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User talk:Ems57fcva/archive 1

Hi Ems,

here is some of my documentation. --Cleon Teunissen | Talk 22:13, 24 Mar 2005 (UTC)

The following text is from an article by Neil Ashby. Source of the article: Reference frames and the Sagnac effect
 * Now consider a process in which observers in the rotating frame attempt to use Einstein synchronization (that is, the principle of the constancy of the speed of light) to establish a network of synchronized clocks.

 * Observers fixed on the earth, who were unaware of earth rotation, would use just use the coordinate distance for synchronizing their clock network. Observers at rest in the underlying inertial frame would say that this leads to significant path-dependent inconsistencies, which are proportional to the projected area encompassed by the path. Consider, for example, a synchronization process that follows earth’s equator in the eastwards direction.

 * From the underlying inertial frame, this can be regarded as the additional travel time required by light to catch up to the moving reference point. Simple-minded use of Einstein synchronization in the rotating frame uses only the coordinate distance, and thus leads to a significant error. Traversing the equator once eastward, the last clock in the synchronization path would lag the first clock by 207.4 nanoseconds. Traversing the equator once westward, the last clock in the synchronization path would lead the first clock by 207.4 nanoseconds.

 * In an inertial frame a portable clock can be used to disseminate time. The clock must be moved so slowly that changes in the moving clock’s rate due to time dilation, relative to a reference clock at rest on earth’s surface, are extremely small. On the other hand, observers in a rotating frame who attempt this, find that the proper time elapsed on the portable clock is affected by earth&'s rotation rate.

 * Path-dependent discrepancies in the rotating frame are thus inescapable whether one uses light or portable clocks to disseminate time, while synchronization in the underlying inertial frame using either process is self-consistent.

 * GPS can be used to compare times on two earth-fixed clocks when a single satellite is in view from both locations. This is the common-view method of comparison of Primary standards, whose locations on earth's surface are usually known very accurately in advance from ground-based surveys. Signals from a single GPS satellite in common view of receivers at the two locations provide enough information to determine the time difference between the two local clocks. The Sagnac effect is very important in making such comparisons, as it can amount to hundreds of nanoseconds, depending on the geometry. In 1984 GPS satellites 3, 4, 6, and 8 were used in simultaneous common view between three pairs of earth timing centers, to accomplish closure in performing an around-the-world Sagnac experiment. The centers were the National Bureau of Standards (NBS) in Boulder, CO, Physikalisch-Technische Bundes-anstalt (PTB) in Braunschweig, West Germany, and Tokyo Astronomical Observatory (TAO). The size of the Sagnac correction varied from 240 to 350 ns. Enough data were collected to perform 90 independent circumnavigations. The actual mean value of the residual obtained after adding the three pairs of time differences was 5 ns, which was less than 2 percent of the magnitude of the calculated total Sagnac effect.

External link: Reflections on Relativity, Section 2.7 The Sagnac effect.

External link: [http://www.phys.canterbury.ac.nz/research/laser/ring_2000.shtml Ring interferometry experiment. University of Canterbury, New Zealand]

External link to a PDF document (1,086 KB) featuring the 1984 GPS validation of the predicted Sagnac effect. IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT

External link: GPS overview According to this source, the first GPS satellites that were launched could switch to either a newtonian compliant mode, or a relativistic compliant mode. It soon became clear that the system had to comply with general relativity in order to be accurate. --Cleon Teunissen | Talk 22:13, 24 Mar 2005 (UTC)

Sagnac interferometry and space-time geometry
I looked over your reference. I don't see where you got the "prefered frame" business from with it. Please take a careful look at my edit. I have done my best not to overly disrupt your write-up, which overall is actually quite good. However, that one point needed dealing with. EMS

 * Relativistic physics is a theory of the properties of space-time geometry, and how matter and energy interacts with space-time geometry.

 * I assure you I have not confused the ring setup with an inertial frame of reference. Sagnac interferometry measures rotation with respect to the local space-time geometry. According to general relativity, is it possible for space-time geometry to rotate with respect to its surrounding space-time geometry, but the amount of rotation is exceedingly small. See frame dragging and Gravity Probe B. The amount of space-time geometry rotation that general relativity predicts is too small for current ring interferometers to detect. Because of this a Sagnac interferometry measurement of the rotation rate of Earth, and astronomical observation of the rotation rate of Earth agree exactly. --Cleon Teunissen | Talk 22:53, 24 Mar 2005 (UTC)

 * You wrote:
 * The Sagnac effect has been used to claim that a prefered frame of reference exists. This is due to a misunderstanding of the nature of the propagation of light and treating the rotating Sagnac ring as an inertial frame of reference.
 * I did not treat the rotating Sagnac setup as an inertial frame of reference. I stated that a Sagnac interferometer shows a displacement of the interference fringes when it is rotating with respect to the local inertial frame. --Cleon Teunissen | Talk 22:59, 24 Mar 2005 (UTC)

wikipedia conversation
P.S. You seem to be sending me messages through a means other than what I am using. How do you send Wikipedia messages?

 * I use the following procedure: on my own talk page I open an edit window. I copy some text, and then I cancel that edit window. Then I go to the talk page of the 'other guy' and I paste what I've copied, and then I add text of my own. This has the advantage of making the thraed readable in one place. I appreciate it that you put your answers on my talk page, relieving me of the task of monitoring your talk page. Please insert four wavy lines ~ at the end of what you write, then your name and the time and date will automatically be added. --Cleon Teunissen | Talk 09:04, 25 Mar 2005 (UTC)

Preaching to the converted
Hi Ems, I am quite sure we will be able to work it out. By the looks of it we use some technical terms somewhat differently, leading to misunderstanding. The things you are explaining to me are the very things I am explaining to other people. I will try and identify the misunderstanding, so we can address them.

Personally, I prefer an explanation of the Sagnac effect without invoking formulas. I think that is possible.

I would like to see a statement like "wanted to debunk special relativity" not in the article, that sounds so agressive. I'd prefer a neutral: "Sagnac's motivation to conduct the experiment was based the interpretation in terms of classical mechanics". Do you have a solid historical source for agressive motives on the part of Sagnac? --Cleon Teunissen | Talk 10:17, 25 Mar 2005 (UTC)

I have written a text aimed at addressing misunderstandings. I have put that text on the User:Ems57fcva/sandbox/Sagnac_Effect page.  How did you create that page? I'd like to create a sandbox of my own.

The story about gyroscopes is not necessary, I'm OK with removing that. just the remark that Sagnac interferometry is the electromagnetic counterpart of gyroscopes will suffice.

I don't think it is neceessary to tell how Sagnac interpreted the experiment, since he erred. In general I concentrate on presenting a correct interpretation as clear as possible, I usually do not bother to refute wrong interpretations. --Cleon Teunissen | Talk 12:45, 25 Mar 2005 (UTC)

 * Hi Cleon, the equation can be skipped by those who are not proficient with such stuff, while those who are can use it to verify the assertions being made.
 * [...] equations [...] establish the proper basis for justifying the blanket assertions that Sagnac is consistent with relativity. [...] to be honest with you, you are groping with the issues of SR and GR in your version, while the metric equation itself is the necessary description that handles those issues. EMS

Yes, if it is asserted that general relativity predicts the Sagnac effect, then it is good to actually show that. I agree that what I wrote about SR and GR in the current article won't do. I was struggling to be brief. I think the section on GPS should go too. I wrote about it to emphasize that the sagnac effect is important and relevant. Currently, we are discussing the article on three locations: the sagnac effect talk page, your talk page, and your sandbox page. Let's limit that to two locations: your talk page and your sandbox page. --Cleon Teunissen | Talk 16:09, 25 Mar 2005 (UTC)

It must be shown that GR complies with SR in this matter, but I feel the fundamental explanation of the physics is not to be attributed to general relativity. I'd like your opinion on that. --Cleon Teunissen | Talk 16:09, 25 Mar 2005 (UTC)

Harress
You wrote:
 * The first to perform a ring interferometry experiment aimed at observing this correlation of angular velocity and phase-shift was the Harress in 1911

Actually, the experment done by Harress was aimed at finding out some physics of light moving through glass. Other physicists recognized in retrospect that the Harrass 1911 experiment constituted a Sagnac interferometry experiment. However, showing the Sagnac effect was not on Harress' mind at the time. The article that Harress wrote deals only with the physics that Harress was investigating.

That is why I wrote that the sagnac experiment was the first one that was specifically aimed at obtaining a sagnac effect. To my understanding, that explains why the effect was named after Sagnac rather than after Harress. --Cleon Teunissen | Talk 17:04, 25 Mar 2005 (UTC)

 * Can you provide me with a reference --EMS 18:52, 25 Mar 2005 (UTC)

Pfew, I'd have to try and google the site where I read that. Light travels at 200.000 km/s in glass. Harress used a turntable and a path for the light that sent it twice through the glass, in both directions. With the turntable rotating, the light was traversing moving glass. His aim was to find out whether certain effects cancel or not. (As a matter of fact they do, the magnitude of the Sagnac effect remains the same if the light moves slower than lightspeed-in-vacuum). It was a ether-theory inspired experiment. --Cleon Teunissen | Talk 00:37, 26 Mar 2005 (UTC)

Stedmanreview1997 1.5 MB PDF-file see section 1.2 Early history of Sagnac effect, Harress experiment was aimed at finding out properties of Fresnel drag. I remember reading a site whith an actual drawing of the light path on the Harress turntable. I haven't found that site yet. --Cleon Teunissen | Talk 01:06, 26 Mar 2005 (UTC)

The Stedman Review article will do, I think. Einstein's thinking was influenced by Fizeau's interferometric experiment of light traversing a tube in which water is flowing. Fizeau's results were unsupportive of ether-drag theories. In section 2.4 of the Stedman article (2.4 Corrections from the media; drag effects) describes attempts to find ether-drag in glass mounted on a rotating turntable. It was only after Harress' early death that his experiment was reinterpreted as constituting a Sagnac experiment. --Cleon Teunissen | Talk 01:38, 26 Mar 2005 (UTC)

Sagnac effect article march 27th
I think that the Sagnac Effect article is now ready for "prime time", unless you have some objection to it (which I would doubt since I noticed that you have tweaked it some). I have chosen to put in a section of uses of the effect, including a reference to the GPS. The more I thought about it, the more it seemed to me that this did belong in there.

 * I have several objections.Yesterday I placed several comments on the discussion page: User_talk:Ems57fcva/sandbox/Sagnac_Effect I prefer to address those issues first.

 * In anticipation of the merger, I have made some changes to the current sagnac effect article

 * The content of your version and the content of mine must be merged somehow. There are differences in emphasis between us, differences as in judging what are the important features. I'd very much like to address these differences. User_talk:Ems57fcva/sandbox/Sagnac_Effect --Cleon Teunissen | Talk 07:44, 27 Mar 2005 (UTC)

Another sandbox
I have created a sandbox with my User Name. It shows my proposal for a merged version of the articles User:Cleon_Teunissen/sandbox/Sagnac_Effect --Cleon Teunissen | Talk 20:34, 27 Mar 2005 (UTC)

covariance and invariance
Dear Cleon,

Overall I liked your merger. I have updated your edit, removing a sentence from the 4th paragraph about the viewpoint being an intertial frame of reference. You aleady cover that issue in the previous sentence by saying that the rotation is with respect to an inertial frame, and I would leave it at that. You later on note that the Effect must be the same as viewed in any frame of reference. That really is the crux of Relativity anyway -- all phenomena should be the same a viewed in any reference frame(s).  (It really is a good question that the anti-relativists ask when they question why the Effect should appear even to a co-rotating observer. Unfortunately for them there is a good answer to it.)  Beyond that, I do think that the Sagnac magnitude calculation belongs in that page, but that is a minor issue since it can be gleamed from the references.  Overall, I think that it is time to put the new page out there.  EMS

 * Dear EMS, I have made the test page into the current Sagnac effect article  There is a profound philosophical difference between us. For now I will gloss over that, but I want to address it

 * My position is that general relativity equips the physicist with a full set of transformations, all transformations can be handled. This property of the mathematical formulation of the theory is called 'general covariance'. It can be shown that any theory can be formulated in general covariant form. Newtonian dynamics can be formulated in general covariant form, just like general relativity. (However, newtonian dynamics looks ugly in general covariant form, and GR looks elegant in covariant form. The source of this informations is the 1200 page book Gravitation' by Misner, Thorne, and Wheeler.)
 * According to my sources, general relativity is not generally invariant, and I think the sources I have consulted are knowledgable in this. Usually the covariance group of a physics theory and its invariance group coincide, like in the case of special relativity. This is not the case with general relativity.
 * The philosophical conclusion that I draw is that physical phenomena relate to local inertial frames. It seems to me that physical phenomena take place in local inertial frames exclusively. The mathematics of general relativity can handle any choice of coordinate system, including coordinate systems that rotate with respect to the local inertial frame. Calculations performed this way yield outcomes that are consistent with the outcomes of other appropriate calculations. However, it seems to me that coordinate systems that rotate with respect to the local inertial frame do not represent actual physics.

 * I draw a distinction between 'performing calculations in the context of coordinate system that is rotating with respect to the local inertial frame' on one side, and on the other side, 'thinking about physics from the point of view of a rotating frame.
 I acknowledge that the calculations yield correct outcomes. I state that attempts to think about physics from the viewpoint of a rotating coordinate system do not have physical meaning. --Cleon Teunissen | Talk 17:57, 28 Mar 2005 (UTC)

 * Well, I overstated the above remark. At least it has less physical meaning to use a coordinate system that rotates with respect to the local inerital frame. Both in classical mechanics and in relativistic mechanics. --Cleon Teunissen | Talk 18:13, 28 Mar 2005 (UTC)

[...] With this I must strongly disagree. The general principle of relativity states that "the laws of physics are the same in all frames of reference" [...]. --EMS 22:27, 28 Mar 2005 (UTC)

 * Dear EMS, I will need some time to prepare a thorough answer. For now, just a single remark:
 What you are stating is the wording of the 1916 article by Einstein that presented the equations of GR in its completed form. In the next years there was much correspondence between Einstein and his collegues on how to interpret GR. Felix Klein, Herman Weyl, and several other mathematicians. After a couple of years Einstein agreed with his collegues that GR is not generally invariant. In later years Einstein is seen to have retreated from the position he had taken earlier, and in later articles he adjusted his wording accordingly, relying on a narrower (but still sufficient) principle of equivalence.
Not being invariant didn't diminish the importance of GR, so it wasn't a real bother to Einstein. Only GR can provide the unification of a theory of gravity and minkowski space-time, GR is indispensible. Special relativity can handle the motion of accelerating bodies in Minkowski space-time. What SR cannot handle is the consequences of gravitation. --Cleon Teunissen | Talk 08:15, 29 Mar 2005 (UTC)

[...] Are you saying the the fall of the water when you accidentally knock a glass over is not "actual physics"? [...] --EMS 22:27, 28 Mar 2005 (UTC)

 * Here is what I say:
In the curved space-time surrounding Earth the following is valid:
When a test mass is released into free fall, it will from then on follow a geodesic (ignoring air resistence for now). In this particular case, that geodesic is a straight line towards the center of gravity. The curvature of space-time manifests itself in the fact that this motion straight towards the center is accelerating with respect to the center of the Earth. The motion of the test mass is a result of an interaction of the test mass with the local inertial frame (the interaction with the local space-time geometry.

 * When the object is not released into free fall, the physics of the test mass is a result of the interaction of the test mass with the local inertial frame (just as in the free fall situation, interaction with local space-time geometry).
 A mechanical force is deviating the test mass from moving along a geodesic. According to general relativity, the force exerted by the surface of the Earth on objects, preventing them from moving along a geodesic, is the same physics as the thrust of a space-ship rocket engine, accelerating a space-ship with respect to the local inertial frame. In general relativity, being accelerated with respect to the local inertial frame, and being deviated from moving along a geodesic are one and the same thing.

 * My point is: both in the free fall physics and in non-falling physics, the physics of the object (either the motion or the magnitude of the force that is required to maintain positon) is the result of interaction of the object with local space-time geometry. --Cleon Teunissen | Talk 10:09, 29 Mar 2005 (UTC)

 * I think I need to explain something else. On several occasions, I have used the expression 'local inertial frame' as a substitute for 'local space-time geometry. That is unconventional terminology, and it has led to confusion, I'm afraid, and I apologize for that.

 * I think I should explain how I use the expression 'inertial frame'. I tend to think of the inertial frames of Minkowski space-time as a mathematical group. All members of the group of inertial frames are symmetrical with respect to each other, in the sense that a single transformation procedure transforms any member into any other member. I have come to think of the group of inertial frames of Minkowski space as a single frame, because the members of the group are indistinguishable. So when I write: 'local inertial frame' I am thinking of the inertial frame that is co-moving with a test mass, plus all the other members of the group of inertial frames. --Cleon Teunissen | Talk 11:15, 29 Mar 2005 (UTC)

Principle of relativity.
Hi EMS, you need not have apologized for writing long texts. I am much worse.

I'd like to go back to the basics. Frst I will recapitulate very elementary stuff, to lay a foundation. then I will come to the point.
 Recapitulating
 When two objects collide with each other, and they remain stuck to each other, a lot of kinetic energy is converted to heat. For the calculation of the amount of kinetic energy gets converted to heat any inertial coordinate system can be chosen, the outcome of the calculation is always the same. (The most symmetrical choice of coordinate system being the coordinate system that is co-moving with the center of mass of the two objects that are going to collide.)

The reason that any inertial coordinate system can be chosen is that in all physical interactions there is no dependency on velocity, only relative velocity matters. You can set up the collision, measure the amount of heat that is released. Then the objects are co-accelerated for a while, and after this acceleration stage, the center of mass of the two object has a relative velocity to the initial situation. The two object are given the same relative velocity to each other again, and at collision exactly the same physics will occur.

The core concept of the principle of relativity is the conviction that everytime the relative velocity is the same, the same physics is occuring at the moment of collision. Any transient change-of-velocity stage is undetectable after the fact.

Ring Laser interferometer
 Now I'd like to look at the Ring Laser interferometer. The Canterbury (New Zealand) RLG uses a laser with a frequencyof 473 THz. Suppose that ring laser (like the original Sagnac setup) is build on a platform that can rotate. When that platform cancels the Earth rotation by counterrotating, then the counterpropagating beams are monochromatic coherent light, as is normal for lasers. But when this ring laser interferometer is co-rotating with Earth, then the laser light splits in two frequencies, and in the case of the Canterbury University RLG the frequency difference between the two counterpropagating beams is around 70.7 Hz. The thing to note is that a ring laser interferometer measures straight away, no calibration by outside comparison. Every real time measurement by a ring laser gyroscope is a measurement without memory of earlier measurements!

Initially the ring interferometer had a rotation rate of zero. Then a torque was applied to the platform to bring the rotation rate to one revolution per day, co-rotating with Earth. So there has been a transient torque, resulting in a new angular velocity that is a constant angular velocity. The changing of the angular velocity was transient. What is observed is that after the change of angular velocity there is different physics going on as compared to the initial situation. In the new situation there is frequency splitting. The transient change-of-angular-velocity stage is detectable after the fact.

The core concept of the principle of relativity is the conviction that everytime the relative velocity of two or more objects is the same, the same physics will occur. Any transient change-of-velocity stage (change of velocity of the common center of mass of the system under observation), is fundamentally undetectable after the fact.

On the other hand. If a change is detectable after the fact, by an instrument that operates without calibration by outside comparison, then it is shown that the physics has changed: a different physical interaction must be taking place as compared to before. --Cleon Teunissen | Talk 14:06, 29 Mar 2005 (UTC)

Blooper
Hi EMS,
 I reread one of my sources, and I discovered I made a blooper. I used the word 'invariant' very inappropriately, making my intention unintelligable. Here is a link to one of my sources.
 External link: History of relativity I knew I should have taken my time, but I didn't. I should have paced myself. --Cleon Teunissen | Talk 16:20, 29 Mar 2005 (UTC)

Unification

 * The goal of relativity is to permit all observers to reconcile their views of the same events. --EMS 16:03, 29 Mar 2005 (UTC)

There we are on common ground. Many authors make it seem as if different observers disagree, and I find it annoying when authors present relativity in that way.

Any observer can transform his instrument readings to what another observer's instrument readings would be. Relativity theory facillitates agreement between observers and the mathematical form provides independence of choice-of-coordinate-system.

We have several times now jumped to wrong conclusions as to what the other's thoughts are. In my very first response to you, after you had made some edits, I had jumped to conclusions.

 * You want to treat one of those views as "correct". My point is that both views are correct! --EMS 16:03, 29 Mar 2005 (UTC)

I will try to explain my philosophical problem with that.
 Before the introduction of special relativity, the following two situations were interpreted as being different physics. A moving magnet, inducing current in a stationary coil, and a moving coil, moving through the field of a stationary magnet, which also induces current. If it was assumed that the galilean transformations are the appropriate transformations then there are two really different mechanisms, producing, as it turned out, the same current strength.

This strange doubleness went against Einstein's intuition. Einstein was eager to bring a principle of relativity back to physics. But that meant that he had to resolve that double mechanism situation. If only relative motion is supposed to exist, how does nature "decide" which mechanism is going to actually "do the job"? Einstein looked for an electrodynamics in which there is only one mechanism, no need for nature to "decide". As it turned out, the only way to reduce it from two mechanisms to one mechanism was to recognize that space and time are different aspects of a single entity, space-time. With the unification of space and time, several things slotted together into a single electrodynamics.

So I'm not happy with the idea of recognizing two incompatible mechanisms for causing the Sagnac effect. A unification seems in order, or at least a disambiguation. I follow my sources in thinking that the mathematical framework of general relativity can be interpreted in such a way that this unification is achieved. Key elements in this interpretation are the principle of equivalence and Einstein's views on Mach's principle. --Cleon Teunissen | Talk 19:49, 29 Mar 2005 (UTC)

Modeling the Earht's atmosphere
By the way, you probably should remove the hovercraft business from your Coriolis Effect page since that is due to multiple causes. :--EMS 16:03, 4 Apr 2005 (UTC)

 * Well, the rotating mercury mirror is intended to model atmospheric motions. The surface of the rotating mercury mirror is concave, and the surface of the Earth is an ellipsoid. The dynamic equilibrium that is reached is similar in both cases. The rim of the "saucer" being higher models the greater distance to the center of the Earth at the Equator. In the coriolis effect article I describe a counterclockwise eddy on a counterclockwise rotating mercury mirror. The counterpart of that motion in the atmosphere is in meteorology called 'inertial wind'. A weather balloon that is co-flowing with inertial wind is following a trajectory around the axis of the Earth that is somewhat saddle-shaped. An accelerometer onboard that weather balloon (co-flowing with inertial wind) will not measure acceleration in a direction parallel to the surface of the earth.
The coriolis effect in the atmosphere is due to the fact that the way the air is moving is a form of orbital dynamics. Everywhere on each hemisphere gravity provides the necessary centripetal force, and the air can move with little friction in any direction where there is room to move to. --Cleon Teunissen | Talk 19:21, 5 Apr 2005 (UTC)

Two spectrums of weak vs strong
Hi EMS,

I performed a google search, using the following search words:
 relativity principle equivalence weak strong.

I get the impression that on all of the pages that google lists the following meaning of 'Principle of Equivalence' is used. (A meaning that I was previously unfamiliar with).
 A weak conjecture would be to hypothesize that the Principle of Equivalence only holds for laws of motion of objects. A stronger conjecture would be to hypothesize that all properties of physics are equally subject to local space-time geometry. Locally, the description of space-time geometry can be approximated by a Lorentz frame that is tangent to the local space-time curvature. Strong equivalence is to conjecture that these local Lorentz frames are as indistinguishable as the Lorentz frames of Minkowski space-time.

I had always assumed that the spectrum of weak vs strong principle was about the tidal-effects-objection to the Principle of Equivalence.

It appears that the general physics community regards the tidal-effect-objection as non-problematic, and that the physics community is much more interested in whether really all laws of physics follow local space-time geometry in perfect unison.

As far as I can tell on the basis of my google search, Joke137 is better informed than you on this particular matter. I hope that your contributions and the contributions of Joke137 can be merged. --Cleon Teunissen | Talk 17:54, 6 Apr 2005 (UTC)

 * Personally, I see the "strong equivalence principle" in its various variants as being an abuse of the EP, but if I am to "hold" that page I have to be a reporter of the EP and how it is used instead of an enforcer of the WEP.
 * I have looked at Joke137's references, and I agree with you that he has a good point about the SEP and that it has to be represented. I just need a few days to think on this and get stuff like my taxes done before I edit that page some more.  Also, there seems to be multiple versions of the SEP, including the misstatement that I am opposed to.  The goal now is not to have the last word here but instead to get it into a shape where others can flesh it out more.  My real target is the GR article itself anyway.  The goal here is to have the EP page support the new GR page (when I finally develop it).

 * --EMS 18:56, 6 Apr 2005 (UTC)

Uniform graviational field
In your first example, uniform acceleration, there is a gradient of gravitational potential (at least for the accelerated observer). :--EMS 19:19, 12 Apr 2005 (UTC)

 * Are you perhaps referring to the following? In the article by Peter M. Brown, it is stated on page 16 (page 16 of the PDF-version of the article)

 * A very important gravitational field with zero space-time curvature in general relativity is the uniform gravitational field. The gravitational acceleration of an object in such a field will be calculated here since there will be occasion to use it below.

 * $$ d^2 z/d \tau ^2 = - (g/c^2)(1 + gz/c^2)/[(1 + gz/c^2)^2 - v^2/c^2] $$

 * This expression gives the local acceleration of an object whose velocity is v. Observers at different positions z in the field system will not measure the same local value of acceleration. Not only will the acceleration depend on position but also on velocity. This is contrary to what one would normally assume for a uniform gravitational field.

 * I'm out of my depth here, I cannot judge the importance of this. But by the looks of it, its not a slope; it doesn't look linear. --Cleon Teunissen | Talk 05:43, 13 Apr 2005 (UTC)

In this case, the "potential" is $$gz$$. It is no coincidence that this is the same as the Newtonian equation. As for the above equation for coordinate acceleration: You are quite correct that the acceleration is not linear. A uniform local acceleration in relativity produces a result called "hyperbloic motion" because the velocity with respect to an inertial observer will approach but never equal or surpass $$c$$. There are also other wierdnesses in there: For example, the coordinate speed of light in this case is $$c ( 1 + gz/c^2 )$$. (This is only how the movement of light is being measured. Locally, the speed of light is always $$c$$, but between due to gravitational time dilation, the coordinate velocity becomes different.)  So the limiting velocity ends up being a function of position instead of being constant throughout the observed spacetime (as is the case for an inertial observer). I would also point out the this result comes from SR, even though it helps to provide on a handle on how things behave in GR.

--EMS 16:08, 13 Apr 2005 (UTC)

Diamagnetic levitation
The weightlessness of astronauts in a space-station that is orbiting a planet is fundamentally different from the approximation to weighlessness that can be achieved with for example diamagnetism. Most atoms are diamagnetic and a uniform 20 Tesla magnetic field will levitate any object (unless it happens to be a non-diamagnetic material.) --Cleon Teunissen | Talk 14:24, 15 Apr 2005 (UTC)

 * Magnetic levitation is not weightlessness. Instead you have replaced the repulsion of the ground with a magnetic effect exerting the same force in a different manner. A magnetically levitated man will still feel his own weight. --EMS 16:44, 15 Apr 2005 (UTC)

Actually, diamagnitism can come pretty close to producing real levitation. External link: diamagnetic levitation inside a Ø32mm vertical bore of a Bitter solenoid in a magnetic field of about 16 Tesla at the Nijmegen High Field Magnet Laboratory.

In the case of diamagnetism, each atom contributes individually to the levitation, diamagnetism will levitate a drop of water!
 [quote]
 We have observed plenty of other materials floating in magnetic field - from simple metals (Bi and Sb), liquids (propanol, acetone and liquid nitrogen) and various polymers.
 [end quote]
 --Cleon Teunissen | Talk 18:50, 15 Apr 2005 (UTC)

From the page you provided a link to: "In the case of diamagnetic levitation, the gravitational force is compensated on the level of individual atoms and molecules."

The object is floating at a level such that if it fell further into the magnetic field the repulsion would become greater than that the force of gravity, and above it the repulsion would become less than the force of gravity. It is levitation. It is not intertial motion and it is not wieghtlessness. --EMS 20:29, 15 Apr 2005 (UTC)

 * OK, it has been firmly established that we agree on that. I wrote:
 * The weightlessness of astronauts in a space-station that is orbiting a planet is fundamentally different from the approximation to weighlessness that can be achieved with for example diamagnetism.
 * And you have confirmed that you agree with me that levitation is not weightlessness. I notice in retrospect that it didn't help that I contrasted diamagnetic levitation with true weightlessness. It triggered you into exclaiming that diamagnetic levitation is not weightlessness.
 * I shall attempt to avoid this sort of getting sidetracked. ---Cleon Teunissen | Talk 07:26, 16 Apr 2005 (UTC)

Long buried theory
With regards to geometrodynamics, please see http://www.physicsdaily.com/physics/Geometrodynamics. Suffice it to say that I see little value in gravitation being confirmed as a fundamental interaction by a dead theory. --EMS 20:58, 15 Apr 2005 (UTC)

 * I was not aware that at some point in time the name 'geometrodynamics' has been in use for a theory different from the theory of general relativity. I have encountered the name 'geometrodynamics' many times, and always it seemed to be used as an alternative to the name 'general relativity', rather than referring to another theory.

 * I did some googling, and I encountered references to 'geometrodynamics' and to 'topological geometrodynamics'. I guess the distinction between 'general relativity' and 'topological geometrodynamics' was never very obvious since the program was intended to be an extension of general relativity. Topological geometrodynamics has been abandoned long ago, I hope that 'geometrodynamics' can become a common name for the theory of general relativity. I think the name 'geometrodynamics' suits the theory well. --Cleon Teunissen | Talk 10:17, 16 Apr 2005 (UTC)

 * What I often head said about GR is that it is a geometric theory, and there is broad agreement that any successor to GR will itself be a geometric theory. By geometric they mean that it will be a theory which provides a metric description of spacetime.  I assume that you know what a metric is by now, especially after my demanding that one appear on the Sagnac Effect page.

 * As for 'geometrodynamics': I don't recall having ever heard that term before, and most certainly not in my taking of GR classes back in '99-'00 or in any of the various GR-related meeting that I have attended as part of a GR-related project of mine.  Based on that, I think that it is fair to say the geometrodynamics is not a commonly used term for GR, and indeed I find it hard to understand why anyone would try to rename GR anyway:  Its name very adeptly describes what it is and what it does.  My guess is that geometrodynamics is exactly what the web indicates that is:  The name for an attempt to create an even more general theory that accounted for GR and the other "interactions".  So the bottom line for me is that I see little need to either rename GR or redefine geometrodynamics.

 * As for the GR page itself: Except for the mentioning of alternate theories in the legitimate context of doing so, I will not be seeking in the least to bring in differing ideas and concepts.  This desire is based on the rules of Wikipedia, my own desire to properly inform people about GR, and my own experiences with alternate ideas and theories.

 * --EMS 17:32, 16 Apr 2005 (UTC)

GR terminology

 * [...] centrifugal force can create a "gravitational field" comparable to the gravitational field of gravity. --EMS 20:58, 15 Apr 2005 (UTC)

I think the expression 'centrifugal force' should not be used. I avoid using the expression centrifugal force. It is not a force; it does not involve the exchange quanta of action, there is no exchange of either photons, (W+,W-, or Z)-bosons, or gluons or some other quanta of action. I use the expression 'centrifugal manifestation of inertia'.

I use the following reasoning:
 We know that the physics of acceleration is that when a latticework of measuring rods and clocks is being accelerated by a force then the clocks will not count time at exactly the same rate, there is a anisotropy of the rate of time.

I need an expression for that anisotropy in the rate of time. Using the expression "gravitational field" as a metaphor will not do. A gravitational field is curvature of space-time and acceleration is not curvature of space-time, that distinction is crucial for proper understanding of gravitation. So another metaphor is needed, and I settle for 'an incline in the rate of time' (an incline in space-time geometry).

A strong centrifugal manifestation of inertia can for example be elicited in a really big wheel-shaped space-station, big enough to pull 1 G of acceleration at the perimeter. Pulling 1 G of acceleration does not result in a centrifugal force.
 Objects inside a cabin in the rotating space-station rest on the floor of the cabin. The floor of the cabin is exerting a force directed towards the center of rotation. In response to that force being exerted there is a centrifugal manifestation of inertia.

You said that gravitation should not be called a force since no force is involved.
 That reasoning applies equally in the case of centrifugal manifestation of inertia. It should not be called a force because it is not a force. --Cleon Teunissen | Talk 07:51, 17 Apr 2005 (UTC)

 * I will use the term "centrifugal force" since everyone else does. However, it is worth noting that when a centrifugal force is detected, the real force is a cetripetal (or towards-the-center) force which is keeping the observer going in a circle.

 * Kindly do me a favor and stop trying to rearrange the lexicon of physics. It makes communications difficult, especially with other physicists.

 * Beyond that, of course centrifugal force is not a real force. If it wasn't an inertial "force" it wouldn't be able to generate a gravitational field after all. --EMS 15:18, 18 Apr 2005 (UTC)

I am reluctant to use the expression 'centrifugal force' because many people do not see that expression as a metaphor. Many people, it seems, believe that 'centrifugal force' is a true force. I'm not particularly eager to rewrite the lexicon, but I really need the expression 'manifestation of inertia'. Without it, I cannot explain physics. It's a dilemma. I am aware that the fact that I use novel expressions hampers efforts to cooperate. --Cleon Teunissen | Talk 18:40, 18 Apr 2005 (UTC)

 * I think that you need to realize that the average man in the street is not budding relativist or even cares to be a competent physicist. When push comes shove, "centrifugal force" actually describes what they are experiencing in their own frame of reference.  That the physical reality behind what they perceive as a force is quite different is another matter.  The botton line remains that if you don't hold onto the bars when you are near the rim of that spinning piece of playground equipment that you are going to go flying off of it.

 * Then again, unlike you I have no problems with the idea of being at rest in an accelerated reference frame. Being on or in a spinning device and experiencing cetrifugal force is fine and dandy by me.  I remember being in a carnival centrufuge and thinking jokingly of the force that is keep someone suspended "above" me a being a personal "gravity", only to discover years later that in GR that is exactly what it is.  (Actually what I had in GR terms was a personal gravitational field, at least for my sector of that centrifuge.  And it was personal:  Everyone else had a different idea of where "up" had gone.)

 * So my overall point is that centrifugal force is perfectly real in the appropriate frame of reference. That it is no more real than gravity is is irrelevant unless you are a physicist.

 * --EMS 20:56, 18 Apr 2005 (UTC)

What a metric is

 * By geometric they mean that it will be a theory which provides a metric description of spacetime. I assume that you know what a metric is by now, especially after my demanding that one appear on the Sagnac Effect page. --EMS 17:32, 16 Apr 2005 (UTC)

You can judge my understanding of aspects of the Minkowski metric from what I have written on the Talk page of the Twin paradox article. The Sagnac effect and the Twin paradox have in common that they can be interpreted in terms of the physics of time dissemination. The Twin paradox and time dissemination.
 I present an interpretation of the Twin paradox in purely geometrical terms. The essential feature is that in both the Sagnac effect and the Twin paradox a loop is closed. That is why I decided to mention in the Sagnac effect article that the Sagnac effect is recognized in (GPS) synchronisation procedures. The first message I posted here, on your talk page, was a lengthy quote from an article by Neil Ashby, who discusses time dissemination. --Cleon Teunissen | Talk 09:58, 18 Apr 2005 (UTC)

 * It is pretty much as I had hoped: You know a metric when you see it, or at least Minkowski's metric.  You bring in Pythgarus, but metrics go far beyong his insights.

 * A metric is an equation the describes the square of the separations between coordinates on a manifold. In relativity, metrics are  Lorentzian with a temporal component having a the square of its separation given in a sign opposite that of the spatial separations.  Overall, the metrics in Relativity give the proper time experienced in traveling a path, which is why a geodesic in relativity maximizes the distance travelled (since any deviation generated time dilation with respect to the inertial path), instead of minimizing it as in a Riemannian manifold.

 * --EMS 15:38, 18 Apr 2005 (UTC)

Reality

 * centrifugal force is perfectly real in the appropriate frame of reference. That it is no more real than gravity is is irrelevant unless you are a physicist. --EMS 20:56, 18 Apr 2005 (UTC)

I'd like to contrast the following two situations.

First situation: I am standing on a rotating disk near to the perimeter, and a rope is attached to a climber's harnass I am wearing to keep me from falling of the disk. The disk is at ground level. A hundred meters away from the disks is a solid wall. The radius of the disk is 15 meters and at one revolution per 8 seconds the rope is pulling 1 G of centripetal acceleration. If I cut the rope I will fall of the disk, hit the ground, and I will probably sustain abrasive wounds, but I'll live. The idea is: as long as the rope is attached to the harnass I am being accelerated. The very femtosecond I cut the rope I cease to be accelerated (if not sooner). There is no way I am going to hit that wall a hundred meters away: if I cut the rope I will only have to deal with my velocity at that moment, which is about 40 kilometers/hour; cutting the rope is a good first step to freeing myself.

Second situation: I am abseiling. The rockface is right under my feet and the ground below is still a hundred meters away. In that situation there is no way I am going to cut my rope first.

In assessing the situation it depends on how much I "zoom in", or how far I "zoom out". If I zoom in to the smallest perspective, then centrifugal manifestation of inertia and gravitational manifestation of inertia are alike: I can feel it as long as the rope is attached, and as soon as the rope is cut the manifestation of inertia is gone.

I prefer to zoom out to the widest possible perspective, so that I can gather as much relevant information as I can. As seen from a more comprehensive perspective, I predict that on the rotating disk cutting the rope is a good way of getting out of the situation. When I am abseiling, I will not cut the rope.

So my overall point is that curvature of space-time has real consequences in all frames of reference, and in all frames of reference centrifugal manifestation of inertia ceases as soon as I cut the rope.

Physics is about the underlying properties of nature, the properties that are independent of the choice of reference frame. --Cleon Teunissen | Talk 23:36, 18 Apr 2005 (UTC)

 * I don't see how your little diatribe (which from a physics standpoint is quite correct BTW) in any way contradicts my words as quoted above it. As you noted, the cetrifugal force is gone once you cease to be in the accelerated frame of reference.

 * BTW - After you cut the harness while on the side of a cliff, gravity has also vanished for you. However, that is not going to stop the base of the cliff from accelerating towards you (in your frame of reference that is).

 * --EMS 01:51, 19 Apr 2005 (UTC)

 * P.S. I also forgot to mention that my remark also dealt with things from the viewpoint of an (admitedly naive) observer.  After all, knowing that being thrown off of a rotataing disk may be uncomfortable but not fatal while falling off of a cliff may well be fatal does not require any knowledge of GR.  I repeat:  There is nothing wrong with an observer on a rotataing disk describing his experiences as being under the influence of a centrifugal force.  If nothing else, it is quite in accord with Occam's Razor:  The use of the simplest explanation that explains the facts.

 * We just have more facts to deal with.

 * --EMS 03:25, 19 Apr 2005 (UTC)

A model that breaks down

 * There is nothing wrong with an observer on a rotataing disk describing his experiences as being under the influence of a centrifugal force. --EMS 03:25, 19 Apr 2005 (UTC)

I think the following example is interesting: an observer inside a rotating wheel-shaped space-station. As long as the observer is in physical contact with something inside the space-station, strong enough contact to keep the observer in co-acceleration with the wheel, then what he measures is consistent with being in a pervasive force-field.

But when the observer is free-floating inside the rotating space station the force-field model breaks down. The observer can be floating inside the space-station with a velocity of, say, 1 centimeter per second with respect to the center of gravity of the space-station. He will not accelerate away from the center of gravity of the space-station, that velcity will remain constant. (Of course, when he finally does come in contact with the perimeter it will be hazardous, for the perimeter is moving fast in a perpendicular direction.)

The 'floating observer' thought experiment illustrates the fact that in the case of rotational motion there is no pervasive alteration of the rate of time, no field. The perimeter is moving faster than the hub and that corresponds to different rates of time for objects co-moving with different parts of the rotating structure, proportional to the distance to the hub.

I am primarily interested in the physical difference between gravitation on one hand, and acceleration and rotation on the other hand. Gravitation is a pervasive alteration of space-time geometry itself, spherically symmetrical around a celestial body. But when a structure is rotating in flat space-time (pulling G's), then the space in and around that rotating structure is still plain old flat space-time.

I suspect that Einstein was thinking about propagation of electromagnetic radiation in formulating the equivalence principle. Einstein's first quantative prediction was about frequency shift of light, and I think that is not a coincidence. I think the equivalence principle is particularly striking when thinking about propagation and detection of photons. --Cleon Teunissen | Talk 06:13, 21 Apr 2005 (UTC)

 * If the observer is not being accelerated, there is not need for him to perceive the existance of a "force field" acting on himself and the surrounding objects. Take your observer and have him fire rockets so that he comes be and stays at rest with respect to rotataing space station, and he will be dealing with centrifugal force until he stops firing his rockets.

 * I assure you the centrifugal force and gravity and heuristically very much the same. You will find between at-rest positions at different potentials both gravitational time dilation and gravitational red-shifting for instance.  And why shouldn't you?  After all, compared to an inertial frame of reference the station/disk is moving faster and faster the farther you go from the center.  So of course the clock of a position "below" you will tick slower than yours.

 * So kindly stay in the desired frame of reference. Yes.  You can enter an inertial frame of reference any time you like in a rotatating frame of reference.  Then again, you can also do the same here on the Earth:  Your (natural and reasonable) reluctance to jump out of a tall building or off of a cliff does not change the fact that you can do so.

 * --EMS 14:37, 21 Apr 2005 (UTC)

Applying Occam's Razor

 * Take your observer and have him fire rockets so that he comes be and stays at rest with respect to rotataing space station, and he will be dealing with centrifugal force until he stops firing his rockets. --EMS 14:37, 21 Apr 2005 (UTC)

In a roundabout way you have confirmed what I said. Gravitation is pervasive, and centrifugal manifestation of inertia is present exclusively in response to a centripetal force being exerted.

 * So kindly stay in the desired frame of reference. Yes. You can enter an inertial frame of reference any time you like in a rotatating frame of reference.

I'd like to point out that I stayed in one frame of reference from the beginning to the end: the local inertial frame of reference of the part of the universe where the wheel-shaped space-staton is residing. Possibly you have used two frames of reference. It may be that you started with a rotating frame of reference, and that you then inserted an inertial frame of reference.

Occam's Razor applies well here. Do not enter more frames of reference into the picture than you need. We have a wheel-shaped space station. We consider two equally possible situations: (1) the observer is sitting or standing or hanging on to something, and the structure is exerting a centripetal force on him; (2) we have the same observer floating somewhere inside, with a velocity of say, one centimeter per second with respect to the center of gravity of the space-station. One frame of reference suffices to give a coherent account of the physics going on in both the situations; I used the same frame of reference throughout. --Cleon Teunissen | Talk 06:50, 22 Apr 2005 (UTC)

Too many cooks
I have ordered myself to stay away from the Equivalence principle article for at least weeks, preferably months. Too many cooks spoil the broth.

I regret that a choice has been made to write an article exclusively for people who are experts on the subject. As it stands the article goes straight into discussing items like the fine structure constant and fifth forces. Clearly the article is aimed at people who are already quite familiar with the equivalence principle, people who have PhD in physics. I wish it would be otherwise.

Anyway, flooding talk pages with my words is counterproductive, I should step back. --Cleon Teunissen | Talk 19:31, 25 Apr 2005 (UTC)

The use of jargon

 * However, if you can get more specific about how you think the EP page is going over people's heads, I am willing to listen. --EMS 20:02, 25 Apr 2005 (UTC)

I am convinced that Einstein moved the understanding of physics to a deeper level. I believe that the following words of Einstein are incredibly potent words:  >>[...] we shall therefore assume the complete physical equivalence of a gravitational field and a corresponding acceleration of the reference system. <<   That is the point of departure from newtonian thinking about gravitaion.

Recapitulating: before 1905, before the discovery of special relativity, both an inertial frame of reference and an accelerated frame of reference were seen as euclidean. Special relativity showed that besides the obvious difference there is a profound difference between an inertial frame and an accelerated frame that had never been suspected before, because space and time were seen as separate.

I think that to people who have immersed themselves in relativity, the expression 'accelerated frame of reference' feels transparent, and obvious. I think it should be recognized that the expression 'accelerated frame of reference' is highly technical jargon. Only people who hold a PhD in physics can be reasonably expected to be familiar with the non-obvious meaning of the expression 'accelerated frame of reference' in the context of relativistic physics.

Another Einstein quote (that I have quoted frequently):
 * A falling man does not feel his weight because in his reference frame there is a new gravitational field, which cancels the gravitational field due to the Earth. In the accelerated frame of reference, we need a new gravitational field. (Translation of a talk that Einstein had given in Japan in 1922, published in the aug.1982 issue of Physics Today, p. 45-47)

This is a translation (or possibly it is translated twice), so none of the expressions used can be relied on as meant literally, but apart from that, this quote features the key element of complete cancelation. NASA plans a test of the equivalence principle with atom interferometry. Interferometric experiments are the spirit of the equivalence principle as introduced in 1907 by Einstein.

My objection against the article as concieved by Joke137 and you is that it assumes the reader to have full knowledge about the core issues of the equivalence principle. Effectively the article skips the core and instead fills the reader in on highly technical matters: the different flavors of the equivalence principle, which are peripheral issues. When Einstein introduced the equivalence principle in 1907, thoughts about different flavors were still far away, in 1907 one equivalence principle is stated, and what is stated in 1907 corresponds to what today is referred to as the strong equivalence principle.

The only reason for the subdivision in different equivalence principles was to serve as a categorizing tool in presenting the long list of concievable violations of the relativistic equivalence principle, the subdivision is not a core issue. --Cleon Teunissen | Talk 04:43, 26 Apr 2005 (UTC)

First of all, with SR: SR is a Euclidean theory. It was an advance but it needs a force of gravity just the same as Newtonian mechanics did. Also SR does not directly deal with acceleration. Like Newtonian Mechanics, SR assumes the existance of inertial frames of reference, and assumes a flat spacetime in doing so. The WEP specifies a technique for identifying inertial frames of reference, and the EEP and SEP specifies ways in which all such inertial frames are identical.

Secondly, I would avoid the use of "cancellation" as a concept with this. Einstein is introducing a second "field", which is the acceleration of objects at rest with respect to the Earth as the observer free-falls. He then realizes that this second field is of the same ilk as the original gravitational field, and hence the equivalence. I don't see that this is the best way of getting to the point, although describing that as part of the development of the EP may be helpful.

Thirdly, the 1907 EP is the WEP, not the EEP or the SEP. The WEP is embodied in the "physical equivalence" statement of Einstein's and which I intend to incorporate in the next edit. The EEP is a statement of the uniformity of observation in inertial frames of reference, and is a more rigid statement than the WEP. It also is of a different orientation, since it is postulating an equivalence of all inertial frames instead of specifying what an inertial frame is. For that reason, although I would like to avoid the subdivisions myself, I am forced to live with them and see to it that they are properly documented.

I will try to come up with some way of describing what is going on. Perhaps a good way is to use the rocket ship example: In an accelerating rocket ship, you will see objects as being accelerated downward with respect to yourself not because they are beging accelerated by because you are. This is the same situation as exists when standing on the surface of the Earth under the WEP.

--EMS 18:07, 26 Apr 2005 (UTC)

The powerful physics concept of superposition
Unfortunately I have too few clues to reconstruct which version of WEP you have in mind, among the dozens of versions. You'd have to describe what you have in mind from scratch.

 * It is there on the Equivalence principle page itself: The rule for determining that one is in an accelerated frame of reference.  It does need elaboration, along the lines that you outline at the end of this message.

It is sometimes argued that Minkowski space is non-euclidean; I am happy to go along with the interpretation that Minkowski space is quite Euclidean, because it is all straight, all flat. all parallel. I concur with Joke137 that huge swathes of interstellar and intergalactic space are exceedingly close to Minkowski space-time.

 * No argument here. SR is Euclidean, and in places distant from any "gravitaional sources" indeed spacetime should be flat.  (Whether the existance of dark energy means that the spaces between the galaxies really is distant from any gravitational source is another can of worms, and the Robertson-Walker solutions to the EFE call for curvatures to exist on a truly cosmic scale.  However, as a practical matter interstellar and intergalactic space is in general "exceedingly close to Minkowski spacetime".)

Whenever possible I use the expression 'curved space-time' rather than the metaphor 'gravitational field', because curvature of space-time is so unlike the concept of 'field' as in for example the electrostatic field.

 * A gravitational field is a matter of your frame of reference. If you are in an accelerated frame, you will find objects being accelerated with respect to you by a "gravitational field".  Note that the field exists when you are being accelerated.  That is the trick.

 * Curvature, OTOH, is always there whether you are in inertial/geodesic motion or not.

Newton had showed (assuming Euclidean space) that if gravity is assumed to be a force then angular momentum is conserved only if the force acts instantaneously. A relativistic theory of gravitation would have the mediator of that force propagate at lightspeed, making it difficult to recover conservation of angular momentum. Einstein was dissatisfied with the direction his first attempt led him.

 * Global energy-momentum conservation does not exist due to the lack of an appropriate background spacetime against which to describe it. However, it still exists locally and in bound systems.  One of Einstein's insights, which does work out, is that the gravitational field can transmit changes in the energy/momentum distribution of spacetime through gravitational radiation.  This has been verified using the binary pulsars.

Einstein describes his breakthrough moment as follows: Einstein about free-fall

 * Just as is the case with the electric field produced by electromagnetic induction, the gravitational field has similarly only a relative existence. For if one considers an observer in free fall, e.g. from the roof of a house, there exists for him during his fall no gravitational field---at least in his immediate vicinity. (A. Einstein, manuscript written in 1919, quoted from G. Holton, Thematic Origins of Scientific Thought, Harvard Univ. Press, 1973, 364. The original manuscript in Pierpont Morgan Library, New York, and in Einstein Archives, Hebrew University of Jerusalem.)

A suitable expression, I think, is to describe the physics of free-fall as a superposition of two effects: gravitational anisotropy and accelerational anisotropy. Amazingly, the superposition of the two effects restores isotropy: the velocity of light is once again the same in all directions
 Free-fall is then a dynamic state in which the two effects exactly even out (only tidal forces remain). The atomic clocks in the GPS satellites are in uniform motion in their local inertial frame of reference and so are atomic clocks onboard ISS, the Space station in low Earth orbit. In those two inertial frames time progresses at dissimilar rates.

 * I do not see superposition as being a useful concept. Free-fall is inertial motion.  That is the gist of it.  In falling, you have not added an effect, but instead have lost one (i.e., being accelerated by the surface of the Earth).

In summary: In my interpretation I distinguish conceptually four different situations: --Cleon Teunissen | Talk 20:22, 26 Apr 2005 (UTC)
 * 1) Free floating in (exceedingly close to) flat space-time.
 * 2) Being accelerated in flat space-time.
 * 3) Positioned on a planet, prevented from free-falling. Is (locally) indistinguishable by way of measurement from 2.
 * 4) Free-fall: a dynamic state of superposition of gravitation and acceleration. Is locally indistinguishable from 1.

 * I see 2 and 3 as being functionally equivalent, and 1 and 4 as being similarly related. I am loath to use the term "indistinguishable" due to the tidal effects.

 * --138.88.225.11 02:51, 27 Apr 2005 (UTC)

Either addition of effect or loss of an effect
The atomic clocks in the GPS satellites are in uniform motion in their local inertial frame of reference and so are atomic clocks onboard ISS, the Space station in low Earth orbit. In those two inertial frames time progresses at dissimilar rates. --Cleon Teunissen | Talk 20:22, 26 Apr 2005 (UTC)

 * I do not see superposition as being a useful concept. Free-fall is inertial motion.  That is the gist of it.  In falling, you have not added an effect, but instead have lost one (i.e., being accelerated by the surface of the Earth). --EMS 02:51, 27 Apr 2005 (UTC)

 * Let me get this straight: do you claim that for the GPS satellites time progresses at the same rate as for clocks onboard ISS? Or do you agree that in those two inertial frames of reference the rate of time is dissimilar?

 * Let me put it to you this way: Intertial motion occurs along geodesics of spacetime as parameterized by the passage of proper time, where "proper time" refers to the local passage of time for an observer.

 * This means that locally, all clocks tick at the same rate!!! What you are up against with GPS and ISS is how their clock rates are perceived by an observer here on the surface of the Earth.  For that, you need to use the metric tensor, and doing so works quite well, giving the observed relative rates of the passage of proper time with respect to a reference clock for the ISS, GPS constellation, and the surface of the Earth.  It is those proper time rates to which you refer.  BTW - Do note that the faster clock rates (with respect to coordinate/callibrated time) for the ISS and GPS are due to their experiencing less gravitaional time dilation than we do.

 * Do you claim that the curvature of space-time of the planet Earth has no effect at all on the physics onboard ISS and onboard the GPS-satellites? --Cleon Teunissen | Talk 06:25, 27 Apr 2005 (UTC)

 * Yes. That is the point of the EEP and SEP.

 * --EMS 16:17, 27 Apr 2005 (UTC)

The transition from SR thinking to GR thinking
Unfortunately I have too few clues to reconstruct which version of WEP you have in mind, among the dozens of versions. You'd have to describe what you have in mind from scratch. --Cleon Teunissen | Talk 20:22, 26 Apr 2005 (UTC)

 * It is there on the Equivalence principle page itself: The rule for determining that one is in an accelerated frame of reference.  It does need elaboration, along the lines that you outline at the end of this message.  --EMS  02:51, 27 Apr 2005 (UTC)

In the transition from newtonian thinking to GR thinking many things remain the same, but the concept of 'acceleration' is profoundly different in the two paradigms.

Recapitulating: in newtonian thinking, the concept of acceleration is anchored on the concept of the common center of mass. It is assumed that the common center of mass of an assembly of objects will always continue in inertial motion. Newtonian thinking is to assert that to maintain constant distance and direction with respect to the common center of mass is what fundamentally constitutes inertial motion. (Also uniform change of distance is defined as inertial motion.)

In GR context: the referencing to the 'common center of mass' must be relinquished. What remains is to define acceleration as 'acceleration with respect to the local inertial frame of reference'. The 'local inertial frame of reference' is defined as: 'the local frame that is stationary with respect to a free-falling test mass'.

GR asserts the following two statemens:
 (1) Standing on the surface of a planet, you are being accelerated with respect to the local inertial frame of reference.
 (2) Standing on the surface of a planet, your distance to the center of gravitation of that planet remains the same.

 * The rule for determining that one is in an accelerated frame of reference.  --EMS  02:51, 27 Apr 2005 (UTC)

You give no clues as to what concept of acceleration you have in mind. Clifford Will associates the WEP exclusively with Newtonian thinking.

Concepts like rest mass, center of mass, distance, time, relative velocity, energy, remain by and large unchanged in the transition from special relativity thinking to General Relativity thinking. But the concept of acceleration gets a huge make-over (along with gravitation). --Cleon Teunissen | Talk 10:46, 27 Apr 2005 (UTC)

 * I think that you are doing a very good job of confusing yourself. Acceleration occurs with respect to the center of mass in GR too, but that issue is dwarfed by many other conceptual changes.

 * In GR we often talk of a "coordinate acceleration". For example, you can treat distance from the center of the Earth as a radial coordinate, with respect to which objects initially at rest with respect to the Earth are accelerated.  Of course those objects are following timelike geodesics and so are in inertial motion.

 * On the other hand, there is physical acceleration, which is the use of a force to cause a deviation from inertial motion. That is why GR is so wierd when it comes to acceleration:  Being at rest on and with respect to the surface of the Earth places you at (radial) coordinate rest, but physically you are being accelerated; while freefall is physically inertial motion but is also (radial) coordinate acceleration.

 * BTW - Do note that I have avoided talking about coordinate acceleration before this. I felt that it did not help this discussion, and I worry that it still may not.  (One note: being in a circular orbit above the equator is a case of inertial motion without coordinate acceleration, at least when using Schwarzschild coordinates.  You are in coordinate motion through both time [which is unavoidable] and longitude, but no rate change in that motion is occuring.)

 * --EMS 03:56, 28 Apr 2005 (UTC)

Yep, what you describe is a resolution I had reached for myself a long time ago. I invented (and for while advocated publicly) the following two expressions: 'geodesic acceleration' and 'non-geodesic acceleration'. The acceleration towards a center of gravitation in free-fall is then the 'geodesic acceleration', and what you call 'physical acceleration' I call (for myself): 'non-geodesic acceleration'. (Being deviated from moving along a geodesic by a mechanical force)

One can argue that GR features two kinds of acceleration, where Newtonian thinking features only one. It is a dilemma of didactics whether to mention that explicitly or not.

The newtonian inheritence is that the concept of acceleration is associated with inertia, to accelerate you must "overcome" inertia. Gravitation is "cheating", bypassing the rules of "well-behaved" newtonian motion. When the coordinate acceleration of free-fall in curved space-time is prevented the inertia is pointing in the opposite direction of where newtonian thinking expects it to point.

Lately I have come to the conclusion that maintaining a distinction between 'coordinate acceleration' and 'physical acceleration' is not an absolute necessity. I want to merge those two perspectives on acceleration again. I have decided for myself to reinterpret in such a way that the two views on acceleration are brought into one perspective.

Gravitational interaction between two masses causes the two masses to accelerate towards the common center of mass. The conceptual change is that I skip the word 'force'. I just say: gravitational interaction between two masses causes the two masses to accelerate towards the common center of mass. --Cleon Teunissen | Talk 06:14, 28 Apr 2005 (UTC)

 * I strongly council you against trying to re-integrate coordinate and physical acceleration.

 * Look again at what Newton did: He treated spacetime as a flat spatial manifold seperate from time and mapped with a Cartesian coordinate system.  This gave him geodesics which do not deviate:  Given a coordinate direction of motion for an object, inertial motion will maintain that direction of motion (and also by definition the rate of motion).

 * However, if you change the coordinate system (or the "map" of space), then this correspondence of coordinate and physical accelerations will vanish. For example, an object traveling on a chord in a spherical coordinate system will go from moving in a mostly inward direction to moving in a pure tangetial direction and them to moving in a mostly outward direction.  Technically, it is still a straight line, a geodesic, but becuase the map has changed there is now coordinate acceleration!  And this is with Newtonian space!

 * Einstein introduced the principle of general covariance: The laws of physics are independent of the coordinate system against which the spacetime is mapped.  As a result, you can always identify a coordinate system against which a given object is not undergoing a coordinate acceleration as it moves inertially, but as a practical matter you can use whatever coordinate system that you like.  For example, in the above discussion on the GPS and ISS, it is best to use a coordinate system which is a non-rotating Earth-centered frame, which neither the GPS, ISS, or ourselves are at rest in:  It makes the calculations the easiest.

 * My advice is to get used to thinking about two different types of acceleration. Since you already have an elementary grasp of the concepts (and I apologize for underrating you with respect to that), you are in a good position to use them and get better familiarized with what is really going on in GR.

 * --EMS 13:44, 28 Apr 2005 (UTC)

Comparing local rates of time
It has been experimentally confirmed that clocks that have been at altitude, and that were later rejoined with other clocks that had remainde deep in the gravitatonal potential had counted a dissimilar amount of cycles. Gravity probe A

This is reminiscent of the Twin paradox. Two clocks are separated, they are taken on journeys with dissimilar pathlength, and when they are later rejoined, they have not counted the same number of cycles.

Currently, the second is defined as a particular number of cycles of a particular Cesium133 atomic transition. When two Cesium clocks are located on a rotating disk, at dissimilar distance to the center of rotation, then time will not progress at the same rate at the two locations. Light (from that atomic transition) that travels from one clock to the other will itself not change during the journey, but due to the difference in rate of time of the two locations, the light from "the other Cesium clock" will under measurement not show the same frequency as the locally produced Cesium133 transition photons. When clocks are rejoined, they are seen to have counted a dissimilar amount of cycles.

Gravitational alteration of the rate of time is that somehow matter at dissimilar distances to a center of gravitation is in dissimilar rate of time. We don't know what happens to photons while traversing curved space-time; each photon can be measured only once. On measurement, the gravitational frequency shift is measured, consistent with the relativistically predicted difference in rate of time for the two locations.

 * This means that locally, all clocks tick at the same rate! What you are up against with GPS and ISS is how their clock rates are perceived by an observer here on the surface of the Earth. :--EMS 16:17, 27 Apr 2005 (UTC)

I'm not sure what you mean here. The gravitational alteration of the rate of time is in the same category as the dissimilar amount of cycles counted in the Twin paradox and the dissimilar amount of cycles for dissimilar distances to a center of rotation of a rotating disk. It can be verified as being factual by separation and later rejoining of clocks. --Cleon Teunissen | Talk 07:06, 29 Apr 2005 (UTC)

 * First of all, don't lose track of those observations. They are important.

 * I repeat that locally (and do note that I emphasize locally), all clocks (or at least all "good" clocks) tick at the same rate. This is not to say that identical, callibrated clocks cannot be separated, sent on different paths through spacetime, and then rejoined without showing different times.  Instead, what I am saying is that those clocks are all measuring the same thing:  proper time.

 * Here is Minkowski's metric: $$ds^2 = dt^2 - dx^2/c^2 - dy^2/c^2 - dz^2/c^2$$.  Note that $$ds$$, which acts as the length of an incremental path, is also the incremental proper time experienced by an observer traveling along that incremental path. Technically, to use the metric we need to use integration, but for inertial motion in this coordinate system we can just treat "d" as refering to the difference between the start and stop positions on the path.  So in terms of the coordinates, let us have one observer "move" inertially between the spacetime coordinates of (0,0,0,0) and (10 years, 0, 0, 0) (which means that the observer stayed at $$x=y=z=0$$ for 10 years).  For this observer, $$ds^2 = dt^2 - dx^2/c^2 - dy^2/c^2 - dz^2/c^2 = (10\;\mathrm{years})^2$$. So this first observer experiences 10 years of proper time.

 * Now have another observer move inertially between spacetime coordinates of (0,0,0,0) and (5 years, 4.33 light-years, 0, 0) and then accelerate so that they then move inertially from (5 years, 4.33 light-years, 0, 0) to (10 years, 0, 0, 0). You will find that $$ds^2 = (5 \;\mathrm{years})^2 - (4.33\; \mathrm{years})^2 = 6.25\; \mathrm{years}^2 = (2.5 \;\mathrm{years})^2$$.  So On each leg of the path, the second observer experiences 2.5 years of proper time, and comes back to the first observer having experienced only 5 years of proper time instead of 10 years.

 * I assume that you know what I just did, albeit in metric form. The point that I am trying to make is that each observer was subject to the same physics.  Neither clock ran slow!  Instead, due to the laws of physics themselves (and the different paths taken through spacetime), the observers/twins experienced different amounts of proper time.

 * You seem to think that the physics for the various clocks on the Earth, in the ISS, and in the GPS constellation are different. My point is that it is the same.  The differences in the times they report are due not to the clocks being physically different or subject to different physical laws, but instead due to the metric structure of spacetime.  In fact, as you noted in your last paragraph above, the same situation as exists in the Twin Paradox exists in the Earth/ISS/GPS situation and also the rotataing disk situation.  Look again at each, and you will see clocks which are experiencing different rates of proper time due to the different paths that they are taking through spacetime.

 * Take the Schwarzschild solution and figure out the path lengths in the on-Earth, GPS and ISS cases. Do note that the temporal coordinate will be for an observer distant from the Earth, and that you need to account for the rotational motion of the objects due to the rotation of the Earth (for us) or orbital motion (for the spacecraft).  However, if you do it properly, you will get the observed relationship for the passage of proper time in each case.

 * So "good" clocks never run fast or slow. They just follow paths of different (proper time) length through spacetime.  That, in a nutshell, is what "time dilation" is all about.

 * --EMS 16:28, 29 Apr 2005 (UTC)

Differences in the amount of proper time
I take the two-clocks-on-a-rotating disk arrangement, for that is the most symmetric one. As soon as one of the clocks reaches the point of one year of proper time counted the clocks are rejoined and compared.

What needs to be adressed is this: the Cesium133 clocks as a whole setup were moving through space, which can be regarded as macroscopic kinematics. On rejoining they are seen to have counted a dissimilar amount of cycles, which is a difference that is quantumphysical in nature; transition of electrons; the smallest scale physics.
 It seems to me that it is not enough to refer to longer pathlength only. What is the nature of the physics that is converting pathlength in space to differnence in quantumbehavior?

The mathematics of the metric structure of space-time describes how much difference in proper time is to be expected. It does not offer explanation of the underlying physics of this difference.

It is tempting to make a comparison with for example mechanical clocks that are sensitive to temperature variation. You take one of the clocks up a cold mountain, and on rejoining with a clock in the valley a dissimilar amount of cycles is counted.

It is tempting to hypothesize that in the case of the Twin paradox and the two-clocks-on-a-rotating disk arrangement something is tampering with the rate at which quantumprocesses are occurring. This "tampering with the rate of time" would have to be in the same proportion for all quantumprocesses, for no anomalies are known.

Be it as it may, all observations are consistent with a slower rate of all physical processes at greater depth in a gravitational potential, consistent with a slower rate of time itself.

When Einstein predicted that gravitation will bend the path of light, he did that on the basis of the wave-properties of light. Einstein treated space-time as a dispersive medium, closer to the Sun the wave-front is propagating slower, hence a bending. (And later the theoretical discovery that close to the Sun there is a "surplus" of space, also affecting the propagation of the wave-front.)

About the clocks:
 Of course the clocks are fine!! It is puzzling that you bother to assert that the clocks are fine, that they run neither fast or slow; that is as superfluous as taking the trouble of asserting that the Earth is spherical and not flat. Of course the clocks run according to the laws of physics! In this particular case the relevant law of physics is the law that relates amounts of proper time in Minkowski space-time (or under the Schwarzschild metric) --Cleon Teunissen | Talk 19:07, 29 Apr 2005 (UTC)

"The mathematics of the metric structure of space-time describes how much difference in proper time is to be expected. It does not offer explanation of the underlying physics of this difference."

The metric structure is the underlying physics explaining that difference.

In the frames of reference of the traveling twin in the Twin paradox, the "stay at home" twin is also subject to time dilation. However, because of the change of frames of reference when he accelerates, the traveling twin sees the stay-at-home twin move through 20 years of coordinate time at a time dilation factor of 2:1 (traveling twin:stay-at-home twin) (in the sitaution in my example above that is).

From the Schwarzschild solution for an observer at rest in the earth-cetered inertial frame of reference: $$ds^2 = (1 - 2m/r)\,dt^2$$. Since $$2m/r$$ is less for an observer in the ISS than for ourselves, it follows that $$ds$$ over some coordinate time the elapsed proper time will be greater in the ISS (ignoring its orbital motion of course) than for us here on the Earth (when ignoring our rotational motion).

You acknowledge that the clocks are the same, and then you turn around and ask what makes them different. The answer is their path through spacetime. that really is all that there is to it.

If you want a different explanation of the time dilation effect, then realize that for observers in the gravitational field of an accelerating rocketship, there also is time dilation with the observer lower down appearing to have a clock that ticks slower. In this case, the explanation is the relativity of simultaneity combined with the change of inertial frames of reference as one accelerates. The more the acceleration, and the more separated the observers, the greater this effect.

The same explanation works in the gravitational field of the Earth. However, the "why" behind that is, once again, the metric structure of spacetime.

--EMS 20:09, 29 Apr 2005 (UTC)

The analogy with electromagnetic induction
I'd like to show you something that I encountered in my early searches of information on GR. It is how the physicist and historian of science Michel Janssen explains the view that Einstein took.

Einstein had referred to an analogy with electromagnetic induction. For a charged particle that is at rest with respect to a current carrying wire there is no magnetic field. On the other hand, when the charged particle is moving with respect to the current carrying wire a magnetic field manifests itself. In a representation in a Minkowski space-time diagram this can stated as follows: there is one field, an electromagnetic field, and how that field is percieved is dependent on what "slice" you cut in space-time. It is, in terms of the Minkowski space-time diagram, dependent on the direction of the "slice" that is cut in space-time.

Likewise, Einstein envisioned a reinterpretation of the concept of gravitational field, in which it presence or non-presence is a relative quality, dependent on your relative acceleration; dependent on what "slice" you cut in (curved) space-time.

This thinking, I infer, centers around a principle that acceleration of objects (relative to the observer) can fundamentally only be meaningfully defined in relation to a chosen frame of reference. For every choice of reference frame there is a corresponding d'Alembert acceleration. (Including frames with zero d'Alembert accereration)

I can see the logic and self-consistency of that approach. I can see how it can be made to work. (In order to make it work in curved space-time, a distinction between coordinate acceleration and physical accceleration is introduced.)

Based on the information provided by sources like Michel Janssen, I have made my choice as to which interpretation of GR to follow. --Cleon Teunissen | Talk 11:15, 30 Apr 2005 (UTC)

Reliable sources of information
Michel Janssen is one of my most important sources of information.
 External link: Einstein's first systematic exposition of general relativity
 * In the presence of a gravitational field the laws of nature will in general not be particularly simple in any one frame or in any one class of frames.The simplest formulation is a generally-covariant one, a formulation that is the same in all frames,including frames in arbitrary motion with respect to one another. In this sense of relativity, general covariance guarantees general relativity (Einstein 1916a,770). This does not mean that observers in arbitrary motion with respect to one another are physically equivalent the way observers in uniform relative motion are. In that more natural sense of relativity, general relativity does not extend special relativity at all. - Michel Janssen

 * I don't like the context in which you are presenting this. On one level, this is true.  For example, in an accelerated box the observer in the top of the box experiences a different proper acceleration than the observer in the bottom of the box.  They also differ in terms of potential energy and clock rate.  However, this obscures the ways in which they are the same, and the fact that potential energy and the like are a matter of how the situation in the accelerate box is perceived.

 * None-the-less, the statement about the physical equivalence of observer in arbitrary motion is correct and important. However, there is an extension of SR in to GR, namely Local Lorentz Invariance, which states that locally in the vicinity of an observer the rules of SR do apply.

Another important source of information for me is the online book, reflections on relativity by the mathematician and astrophysicist Johathan Vos Post. Jonathan Vos Post writes that a Sagnac interferometer measures absolute rotation.

I infer that he uses the expression 'absolute rotation' to emphasize the contrast with the concept of 'relative measurement'. Velocity can fundamentally only be expressed as velocity with respect to other mass. A Sagnac infermeter works straight away, the way it works does not require comparison with an outside reference. Instead, a Sangac interferometer performs a local, geometric measurement. That is particularly striking in the case of the ring laser gyroscope: the beat frequency is proportional to the angular velocity of the ring laser gyroscope.

A Sagnac interferometer measures the amount of rotation with respect to the local inertial frame of reference. Since frame dragging is a rare an exceedingly small effect, effectively all the local frames of reference of the universe do not rotate with respect to each other.

The point is the finding (in the years between 1915 and 1920) that in Einsteinean space-time rotation is not relative. The general covariance form of the equations facilitates the unification of gravitation and special relativity, but this general covariance has no bearing on the physics of rotation.

Calculations have been performed (notably by Thirring) on what the metric is of the space-time inside a hollow, rotating sphere. These calculations have shown that in GR rotation is not reciprocal. Visually the two following situations look the same: a planet is itself rotating, or a very large hollow spere is rotating around the planet. But the physics is not the same in those two cases. This is documented in the article by Michel Janssen Einstein's first systematic exposition of general relativity

 * Very good. This is a point that I tried to make in our Sagnac Effect discussions:  Rotataing the coordinate system is not the same as rotataing the aparatus/planet.  (There is no Sagnac Effect if you spin but the apparatus does not.)

 * As for rotation in general: I will split hairs here.  IMO, rotation is relative.  I have no problems with that.  What is not relative is proper acceleration, and that is what is used to distinguish the rotating and non-rotataing situations.  The bottom line is none-the-less much the same:  There is a state for a disk which all observers will agree is physically non-rotating whether the disk is undergoing a coordinate rotation (with respect to some observer's chosen coordinate system) while in that state or not.

Peter M Brown documented the shift of interpretation from the Einstein interpretation of GR to the modern interpretaton of GR. You haven't spoken out on the subject lately, but as far as I can tell you reject the modern interpretation of GR and you regard the 1916 Einstein interpretation of GR as the only possible interpretation. (Michel Janssen documents that after about 1920 Einstein did not endorse his 1916 interpretation of GR anymore.) --Cleon Teunissen | Talk 08:37, 3 May 2005 (UTC)

 * As far as I'm concerned, you don't yet truly understand either version of GR. I don't so much endorse the 1916 interpretation as I use the 1916 semantics.  There is value in refering to a gravitational field, even that is only a convenient description of the observed action of inertially moving bodies with respect to yourself.

 * I also don't see much value in Dr. Brown's article. How GR came to be in interesting in its own right, but what matters is how GR itself functions, and articles like this are not going to help you to understand GR all that well.  In your cases there are specific issues that need to be tackled, and the history of GR is not one of them.  Indeed, I chose not to comment on that "EGR vs MGR" article because I saw noting there to disagree with.  In terms of interpretation, things have advanced and continue to do so.  However, the underlying theory is still Einstein's.

 * --EMS 15:52, 4 May 2005 (UTC)

 * P.S. You are making progress.  Just don't confuse progress with completion.

Good move
Good move to move the Talk:equivalence principle page, that was long overdue.

Now that I'm here: it was also good to comment out the category tags on the sandbox pages; it hadn't occured to me the sandbox articles might get listed on a central page. --Cleon Teunissen | Talk 21:39, 4 May 2005 (UTC)

 * Thank you for agreeing with me on something! :-)

 * --EMS 04:00, 5 May 2005 (UTC)

Connections between Sagnac effect and inertia

 * I think that you are finally starting to grasp the significance of the EP and where it fits into things. --EMS | Talk 14:44, 12 May 2005

Well, my grasp has changed very little. What is mainly happening is that you often read something very different from what I write. Apart from the actual differences of opinion between us, you have on many occasions chased imaginations, attributing thoughts to me that are alien to me.

 * In that case you need to do a better job of communicating your ideas. I do my best to deal with what you write, and try to give you the benefit of the doubt, but sometimes I must just plain disagree.  Perhaps what you need is less to learn GR than how to communicate what you have learned.  Personally I think that the two are intertwined.

I am confident that my judgement of the quality of sources of information is good. When different sources contradict each other, I judge for myself how to piece together a coherent picture. Your version of GR contradicts sources of information that I regard as reliable. (Jonathan Vos Post, John Wheeler, Michel Janssen, Max Planck institutute for the history of science, Kyoto institute of history of science.)
 (Much of the helpful information I found comes from physicists that have turned to history of science. Historians of science trace the development of ideas, so their texts tend to focus on the fundamental assumptions underlying the theories of physics)

The equivalence principle article
It is the Wikipedia way that I can only try. It has been clear for weeks that I did not get support from Joke137, so that was it.

 * My advice is to leave it be. Minor edits are OK, if they are needed, but you have a viewpoint on it that is inconsisent with ours.  I need to polish that off at some point.

The Sagnac effect and time dilation
I remain keenly interested in the subject of proper time, because of the connection with the Sagnac effect.

Recapitulating: the Twin paradox scenario and the two-clocks-on-a-rotating-disk scenario have in common that it is the difference in pathlength that counts: to calculate the time dilation, a path integral of the path with respect to the inertial frame of reference must be calculated.

In the Twin paradox scenario the acceleration phase can be short and concentrated, in the two-clocks-on-a-rotating-disk scenario the acceleration is distributed uniformly. For example, in a twin paradox scenario the traveling twin can make a lot of zig-zags, accelerating much more often, but that does not lead to more time dilation if the pathlength is the same as one big haul away and one return journey. The (accumulated) difference in pathlength counts, not the (accumulated) acceleration.

The Twin paradox can be represented in a space-time diagram with one dimension of space and one dimension of time, the two-clocks-on-a-rotating-disk scenario needs a space-time diagram with 2 dimensions of space. If you start with the two-clocks-on-a-rotating-disk scenario and you omit one of the two dimensions of space, then what remains is a form of the twin paradox scenario.

 * You only need one dimension of space for the Saganc experiment, but that dimension is θ where v=rω.

In GPS synchronisation procedures the Sagnac effect must be taken into account. Neil Ashby describes that the Sagnac effect also occurs if time is disseminated with portable clocks instead of with radio-signals. The Twin paradox, the two-clocks-on-a-rotating-disk scenario and the Sagnac effect are only different in appeareance. The aspects that they have in common are the aspects that count: dissimilar pathlenths, and a loop is being closed.

This view implies that the double-slit experiment and the Twin paradox in Minkowski space-time are seen as involving the same space-time geometry. In the case of interferometry the time difference is measured by measuring a phase shift, in the Twin paradox scenario the time difference is measured by comparing clockreadings. (This is all based on the principle that isotropy of inertia and isotropy of quantumwave propagation always coincides.)

 * I would be careful here. I see no reason for such a theoretical coincidence, except at macroscopic levels.  The quantum view can be very different than the classical one.  Only on macroscopic scales is it demanded that they correspond.

Inertia
The recurring theme, it seems, is that inertia is correlated whith the temporal relation of an object with its surroundings. This is particularly visible in the case of the Twin paradox. The traveller that changes his velocity is the one who changes the way he relates to his surroundings. I follow the expectation that in the future a theory will be found that describes the quantumphysics of inertia.

I have read what you have written on User:Ems57fcva/sandbox/General_Relativity. I am curious in what direction that will develop.

 * It will develop if and when I can get back to it. It may become a seperate article on inertia and GR instead of replacing the GR page itself.  I am beginning the think that the GR page has to be general, and that write-up is getting too specific.  I also think that redoing the GR page in one fell swoop is not advisable, based on my EP experiences.

 * --EMS | Talk 16:59, 16 May 2005 (UTC)

--Cleon Teunissen | Talk 16:33, 16 May 2005 (UTC)

Spatial dimensions involved in the Sagnac effect
You only need one dimension of space for the Sagnac experiment, but that dimension is θ where v=rω. --EMS | Talk 16:59, 16 May 2005 (UTC)

 * The Sagnac effect involves circumscribing an area; the magnitude of the Sagnac effect is proportional to the size of that area, so there are two spatial dimensions involved, in polar coordinates both θ and the radius matter. --Cleon Teunissen | Talk 12:12, 18 May 2005 (UTC)

We were talking time dilation, and it is with respect to time dilation and the length of the path taken by an observer on a rotating disk [who is constantly accelerating but going at a constant speed with respect to the center of the disk (as viewed by an intertial observer)] that my remark applies.

For example, in the twin paradox, the observer goes out and back along the x axis. If he also moves with respect to the y axis independently of his x motion, you then need to use two spatial dimensions in that case. Similarly on the rotating disk if you move with respect to r then r must be taken into account.

The bottom line is that there is nothing wrong with what you wrote. I was just playing a coordinate game, which admitedly is only good in the idealized Sagnac case where the light is staying at a constant r. --EMS | Talk 15:08, 18 May 2005 (UTC)

The relation between quantum physics and gravitation
This is all based on the principle that isotropy of inertia and isotropy of quantumwave propagation always coincides. --Cleon Teunissen | Talk 16:33, 16 May 2005 (UTC)

 * I would be careful here. I see no reason for such a theoretical coincidence, except at macroscopic levels.  The quantum view can be very different than the classical one.  Only on macroscopic scales is it demanded that they correspond. --EMS | Talk 16:59, 16 May 2005 (UTC)

There is the Heisenberg uncertainty, of course. As is the case with all quantummechanics, the correspondence holds good for the average behavior. The larger the number of quanta of action involved, the tighter the correspondence. The average is affected in the way it is because the probability distribution of each quantum of action is affected individually.

In the Sagnac effect article I wrote 'interpreted in terms of classical wave mechanics there is a standing wave'. In terms of quantum mechanics: the shape of the probability distribution is stationary with respect to the local inertial frame of reference.

Macroscopic behavior of matter is an epi-phenomenon of the physics taking place at the quantum level. If gravitation would not affect the probabilitiy distribution of de Broglie waves, then there would be no gravitational effects at all.
 External link: arXiv.org/abs/physics/0411052 Atomic Interferometric Tests of the Equivalence Principle
 --Cleon Teunissen | Talk 12:17, 18 May 2005 (UTC)

 * That last sentence is an interesting remark. I have no argument with it's point.

 * What disturbed me was that you made a very asture remark about the twin paradox and Sagnac effect being related phenomena since they involve path lengths, and then suddenly dragged quantum mechanics and the double-slit experiment into the mix. Path lengths are also involved there, but the association between the double-slit and Sagnac is very different that the association between Sagnac and the twin paradox.  You cannot describe the twin paradox as being due to the quantum effects behind the double-slit experiment, but your train of though implies that you think so.

 * People have been trying to unify GR and QM for decades. Unless you are very, very lucky you are not going to solve that puzzle yourself. --EMS | Talk 15:24, 18 May 2005 (UTC)

I know of course that so far attempts to find a quantum theory of gravitation have been unsuccesful. But it seems justified to suppose that whether we humans have a working theory about it or not, it is happening in nature. It seems to me that we humans may feel a need for such a theory, nature does not "feel" such a need. It just happens. --Cleon Teunissen | Talk 07:12, 19 May 2005 (UTC)

 * What are you saying here? If it that nature does not use theories, I can go along with that.  Nature simply is, and is and it is.  Our theories, no matter how correct they are, and not nature but instead a model of how nature operates.

 * That is pretty much my view, yes. Among my assumptions is that the properties of nature are what they are, independent of the past, present or future stage of human refinement in modeling nature. --Cleon Teunissen | Talk 16:08, 19 May 2005 (UTC)

 * No argument here. (I would not have bother to respond, but I wanted to indent your response to make the thread more readable, and my having done an edit would be seen in your watchlist.  Therefore ... .) --EMS | Talk 03:44, 20 May 2005 (UTC)

 * I would think that it is possible to create an appropriate model, and that it will be done at some point. Part of the issue may be the identification of the right theoretical mechanisms and also the development of the right theoretical tools.  (Newton had to develop calculus to do his theory.  Einstein needed the newly developed tensor calculus for non-linear geometries to do GR.)  My point is that there are a lot of very capable people working on this, people who already know GR and QM quite thoroughly. --EMS | Talk 13:51, 19 May 2005 (UTC)

The Twin paradox cannot be described as due to quantum effects
You cannot describe the twin paradox as being due to the quantum effects behind the double-slit experiment, but your train of though implies that you think so. --EMS | Talk 15:24, 18 May 2005

 * Actually, the above is an example of you following an imagination, attributing a thought to me that is not mine.

 * I did not mention quantum mechanics when I mentioned the double-slit experiment. I did not suggest that the quantumphysical description of the double-slit experiment helps to elucidate the twin paradox. It doesn't. The 'train of thought' that you attribute to me comes from your own imagination.

 * But what I described is not obvious, so I think it is worth some elaboration. --Cleon Teunissen | Talk 12:05, 20 May 2005 (UTC)

 * You wrote:

 * This view implies that the double-slit experiment and the Twin paradox in Minkowski space-time are seen as involving the same space-time geometry.

 * I'm sorry that I got sloppy in my analysis of it. Even so, the double-slit experiment does not use the time dilation aspects of spacetime.  The twin "paradox" involves time-like paths and acceleration.  The double-slit experiment involves light-like paths and differing spatial path lengths.

 * The double-slit experiment can and is best described classically. Relativity has nothing to do with it.  It is on another level that the two will be merged. --EMS | Talk 12:47, 20 May 2005 (UTC)

The Sagnac effect, the Twin paradox, and Minkowski space-time

Let there be a fleet of four spaceships, numbered 1, 2, 3 and 4. The fleet is moving inertially in Minkowski space-time, and they are not moving with respect to each other, so they can use radio pulses at regular intervals to monitor and maintain a synchronised standard fleet time. The following procedure is used: one regularly spaced train of pulses is directionally beamed from ship 1 to ship 3, and one signal is beamed from ship 1 to ship 4, and ship 4 relays the signal to ship 3.

Clearly, because of the difference in pathlength, the radio-pulses will not arrive simultaneously at ship 3 (as measured in standard fleet time). When the radio-pulses are seen as (collections of) propagating photons then the elapsed proper time (for those photons) from emission to reception is zero. The photons arrive at ship 3 at different moments in standard fleet time. This difference between proper time along the lightlike path and time as measured onboard ship 3 is described by the Minkowski metric.

Now let ship 4 be very close to ship 2. Then the difference in pathlength can be so small that it is about as large as a wavelength of a continuous sinuswave radio-signal. Let a single beam be sent from ship 1. Some of the radio-energy propagates along a straight line towards ship 3, some of the radio-energy reflects on the hull of ship 4 and then reaches ship 3. Under those circumstances ship 3 can obtain an interference pattern.

The above scenario is quite like a double-slit experiment:
 You can set up a double-slit experiment with one point/slit source of monochromatic light, and a mirror perpendicular to the viewing screen, very close to the point source, so that an interference pattern is obtained.

 * Measuring a difference in arrival time, and obtaining an interference pattern can appear to be different types of measurement, but given the nature of light they are in a more fundamental sense the same type of measurement.

Of course, this does not explain the Twin "paradox" in terms of another theory. It only illustrates a well known aspect of special relativity: the geometry of Minkowski space-time describes the time dilation that is involved in the propagation of light.

G E Stedman and Neil Ashby describe the following:
 When on Earth time is disseminated along the equator by way of radio-pulses, then a westward time dissemination relay does not arrive back at the originating station at the same moment as the eastward time dissemination relay. Also, a clock circumnavigating Earth in an eastwards (westwards) direction loses (gains, respectively) 207.4 ns from the Sagnac effect. (Provided the clocks remain in uniform circular motion, etc etc.)

The Sagnac effect can be elicited with light-pulses as the time bearers, or with portable clocks as the time bearers. In both scenario's the amount of time dilation that build up from start to finish can be calculated with special relativity formulas.
 When light is used as a time bearer then the time difference can be measured interferometrically, or the time difference can be measured by comparing arrival time as measured by a clock.

The fleet of spaceships can also use shuttlecrafts with onboard atomic clocks to disseminate time among the fleet. Then both the transit time and the elapsed proper time with respect to standard fleet time must be taken into account. The transit time will of course be much longer than in the case of disseminating time with lightpulses. Let two shuttlecrafts be used, one disseminating time to the ships of the fleet in the following order 1-2-3-4-1 and the other in the opposite direction: 1-4-3-2-1. On returning to ship 1 the two shuttlecrafts should have counted the same amount of proper time.

Properties of double slit interferometry
 Interference fringes can also be obtained with matter interferometry. In various types of interferometry it has been experimentally demonstrated that interference fringes will also be build up if the luminosity of the beam is so low that there is at all times only one quantum of action present in the setup. This implies that for quanta of action a process of self-interference is perfectly normal. Paul Dirac was the first to draw the conclusion that each photon interferes only with itself.

This is a quite peculiar aspect of the propagation of light. Whenever a non-laser source of light is used to obtain an interference pattern then each photon will only contribute to the interference fringes by way of a self-interference process.

I suppose that the above conundrum is related to the reasons why attempts to unify GR and QM have been unsuccesful so far.
 --Cleon Teunissen | Talk 12:15, 20 May 2005 (UTC)

You continue to mix apples and oranges. You as confusing yourself with the difference in spatial path lengths for the double-slit experiment (and hence the number of wavelengths on the path), and the path difference for the twin paradox.

Here is something cute to consider: Along a purely spatial or Riemannian manifold, a geodesic is a path which locally always covers the shortest spatial distance. In a Lorentzian manifold such as the spacetimes of relativity, a timelike geodesic is a path which locally experiences the longest proper time.

You can use relativity to reconcile different views of the double-slit experiment, but that is a fairly trivial exercise, and does nothing to help unify the QM and GR. --EMS | Talk 13:13, 20 May 2005 (UTC)

Particle/wave duality and special relativity
The double-slit experiment can and is best described classically. --EMS | Talk 12:47, 20 May 2005 (UTC)

 * Well, according to classical wave dynamics an interference pattern can occur when the light is coherent light. In fact an interference pattern can also be obtained with incoherent light (for example sunlight). Describing the double-slit experiment demands facing up to particle/wave duality.

 * The version of the double slit experiment that uses one slit and a mirror is called "Lloyd's mirror" External links: principle of Lloyd's mirror Interference fringes in a Lloyd's mirror setup

 * You don't need GR for it. That was my point.  You can also get away without using QM either, but that is not a very productive exercise. --EMS | Talk 05:19, 21 May 2005 (UTC)

You can use relativity to reconcile different views of the double-slit experiment, but that is a fairly trivial exercise, --EMS | Talk 13:13, 20 May 2005 (UTC)

 * I agree that it is a fairly trivial exercise.
 The Lloyd's mirror version of the double slit experiment is the light propagation analog of changing direction of motion. Light imparts momentum when it reflects against a surface. In a sense the light bounces against the reflecting surface.

The twin "paradox" involves time-like paths and acceleration. --EMS | Talk 12:47, 20 May 2005 (UTC)

 * Recapitulating: Lightlike worldlines are the extreme limit of very fast timelike worldlines. Simplified calculations of timelike worldlines often assume instantaneaous U-turns. Instantaneous U-turns are physically unrealistic, but in thought experiments they are OK, for instantaneous U-turns do not affect the logic of the thought experiment. I will call such an instantaneous U-turn a "bounce"

 * In the Proper time time article you present a calculation in which the traveling twin "bounces" once. Alternatively, you can have the travelling twin bounce three times: travelling away 2.5 years of coordinate time, bouncing, travelling back for 2.5 years coordinate time, bouncing, and away and back again. Then the accumulated time dilation of the travelling twin will be the same as in the 'one bounce' scenario, even though he has gone through three times as much acceleration. It is the (accumulated) difference in pathlength that determines the (accumulated) time dilation. The acceleration that is involved is, although a necessary factor, not a determining factor.

You continue to mix apples and oranges. You as confusing yourself with the difference in spatial path lengths for the double-slit experiment (and hence the number of wavelengths on the path), and the path difference for the twin paradox. --EMS | Talk 13:13, 20 May 2005 (UTC)

 * I follow Jonathan Vos Post in thinking that particle/wave duality is at the heart of relativistic physics. I regard it as a principle of physics that the propagation of light in Minkowski space-time, and the propagation De Broglie waves in Minkowski space-time is the same fruit.

 * Currently the largest molecules for which diffraction and interference has been achieved are C60 and C70 fullerenes. External link: de broglie interferometry. This is supportive of the idea in principle all lumps of matter propagate through space as de Broglie waves. Of course, the bigger the lump of matter, the less the probability of observing interference.

 * I know that it is pretty audacious to see particle/wave duality at the heart of relativistic physics, but I would like to point out that there is a difference between being audacious and being confused. I'm not confused here.

 * I studied QM as an undergraduate in college. Even without a formal QM/GR unification, deBroglie waves must still transform properly between coordinate systems and under the Lorentz transformations for both theories to be tenable.  I know of noone that has found a problem on that level.  You can study that association if you like, but for the metric structure is what is important to me, not whether the geodesics are traveled by waves or particles.

 * As for being audascious: Be my guest.  Just remember that Wikipedia is looking for people to be bold, not audascious.  They are after factual articles, not research articles and not audascious ideas.  Einstein would not have been welcome to post an aticle on relativity here in 1905 (if WIkipedia had existed then), and that is quite good and proper.   It is only after the theory becomes endorsed enough to be controversial (1907/8) that describing it and the debate surrounding it becomes proper. --EMS | Talk 05:19, 21 May 2005 (UTC)

It is on another level that the two will be merged. --EMS | Talk 12:47, 20 May 2005 (UTC)

 * I agree with that. The idea that special relativity accommodates particle/wave duality does not constitute a new theory. For example, Thomas precession is described as a relativistic quantum effect, this illustrates special relativity and quantum physics have been merged ages ago.

 * My intention was to investigate the relation between Special Relativity and QM. It is puzzling why you keep repeating the obvious: 'it does not help to unify GR and QM' I know that it does not help to unify GR and QM. If you respond to me, please respond to things I actually claim. When you read, please search fiercely for the most cautious, the most unassuming interpretation of what you read. You have a habit of over-interpreting wildly.

 * --Cleon Teunissen | Talk 00:25, 21 May 2005 (UTC)

 * If you are not seeking a unification or at least a deeper relationship than a certain reciprocity between them, then why are you bringing it up!!??. You keep over and over and over again pointing out this supposed commonality between time dilation and wave interactions.  You even declare your audasciousness above.

 * I'm not all that sure that you are not over-interpreting my writings. My goal is to show you where you are heading with some of this stuff.  If it looks properly ridiculuos, then good.  If you were not heading in the indicated direction, then you should look again at your writings.  Remember:  It is your job to communicate here.  --EMS | Talk 05:19, 21 May 2005 (UTC)

The search for interconnections

 * If you are not seeking a unification or at least a deeper relationship than a certain reciprocity between them, then why are you bringing it up!!??. --EMS | Talk 05:19, 21 May 2005 (UTC)

Yes, I am seeking for deep interconnections. The way I see the Twin "paradox" scenario has been influenced by what I have learned about the Sagnac effect. (From now on I will refer to the loop-closing Twin scenario, I am fed up with referring to the Twins scenario as a "paradox".)

The Sagnac effect can be recognized in the following three situations: (1) interferometry with counterpropagating light in a loop trajectory. (2) Time dissemination relays with a loop topology. (3) Two clocks on two rotating disks, the disks either rotating in different directions or in the same direction, the two disks rotating with dissimilar angular velocity with respect to the local inertial frame.

Version (3) can be seen as relatively elaborate version of the loop-closing Twin scenario. Conversely, the loop-closing Twin scenario can be seen as a truncated Sagnac cycle.

 * You have a way of creating connections where they do not belong. That is what has gotten you into trouble with the Equivalence Principle page.  That is touble for you here also.  Sagnac involves the propagation of light, and therefore light-like paths.  Time dissementaion is done with signal synchonization, and therefore also involves light-like paths, and will display a legitimate Sagnac effect.  The loop-closing Twin paradox, on the other hand, involves time-like paths!  See my revised proper time article for how that works, using path lengths (which you now seem to be used to).

In visualising each of the versions, I visualize a space-time diagram with two spatial dimensions and one time-dimension. I visualize how the physica progresses in time. I consider the space-time diagram representation as the most fundamental representation of the physics taking place. This opinion of mine is strongly influenced by the Usenet Physics FAQ discussion of the loop-closing Twins

In the Sagnac effect article I have only added the description of (2) so as not to overburden the article. I have structured the article in such a way that the most accessable information is given first. As the article progresses, it deepens.

 * I think that (3) is worse that a "burden". IMO it is actually a misleading red herring.  I'm not even sure of the status of (2), but the last I saw of the Sagnac effect article you had it well in hand and I felt little need to get involved with it again.  If anything, your knowledge of the mechanisms behind it has increased.  Just be aware that your studies have now moved away from the Sagnac effect itself to the dynamics of the rotataing disk in general.  The Sagnac effect is just on aspect of the rotataing disk in relativity.  The loop-closing twin paradox is another.

The information in an article is always only the tip of an iceberg. The conceptual background of the author resonates in how the information is presented.

If I were to rewrite the Twin paradox article, I would present pathlength difference as the crucial element. The current Twin paradox article presents change of the plane of simultaneity at the moment of the U-turn as pivotal, but I would describe the change of plane of simultaneity as a downstream consequence, not as an upstream causal aspect.

If I would rewrite Twin paradox article, I would probably not mention the Sagnac effect, but the connection is prominent in my mind and that mindset as a whole resonates in what aspect of the loop-closing Twin scenario I focus on.

 * The simultaneity shift is not just a "downstream" consequence. It is really quite crucial.  However, the current twin paradox particle does not correctly state why it is crucial.

 * Year ago, I posted on the USENET relativity group an article of the twin "paradox" resolution. It goes over the math of what the traveling twin views.  I advise reading it.  I would love to see that math placed into the twin paradox page.

In the case of the Minkowski metric the following is in my mind:
 $$ c^2 dt^2 - dx^2 - dy^2 - dz^2 $$ adds up to zero in the case of propagation of light. A flash of light expands spherically symmetrical into space, and all inertially moving observers monitoring the expansion of the light observe a spherically symmetrical expansion. (This is, of course, only one of many ways to formulate the relativity of inertial motion, this one focuses on wave-propagation.)

Particle/wave duality is not possible in a space with a Euclidean metric, but I am intrigued by Jonathan Vos Post's assertion that a Lorentzian manifold has the property that it allows particle/wave duality. (As I understand it, the technical term 'pseudo-Riemannian manifold' refers to a special case of Riemannian geometry, with pseudo-Riemannian geometry sharing the (+,-,-,-) property of Minkowski space-time geometry.)

 * Correct. Most relativists use the term Loretzian for any relativistic spacetime, including those of GR.  For the mathematician, "pseuso-Riemannian" is prefered.  Personally, I won't fight the math freaks over this.  I'm more interested in the substance than the semantics.

In writing a wikipedia article I would not write explicitly about such matters, because wikipedia is not the place to go that far into detail, but the general frame of mind does influence the way information to be presented is selected, and how it is presented; hence it is often that on the Talk page the physics is discussed at a deeper level than the level of the article.

In the Sagnac effect article, I describe briefly the physics of the ring laser interferometer. Normally the laser process converges rapidly to monochromatic light. But in the case of the ring laser interferometer there is a splitting of the frequencies. So what drives that splitting? As I present the physics, the splitting of the frequencies is to be understood by considering the geometry of the setup: the difference in pathlength, combined with the condition that the two counterpropagating beams of laserlight must have the same amount of cycles (the same amount of nodes and anti-nodes).

I take the following as a recognizable physics principle and I use it to unify physics explanations: all forms of time dilation that occur in Minkowski space-time can be accounted for in terms of dissimilar pathlengths.
 --Cleon Teunissen | Talk 09:09, 23 May 2005 (UTC)

 * That last statement is quite correct. Just please don't treat the Sagnac Effect as being a time dilation effect or directly related to time dilation.  The connection through the rotataing ring is there, but the loop-closing twin paradox really, really is a horse of a different color. --EMS | Talk 14:13, 23 May 2005 (UTC)

The loop-closing Twins scenario

 * I posted on the USENET relativity group an article of the twin "paradox" resolution. It goes over the math of what the traveling twin views.  I advise reading it.  I would love to see that math placed into the twin paradox page. --EMS | Talk 14:13, 23 May 2005 (UTC)

Well, the best thing to do would be to replace the current Twins article with just a straight link to the Usenet Physics FAQ Twin paradox discussion

As usual Jonathan Vos Post's X-ray perception has seen deeper than any other author on the subject Reflections on relativity chapter 4 section 7
 * Ultimately the answer depends on what sort of satisfaction is being sought, viz., on whether the paradox is being presented as a challenge to the consistency of special relativity or to the completeness  of special relativity.  [...] if it is the completeness (rather than the consistency) of special relativity that is at issue, then the naive acceptance of inertial frames is precisely what is being challenged.

With the Twin paradox, one must distinguish between two kinds of suspicion:
 (1) Are we baffled because there is an inconsistency in the theoretical framework of relativistic physics?
 (2) The theory is self-consistent, but incomplete.

It is not enough to show that special relativity is self-consistent in its description of the loop-closing Twins scenario, that does not alleviate the uneasy feeling of facing something very counterintuitive.

Showing that it is all perfectly consistent moves the problem sideways, but it does not move the understanding of the physics taking place to a deeper level. Why is the Minkowski metric the way it is? What is time? What is space? What is space-time?

My point is that is is an error to think that the loop-closing Twins scenario is exhaustively resolved by showing that special relativity is self-consistent. I do not doubt the selfconsistency, that's not an issue. I want to know why it is the way it is, I crave for a theory that digs even deeper. (Possibly no deeper physics exists, maybe the Minkowski metric is already 'rockbottom', as quarks appear to be the 'rockbottom' of particle physics.)

Anyway, it is rather hilarious that you triumphantly claim to have resolved the "paradox" where compared to others who have written on the subject you haven't even scratched the surface.
 --Cleon Teunissen | Talk 16:40, 23 May 2005 (UTC)

 * Those are excellent references. I counsel against outright replacing the existing twin paradox page, but you are encouraged to add those references and any others that you may be aware of to the SEE ALSO section of that article.  (The ability to find good web references is one of your strengths.)  I really think that Wikipedia deserves a stand-alone article on the Twin Paradox in its own right, but it does not need to be (and probably should not be) as comprehensive and the USENET FAQ pages.

 * As for my math exercise: I think I did more than scratch the surface with it.  The gist of the paradox is "why doesn't the traveling twin see the stay-at-home twin undergoing time dilation?".  The answer is that the traveling twin does, but for the stay-at-home twin's passing through a lot more coordinate time.  To me it answers the questions, and perhaps moots the need for some of these explanations that need more explanation.

 * I think that you are still grappling with the issue of "what is the Minknowski spacetime?" to some extent. It really is counter-intuitive, at least at first.  So feel free to dig as you please.  Just realize that you are trying to figure out the lay of the land, and a land that is fairly well known to others.  A scientific Daniel Boone you are not. --EMS | Talk 20:19, 23 May 2005 (UTC)

Minkowski space-time and the ordely behavior of time.
Sure I'm grappling with Minkowski space-time.

I will describe a model. It won't work, but the way it doesn't work may be informative.

Let Minkowski space-time have material properties, like the luminiferous ether was thought to have material propeties. I will call this 'Lorentzian ether'. Let this Lorentzian ether have the property that it enables the existence of time. (Let's say the ether causes matter to move forward in time by coupling to that matter, like the millions of switches in computer memory chips are simultaneously refreshed (occasionally overwritten) with each pulse of the central clock.)

Let this Lorentzian ether have the property that an object that is stationary with respect to that ether experiences more proper time than any other object. Let this Lorentzian ether have the property that to move in that ether has the effect of weakening the coupling, so that the (accumulated) proper time for a moving object is less than for a stationary object.

The Lorentz Ether theory made the same physical predictions for the outcomes of experiments. According to the Lorentz ether theory Nature contrives to appear relativistic. According to Lorentz ether theory as objects approach lightspeed Nature has to really squeeze them into Lorentz-FitzGerald contraction to keep up the appeareance. So in Lorentz Ether theory you expect to run out of "squeezing-capacity" as you approach lightspeed.

In special relativity there is no such running out of capacity. Let there be a very large number of spaceships arranged in a straight line in Minkowski space. Ship number 2 is moving away from ship number 1 at 1/10th of the speed of light. Ship number 3 is moving in the same direction as ship number 2, and it is moving away from ship number 2 at 1/10th of the speed of light, etc etc. In special relativity there is no end to that sequence. Each individual ship is fine, no proper "squeezing"; therefore an ether-type theory (with its fixation of absolute velocity) cannot account for the formulas of special relativity.

In physics, when there is no mechanism, then there is randomness. When something always happens in a repeatable way, there must be an underlying mechanism. Special relativity formulas allow calculation beforehand of the (accumulated) time dilation of any loop-closing scenario. Proper time is a very orderly behaving phenomenon (as far as we are able to tell). Therefore there must be an underlying mechanism, but it is unclear in what direction the nature of that mechanism is to be sought.

So I am really curious: a mechanism for newtonian absolute time would be something like a coupling to a universal background scalar mechanism. On the other hand: the rate of proper time as described by special relativity couples to both a scalar time and to three dimensions of a vectorial time, it seems. Proper time, it seems, is a resultant of the scalar time minus a "reverse time" due to motion through space.

There is the (somewhat inaptly named) transverse doppler effect. When there are two clocks, one moving inertially, the other in circular motion with the inertially moving clock at the center of circular motion, then the (accumulated) time dilation can be accounted for in terms of the transverse doppler effect.

All loop-closing scenario's in special relativity have in common that the time dilation can be accounted for in terms of dissimilar pathlength. The dissimilarity of pathlength can occur due to symmetry breaking by physical acceleration. When an object is being accelerated, its time-relationship with its surroundings is changing.

There is something that I am very curious about. Let there be a clock, falling straight towards a center of gravitation. The clock beams (at one second proper time intervals) electromagnetic pulses to a far away observer. The observer is located so far away, and in such a position, that effectively the whole length of the fall the motion of the clock is a transverse motion in the frame of the observer. So the resultant time separation of the pulses on reception is in part due to the Schwarzschild metric, and in part due to the transverse doppler effect. Is this reasoning correct, and what, to a reasonable approximation, is the time spacing of the pulses on reception?

I am so curious about that because in SR one of the characteristics of inertial motion is that the time-relationship with the surroundings remains the same during inertial motion. I am curious whether, under special circumstances, that characteristic can also occur in curved space-time.
 --Cleon Teunissen | Talk 11:42, 24 May 2005 (UTC)

Cleon - You wrote:

 * Proper time, it seems, is a resultant of the scalar time minus a "reverse time" due to motion through space.

Proper time is time as experienced locally by an observer. Each observer can use that proper time to set up a coordinate system with a temporal coordinate defined by clocks synchonized with their own clock. In addition, the observer can use rods or parallax to set up a spatial coordinate system (preferably a system of linear orthogonal x, y, and z coordinates) such that there are four coordinates being used to map spacetime (not just space).

Special relativity fundamentally is a means of converting between the coordinate systems of different observers, all of whom have used the above means to set up their own coordinate system. Proper time for another observer who is in motion with respect to myself is given is given by my proper time minus how that observer is moving through space and time in my coordinate system. Similarly, the other observer figures out my proper time with respect to his coordinate system. Time dilation is one observer finding another observer's clock running slow with respect to that observer's temporal coordinate system.

You have to do this on the basis of coordinate systems. That way there is no absolutism to it. (Absolutism would violate the principle of relativity).

Now step back. All inertial observers in SR see spacetime as being described by the Minkowski metric. In fact, there are 10 isotropies of spacetime (or ways that you can change your view but still have the spacetime look the same) in SR: Four translations (one for each axis, including time), three rotations (x-y, x-z, and y-z), and three velocities (which act as rotatations with time). Note that while a rotation is OK, rotational velocity is not: The metric for an observer co-rotataing with a Sagnac interferometer is not the Minkowski metric, after all. (See my part of the Sagnac effect page if you doubt that.)

Of course if spacetime is curved the Minkowski metric goes out the door, but curved spacetimes still have metrics, and the proper time formula still applies. For your observer falling towards a massive object from a distant position, it turns out that his time dilation due to velocity from the free-fall is the same as the time dilation for an object at rest with respect to the central object at that position. The two effects multiply, and so his pulse rate with be determined to be 1 - 2m/r. Note that this is with respect to the distant observer's temporal coordinate system (as set up using synchonized clocks). The observed pulse rate will be less due to each pulse being emitted from further away, and I am not interested in computing that right now.

--EMS | Talk 15:50, 24 May 2005 (UTC)

Theories of local physics versus action-at-a-distance physics.
The odd thing about your reaction is that you call the references excellent, but then it becomes clear that you haven't grasped the point they are making.

You seem unable to recognize that the Usenet physics FAQ discussion of the loop-closing Twins and Jonathan Vos Post's discussion are not only lengthier, but that they adress the issue at a deeper level. It's not that you disagree with them, it seems that you do not percieve what it is they are saying. Usenet Physics FAQ, review from a more abstract level

My thinking is very much influenced by the Distance dependence objection as discussed in the Usenet Physics FAQ.
 * With our "standard example", Stella's accounting of Terence's ageing runs like this: one-seventh of a year on the Outbound Leg, one-seventh of a year on the Inbound Leg, and the rest --- 14 years minus two-sevenths --- during the Turnaround.  You may recall she does the Turnaround in a day, according to Terence, or about 15 hours by her own clock.  (Let's just say 15, and hang the minutes; the exact figure won't matter.)

 * Say Stella takes a longer journey, spending 2 years on both the Inbound and Outbound Legs, for a total of 4 years of her time, or 28 years according to Terence. But she still takes the same 15 hours for the Turnaround.

What are the logical consequences if it is assumed that the physics of the loop-closing Twin scenario takes place during the Turnaround-phase?

 * It kind of does occur during the turn-around phase. Actually what changes is how Stella views the spacetime, and for the purposes of this exercise where she places her simultaneity volumes.  Realize that Terrence isn't aging due to Stella's turnaround.  Instead her view of "the same time" is being moved by almost 14 years with respect to Torrence's time.  On one level it is quite correct.  On another it is an odd form of relativistic accounting that is IMO more confusing than enlightening.

Overall, the following can be seen: the difference of elapsed proper time between Terence and Stella does not significantly depend on how briskly Stella performs her turnaround. On the other hand: the larger the distance between Terence and Stella at the moment of turnaround, the larger the difference in amount of elapsed proper time.

 * I will not argue with this. it comes from the path-distance business that you recently noted.  However, I will argue with what follows.

So the Turnaround-phase-theory is an action-at-a-distance theory. The same amount of acceleration by Stella has different outcomes, depending on how far away from Terence she is.

I think action-at-a-distance is unsatisfactory as a physics theory.

 * This is not action-at-a-distance! Because Stella accelerated, her view of spacetime was changed.  Torrence was not acted on at all!  Torrence was aging all along in his own frame of reference, without any aid from Stella at all.  Due to the relativity of simultaneity, when on Terrance's world-line Stella considers to be "at the same time" as her own time was shifted by 14 years due to Stella's acceleration.

 * You chide me for not understanding the USENET FAQ article, and then you show ignorance of the most fundamental aspect of relativity theory: It is fundamentally a set of transformation rules, so that observations in different frames of reference can be reconciled.  In this case, there are three operational frames of reference:  Torrence's, Stella's outbound frame, and Stella's inbound frame.  That is the key.  (You should be aware of that.  That article makes that point up front and repeatedly.)

In the history of physics, physicists have recognized the existence of fields, and how these fields remove the necessity to postulate action-at-a-distance. For example: the electrostatic force is described as mediated by a field. This field is pervasive and a charged particle interacts with the field, instead of interacting directly with the originator of the field. (Changes of the originator of the field propagate at finite speed so the field must be able to carry energy and momentum independently, otherwise conservation of energy and momentum would be violated. Thus a field is a physical entity.) A key element of field physics is that at each moment in time the physics taking place is "local physics".

I prefer an interpretation of the loop-closing Twins scenario in which the physics is at all moments in time local physics. I assume that the physics taking place is distributed over the whole length of time. I put the difference in pathlength at the central position, and I categorize the acceleration at the moment of turnaround as a necessary condition.

The decision to go for an interpretation with local physics during the whole time implies a field concept of space-time. Space-time itself must be a physical entity, with physical properties. The nature of this field must be such that it affects proper time, leading to path-dependent proper time.

This is what Johathan Vos Post refers to in his discussion of the loop-closing Twins scenario. Mach's criticism of newtonian dynamics was that the assumption of absolute time and absolute space is unsatisfactory if the physics expectation is that all physics is interactions between physical entities. Newtonian space acts on matter but is not being acted upon. Minkowski spacetime is unsatisfactory in the same way: it acts on matter/energy in it without being acted upon.

In the theory of general relativity the actual physics does have the property that it is all physical entities, all interacting. In General Relativity, matter/energy acts upon space-time geometry, curving it, and spacetime geometry acts upon matter/energy, affecting its motion.
 --Cleon Teunissen | Talk 09:56, 25 May 2005 (UTC)

 * I see the USENET Physics FAQ twin paradox article as being overly long-winded, somewhat dense, and not dealing with the central issue behind the so-called paradox. All that your diatribe here has done is to confirm that opinion.  It has also confirmed to me that you have a lot to learn.

 * --EMS | Talk 16:18, 25 May 2005 (UTC)

 * P.S. I really prefer my own example.  In this sub-thread, it is helpful since it shows how the view of "Stella" changes.  I strongly advise looking at it again.

The author of Mathpages.com
I discovered I have made a mistake.
 I was in error in stating that the author of the online boek reflections on relativity is Jonathan Vos Post. I discovered that the site Mathpages.com  is maintained by someone called Kevin Brown. I have not been able to find background information about this Kevin Brown. Possibly it is a pseudonym.

Jonathan Vos Post is a mathematicion and he also has math material online: MATH Pages of Jonathan Vos Post. It seemed to fit.
 --Cleon Teunissen | Talk 22:34, 25 May 2005 (UTC)

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