C S Unnikrishnan
email: unni@tifr.res.in

General Theory of Relativity and the Universe Between Beauty and Truth

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The centenary year of the general theory of relativity (GTR) is being celebrated with universal appreciation of Einstein's genius and the beauty of his theory, which it truly deserves given its well-verified predictions and all-encompassing applicability from terrestrial navigation to astrophysics and cosmology. The theory is now more or less accepted as perfect, requiring structural modifications only when quantum effects are important in gravity. A recent article of appreciation by T. Padmanabhan in Current Science 1 highlights these features from essentially the standard point of view, while pointing to the modifications suggested by quantum gravity and also to new possible conceptual developments relating gravity and thermodynamics of space-time.

During such a celebration feast, dissenting or even apprehensive remarks may be seen as tasteless. But there could be a gap between truth and beauty (as apparent in the well discussed Tagore-Einstein dialogues 2

). One may ask, isn't the body of experimental verifications an indication of the truth of the theory. Yes, indeed and there should not be any doubt about its empirical support. Essentially all its predictions are verified to remarkable precision. However, empirical support is always limited to a finite number of instances and scenarios, often dictated by the theory itself and there is always the possibility that something right at the core, at the level of postulates and interpretation of the theory, remains to be deciphered. Also, there is no guarantee that there are no phenomena outside the predictions of a 'verified' theory, unnoticed or ignored due to some circumstances. Therefore, even the most beautiful theories will need to pass any conceivable test, both in predictions and foundations. This is particularly so when the theory has foundational postulates that remain as mysteries. The case of GTR is particularly so.

If there was one thing that remained obscure and incomprehensible in the fundamental physics of dynamics, it is the origin of inertial forces, as was made amply clear by Mach's criticism of Newton. [START_REF] Mach | The Science of Mechanics[END_REF] This is why such experiential forces in non-inertial frames remained as 'pseudo-forces' in physics. In the standard model paradigm there is no place for a pseudo-force remaining outside the scope of particles and their interactions, with well defined couplings. While bringing all imaginable gravitational effects within a framework that treated gravity and acceleration as equivalent locally, GTR reduced gravity itself to an inertial effect and separated it in character from all other known forces. The observed fact that inertia to motion is identical to the charge of gravity, and not related to the charge of any other known interaction, remains a puzzle and this equivalence is the fundamental building postulate of GTR. [START_REF] Einstein | Relativity: The special and general theory, Translation[END_REF] By reducing gravity to an inertial effect, GTR closed the path to a correct understanding of pseudo-forces. As Einstein himself regretted, he was not able to incorporate Machian ideas into general relativity. Equating gravity and inertia allowed Einstein to construct a mathematically beautiful theory in which gravity was described entirely as the geometrical property of the unobservable space-time, much in consonance with Newton's invoking of absolute space to justify pseudo-forces. However, the status of pseudoforces in general relativity remains the same as in the days of Newton [START_REF] Wilczek | Total Relativity[END_REF] and in this sense general relativity did take a large retrostep from Mach, when it could have taken an equally large step forward. As I will show, this renders the theory incomplete and even inadequate to deal with some laboratory experiments.

Our many successes in describing physical nature have been celebrated with triumph and relief; the near completion of the standard model physics, a century of theory of special relativity, and now a century of general relativity. We are already into the centenary era of quantum theory. However, all these triumphs, without exception, are damped in bewilderment (whether one is aware of it or not) when faced with one physical system -the Universe.

Universe is 'once-given', as Mach emphasized and it is a single physical system with its dynamics governed by the properties and interactions of matter and energy it contains. It is self-dynamical. It is too large to be tweaked for a physical test. But it is not too large any more to be studied in depth, literally. Today, we know about its expansion dynamics, age, average matter density, its matter and radiation content, temperature of the background radiation (CMBR), its evolution and fluctuations etc., and we also know where we lack true understanding -dark or missing matter and a seemingly uniform distribution of unobservable energy. What we understand well is the relation between the expansion dynamics of the universe and its matter-energy content. The nearly isotropic and homogenous background radiation provides an absolute space marker enabling us to measure our velocity relative to the cosmic frame to good precision. Its monotonically decreasing average temperature is an absolute universal clock, synchronized everywhere in the universe good to a part in 10 5

. The fundamental premise of the rejection of absolute space and time by the special theory of relativity is made null and void by just this thermal clock of the universe. The 'de-synchronization' term δt = vx/c 2 in the Lorentz transformation is in direct conflict with this cosmic absolute time.

Coming to the compatibility of other fundamental theories with cosmology, we already know that the zero-point energy of quantum field theories are in huge conceptual conflict with cosmology because the measured expansion rate demands an average energy density that is smaller than 10 -29 g/cm 3 , whereas the zero-point energy density in any calculation is far greater.

What about general relativity? Is it immune to the knowing smile of the real universe, the understanding of which was entirely dependent on the theory itself? Alas, it is not. The reason is physically simple -general relativity is written down and tested in this very universe with its enormous matter content and its gravity, the theory itself is constructed assuming explicitly empty space as its fundamental space. In other words, away from clustered matter like a star or celestial objects, the theory asserts that space-time is the empty Minkowski space-time of special relativity, whereas in reality, unknown to the theory, space it is permeated by a uniform distribution of matter and energy. GTR is a theory of gravitational charges and their fields, but it is oblivious to the fact that it is operative within a large cloud of gravitational charges with their enormous collective potentials. Since this fact was not known when general relativity was constructed, it is missed out in the theory and the theory pays a heavy price for this slip. (All our fundamental theories were completed well before any deep observational cosmology emerged). GTR misses Mach precisely because of this conceptual error, as we will see. Consistent with the fact that the theory does not incorporate the Machian insistence that pseudo-forces should have a physical origin in some interaction with matter, the inertial forces remain as pseudo as ever in general relativity. To make matters worse, at least in the eyes of philosophers of science, even the force of gravity is reduced to a pseudo-force in general relativity, similar to the inertial forces arising in coordinate transformations. GTR remains silent to the origin of those 'forces without sources' in non-inertial coordinates.

We could have gone ahead with this, trading truth for beauty, but for a severe conflict with the results of a class of laboratory experiments! This sounds blasphemous at first, daring to discuss a conflict between the general theory of relativity and any conceivable experiment. However, empirical rigour is the privilege of the physicist, never to be compromised. Let us therefore briefly examine the actual conflicts, conceptual and empirical.

For any observer moving though the universe at a constant velocity ⃗ v, the relative matter flow is in fact a large current of the charge of gravity (mass and energy) in the direction -v, and it is clear that the resulting space and its metric should be anisotropic, while remaining homogenous. This is because moving matter should generate new relativistic gravitational potentials (metric coefficients in the mathematical description) in the correct theory. [START_REF] Unnikrishnan | Cosmic Relativity: The fundamental theory of relativity, its implications and experimental tests[END_REF][START_REF] Unnikrishnan | Physics in the 'Once-Given' Universe[END_REF] One brief glimpse at electrodynamics would immediately warn us about the large magnetic effects of flowing charges, or currents. Since Lorentz transformations (LT) preserves isotropy, the metric components g 0i that should represent the gravity of moving matter remains invariant as zero under LT. Large matter currents with no magnetic potentials! Therefore, the LT is physically inconsistent in non-empty space. In contrast, the Galilean transformation (GT) gives the correct anisotropic metric and also, the correct relativistic factor for time dilation due to the change in the metric factor g 00 .Under GT, with the universal time for all observers at rest (comoving) in the cosmic frame,

x ′ = x -vt; t ′ = t (1)
the metric (2D for brevity) changes as

-1 0 0 1 → -(1 -v 2 /c 2 ) v/c v/c 1 = g 00 g 0i g i0 g 11 (2)
Therefore, the physical time of a moving clock becomes (-g 00

) 1/2 dt ′ = dt ′ (1 -v 2 /c 2 ) 1/2
. Here, v is the 'absolute' velocity in the cosmic frame and hence without usual paradoxical ambiguity associated with relative velocities. [START_REF] Unnikrishnan | On Einstein's resolution of the twin clock paradox[END_REF] Note that this does not lead to the synchronization term vx/c 2 in the relativistically modified time. Consequently, and since the cosmic frame is the absolute preferred frame, this new paradigm of relativity that is made consistent with cosmology predicts that velocity of light relative to a moving observer is Galilean to first order (v ± c). Combined with this feature, the time dilation factor also implies the correct length contraction. It is worth reassuring that this theory that attributes all relativistic effects to the gravitational influence of the matter and energy in the universe reproduces every tested relativistic result that is conventionally attributed to the special theory of relativity, while retaining the Galilean nature of the relative velocity of light. This should not be surprising once we have the time dilation and length contraction evident in the structure. In fact, the Lorentz-Poincare theory had these features, but relied on an unphysical ether instead of the very physical universe and its gravity, unknown in their time.

Some may already squirm and ask, isn't the relative velocity of light proved to be isotropic in numerous experiments?! One just finds even more squirming in face of the question 'which experiment?', and then the standard degenerate answer is 'Michelson-Morley experiment'. This is clearly unfortunate because it should have been widely known that the null result obtained almost two decades before the special theory of relativity is in fact consistent with an ether-like absolute frame theory with Lorentz contraction and anisotropic relative velocity (Lorentz-Poincare theory) as well as with special relativity that postulated isotropic relative velocity and no length contraction in the comoving frame. Besides, M-M experiment compared the two-way relative velocity and not the one-way relative velocity and this cancels any first order Galilean effect (the residual second order effect is then cancelled by a real length contraction in the preferred frame theory). So, the failure to detect the motion of the inertial frame by a local experiment is not in conflict with the anisotropic propagation of light relative to such a frame. The question is how to test for such an anisotropy, if it truly exists, since one cannot 'see' or measure how far the light wavefronts are while chasing them. It was generally believed that the true one-way relative speed of light can never be measured because of the impossibility to synchronize distant clocks in a way that is independent of the theory. However, from CMBR we now know that given sufficient distance between the clocks there is even a practical way of synchronizing two distant clocks good to about 10 -5

. Unfortunately, the distance required for a test of isotropy of the relative velocity of light is too large to be practical because of temperature decreases way too slowly, over cosmological time scales. Some years ago, we discovered a way to test for the isotropy of relative one-way speed of light, without the need of synchronizing two distant clocks. [START_REF] Unnikrishnan | Physics in the 'Once-Given' Universe[END_REF][START_REF] Unnikrishnan | Precision measurement of the one-way speed of light and implications to the theory of relativity[END_REF] To fix the ideas, let us consider propagation of a pulse of sound, which we know for sure is Galilean. If the pulse starts at the location of the inertially moving observer O ′ , the separation ∆L between O ′ and the pulse increases linearly with his time t ′ ,

∆L = v r ∆t ′ = (c s -v o ) ∆t (3)
where t refers to time in the stationary laboratory O. Then v o and c s are the velocities of the observer and the pulse of sound in the fixed frame O. The relative velocity is denoted v r . Therefore v r = L/∆t ′ r independent of the shape of the one-way path. In particular, if the path joins back on the observer, as in a stadium track of round trip distance L, the pulse has travelled a distance ∆L = L relative to O ′ when it catches up with the observer after one round trip. This does not require any synchronization because the same clock is maintained. It is trivial to confirm that this gives the correct relative velocity for sound and in any case this has been confirmed by a real experiment (figure 1). Since ∆t ′ = ∆t to first order, independent of theory, measured relative velocity is v r = (c s ± v o ) depending on the direction of propagation of the pulse A plot of ∆t ′ vs. v o gives a linear graph with slope v o /c s if and only if the relative velocity is Galilean. (The much smaller second correction v 2 /c 2 is not relevant for this first order result). A laboratory experiment with exactly the same protocol and interferometric precision for comparing the one-way relative speed of light returns exactly similar results, proving that the relative speed of light is Galilean to first order, as in the case of sound! What we believed all along is not what we see in the experiment that avoids the logical circularity of clock synchronization. Hence, the crucial foundational postulate in the construction of the theories of relativity is falsified by a direct experiment. [START_REF] Unnikrishnan | Physics in the 'Once-Given' Universe[END_REF][START_REF] Unnikrishnan | Precision measurement of the one-way speed of light and implications to the theory of relativity[END_REF] Then how is it that GTR manages to predict all known and imaginable gravitational effects so precisely and exquisitely, in its elegant framework? The clear answer is that GTR does not necessarily require the constancy of the relative velocity of light for deriving its results, even though that was the historical device in Einstein's early derivations. One example will suffice to show the essential fact. Consider the derivation of the gravitational redshift. The redshift in an accelerated frame happens both in the special theory as well as in the preferred cosmic frame theory. In the former picture it is interpreted as due to separated clocks running at different rates and in the later it is simply because the relative velocity is Galilean, as in the case of sound. Therefore, the mere application of the equivalence principle -that the physical effects in a uniform gravitational field and in a uniformly accelerated frame are indistinguishable -is sufficient to deduce gravitational redshift of radiation. What about the relative gravitational time dilation of clocks? Since the clocks in the accelerated frame are at relative rest they run at exactly the same rate. However, comparing them requires bringing them together in the frame moving at absolute velocity v and this entails the relative time dilation vx/c 2 = tgx/c 2 , exactly the same as in the derivation by Einstein. [START_REF] Einstein | On the influence of gravitation on the propagation of light, in The principle of relativity[END_REF] We now turn to gravitational phenomena that GTR does not predict or explain. For every experiment done near the earth, GTR calculates the physical effect by considering the Schwartzchild metric or the Kerr metric, when the slow rotation of the earth is taken into account. In rotating frames or in freely falling orbits, the so called gravitomagnetic effects are small, of order ω ≃ (GM/c 2 R) Ω or ⃗ v ×⃗ g. This field can exert a torque on a gyroscope, inducing a precession that has been measured in sophisticated satellite experiments. [START_REF] Everitt | Gravity Probe B: Final Results of a Space Experiment to Test General Relativity[END_REF] The magnitude of these effects are negligibly small in laboratory situations, according to Einstein's general relativity.

However, consider the current-current interaction in electrodynamics. Magnetism is the real evidence for relativistic features of electrodynamics. In Ampere's experiments, it was established that parallel currents experience an attractive force and opposite currents repel. If the currents are in a loop, one can rewrite this in terms of a magnetic moment interacting with a uniform magnetic field, and the torque on the current loop due to the magnetic field τ = µ × B will flip the loop (or a small magnet) to the lower energy configuration of parallel currents.

In the rest frame of a laboratory under slow rotation at rate Ω, the entire matter in the universe -an enormous amount of the charge of gravity -is in circulation and should be generating a very large gravitomagnetic field B g . Given the density ρ of matter-energy in the universe this can be calculated as approximately B g ≃ (GρR 2 H /c 2 ) Ω where R H is the Hubble size. In fact, this is just the quantity ∇ × (g 0i ), where g 0i is equivalent to a gravitational vector potential A i due to the matter current in the direction i. The metric factor g 0i is in fact (GρR 2 H /c 2 ) v, clearly revealing the coupling constant for both inertial forces and Newton's law of dynamics as the gravitational constant G. (The gravitational potential Φ U ≈ GρR 2 H is numerically close to c 2 , with obvious implications to the correct interpretation of Lorentz factors and the theory of relativity). Creating the analogue of a small current loop in gravity is easy because setting a piece of the charge of gravity is achieved by rotating a small massive disk. The spinning disk indeed flips its direction promptly when a large matter current of cosmic matter is also generated by slow rotation relative to the cosmic frame, fully consistent with the relativistic interaction with the matter in the universe. [START_REF] Unnikrishnan | Dynamics, relativity and the equivalence Principle in the 'once-given' universe[END_REF][START_REF] Unnikrishnan | New Experimental Results on Cosmic Gravitational Effects and the Centenary Einstein Equation[END_REF] The measured torque agrees with (s × B g ) /2 = s × (∇ × v) /4 and the experiment shows that parallel currents repel in gravity. Since there is frame-independent transfer of energy and angular momentum due to the action of an external force, we have no choice but to trace the force to the only known long range interactions in physics that can act on the electrically neutral disk. Therefore, the interaction responsible is definitely gravity. However, such an interaction of the right magnitude is not contained in the vacuum solutions of Einstein's equation, and it does not explain the effect, not any more than Newton's pseudo-explanation in which a non-force from absolute space is invoked to keep the equations correct. That single most important lacuna in GTR, ignoring cosmic matter in the equation itself, hits back at the theory as soon as we look at a phenomenon that is induced by the gravity of the matter in the universe Therefore Einstein's general relativity needs an important modification to permanently incorporate the gravitational effects of the matter in the universe because the equation is to be operative always in the presence of all this matter without exception. The proposed modification does not alter other tested predictions of general relativity and I call the new equation the Centenary Einstein Equation, 13 R ik -1 2

g ik R + Λg ik -κT ik(u) = κT ik (4)
(κ = 8πG/c 4 ) .which does not allow a vacuum Einstein equation, R ik = 0, except as an approximation that cannot predict the result of the experiment we just discussed. Without this modification Einstein's equation cannot claim that it is a complete theory of gravitation.

We now see how Machian speculation is properly integrated into the relativistic theory of gravity. For an observer in uniform motion in a circular path, the direction of velocity and hence g 0i is time dependent resulting in the centrifugal force, F cf = m g dA/dt = m g v 2 /r. In frames of pure rotation, dA/dt = 0, but ∇ × A = ∇ × v = 2Ω and this is exactly the cosmic gravitomagnetic field in the fully relativistic theory. The Coriolis-Lorentz force F C = m g v × 2Ω on a moving mass is an immediate consequence. It can be shown that the Newton's law of dynamics itself is a relativistic consequence of cosmic gravity and it is indeed a gravitomagnetic law, similar to Lenz's law in electrodynamics. This also reveals the origin of Newton's law of motion, the equivalence principle, both the weak equivalence principle and the Einstein equivalence principle [START_REF] Unnikrishnan | True dynamical tests of the equivalence principle[END_REF][START_REF] Sciama | On the origin of inertia[END_REF] because in an accelerated frame, g a = dA/dt = -dv/dt. Since spin in general is the rotational current of the charge of gravity, many gross spin dependent effects in fundamental physics, from certain geometric phases to spinstatistics connection, can also be linked to the interaction with cosmic matter. [START_REF] Unnikrishnan | Physics in the 'Once-Given' Universe[END_REF][START_REF] Unnikrishnan | New Experimental Results on Cosmic Gravitational Effects and the Centenary Einstein Equation[END_REF] Though not evident in the metric description, the expression B g ≃ (GρR 2 H /c 2 ) Ω stresses that inertial forces are evidently gravitational, and not just locally equivalent to gravity. Obviously, the constant vector potential field in a uniformly moving frame cannot be detected and this becomes the principle of relativity. However, it is only as good as the homogeneity of the matter-energy distribution in the universe.

We have seen that in spite of the much admired beauty and impeccable empirical record of the general theory or relativity, the theory has a serious flaw in its structure and foundations, which can be remedied by accepting new experimental results and basing the theory on a new relativity framework in which the gravity of the cosmic matter determines relativistic dynamics. This paradigmatic framework is called Cosmic Relativity. [START_REF] Unnikrishnan | Cosmic Relativity: The fundamental theory of relativity, its implications and experimental tests[END_REF][START_REF] Unnikrishnan | Physics in the 'Once-Given' Universe[END_REF] The basis of the correct theory of gravitation should inherently include the gravity of the environment in which it is applicable and tested because universe is not gravitationally neutral and gravity cannot be shielded. This is a situation peculiar only to gravity. Though all fundamental theories of physics were constructed without accounting for the gravitational interaction with cosmic matter-energy, all experimental tests necessarily include the effects of such an interaction, whether measurable or not. Considering all that we discussed here, the theory of gravitation and relativity in particular were rendered incomplete because of this, in spite of their apparent and much admired beauty. Fortunately, today on the centenary of the theory, we know how to mend this gap between beauty and truth.

FIG. 1 :

 1 FIG.1:The left panel shows the expected Galilean result for relative velocity from the validation experiment with sound. The right panel result proves that relative velocity of light is indeed Galilean to first order. The picture frame depicts the experimental strategy for measuring one-way velocity relative to the inertial observer.

FIG. 2 :

 2 FIG.2: Panels A and B indicate how a small current-loop or magnet flips its direction when the current in the larger loop is in a direction opposite to that of the test loop current. Panel C: When a spinning disk is taken into a frame slowly rotating relative to the matter in the universe (indicated by dual arrows on top), the spinning disk flips due to the large cosmic gravitomagnetic force, until the two matter currents become opposite[START_REF] Unnikrishnan | Dynamics, relativity and the equivalence Principle in the 'once-given' universe[END_REF]

1

  Padmanabhan, T., One hundred years of general relativity: summary, status and prospects, Current Science, 2015, 109, 1215-1219. 2 Tagore, R., The Religion of Man, Appendix II, (The Macmillan Company, New York), 1931, pp. 221-225.


C S Unnikrishnan
email: unni@tifr.res.in

Does Lorentz Force Law Contradict the Principle and Theories of Relativity for Uniform Linear Motion?

I show that no force or torque is generated in cases involving a charge and a magnet with their relative velocity zero, in any inertial frame of reference. A recent suspicion of an anomalous torque and conflict with relativity in this case is rested. What is distilled as 'Lorentz force' in standard electrodynamics, with relative velocity as the parameter, is an under-representation of two distinct physical phenomena, an effect due to Lorentz contraction and another due to the Ampere current-current interaction, rolled into one due to prejudice from special relativity applied only to linear motion. When both are included in the analysis of the problem there is no anomalous force or torque, ensuring the validity of Poincare's principle of relativity. The issue of validity of electrodynamics without the concept of absolute rest, however, is subtle and empirically open when general noninertial motion is considered, as I will discuss in another paper.

The modern theory of electrodynamics was built by Maxwell by distilling various experimental results and then including the phenomenon of displacement current he discovered from a consistency analysis. This was well before the theories of relativity by Lorentz, Poincaré and Einstein came into discussion. The relativity principle expounded by Poincaré ensures the impossibility of detecting uniform linear motion by experiments in electrodynamics Figure 1: The charge moving at velocity v is physically equivalent to magnet moving at velocityv in Einstein's special relativity. Both forces are given by the Lorentz force law with v as their relative velocity.

and mechanics [START_REF] Poincaré | L'état actuel et l'avenir de la physique mathématique[END_REF]. Thus the state of uniform rectilinear motion is equivalent to the state of rest. It was Einstein who asserted, in the opening paragraph of his 1905 special relativity paper [START_REF] Einstein | Zur Elektrodynamik bewegter Körper[END_REF], that the reciprocal electrodynamic action of a magnet and a conductor depends only on the relative motion of the conductor and the magnet. See figure 1 for the relevant situation. He further wrote, "examples of this sort, together with the unsuccessful attempts to discover any motion of the earth relatively to the "light medium", suggest that the phenomena of electrodynamics as well as of mechanics possess no properties corresponding to the idea of absolute rest".

While analyzing the cases involving a conductor and magnet in various states of relative motion between them, I had realized that current electrodynamics, as represented in Maxwell's equations and the Lorentz force law, is actually an under-representation of the fundamental physical phenomena involved [START_REF] Unnikrishnan | New experiments and results on the relative velocity of light and on the electrodynamics of currents, and their links to gravity[END_REF]. In particular, the Lorentz force law and its relativistic transformations involving only the relative velocity between charges and magnets mix up two distinct physical phenomena into a single expression that does not adequately represent the physical effects for general motion involving non-rectilinear motion. Something has been lost in translation by Maxwell and Lorentz, from the body of results arrived at by painstaking experiments over decades by Faraday, Ampere, Weber and others. However, that shows up only in the case of non-rectilinear motion and the subject of this paper is the analysis that shows that there is no torque or force when a charge and a magnet that are relatively stationary are observed from a uniformly moving frame.

The physical phenomena that are relevant are (a) Ampere's currentcurrent interaction and (b) the modification of charge densities involved in the effective equivalent currents in a magnet due to Lorentz contraction in motion. These are two different physical phenomena, with different physical origins and mathematical expressions, which coincide exactly for the case of force on a charge moving uniformly relative to a magnet. Usually, the force is written as the Lorentz force,

F = q( E + v × B) (1)
Since v is interpreted as the relative velocity between the magnet and the charge, there is no force when a charge is at rest relative to a magnet and no force appears when the system is viewed from another frame moving relative to the physical system. However, instead of using the formula, if one tries to calculate the force from the interactions of the charges and currents involved in the problem, there could be an apparent conflict that is spurious if one of two fundamental physical effects we discussed is not taken into account. Indeed, the current-current interaction is often forgotten in discussions since it is assumed that Maxwell's equations contain fully its manifestations. This is perhaps true, except that there is certainly one ambiguous element in the formulation of modern electrodynamics, and that is the interpretation of the velocity that appears in the transformation equations: relative or absolute? When the Lorentz force law is discussed in moving frames, usually only the Lorentz contraction effect is considered. In particular, the case of a charge and a magnet there is a spurious force or torque unless the current-current interaction is included [START_REF] Unnikrishnan | New experiments and results on the relative velocity of light and on the electrodynamics of currents, and their links to gravity[END_REF]. This seems to be the case in a news and analysis article announcing a serious conflict between relativity and the Lorentz force law, in the case of a charge and a magnet that are relatively stationary, when observed from a moving frame [START_REF] Cho | Trouble with the Lorentz law of force: Incompatibility with special relativity and momentum conservation[END_REF]. The magnet is equivalent to a current loop involving two opposite currents separated by distance. In a moving frame Lorentz contraction generates asymmetric charge densities and an electric field (see below). If this is the only effect that is considered as the basis of Lorentz force, an anomalous torque is indicated and if true, it would conflict with relativity since a real force or torque and resultant motion (dynamics) cannot appear within this physical system merely due to uniform motion of an observer. Now I show that this paradox arose precisely because of not taking into account the fundamental phenomenon of current-current interaction in the moving frame. Including that effect makes the torque vanish. Indeed, the system considered in the news analysis is a variant of an example I have analyzed earlier with the difference that he was considering a system where the charge is separated from the magnet and a torque is generated, whereas I have been dealing with examples where the charge is right near the surface of the large magnet [START_REF] Unnikrishnan | New experiments and results on the relative velocity of light and on the electrodynamics of currents, and their links to gravity[END_REF]. (This is because we are attempting to make measurements on the dynamics of charges near moving magnets in various configurations and the possibility of good measurements reduces with increasing distance between the charge and the magnet). In the particular case of linear motion, the analysis can be done either with relative velocities or with velocities with respect to a preferred absolute frame and the results are identical, reiterating the fact that no experiment in linear motion can be used as a demarcating test between different theories of relativity obeying the relativity principle. Three such theories are the Lorentz-Poincaré relativity theory [START_REF] Poincaré | L'état actuel et l'avenir de la physique mathématique[END_REF][START_REF] Lorentz | Electromagnetic Phenomena in a System Moving with Any Velocity Less Than That of Light[END_REF], Einstein's special relativity [START_REF] Einstein | Zur Elektrodynamik bewegter Körper[END_REF] and the new paradigm of Cosmic Relativity [START_REF] Unnikrishnan | Physics in the 'Once-Given' Universe[END_REF][START_REF] Unnikrishnan | Cosmic Relativity: The Fundamental Theory of Relativity, its Implications, and Experimental Tests[END_REF] that I have been advocating in which all relativistic effects are due to the gravitational effects of cosmic matter and cosmic frame is a preferred frame perfectly replacing the old ether.

Consider a charged particle in close vicinity of a bar magnet with large polar area, close to one of its poles. Moving the charge relative to the magnet will make it deflect transversely and moving the magnet also will produce the same physical effect (figure 1). The force is given in both cases, as in modern electrodynamics, by the Lorentz force law,

F = q( E + v × B) (2)
with E = 0 in this case. This is the example that guided Einstein to (hastily) conclude that all electrodynamic phenomena are completely symmetric in relative motion. Now consider the entire system of the magnet and the charge at rest. In special relativity, v is the relative velocity between the magnet and the charge, as originally asserted by Einstein. When the relative velocity is zero, there is no force on the charge and it remains at rest. However, viewed from a frame moving at velocity V , the magnet becomes charged, with opposite charges on its two sides parallel to the motion of the observer due to Lorentz contraction (figure 2). This is because the magnet is equivalent to a current loop and on one side the velocity of the charged particles corresponding to the current add to the motion of the observer and on the other side, it subtracts. If the speed of the moving charges in the magnet is u, the Lorentz contraction factors for the two opposite currents are different, 1 In a frame moving right with velocity V , the originally stationary charge becomes a current with velocity -V . the observer, these can be written as

-(V + u) 2 /c 2 1/2 and
(1) ∆l 1 = -L(V 2 + u 2 + 2uV )/2c 2 (1) ∆l 2 = -L(V 2 + u 2 -2uV )/2c 2 (3)
and the difference for low velocities is -2LV u/c 2 . (the similarity to the Sagnac term is not accidental. See reference [START_REF] Unnikrishnan | Physics in the 'Once-Given' Universe[END_REF][START_REF] Unnikrishnan | Gravito-Electromagnetism: Glimpses Glimpses of Unexplored Connections[END_REF]). The change in the linear density will be then -2V u/c 2 . This multiplied by the negative charge density λ is the difference in charge densities, creating a transverse electric field E in the direction V × (∇ × u) , of magnitude

E = 2λV u/2πε 0 rc 2 (4)
However, now we have a conflict with principle of relativity if there is only the Lorentz contraction, since the charge should start moving due to this electric field, which is unphysical since an observer's mere motion should not physically displace the charge relative to the magnet! However, note that in the same frame, the charge becomes a current -q V and there are forces of opposite sign to that of the Lorentz contraction from the Ampere current-current interaction that exactly bring the net force to zero. Parallel current attract and opposite ones repel, where one current i q = qV is from the moving test charge and the other two oppositely directed ones i m from the current loop in the magnet. This current-current force is exactly same in magnitude and opposite in direction to the one generated by the Lorentz contraction. The two cancel, and the charge remains at rest, as if there is no force. The Ampere interaction from the two opposite currents on the current The current-current interaction cancels this.

of the charge q, now moving with velocity V in the new reference frame is

F A = 2µ 0 2π i q i m r = µ 0 π qV i m r = µ 0 π qV λu r (5)
and the (oppositely directed) force from Lorentz contraction and the electric field of the modified charge density of the currents in the magnet is

F = qE = qλV u πε 0 c 2 r = µ 0 π qV λu r = µ 0 π i q i m r (6)
if we identify µ 0 = 1/ε 0 c 2 , which is the case in electrodynamics! If the charge, instead of being near the pole of the magnet, where the field is uniform, is far away as illustrated in reference [START_REF] Cho | Trouble with the Lorentz law of force: Incompatibility with special relativity and momentum conservation[END_REF] then we get a (spurious) nonzero torque from just the Lorentz contraction (figure 3).

The problem posed as a paradox conflicting relativity is completely solved if the torque is recalculated with the current-current interaction added. That generates an equal and opposite torque to what was calculated from Lorentz contraction and the net torque is zero. The factual situation is that there are two equal and opposite forces (or forces and torques in the general case), which balance in the case of linear motion. This should not be trivialized, as is done in standard electrodynamics, to a 'zero force' situation since this balance is broken in the case of rotation motion as we shall see [START_REF] Unnikrishnan | Complete Solution of the Fundamental Problems of Unipolar Induction and Related Phenomena[END_REF]. A 'zero' as genuine nothing and as a delicate and special balance of two equals are completely different, conceptually and physically.

It is clear that, for the case depicted in fig. 3, one may take the limit of the current loop area shrinking to infinitesimal values with the magnetic moment remaining constant and the analysis, with the current-current interaction included, gives zero torque in all frames in the presence of the charge. I may add here is that what we have done is to derive the relation between µ 0 , ε 0 and c from the principle of relativity with Ampere's current-current interaction and the Lorentz contraction as the ingredients, without entering the plane of the electrodynamic wave equation. It is very important to recognize that these phenomena of linear motion does not allow us to demarcate between special relativity and an absolute frame theory as the empirically valid theory because both incorporate Poincaré's principle of relativity. Explanations can be found for all electrodynamic phenomena in linear motion in both theories by interpreting the velocities involved as absolute velocities in absolute frame theories, and as relative velocity between the magnet and the conductor in special relativity. Both predict zero force and zero torque in the problems discussed above.

Even in the simpler problem of a single conductor and an external charge, the paradox appears if the current-current interaction is ignored. But such anomalies are spurious since in the same moving frame the charge is transformed to a current that interacts with the current in the conductor cancelling the force from Lorentz contraction. Principle of relativity in rectilinear motion remains intact. However, the respite is temporary, as I will elaborate in another paper dealing with cases of uniform rotational motion [START_REF] Unnikrishnan | Complete Solution of the Fundamental Problems of Unipolar Induction and Related Phenomena[END_REF]. It is also important to recognize that the wise do not consider that modern electrodynamics as discussed in standard text is the last word on the electrodynamics of the real world and several issues related to the exact nature of the currentcurrent interaction, unipolar induction, action and reaction etc. are being actively discussed and experimented with, albeit in a relatively small yet competent community.

Disclaimer: The discussion in this paper pertains to the news and analysis, reference [START_REF] Cho | Trouble with the Lorentz law of force: Incompatibility with special relativity and momentum conservation[END_REF], and not directly to the original paper, which was not available at the time of writing or submitting this paper. The paper by M. Mansuripur is now available in arXive.org as arXiv:1205.0096.

Figure 2 :

 2 Figure 2: Lorentz contraction of currents in the magnet generates asymmetric charge density and electric field. The long arrows depict the current elements.In a frame moving right with velocity V , the originally stationary charge becomes a current with velocity -V .

Figure 3 :

 3 Figure 3: Spurious torque on the magnet due to a charge on the far left, considering Lorentz contraction alone in the problem in the moving frame. The current-current interaction cancels this.

-(Vu)

/c 2 1/2 . For low velocities involved for both the current and