text:
User:Methawee

HW for 23/10/10

1.	If transportation have accident. Maybe late. The driver can’t send order on time. 2.	The driver can swindle. Because customer pay money at him. 3.	Customer call to employee for order. when they record in note book. Sometime can mistake.

title: User:Methawee


text:
How does engineering tie with some other careers

Engineering –skillful or artful contrivance; maneuvering

Engineering ties with every career known to man. If you have engineenering skills but can't find a jod in engineering, you should be able to find a job that ties along with it such as an culinarian. Virginia Western has a great culinary program, engineering is used just as much in their program as in regular engineering programs.http://www.virginiawestern.edu/bet/culinary/.

Sheddricka Arthur 16:59, 21 October 2010 (UTC)`Sheddricka Michelle Arthur Ocala Florida

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/


text:
User talk:Sheddricka Arthur

 Hello Sheddricka Arthur, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may

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title: User talk:Sheddricka Arthur


text:
User talk:Metalmania~enwikiversity

 Hello Metalmania, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may

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The developer team at Wikimedia is making some changes to how accounts work, as part of our on-going efforts to provide new and better tools for our users like cross-wiki notifications. These changes will mean you have the same account name everywhere. This will let us give you new features that will help you edit and discuss better, and allow more flexible user permissions for tools. One of the side-effects of this is that user accounts will now have to be unique across all 900 Wikimedia wikis. See the announcement for more information.

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Renamed
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title: User talk:Metalmania~enwikiversity


text: File:2010 10 21 14 05 59.djvu

title: File:2010 10 21 14 05 59.djvu


text: File:2010 10 21 14 48 38.djvu

title: File:2010 10 21 14 48 38.djvu


text:
User talk:Insectlady

 Hello Insectlady, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may

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title: User talk:Insectlady


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User:Swamps42

Hi! I'm a graduate of the UCCS College of Business and would like to go on for my degree in physical therapy should I heal enough to physically be able to manage that kind of workload. In the meantime, I'm trying to keep learning as much as I can to keep myself busy and happy.

title: User:Swamps42


text:
User talk:Gorbetron

 Hello Gorbetron, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may

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title: User talk:Gorbetron


text:
User talk:K-rowe

 Hello K-rowe, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may

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 Hi , I am Percy. Nice to meet you. I love the beach, swimming, fishing, and I am currently doing some research at Wikiversity on oceanography. I am also learning to play piano. What do you like? Can I be your mascot?

title: User talk:K-rowe


text:
User talk:Masatiq

 Hello Masatiq, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may

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 Hi! My name is WikiversityJack. I am a pumpkin and a Wikiversity mascot. My aunt told me that fun + learning = Wikiversity. Let me know if I can help you out.

title: User talk:Masatiq


text:
User talk:Rrowe.msu

 Hello Rrowe.msu, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may

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title: User talk:Rrowe.msu


text: File:X intersection Y.jpg

title: File:X intersection Y.jpg


text: File:X U Y intersection X U Z.jpg

title: File:X U Y intersection X U Z.jpg


text: File:X union to y intersection Z.jpg

title: File:X union to y intersection Z.jpg


text: File:X union Y.jpg

title: File:X union Y.jpg


text:
User talk:Carrie5215

 Hello Carrie5215, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may

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Feel free to leave a message on my talk page if you have any questions or need help. --mikeu talk 07:17, 22 October 2010 (UTC)

title: User talk:Carrie5215


text:
User talk:Jashina~enwikiversity

 Hello Jashina, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may

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Feel free to leave a message on my talk page if you have any questions or need help. --mikeu talk 07:17, 22 October 2010 (UTC)

Your account will be renamed
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The developer team at Wikimedia is making some changes to how accounts work, as part of our on-going efforts to provide new and better tools for our users like cross-wiki notifications. These changes will mean you have the same account name everywhere. This will let us give you new features that will help you edit and discuss better, and allow more flexible user permissions for tools. One of the side-effects of this is that user accounts will now have to be unique across all 900 Wikimedia wikis. See the announcement for more information.

Unfortunately, your account clashes with another account also called Jashina. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Jashina~enwikiversity that only you will have. If you like it, you don't have to do anything. If you do not like it, you can pick out a different name.

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Renamed
 This account has been renamed as part of single-user login finalisation. If you own this account you can |log in using your previous username and password for more information. If you do not like this account's new name, you can choose your own using this form after logging in: . -- Keegan (WMF) (talk) 06:12, 19 April 2015 (UTC)

title: User talk:Jashina~enwikiversity


text:
User talk:Sheepe~enwikiversity

 Hello Sheepe, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may

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Feel free to leave a message on my talk page if you have any questions or need help. --mikeu talk 07:17, 22 October 2010 (UTC)

Your account will be renamed
Hello,

The developer team at Wikimedia is making some changes to how accounts work, as part of our on-going efforts to provide new and better tools for our users like cross-wiki notifications. These changes will mean you have the same account name everywhere. This will let us give you new features that will help you edit and discuss better, and allow more flexible user permissions for tools. One of the side-effects of this is that user accounts will now have to be unique across all 900 Wikimedia wikis. See the announcement for more information.

Unfortunately, your account clashes with another account also called Sheepe. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Sheepe~enwikiversity that only you will have. If you like it, you don't have to do anything. If you do not like it, you can pick out a different name.

Your account will still work as before, and you will be credited for all your edits made so far, but you will have to use the new account name when you log in.

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Yours, Keegan Peterzell Community Liaison, Wikimedia Foundation 23:43, 17 March 2015 (UTC)

Renamed
 This account has been renamed as part of single-user login finalisation. If you own this account you can |log in using your previous username and password for more information. If you do not like this account's new name, you can choose your own using this form after logging in: . -- Keegan (WMF) (talk) 06:22, 19 April 2015 (UTC)

title: User talk:Sheepe~enwikiversity


text:
User:Shayanin

events identification But it has advantage
 * 1) 1.It has opportunity cheat from employee while he send the product to customer and receive the money of fish
 * 2) 2. It has opportunity the worker in office maybe record the orders are exceeded or lacking
 * 3) 3. It has opportunity the worker in office maybe customize account  of revenue
 * 4) 4. The orders have very important must have record in book or computer for protect the orders are loss.
 * 1) 1.The carman send the fish to the restaurant by we don’t go with him. It help save the time and easy to management but we must be careful control over and choose the carman that we can trust.
 * 2) 2. It is convenient with the customer because can call and have service  delivery. In the future  maybe expanding trade.

title: User:Shayanin


text:
User:Silawadee

CPU CPU Speed Bus Speed Cache size Storage type & amount Blackberry 8900 BlackBerry OS 512 MHZ - 256 kB ROM 256 MB iphone ARM 11 400 MHz 100MHz 256 kB EEPROM (flash drive) 32 GB Netbook Intel® Atom™ Processor N450 1.66 GHz 667 MHz 512 kB PROM type 160 GB

In my personal from research i think that iphone is the most technology advance because it has CPU which requires low energy and can use faster than new book although net book has quite bigger number of cache size.

title: User:Silawadee


text:
User:Woralak

Risk :  Opportunities : - Convenient because we do not to pay much money to hire workers. Threat : 1. We should careful to receive order. Maybe false receive order. 2. We should keep document everything into computer too. We just should not note in paper. 3. Driver just should only drive car. They should not receive order and keep money. Should clear assign and share the work that division of labor according to aptitude in each of the people.Especially in finance, we should careful more because if have something false then will be responsibility.

title: User:Woralak


text:
User:Wilasinee~enwikiversity

RISK

About Threat : - Careful order to make a mistake, aren’t targeted  .Save data in the computer. Do not write down on paper only. Bus driver should be driving only .Provide to duty a clear that will have many positions .Devide work that to suitable and aptitudes of each side. Especially in finance. Should be more careful. If it is wrong then they will heavy responsibility.

About Opportunity : - Comfortable .We don’t pay much money in many worker.

Look a supply chain management. Supply chain management; What finance and accounting information does it deal with? Accountants prepare the financial statements, financial statements, Financial reports including the income statement, the balance sheet, and the statement of cash .In preparing financial statements, they adhere to a uniform set of rules called generally accepted accounting principles (GAAP)generally accepted accounting principles (GAAP)Uniform set of rules for financial reporting established by an independent agency called the Financial Accounting Standards Board (FASB).

What are the advantages of using this module?

-There are a lot more careful in their work because they learn about money. The allocation of funds. If it mistake maybe have the problem could be as many

-Trained to be patient with her. -Management of both incoming and outgoing person or organization that is working properly.

title: User:Wilasinee~enwikiversity


text:
User talk:Nano-gilmour

 Hello Nano-gilmour, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may

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title: User talk:Nano-gilmour


text:
User:FraserEngineering

Student of Engineering. Specialising in Aerospace, Astronautics and Space Technology.

title: User:FraserEngineering


text:
User:Egm6936.f09/Gradient of vector: Two tensor conventions

The Jacobian matrix of a vector-valued function of several variables is a collection of partial derivatives that can be ordered in many different ways, among which there are generally two logical orderings of these partial derivatives (see Two conventions for Jacobian matrix further below). Not surprisingly, in parallel, there are also two conventions for writing the gradient of a vector.

It is important to know these conventions to avoid the confusion in writing the term in the vorticity equation (e.g., Batchelor 1967, p.267 ) that corresponds to the vorticity production due to vortex-line stretching (e.g., Tritton 1988, p.86 ) as  $$\displaystyle \boldsymbol \omega \cdot ( \nabla \mathbf U ) $$  or as  $$\displaystyle ( \nabla \mathbf U ) \cdot \boldsymbol \omega$$.

Both ways of writing this term could be correct, depending on which convention one uses for writing the gradient of a vector in terms of the basis vectors. It is important to note that, for any physical relation, regardless of the various possible tensor forms, there is only a unique component form; an example is the vorticity equation itself. There are two ways (conventions) to express the gradient of a vector, i.e., a second order tensor, in terms of the basis vectors.

Here, as in the article Kolmogorov scales, $$\displaystyle \mathbf U$$ designates a (spatial velocity) vector field defined on the domain $$\displaystyle \mathcal B$$, i.e., $$\displaystyle x \in \mathcal B \mapsto \mathbf U (x) \in \mathbb R^3$$. (Ignore the time dependence of $$\displaystyle \mathbf U$$ here.)

= First convention =

The first convention, often used in continuum mechanics (e.g., Truesdell & Noll 2004, p.15 ; Gurtin 1981, p.30 ; Gurtin et al. 2010, p.45 ; Naghdi 2001, p.21, Eq.5.2 ; Gonzalez & Stuart 2008, p.48 ), is

 * {| style="width:100%" border="0"

$$  \displaystyle {\rm grad} \, {\mathbf U} = \nabla {\mathbf U} = \frac{\partial U_i}{\partial x_j} {\mathbf e_i} \otimes {\mathbf e_j} = U_{i,j} {\mathbf e_i} \otimes {\mathbf e_j} $$  (1)
 * style="width:95%" |
 * style="width:95%" |
 *
 * }

in which the index  $$\displaystyle i$$  of the vector component  in the numerator is summed with the index  $$\displaystyle i$$  of the first basis vector   $$\displaystyle \mathbf e_i$$, and the index   $$\displaystyle j$$  of the coordinate  $$\displaystyle x_j$$   in the denominator is summed with the index  $$\displaystyle j$$ of the second basis vector   $$\displaystyle \mathbf e_j$$.

Nabla is not a "vector"
In Eq.(1), "grad" is a differential operator; nabla $$\displaystyle \nabla$$ is simply an abbreviation for "grad", and is not a "vector" in this first convention. In the second convention, on the other hand, nabla is considered as a "vector", and is written here in boldface, i.e., $$\displaystyle \boldsymbol \nabla$$ to distinguish from the above $$\displaystyle \nabla \equiv {\rm grad}$$ differential operator in lightface.

Directional derivative
The first convention is likely to have its root in the definition of the gradient of a vector field $$\displaystyle \mathbf U$$ by the directional derivative of  $$\displaystyle \mathbf U$$ at $$\displaystyle x$$  in the direction $$\displaystyle \mathbf h$$ (e.g., Misner et al. 1973, p.59 ; Truesdell & Noll 2004, p.15 ; Gurtin 1981, p.29 ; Ciarlet 1988, p.41 ):

 * {| style="width:100%" border="0"

$$  \displaystyle \left. \frac{d \mathbf U (x + \epsilon \mathbf h)}{d \epsilon} \right|_{\epsilon = 0} = \lim_{\epsilon \rightarrow 0} \frac{\mathbf U (x + \epsilon \mathbf h) - \mathbf U (x)}{\epsilon}= D \mathbf U (x) \cdot \mathbf h = [{\rm grad} \mathbf U (x)] \cdot \mathbf h \equiv [\nabla \mathbf U (x)] \cdot \mathbf h $$ (1b)
 * style="width:95%" |
 * style="width:95%" |
 *
 * }

In some works, the component form of $$\displaystyle \nabla \mathbf U$$ in Eq.(1) was not given explicitly, but can be deduced implicitly from Eq.(1b).

= Second convention, transpose of the first =

The second convention for gradient of a vector, often used in fluid mechanics (e.g., Batchelor 1967, Bird et al. 2006 , Pope 2000 , Tritton 1988 ), corresponds to the transpose of the gradient in the first convention.

For this second convention, since boldface nabla is difficult to distinguish from lightface nabla, we use  $$\displaystyle \boldsymbol \nabla \equiv \nabla_*$$  (nabla with subscript *) to denote the gradient (of a vector) to distinguish with the symbol  $$\displaystyle \nabla$$  (plain lightface nabla) used for the first convention:

 * {| style="width:100%" border="0"

$$  \displaystyle \boldsymbol \nabla {\mathbf U} = \nabla_* {\mathbf U} = \left( \frac{\partial}{\partial x_i} \mathbf e_i \right ) \left(U_j \mathbf e_j \right ) = \frac{\partial U_j}{\partial x_i} {\mathbf e_i} {\mathbf e_j} = \frac{\partial U_j}{\partial x_i} {\mathbf e_i} \otimes {\mathbf e_j} = \frac{\partial U_i}{\partial x_j} {\mathbf e_j} \otimes {\mathbf e_i} = \overset{\rightarrow}{\nabla} \mathbf U = \nabla^T {\mathbf U} $$ (2)
 * style="width:95%" |
 * style="width:95%" |
 *
 * }

in which the right-arrow nabla $$\displaystyle \overset{\rightarrow}{\nabla}$$ in Malvern 1969, p.58, was introduced.

Nabla is a "vector"
In this second convention, the gradient operator  $$\boldsymbol \nabla \equiv \displaystyle \nabla_* \equiv \overset{\rightarrow}{\nabla}$$  is thought of as the vector  $$\displaystyle \frac{\partial}{\partial x_i} \mathbf e_i$$ (Pope 2000, p.651 ), i.e.,

 * {| style="width:100%" border="0"

$$  \displaystyle \boldsymbol \nabla \equiv \displaystyle \nabla_* \equiv \overset{\rightarrow}{\nabla} = \frac{\partial}{\partial x_i} \mathbf e_i $$  (2b)
 * style="width:95%" |
 * style="width:95%" |
 *
 * }

that acts on the argument (vector ) on its right side (cf. Pope 2000, p.14 ).

Note that boldface $$\displaystyle \mathbf{grad}$$ was also used to designate gradient as a vector (e.g., Landau & Lifshitz 1987, p.3, Eq.(2.2) ), i.e.,

 * {| style="width:100%" border="0"

$$  \displaystyle \mathbf{grad} \equiv \boldsymbol \nabla \equiv \displaystyle \nabla_* \equiv \overset{\rightarrow}{\nabla} = \frac{\partial}{\partial x_i} \mathbf e_i $$  (2c)
 * style="width:95%" |
 * style="width:95%" |
 *
 * }

Again, since it is difficult to distinguish the boldface $$\displaystyle \mathbf{grad} \equiv \boldsymbol \nabla$$ from the lightface $$\displaystyle {\rm grad} \equiv \nabla$$, we will avoid using these boldface symbols, but use $$\displaystyle \nabla_* \equiv \overset{\rightarrow}{\nabla}$$ instead.

Thus equivalently

 * {| style="width:100%" border="0"

$$  \displaystyle {\rm grad} \, {\mathbf U} \equiv \nabla {\mathbf U} = \nabla_*^T {\mathbf U} = {\mathbf U} \overset{\leftarrow}{\nabla} $$  (3)
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where we also introduced the "left-arrow nabla" symbol $$\displaystyle \overset{\leftarrow}{\nabla}$$  used in Malvern 1969, p.58. The left arrow is used to indicate that the differential operator in $$\displaystyle \overset{\leftarrow}{\nabla}$$ acts on the argument (vector  $$\displaystyle \mathbf U$$) on its left side. On the other hand, as a tensor product (or dyadic), vector $$\displaystyle \mathbf U$$ is on the left followed by "vector"  $$\displaystyle \overset{\leftarrow}{\nabla}$$. Thus

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$$  \displaystyle \mathbf U \overset{\leftarrow}{\nabla} = \left( U^i \mathbf e_i \right )\left( \frac{\partial}{\partial x_j} \mathbf e_j \right ) = \frac{\partial U_i}{\partial x_j} \mathbf e_i \mathbf e_j \equiv \frac{\partial U_i}{\partial x_j} \mathbf e_i \otimes \mathbf e_j \equiv {\rm grad} \, {\mathbf U} \equiv \nabla {\mathbf U} $$ (3b)
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which is identical to Eq.(1).

Directional derivative
With the second convention, the directional derivative is written a bit awkwardly by having to move the direction $$\displaystyle \mathbf h$$ in front of the gradient $$\displaystyle \nabla_* \mathbf U (x)$$, i.e.,

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$$  \displaystyle D \mathbf U (x) \cdot \mathbf h = \mathbf h \cdot [\nabla_* \mathbf U (x)] $$  (3c) An example of the use of Eq.(3c) is Pope 2000, p.14, Eq.(2.16), i.e.,
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$$  \displaystyle \frac{d \mathbf s}{d t} = \mathbf s \cdot \nabla_* \mathbf U $$ (3d) = Two conventions for Jacobian matrix =
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Not surprisingly, the above two conventions for writing the gradient of a vector parallels the two similar conventions of writing the Jacobian matrix  containing the derivative of  $$\displaystyle U_i, \ i=1,2,3$$, with respect to $$\displaystyle x_j, \ j=1,2,3$$. The first convention, which is the most used convention (e.g., Battin 1999, p.xxxi ; Ciarlet 1988, pp.28-29 ; Hughes 1987, p.119 ; cf. Malvern 1969, p.58 ; Rappaz et al. 2010, p.13 ), is to write

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$$  \displaystyle \mathbf J = \left[ \frac{\partial U_i}{\partial x_j} \right] = \left[ \displaystyle \begin{array}{lll} \frac{\partial U_1}{\partial x_1} & \frac{\partial U_1}{\partial x_2} & \frac{\partial U_1}{\partial x_3} \\ \frac{\partial U_2}{\partial x_1} & \frac{\partial U_2}{\partial x_2} & \frac{\partial U_2}{\partial x_3} \\ \frac{\partial U_3}{\partial x_1} & \frac{\partial U_3}{\partial x_2} & \frac{\partial U_3}{\partial x_3} \end{array} \right] $$  (4)
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The second convention corresponds to the transpose of the above convention, with $$\displaystyle i$$ being the column index, and  $$\displaystyle j$$ the row index (e.g., Kellogg 1929, p.35 ; Zienkiewicz & Taylor 2005, p.20 ; Fish & Belytschko 2007, p.167 ). Thus if $$\displaystyle \mathbf J_*$$designates the Jacobian matrix in the second convention, then we have (cf. Malvern 1969, p.58 )

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$$  \displaystyle \mathbf J_* = \mathbf J^T = \left[ \frac{\partial U_i}{\partial x_j} \right] = \left[ \displaystyle \begin{array}{lll} \frac{\partial U_1}{\partial x_1} & \frac{\partial U_2}{\partial x_1} & \frac{\partial U_3}{\partial x_1} \\ \frac{\partial U_1}{\partial x_2} & \frac{\partial U_2}{\partial x_2} & \frac{\partial U_3}{\partial x_2} \\ \frac{\partial U_1}{\partial x_3} & \frac{\partial U_2}{\partial x_3} & \frac{\partial U_3}{\partial x_3} \end{array} \right] $$  (5)
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= Matrix decomposition =

From the matrix algebra of the component form, we can deduce the corresponding tensor form. Let's take the case of a 2x2 matrix as an example.

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$$  \displaystyle \hat{\mathbf A} = \left[ \begin{array}{ll} A^1_1 & A^1_2 \\ A^2_1 & A^2_2 \end{array} \right] = A^1_1 \left\{ \begin{array}{l} 1 \\ 0 \end{array}\right\} \left\lfloor 1 \ 0 \right\rfloor + A^1_2 \left\{ \begin{array}{l} 1 \\ 0 \end{array}\right\} \left\lfloor 0 \ 1 \right\rfloor + A^2_1 \left\{ \begin{array}{l} 0 \\ 1 \end{array}\right\} \left\lfloor 1 \ 0 \right\rfloor + A^2_2 \left\{ \begin{array}{l} 0 \\ 1 \end{array}\right\} \left\lfloor 0 \ 1 \right\rfloor = \sum_{i,j} A^i_j \hat{\mathbf e}_i \hat{\mathbf e}_j ^T $$  (6)
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where the superscript denotes the row index and the subscript the column index, and where $$\displaystyle \hat{\mathbf e}_i$$  is a column matrix and  $$\displaystyle \hat{\mathbf e}_i^T$$ is its transpose, i.e., the corresponding row matrix, as shown below:

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$$  \displaystyle \hat{\mathbf e}_1 := \left\{ \begin{array}{l} 1 \\ 0 \end{array}\right\}, \quad \hat{\mathbf e}_1^T := \left\lfloor 1 \ 0 \right\rfloor, \ etc. $$ (7)
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If we think of $$\displaystyle \hat{\mathbf e}_i$$  as the matrix of components of the vector  $$\displaystyle {\mathbf e}_i$$, then the matrix of components of the tensor product  $$\displaystyle \mathbf e_i \otimes \mathbf e_j$$  is  $$\displaystyle \hat{\mathbf e_i} \hat{\mathbf e_j}^T$$; this association is consistent with the following rule of tensor algebra among 3 vectors  $$\displaystyle \mathbf a, \ \mathbf b , \ \mathbf c$$  (e.g., Gurtin 1981, p.4 )

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$$  \displaystyle \left( \mathbf a \otimes \mathbf b \right) \cdot \mathbf c = \mathbf a (\mathbf b \cdot \mathbf c) $$ (8)
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since in terms of matrices of components of these vectors, we have

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$$  \displaystyle ( \hat{\mathbf a} \hat{\mathbf b}^T ) \hat{\mathbf c} = \hat{\mathbf a} ( \hat{\mathbf b}^T \hat{\mathbf c} ) $$  (9)
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which is the matrix of components of the vector $$\displaystyle \mathbf a ( \mathbf b \cdot \mathbf c )$$. Thus the tensor $$\displaystyle \mathbf A$$  with the above matrix of components  $$\displaystyle \hat{\mathbf A}$$ can be written as

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$$  \displaystyle {\mathbf A} = \sum_{i,j} A^i_j \mathbf e_i \otimes \mathbf e_j = A^i_j \mathbf e_i \otimes \mathbf e_j $$  (10)
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With the above explanation, it is then clear that the first convention of writing the gradient of a vector, i.e.,  $$\displaystyle \nabla {\mathbf U}$$  in Eq.(1), corresponds to the usual convention of writing the Jacobian matrix  $$\displaystyle \mathbf J$$ in Eq.(4), whereas the second convention for the gradient of a vector, i.e.,  $$\displaystyle \nabla_* {\mathbf U}$$ in Eq.(2), corresponds to the second (rare) convention of writing the Jacobian matrix (which is the transpose of the usual Jacobian matrix).

In addition, the main rationale for the second convention in writing  $$\displaystyle \nabla_* {\mathbf U}$$, as explained above, is to think of the gradient operator as a "vector", which can then be formed freely with another vector (e.g.,  $$\displaystyle {\mathbf U}$$) into a dyadic (or tensor product).

= Vorticity production by vortex-line stretching =

Now let's return to the vorticity production by vortex-line stretching; the following relationships hold:

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$$  \displaystyle ({\rm grad} \, {\mathbf U}) \cdot {\boldsymbol \omega} = (\nabla {\mathbf U}) \cdot {\boldsymbol \omega} =({\mathbf U} \overset{\leftarrow}{\nabla}) \cdot {\boldsymbol \omega} = {\boldsymbol \omega} \cdot (\overset{\rightarrow}{\nabla} {\mathbf U}) = {\boldsymbol \omega} \cdot (\nabla_* {\mathbf U}) = {\boldsymbol \omega} \cdot (\nabla^T {\mathbf U}) $$  (11)
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We can write:

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$$  \displaystyle \boldsymbol \omega \cdot \overset{\rightarrow}{\nabla} \mathbf U = (\omega_k \mathbf e_k) \cdot \left( \frac{\partial}{\partial x_j} \mathbf e_j \right ) \left( U_i \mathbf e_i \right ) = \omega_k\frac{\partial U_i}{\partial x_j} (\mathbf e_k \cdot \mathbf e_j) \mathbf e_i = \omega_j \frac{\partial U_i}{\partial x_j} \mathbf e_i \equiv \boldsymbol \omega \cdot ( \overset{\rightarrow}{\nabla} \mathbf U ) $$  (12)
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where parentheses were put around $$\displaystyle \overset{\rightarrow}{\nabla} \mathbf U$$  to emphasize the meaning of the gradient of a vector (e.g., Pope 2000, p.14 ). Many authors (e.g., Aris 1962, p.57, p.79 ; King et al. 2003, p.50 ) put the parentheses around  $$\displaystyle \boldsymbol \omega \cdot \overset{\rightarrow}{\nabla}$$, i.e.,

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$$  \displaystyle ( \boldsymbol \omega \cdot \overset{\rightarrow}{\nabla} ) \mathbf U = \left[ (\omega_k \mathbf e_k) \cdot \left( \frac{\partial}{\partial x_j}  \mathbf e_j \right ) \right] \left( U_i \mathbf e_i \right ) \equiv \boldsymbol \omega \cdot ( \overset{\rightarrow}{\nabla} \mathbf U ) \equiv \boldsymbol \omega \cdot \overset{\rightarrow}{\nabla} \mathbf U $$ (13)
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which could originate from the writing of the material time derivative operator as (Aris 1962, p.114 ; cf. Pope 2000, p.13 )

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$$  \displaystyle \frac{D (\cdot)}{Dt} = \frac{\partial (\cdot)}{\partial t} + (\mathbf U \cdot \overset{\rightarrow}{\nabla})(\cdot) $$  (14)
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Even though the same component form would result from such notation, the physical meaning of the gradient of a vector field in  $$\displaystyle \overset{\rightarrow}{\nabla} \mathbf U$$ is lost. Besides, $$\displaystyle \boldsymbol \omega \cdot \overset{\rightarrow}{\nabla}$$ is not the divergence of  $$\displaystyle \boldsymbol \omega$$; its mathematical meaning is a differential operator waiting to operate on  $$\displaystyle \mathbf U$$; one could interpret  $$\displaystyle \boldsymbol \omega \cdot \overset{\rightarrow}{\nabla}$$ as the gradient projected along the direction  $$\displaystyle \boldsymbol \omega$$.

Many other authors simply omit the parentheses to write the vortex stretching term as $$\displaystyle \boldsymbol \omega \cdot \overset{\rightarrow}{\nabla}$$ (e.g., Batchelor 1967, p.267 ; Pope 2000, p.22 ).

= Other uses and notations =

On the other hand, there is no point of avoiding $$\displaystyle {\nabla} \mathbf U$$, since the strain rate is

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$$  \displaystyle \boldsymbol \epsilon = \frac{1}{2}\left[ \nabla \mathbf U + \nabla^T \mathbf U \right] = \frac{1}{2}\left[ {\mathbf U} \overset{\leftarrow}{\nabla} + \overset{\rightarrow}{\nabla} \mathbf U \right] = \frac{1}{2}\left[ \nabla_*^T \mathbf U + \nabla_* \mathbf U \right] $$  (15)
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Note that other authors (e.g., Dhont 2004, p.20 ) even put the tensor product between nabla $$\displaystyle \nabla$$ and  $$\displaystyle \mathbf U$$ (perhaps to emphasize the 2nd-order nature of the resulting tensor) to write

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$$  \displaystyle \nabla \otimes \mathbf U \equiv \overset{\rightarrow}{\nabla} \mathbf U = \nabla_* \mathbf U $$ (16)
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Here again, as mentioned above, the nabla $$\displaystyle \nabla$$  is viewed as a vector, as in Eq.(2b).

= Closure =

As mentioned above, since there is a unique component form for any physical relation, even though there could be several ways to write the same relation in tensor form, some authors write exclusively in component form (e.g., Berdichevsky 2009, Wyngaard 2010 ). The tensor form has its advantage of being concise, compact, and is thus easier to grasp the relation among the different tensor quantities, without being bogged down by the indices and their summations. To avoid confusion, however, the corresponding key components form should always be given, such as the component form of $$\displaystyle \nabla \mathbf U$$ in Eq.(1).

Most continuum mechanics literature uses the first convention, whereas most fluid mechanics literature uses the second convention. Malvern 1969 is a rare exception and an excellent book that presents both conventions, as the book was intended for a course that graduate students would take before taking more specialized topics such as linear elasticity or fluid mechanics.

Unfortunately, these days, the original vision of Malvern (even at the last university where he taught for more than 20 years) is no longer followed perhaps due to practical reasons: Solid mechanics students would take the more specialized linear elasticity before taking continuum mechanics, which includes nonlinear behaviors, whereas fluid mechanics students would shun continuum mechanics completely, as the kinematics of deformation, which is primarily useful for solids, would not be useful for fluids.

= References (order of appearance, with links) =

= References (alphabetical order) =

Aris, R., Vectors, tensors, and the basic equations of fluid mechanics, Prentice Hall, NJ, 1962; Dover, 1989.

Batchelor, G.K., An introduction to fluid dynamics, Cambridge University Press, 1967.

Battin, R.H., An introduction to the mathematics and methods of astrodynamics, revised edition, AIAA, 1999.

Berdichevsky, V.L., Variational principles of continuum mechanics, Vol.II: Applications, Springer Verlag, 2009.

Bird, R.B., Stewart, W.E., Lightfood, E.N., Transport phenomena, Second edition, Wiley, 2006.

Ciarlet, P.G., Mathematical elasticity, Vol.1: Three-dimensional elasticity, Elsevier, 1988.

Dhont, G., The finite element method for three-dimensional thermomechanical applications, Wiley, 2004.

Fish, J., Belytschko, T., A first course in finite elements, Wiley, 2007.

Gonzalez, O., Stuart, A.M., A first course in continuum mechanics, Cambridge University Press, 2008.

Gurtin, M.E., An introduction to continuum mechanics, Academic Press, 1981.

Gurtin, M.E., Fried, E., Anand, L., The mechanics and thermodynamics of continua, Cambridge University Press, 2010.

Hughes, T.J.R., The finite element method: Linear static and dynamic finite element analysis, Prentice Hall, NJ, 1987.

Kellogg, O.D., Foundations of potential theory, Frederick Ungar Publishing Co., New York, 1929; Dover, 2010.

King, A.C., Billingham, J., Otto, S.R., Differential equations: Linear, nonlinear, ordinary, partial, Cambridge University Press, 2003.

Landau, L.D., Lifshitz, E.M., Fluid mechanics, 2nd edition, Pergamon Press, 1987.

Malvern, L.E., Introduction to the mechanics of a continuous medium, Prentice Hall, 1969 (hard cover), 1977 (paperback).

Misner, C.W., Thorne, K.S., Wheeler, J.A., Gravitation, Freeman and Co., 1973.

Naghdi, P.M., ME 185 Lecture notes on continuum mechanics, University of California at Berkeley, Mechanical Engineering, edited by J. Casey, 2001.

Rappaz, M., Bellet, M., Deville, M., Numerical modeling in materials science and engineering, Springer, 2010.

Stephen B. Pope, Turbulent Flows, Cambridge U. Press, 2000.

Tritton, D.J., Physical fluid dynamics, 2nd edition, Oxford Science Publications, 1988.

Truesdell, C., Noll, W., The nonlinear field theories of mechanics, ed. by S. Antman, 3rd edition, Springer Verlag, 2004.

Wyngaard, J.C., Turbulence in the atmosphere, Cambridge University Press, 2010.

Zienkiewicz, O.C., Taylor, R.L., The Finite element method, 6th edition, Butterworth-Heineman, MA, 2005.


text:
User:Stephen Tuck

I was born in Hurst Texas on February 1, 1981. I have two sons named Cayden Drake Richards and Jeremiah Dawson Tuck with Natalie Tuck (with whom I am separated). I was a Class of 2000 honors student that opted for early graduation from Jacksonville High School in summer of 1999. I am highly intellectual with a gift for problem-solving, but have had no college education. Most of my professional career has been as a CSR or Tech Support agent. My fields of research has been in energy, Theoretical Physics, Philosophy, Health, and Computer Science. My heroes growing up have been Einstein, Nikola Tesla, and Thomas Jefferson. My motto is "Strength of Mind and Strength of Heart." I hope to have my work embraced by the scientific community so that I have the opportunity to best utilize my great abilities for the benefit of mankind.

title: User:Stephen Tuck


text:
User:Klyman

My name is Kelly Lyman and I am working on the 2010-2011 fundraising team for the Wikimedia Foundation. This account is used for official edits while officially employed by the Wikimedia Foundation.

Meta user name: Klyman

Freenode IRC nick name: klyman

AIM: klyman, kllylymn

Email: klyman@wikimedia.org

title: User:Klyman


text:
User:Stephen Tuck/Theory of Everything

Tuck’s General Theory of Everything
I have decided to submit my General Theory of Everything (comprising of several theories) to the public and scientific community. I believe that I have unlocked the greatest mysteries of the universe. This should complete the General Theory of Relativity, integrate it along with other theories into a single consistent framework, and help to advance science and technology on a course of further great achievements. I believe my work will prove that leading theories in the scientific community like Quantum Mechanics and String Theories are inaccurate or incomplete. My theories will ultimately be proved by the correct Energy Equivalence equation, which is derrived from the famous equation E=MC^2. Science desperately needs a theory that completely explains how the universe works at the deepest, most intimate level possible. Such knowledge should be an evolutionary leap forward for the future of mankind.

My first theory is that black holes create space, which is also known as “dark energy.” I believe that “dark matter” is ordinary matter that has been consumed by a black hole. It is my understanding of the great theoretical physicist Albert Einstein that gravity is a phenomenon in which space is warped by the presence of matter forming a curved geometry. In this view, the gravitational fields of the objects interact by placing a constant force of acceleration on the objects toward each other. It has been observed that the universe is expanding and that the expansion is increasing at an approximately constant rate. This accelerated expansion did not appear in the earlier universe until sometime after the formation of galaxies. My theory asserts that cold dark matter is primarily massive compact halo objects (MACHOs), which include black holes, neutron stars, white dwarfs, very faint stars, and non-luminous objects like planets. In the Big Bang Theory, space itself expands with time everywhere and increases the physical distance between two points. That explains how the proposed dark energy is able to increase the expansion of the universe. The expansion of space itself acts like the negative pressure pushing distant galaxies and stars away at an increasing rate of speed. The heart of every galaxy seems to be a supermassive black hole, which means that active black holes would push all galaxies away from each other to some extent in addition to holding each galaxy together through gravitation. The point of infinity or singularity within the black hole appears to be the point where this transformation of matter into space occurs. The universe is dominated by dark energy, which permeates all of space and composes approximately 74% of the total energy density. After billions of years of expansion the increased conversion of dark matter into dark energy caused that expansion to slowly begin to accelerate. The Cosmological Principle states that on large scales the universe is homogeneous and isotropic. I believe this is due to the fact that space is expanding at a rate consistent with its creation in black holes, which maintains equilibrium of spatial distribution. Hubble's Law indicates that the universe is uniformly expanding everywhere. The Cuspy Halo Problem seems less of a problem and more like the solution as it points to the fact that cosmological simulations indicate cold dark matter would form cuspy distributions. This implies that the center of the galaxies should exhibit higher dark matter density than other areas. This is exactly where we find massive black holes. During the 1970s and 1980s, various observations showed that there is not sufficient visible matter in the universe to account for the apparent strength of gravitational forces within and between galaxies. This led to the idea that 90% of the matter in the universe is dark matter that does not emit light or interact with ordinary baryonic matter. Vacuum Energy is the underlying background energy that exists in space even when devoid of matter. It is deduced from the concept of virtual particles (which are themselves deduced from the Energy-Time Uncertainty Principle), and is thought to have consequences for the behavior of the universe on cosmological scales. Currently there is no evidence that vacuum energy density varies in space. Special Relativity predicts that energy is equivalent to mass, and therefore if the vacuum energy is "really there," it should exert a gravitational force. Essentially a non-zero vacuum energy is expected to contribute to the Cosmological Constant, which affects the expansion of the universe. Dark energy accounts for approximately 74% of the total mass-energy of the universe. Dark energy is known to be very homogeneous, not very dense, and is not known to interact through any of the fundamental forces other than gravity. That seems to be the very definition of space. It is estimated that dark matter made up 63% of the universe. Now it only makes up about 22% with dark energy making up approximately 74%. Again, I believe this is due to the conversion of matter into space within black holes. Virtual particles can become real particles with the addition of energy such as gravity from a black hole resulting in Hawking Radiation or the acceleration from a strong electromagnetic field. There is evidence that elementary particles are stabilized quantum vacuum fluctuations. Each proton (or neutron) is made up of three quarks but the individual masses of the quarks only add up to 1% off the proton's mass. A field of virtual particles called gluons carries the Strong Nuclear Force. The energy of these vacuum fluctuations has to be included in the total mass of the proton. Quark-antiquark pairs can also pop up momentarily transforming the proton into a more exotic particle. Therefore most of the particle mass comes from virtual quarks and gluons. The Higgs Field is also thought to make a small contribution, giving mass to individual quarks as well as electrons and some other particles. Space and time are often combined in mathematical models into a single entity called the Space-Time Continuum. However, I have come to the realization that this concept is inaccurate. I believe that time travel into the past is impossible without recreating the universe from its exact quantum state of creation that set everything in motion leading to the sequence of events in our past, present, and future. Relativity asserts that observations are dependent upon the observer’s frame of reference, but while time may pass at a different rate for observers, I believe that it is impossible to visit a frame of reference that lies in the past. There can be a difference in the passage of time, but not in causality. It is my assertion that even intelligent life, that is able manipulate the state of the universe, was set into motion from the initial creation of the universe and while possessing free will would respond as defined by our past in a perfect recreation. Another observation is that DNA is a biochemical code that runs within the laws of the physical universe. If you could perfectly model the universe then you could model DNA code, giving you the ability to understand, change, and modify its structure. However the variables and the processing requirements would be incredibly huge. Also dynamic probability is one of the greatest factors in artificial intelligence. People make decisions to fulfill their needs and desires. A logical decision is one that will give a greater probability of success based on all known parameters. The ability to increase success by defining and modifying algorithms dynamically and make decisions based on changing probability I think would best synthesize learning and mimic intelligence. As for the universe, it would be interesting to know what causes unstable vacuum fluctuations (virtual particles) to exist in a limited time and space in accordance with the Uncertainty Principle. It seems like virtual particles are part of the fabric of space. Space appears to interact with matter through the force of gravity thus connecting separated points in space to each other. Therefore it acts as if it has a unifying structure that gives it certain mechanical properties. I believe that we need to probe into the fundamentals of space to determine its mechanics in order to gain understanding of how it interacts with matter-energy at a deeper level and the physics of the underlying process. Perhaps such knowledge will help in understanding the creation and the ultimate fate of the universe. The transformation of mass into space, space into mass, and mass into energy implies that Einstein’s Energy Equivalence equation is incomplete and should be modified to include space as one of its variables. It has been said that the General Theory of Relativity is incomplete because of the lack of a prediction of what happens within a black hole. I believe that my solution fills the hole in that theory. Therefore, it completes the General Theory of Relativity by turning it into a scientific law. It seems only appropriate to rename Einstein’s theories into law such as the “General Law of Relativity” and the “Special Law of Relativity.”

I have also determined that the Higgs Boson does not exist. The Higgs Field is described as having amplitude different from zero, which is a non-zero vacuum value. I believe that mass is a defined characteristic or interaction between matter and space. It would seem that space itself exerts the Higgs Mechanism giving matter its property of mass. It is likely that the structure of space plays role in that interaction. Since matter warps the geometry of space, if the distortion to the surrounding space could be prevented then it may be possible to shield objects from gravitation. This would essentially be the decoupling of objects with mass from space.

I currently believe that black holes do not exist as wormholes based upon my understanding of black holes converting matter into space. My perspective is that a singularity is not a pathway into another universe, but rather into the fabric of space. The inverse effect is when particle/anti-particle pairs are ejected from the plane of space into the universe as real particles. This means that time travel and faster-than-light travel through wormholes would be impossible and would discredit multiple universe theories.

It appears that the gravitation is purely equivalent to acceleration as if the motion of space or matter within space is the cause of gravitation. An interesting thought experiment is that if you were standing on the surface of an incredibly massive object, and checked the time of a distant satellite you would notice a Gravitational Time Dilation in accordance with the Equivalence Principle, which is the same as if you were traveling at a high rate of speed. Obviously, if you are stationary then you may wonder what interaction would cause the effect of time dilation to occur as if you were in relativistic motion. I believe that gravitation is caused by the apparent motion of matter relative to space due to a gravitational field effect induced by mass that causes curvature of its surrounding space. According to Newton's First Law, a body will persist in its state of rest or of uniform motion (constant velocity) in a straight line unless it is compelled to change that state by forces impressed upon it. In a flat space, an object at rest will stay at rest. However in the presence of gravitation (where space is curved) objects of mass have to move with space in order to stay at rest (maintain inertia) in relation to it. Therefore, in order to stay at rest locally within a three-dimensional coordinate system, a counteracting force has to be present to offset the force of gravity. This means an object of mass appears to always be in motion in respect to its surrounding space, but may be at rest within its discrete frame of reference. Newton's Second Law of Motion defines the force generated by the apparent motion of matter. Newton's Third Law might be applied to indicate that gravitation is a reaction directly counteracting the field curvature induced by an object of mass within its vicinity. The equivalence would provide an explanation of a gravitational redshift. Normal redshifts occur when an electromagnetic source moves away from an observer. A cosmological redshift is seen due to the expansion of the universe with sufficiently distant light sources. Interestingly, gravitational redshifts are described as a relativistic effect observed in electromagnetic radiation moving out of gravitational fields. It is interesting to note that photons are massless particles, but are affected by gravitation. Gravity shielding would prove very useful in propulsion. The Frame-Dragging Effect (while miniscule) can provide gravitational shielding. However, the creation or amplification of space kinetics would be a much greater effect if possible. Another option is the use of Hawking radiation from a miniature black hole.

One interesting observation is the scalar connection between the Higgs Boson, space, and quark-gluon condensates. The Higgs Boson is a hypothetical massive scalar elementary particle predicted to exist by the Standard Model in particle physics. At present there are no known elementary scalar particles in nature. During inflation, the universe is flattened (its spatial curvature is critical) and the universe enters a homogeneous and isotropic rapidly expanding phase in which the seeds of structure formation are laid down in the form of a primordial spectrum of nearly-scale-invariant fluctuations. A scalar field can be viewed as a sort of perfect fluid with Equation of State. Although experimental high temperatures and densities predicted as producing a quark-gluon plasma have been realized in the laboratory, the resulting matter does not behave as a quasi-ideal state of free quarks and gluons, but rather as an almost perfect dense fluid. Perhaps variations of the QCD models are correct explaining different aspects of the same entity. This is a model of the QCD vacuum, which at a basic level is a statement that it cannot be the conventional Fock Vacuum empty of particles and fields. In 1977, George Savvidy showed that the QCD vacuum with zero field strength is unstable, and decays into a state with a calculable non-vanishing value of the field. Since condensates are scalar, it seems like a good first approximation that the vacuum contains some non-zero but homogeneous field, which gives rise to these condensates. This would then be a more complicated version of the Higgs Mechanism. However, Stanley Mandelstam showed that a homogeneous vacuum field is also unstable. The instability of a homogeneous gluon field was argued by Niels Kjær Nielsen and Poul Olesen in their 1978 paper “An Unstable Yang-Mills Field Mode.” These arguments suggest that the scalar condensates are an effective long-distance description of the vacuum, and at short distances (below the QCD scale) the vacuum may have structure. It is interesting that the Equation of State describes the properties of both dark energy and quark-gluon condensates and that black holes form quark-gluon plasma. I believe that this is due to the conversion of mass into space by a black hole.

Space is actually composed of something. Sir Isaac Newton and Einstein both expressed belief in a subtle ethereal medium that fills all space. Einstein, in his 1920 address at the University of Leyden stated, “To deny the ether is ultimately to assume that empty space has no physical qualities whatever. The fundamental facts of mechanics do not harmonize with this view.” He concluded by saying, “Recapitulating, we may say that according to the General Theory of Relativity space is endowed with physical qualities; in this sense, therefore, there exists an ether. According to the general theory of relativity space without ether is unthinkable; for in such space there not only would be no propagation of light, but also no possibility of existence for standards of space and time (measuring-rods and clocks), nor therefore any space-time intervals in the physical sense.” Ether is a frictionless medium as required by Newton’s First Law of Gravitation. Black holes are clues to the composition of space. When matter falls into the event horizon it becomes isolated from the rest of space and time and effectively disappears from the universe. At the center of a black hole is a gravitational singularity, which is a region where the space curvature becomes infinite. It supposedly has zero volume but infinite density containing all the mass of the black hole. Once inside the black hole the matter is torn apart into its smallest subatomic components, which are stretched and squeezed until they become part of the singularity, increasing the radius of the black hole. I believe that black holes function similar to the conditions of the Inflationary Epoch. During inflation, the universe is flattened and the universe enters a homogeneous and isotropic rapidly expanding phase. According to the ΛCDM model, dark energy is present as a property of space itself, which begins immediately following the period of inflation, as described by the Equation of State. White holes and wormholes come from ideas of extending the black hole from the singularity in the throat back out to an alternate universe or spacetime. The appearance of singularities in general relativity is commonly perceived as signaling the breakdown of the theory. Since general relativity predicts the inevitable occurrence of singularities, the theory is not complete without a specification for what happens to matter that enters the singularity. This breakdown occurs in a situation where quantum mechanical effects should describe the extremely high-density particle interactions. Currently, science has been unable to combine quantum and gravitational effects into a single theory. I believe my ideas should also resolve the black hole information paradox since matter forms space, which is still part of the universe. It may be possible that some virtual particles created via hawking radiation were matter that had previously fallen into the black hole. It is interesting to note that black hole singularities produce imaginary numbers. According to Superstring Theory, this is interpreted as a higher dimension from the three-dimensional spacetime curvature. Also, black hole graphs show that time on a vertical axis becomes increasingly horizontal approaching the singularity. Another fact that points to an ethereal medium is that gravitational waves propagate through space. They are created by the movement of massive non-uniform bodies of matter or events that redistribute matter within space. Due to the equivalence principle of gravitation and its infinite magnitude, the space around a black hole should reach equivalence to speeds surpassing the speed of light unless prevented from doing so by some underlying process. The invisible boundary where light cannot escape due to spacial equivalence equal to the speed of light is known as the event horizon.

I believe that magnetism is explained by the alignment of charged, dipolar structural units within space around a magnet that form elliptical field lines. Magnetism is typically explained as mediated by virtual photons, but it does not explain the magnetic field line geometry. Photons are defined as having no mass or electric charge and travel in a straight trajectory. An interesting thought is that if a bar magnet became fluid but retained structural bonding, it would naturally curl up into a loop connecting its north and south poles together due to attraction of the opposite charges. A string of such units would form a chain similar to the shape of a pearl necklace. Also, Magnetic Reconnection is an interesting phenomenon. It is the process whereby magnetic field lines from different magnetic domains are spliced to each other, changing their patterns of connectivity with respect to the sources. I believe this is due to dynamic magnetic events that allow the splicing of separate space magnetic field alignments. Magnetic Reconnection is a violation of an approximate conservation law in plasma physics, and can concentrate mechanical or magnetic energy in space. Another interesting but little-known effect is of magnetic field lines smoothing space because they do not like to bend. The effect is small, but under huge gravitational forces the magnetic field lines push back trying to flatten space. This is probably due to the magnetic flux of the field causing resistance to the tidal forces of gravitation. This could be a useful interaction for a Unified Field Theory because it ties the electromagnetic interaction with space, therefore connecting it to gravitation.

Wave-particle duality is another characteristic that I believe can be explained by the fabric of space. Again, I believe this is a property explained by the interaction of mass and space. As particles propagate through space, I think that their path naturally follows a wave-like motion through the framework of space. Perhaps experiments into the wave motion of photons within the electromagnetic spectrum would provide clues to an unseen structure of space. However, space is likely to have dynamic characteristics since matter, energy, and the universal expansion may exert tensor forces upon it. I think that such detailed knowledge would help explain quantum chaos such that we can understand it better than mere probability alone.

The Theory of Quantum Mechanics incorporates four classes of phenomena for which classical physics cannot account: the quantization of certain physical quantities, Wave–Particle Duality, the Uncertainty Principle, and Quantum Entanglement. The centerpiece of this mathematical system is the wavefunction. The wavefunction is a mathematical function of time and space that can provide information about the position and momentum of a particle (but only as probabilities) as dictated by the constraints imposed by the uncertainty principle. I believe that quantum theory makes the mistake of believing that a subatomic particle is in a quantum superposition (combination of all the possible states of a system) until it is observed undergoing a wavefunction collapse into a definite state only at the exact moment of quantum measurement. This is famously illustrated in the Schrödinger’s cat thought experiment, which is thought to be a paradox. Quantum Mechanics seems to be a way to deal with the fact that a subatomic particle is in an “unknown but definite state” at any given moment, which is not currently understood by science. The mathematical formulation of quantum mechanics is abstract and its implications are often non-intuitive. Also Bell's theorem proves that every quantum theory based on quantum principles must violate either locality or counterfactual definiteness. It appears that Quantum Mechanics uses the powerful mathematics of probability because of that uncertainty in knowing the exact state of a subatomic particle, acting as a kind of statistical approximation. I believe that Einstein was correct in his statement that “God does not play dice,” meaning that he believed physical theories must be deterministic to be complete. I also believe that objects have a definite state that determines the values of all other measurable properties (such as position and momentum), and that effects of local actions (such as measurements) cannot travel faster than the speed of light. The no-communication theorem at least substantiates that information cannot be communicated faster-than-light due to the effects of quantum entanglement. Entangled particles are in direct contact with each other in order to get the spin-anti-correlated or spin-correlated case and their values are unknown. Also they are very sensitive to becoming unentangled. As soon as anything disturbes their state they assume a new value that is completely random to their entangled partner. This supports the idea that the values of both particles are defined as equal or opposite in nature by certain types of physical contact and that if kept in a protected state their subsequent measurements will correlate with each other. Observables may be undetermined until some physical intervention is made to measure an observable of the object in question, but that doesn’t mean that the observable is undefined or in multiple states simultaneously. Quantum Mechanics is based on the Heisenberg Uncertainty Principle which states that by precise inequalities certain pairs of physical properties (like position and momentum) cannot simultaneously be known to arbitrary precision. However, I believe this is due to the lack of knowledge of the true nature of the universe at the quantum level rather than being due to the nature of the system itself. I believe that the Uncertainty Principle really means that the act of measuring one quantity of a subatomic particle affects it so that any other measurable quantity changes, thus preventing you from knowing two quantities with arbitrary precision. Entanglement is the only way that you can have several particles in the same state in order to make several measurements to obtain multiple precise measurements. If you could account for all changes introduced during each measurement then you may be able to know precise multiple measurements of the final state of the subatomic particle. Any measuring device uses matter and energy (such as particles or fields) in order to observe and record readings, which changes the state of the subatomic particle during the time of its measurement. Therefore the measured quantities in the EPR paradox are precise values that are known simultaneously about the subatomic particle’s previous state before measurement. The Heisenberg Uncertainty Principle does not directly apply to the measurement of discrete quantizations in entangled subatomic particles. It is interesting to note that if the exact properties of every quantum particle were known, the entire system could be modeled exactly using deterministic physics similar to classical physics. Quantum Mechanics of the twentieth century has enjoyed major success and led to many fields of physics and chemistry including condensed matter physics, solid-state physics, atomic physics, molecular physics, computational physics, computational chemistry, quantum chemistry, particle physics, nuclear chemistry, and nuclear physics. It appears that all of the facts disprove the current theory of Quantum Mechanics (based on quantum superposition wavefunctions) as a completely accurate description of quantum behavior in favor of a deterministic one. I believe that the new quantum theory of the twenty-first century will far surpass Quantum Mechanics in its ability to accurately describe quantum behavior and inevitably enjoy incredible success in the advancement of science. I propose this new quantum theory be called “Deterministic Quantum Mechanics,” and have the abbreviation of DQM.

A Unified Field Theory has been a great pursuit of science, which allows all the fundamental forces and elementary particles to be written as a single field. A Theory of Everything is closely related, but does not require the basis of nature to be fields. The four fundamental forces of nature are: the Strong Nuclear Interaction, Electromagnetic Interaction, Weak Nuclear Interaction, and Gravitational Interaction. I believe that all these forces should come together under the framework of my theory. It appears that all have a basis in being geometrical entities of which space plays an essential role. Work with physics in which quantum gravity is significant may greatly contribute to this goal. Quantum Mechanics has often prevented unification efforts, since it is not deterministic in nature. Further efforts are necessary for the unification of these forces.

Einstein’s equation E = M*C^2 is the most famous equation in history. It is synonymous with human ingenuity and genius. However, I have found that while it provides the correct answer, it is not a completely accurate description of the universe. There are additional variables hidden within C^2. I had predicted that this equation should be modified to account for my theory that black holes convert mass into space. I awoke on day with the thought that this equation was very similar to F = M*A, where force is equal to mass multiplied by acceleration. I carefully considered what Einstein’s equation was stating. At face value, it says that energy equals mass times the speed of light squared. However, the reason that light travels so fast is because the photon is a massless particle. Essentially, the speed of light represents the speed limit of the universe and energy variable is in the form of kinetic energy. Therefore the equation really says that kinetic energy is equal to mass times the maximum speed of kinetic energy squared. A play on semantics would be that the maximum speed of the universe is the “Speed of Space.” While I still believed the notion of Space-Time, I thought that the Speed of Space sounds a lot like Time since time is measured by a constant rate of motion (such as within a clock, atoms, or the distance that light travels). It also occurred to me that space was also defined by the speed of light because it was the maximum speed in which something could travel within it. I decided that Space-Time could replace the variable C^2. Then it occurred to me that a square is a number times itself. I realized that Space-Time should be separated into the two separate variables. Finally, I had discovered a revolutionary simple equation that explained everything. I had discovered E = Space * Mass * Time. The equation has a specific order because Time is the first variable affected by speed. In the case of a black hole, time should stop once matter reaches the speed of light. The next step would be the conversion of mass into space. I imagine that if space accellorated to the level of kinetic energy prior to creation, then it would disappear into a Big Crunch. It appears that Space the first to appear, followed by Mass, and then Time. This should have great ramifications for modeling the universe from the Big Bang to its current state. Also, there are a total of 10 different combinations of possible transformations within the equation. There is Mass into Energy (nuclear fission or fusion), Energy into Mass (sometimes due to particle collisions), Energy into Time (increased temperature increases the rate of reactions), Time into Energy (Chemical energy; decreased temperature decreases rate of reactions), Mass into Time (decrease of velocity), Time into Mass (relativistic mass increase), Space into Mass (virtual particles), Mass into Space (black hole), Space into Time (decreased spacial curvature), and Time into Space (Gravitational Time Dilation). An interesting observation is that it has been observed that in black hole thermodynamics, the maximal entropy in any region scales with the radius squared, and not cubed as might be expected. This observation has lead to the Holographic Principle, which is the idea that that the description of all the objects that have fallen in a black hole can be entirely contained in surface fluctuations of the event horizon. This is probably due to relativistic Length-Contraction. Also, from the equation, I was able to determine that Gravity is a curvature of space due to objects exerting a force on each other through the medium of space. This appears to be due to an interaction between mass and space, which then interacts with any object of mass (a field effect). Just because an object on the surface of a massive body does not move, does not mean that there is no kinetic energy being transferred to it through the force of gravity. According to Einstein’s Equivalence Principle, Gravity is equal to a force. This explains why high gravitational fields cause Time Dilation and Mass Increase. A mathematical proof of the equation is the fact that the Mass Increase and the Time Dilation equations are exactly identical. This is because they have the same mathematical relationship. Basically, as time slows down, the kinetic energy of mass increases at the same rate. After carefull examination of related equations, I was able to construct one that solves for Mass Increase, Time Dilation, and the Kinetic Energy of a moving object. The new equation is Energy = ((Space * Mass * Time) / (1 – (Velocity^2 / C^2))^0.5 – (Space * m0 * Time). While you could solve this Differential Equation using two Simultaneous Equations, it is possible to use an equation solver to solve for any variable through a series of steps.  First set the Space variable to the Speed of Light, Mass to the Rest Mass, Time to the Speed of Light, m0 to 0, and Velocity to the speed.  Next, you calculate the Energy.  Then, zero out the Velocity and calculate the Mass (which is Relativistic Mass).  Next, re-enter Velocity and calculate the Time (yielding Relativistic Time).  You could also get the rate of Time Dilation by setting the Space variable to C^2, Time to 1, entering the Velocity, calculating Energy, zeroing Velocity, and calculating for Time.  However, be sure to reset all the variables before doing further calculations.  Also, if you just want the kinetic energy of a moving object then use the m0 variable.

In conclusion, I had to overcome many hurdles to see what I believe to be the truth about the universe. It started with the understanding that black holes created space from many clues. Then realizing that space wasn’t empty, that it caused the Wave-Particle Duality, and acted like the Higgs Mechanism to give matter the property of mass. I began trying to determine the makeup of space and how black holes created it from matter. I gained insight into magnetism and learned the greater implications of the Equivalence Principle. Next, I tried combining what I learned with Quantum Mechanics, but it didn’t make sense. I was looking for a hidden variable argument, but science had already discounted it. After studying it for a while, I began to doubt quantum superposition in favor of deterministics, while my greatest focus was on Quantum Entanglement. It seemed that Quantum Mechanics was too different (being incompatible with everything else) and had surprising consequences that appeared illogical. A breakthrough was in realizing the incorrect application of the Heisenberg Uncertainty Principle with the contact between the subatomic particles being directly responsible for the correlation. It appears that science had been won over by the power of probabilistic, statistical approximations in its abilities for predicting quantum behavior. However, I had already accepted theories already rejected by modern physics due to unique insight. Finally, I discovered the hidden variables of Space and Time within Einstein’s Energy Equivalence equation in order to change it into its most correct form. With the demise of conventional Quantum Mechanics and my new equation, I finally knew that I had enough evidence to present a complete Theory of Everything. I believe my success came from questioning everything and my ability to connect so many ideas together in order to unveil the truth. I hope that you have enjoyed my theory and I wish you all the best!

“What do you believe is the truth? Whatever you believe is the truth (in your eyes) and nothing else really matters. All I can do is challenge your beliefs; I cannot change them, only you can do that.” – Stephen Tuck

Email: stephentuck.toe@gmail.com

title: User:Stephen Tuck/Theory of Everything


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User talk:Mayank Abhishek

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User talk:EGM6321.F10.TEAM1.HW5

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User talk:Stephen Tuck

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title: User talk:Stephen Tuck