# Thread: Fundamental interactions as a property of space-time

1. ## Fundamental interactions as a property of space-time

Hello, my favorite forum members :-)

I have just posted new manuscript to the journal, so I would like to know your feedback ;-)
Before it will be reviewed and published, it is still ATM, so I post it here.

Please, find below the body of the article

Title: Fundamental interactions as a property of space-time

Abstract:
In the article it is shown, that tiny change in the definition of four-position drives to derivation of electromagnetic field tensor as natural property of the space-time. In presented picture, fundamental interactions are not something additional to the space-time - they become part of it and the derivation comes directly from the foundings of Special Relativity and Relativistic Quantum Mechanics.

1. Section. Introduction
Present days we describe field phenomena in many ways e.g. [1], [2], [3], [4] however we still did not repeat the success of A.Einstein. As it is known, in General Relativity, gravity is not an interaction but some property of the space-time geometry. In most field theories [5], field is still something additional to the space-time (instead of natural result of its presence) or authors modify metric tensor following idea from General Relativity.

The motivation standing behind this article was to find such description of the space-time, which in natural way deliver equations of electromagnetism, mass, and maybe other phenomenas. It looks like it has succeeded much easier, than anyone would expect.

In the article at first we will come back to the root of Special Relativity to state some simple hypothesis about the nature of space-time. Next we will discuss Lagrangian Mechanics and consider consequence of this hypothesis to relativistic mechanics. In effect we will obtain Lorentz force and electromagnetism resulting as natural consequence of discussed space-time definition.

Author believes, that this article may be important step on the path to unify interactions. It also opens new areas for scientific research.

We will use Einstein summation convention and metric signature . We denote as test body proper-time where ; we denote for rest mass and as reduced Planck constant [6].

2. Section. Hypothesis

As it is known in flat Minkowski space-time [7] we define four-position as with proper-time given as . Thanks to above, from historical point of view, we use Minkowski metric with four-velocity giving .

Let us notice, that without affecting metric tensor, we may assume that

(1)

where is some constant chosen such way, that

(2)

This way four-position product gives now

(3)

what gives

(4)

Above redefinition does not affect metric tensor, either four velocity value, however - it will affect action and Lagrangian Mechanics, what we will show below.

3. Section. Results

3.1 Chapter. Preparation

Let us recall classical Lagrangian Mechanics [8] where relation between action (Hamilton's principal function), generalized momentum and Lagrangian we define as follows

(5)

where is for generalized momentum and H for Hamiltonian. Here we will narrow to elementary particles and fundamental interactions only, and following [8] we will define action as we do it in Relativistic Quantum Mechanics

(6)

where we have introduced four-momentum

(7)

With redefined norm of four-position (3), the action in (6) is equal to

(8)

We should here discuss some important issue. In classical mechanics, action is the function of [tex](t, \vec{r})[\tex], thus Lagrangian is function of and Hamiltonian is function of . We therefore have to assume, that action defined this way depends only on .

We will then follow de Broglie hypothesis [9] and assume, that for elementary particles and fundamental interactions, four-momentum may be expressed as

(9)

where is some wave four-vector dependent only on four-position. Thanks to above assumption wave-particle dualism becomes important founding of this derivation.

Thanks to this assumption we get Lagrangian

(10)

Let us introduce four-force

(11)

and four-acceleration

(12)

where . Since

(13)

then we get from (10)

(14)

thus

(15)

Comparing (15) to (4) we get relation which will be important soon

(16)

We may also easy calculate

(17)

thus we may describe dynamics of the system by equation

(18)

where seems to play important role here, determining behavior of velocity and position. Let us therefore introduce four-vector (with the dimension of four-momentum), defined as

(19)

According to (17), it is orthogonal to four-velocity, giving . From (10), using Lagrangian Mechanics property we may calculate generalized momentum as

(20)

We have to stop at this moment to consider, how is dependent on .

T.B.C...

2. ## next part

....

3.2 Chapter. Four-vector

As we we may easy calculate, is present in the wedge product of and . To simplify further calculations, we will introduce related tensor based on four-velocity and four-acceleration as below

(21)

As we will see below, above tensor seems to be more important than we supposed and may serve us in much more sophisticated way.

At first step, to simplify notation, let us introduce dimesionless auxiliary vector related to , defined as

(22)

According to (4), (16) and (17) it gives following relations

(23)

Using [tex]\vec{z}[tex] we may express four-velocity as

(24)

or in more expanded form, thanks to vector calculus rules, according to (23) and (4) and other known vector relations

(25)

Therefore, to create four-velocity, we may easy utilize introduced tensor (21) . At first, let us create four-vector defined as

(26)

Using known relations between vectors, we may express four-velocity as

(27)

and next

(28)

As we see in above results, tensor indeed fully describes curvature of the motion and four-vector is some fundamental vector, giving complete base for mechanics description.

We are used to think, that is the derivative of velocity. As we get from above, vectors and are more fundamental. Indeed, four-velocity and four-acceleration are given by some function based on these four-vectors.

No matter how new this observation seems to be, we indeed accept this phenomena in electromagnetism, where time component of the four-force may be expressed by

(29)

where q is for elementary charge and is for electromagnetic field. Therefore, as we see in (29), is directly related to the electromagnetic field, which is a function of electromagnetic four-potential dependent on four-position only. Therefore four-velocity and four-acceleration are indeed some function of , not otherwise.

As we may easy check, four-vector gives following products

(30)

therefore

(31)

thus

(32)

Thanks to whole above reasoning we may conclude, that vectors and are indeed some functions of four-position.

3.3 Chapter. Field tensor

Thanks to above discovery, using (10) and (20) we may note Lagrange equations as

(33)

Decomposing we get

(34)

where

(35)

We may therefore introduce four-potential defined as

(36)

and define tensor as

(37)

to denote (34) as

(38)

We see strong analogy to electromagnetism, where plays the role similar to classical electromagnetic four-potential. However this time field tensor is indeed immanent property of the space-time definition and wave-particle dualism.

We may easy express by elementary charge [7] as

(39)

where q is for elementary charge, is fine-structure constant and is electric constant or permittivity of free space.

Depending on or , tensor for elementary particles (with elementary charge) would be proportional to the electromagnetic field tensor according to relation (39).

T.B.C...

3. ## last part

...

3.4 Chapter. Frenet-Serret frame

We may transform (41) to the form of

(40)

where we substitute

We see above, that is a measure of the path circled by vectors, subjected to the same angular velocity . Therefore - beside the field equations - we may propose pure geometrical description of the system dynamics, based on the Frenet-Serret formula [11].

According to this description, if we assume as normal vector, as tangent vector and as bi-normal vector, for curvature, for torsion and for the increment of the path, we may describe motion by following system of equations

(41)

To reproduce above for four-vectors, we need third four-vector, orthogonal to four-velocity and four-acceleration. We will introduce such four-vector with the dimension of velocity, denoted as and defined as

(42)

where is some constant with dimension of time , to give this four-vector dimension of velocity . We will explain the orygin of this constant soon. As we may easy calculate, gives following products

(43)

We have to normalize four-acceleration, to keep the same units for all vectors engaged in the Frenet-Serret frame, therefore we will introduce another constant of motion denoted as with dimension of time . Origin of this constant will be explained soon. We will also use imaginary numbers and propose imaginary torsion what will be explained farther.

Let us therefore propose

(44)

thus

(45)

As we see, plays the role of the normal vector here, is tangential and four-velocity plays the role of bi-normal vector. We should be able then to calculate using (41). Basing on Frenet-Serret formula we may conclude

(46)

thus

(47)

Taking proper-time derivative on both and and using known vector products we get

(48)

Now it is clear, why we had to use imaginary rotations. Thanks to such substitution, joining (47) and (48) we get

(49)

what agrees with the invariants' signs (both four-vectors have invariants with negative sign). We also now see, that constant is just the invariant of four-acceleration.

Calculating form (42) we get

(50)

what explains origin of the second constant. This constant is related to dynamic mass-momentum from angular momentum tensor and - indirectly - related to total angular momentum of the motion (including spin). Using (50) we may denote definition of (42) in shorter form as

(51)

where vector points in the direction orthogonal to . Author inentionally use arrow based notation in (51), because of unusual use of as a vector, to stress, that this is vector value.

As we see from above, motion of the body in the Frenet-Serret frame, may be described by two constants and and its proper-time .

Since acceleration four-vector plays the role of normal vector, we should also agree, that this four-vector is more fundamental than four-position or four-velocity and should be treated as the base for further space-time descriptions with more complex metric tensor.

4 Section. Discussion

As we have seen, modified space-time definition works perfectly fine and produce electromagnetism as natural property of introduced four-poition definition. It agrees with foundings of Relativistic Quantum Mechanics (e.g. de Broglie hypotesis, wave-particle dualism), gives some explanation for the nature of rest mass and extends our understanding of four-potentials and Lagrangian Mechanics.

In presented picture, field is not something additional - it is property of the space-time. E.g. we see, that electric field is (partly) equal to gradient of the distributed time dilation factor. We might even try to say, that in this picture space-time it is field, so, it also extends e.g. our understanding of the time flow phenomena.

Beside benefits, this article also brings some issues. If interactions are just properties of space-time, then what with the stong and electro-weak interactions? What would happen if we add some additional vector constant to the vector part of four-position and how it affects metric tensor?

Above questions seems to be good starting point for a further scientific explorations in the subject.

Bibliography

[1] Itzykson, Claude, and Jean-Bernard Zuber. Quantum field theory. Courier Corporation, 2006.

[2] Francesco, Philippe, Pierre Mathieu, and David Sénéchal. Conformal field theory. Springer Science \& Business Media, 2012.

[3] Douglas, Michael R., and Nikita A. Nekrasov. "Noncommutative field theory." Reviews of Modern Physics 73.4 (2001): 977.

[4] Aharony, Ofer, et al. "Large N field theories, string theory and gravity." Physics Reports 323.3 (2000): 183-386.

[5] Weinberg, Steven. "Effective field theory, past and future." International Journal of Modern Physics A 31.06 (2016): 1630007.

[6] Buczyna, Jason R., C. S. Unnikrishnan, and George T. Gillies. "Standard and derived Planck quantities: Selected analysis and observations." Gravitation and Cosmology 17.4 (2011): 339-343.

[7] Rindler, Wolfgang. "Introduction to special relativity. 2." (1991).

[8] Goldstein, Herbert, Charles Poole, and John Safko. "Classical mechanics." (2002): 782-783.

[9] Greiner, Walter. Quantum mechanics: an introduction. Springer Science and Business Media, 2011.

[10] Feynman, Richard Phillips. QED: The strange theory of light and matter. Princeton University Press, 2006.

[11] Wagner, Michael G., and Bahram Ravani. "Curves with rational Frenet-Serret motion." Computer Aided Geometric Design 15.1 (1997): 79-101.

4. That's all folks :-)

How do you like it?
A appreciate your questions and remarks if any.

I really need someone wise, who could ask me some questions about it and give some scientific criticism.
I worked over it too long, so my mind is not fresh enough to push this idea further.

ETA.
If you prefer PDF version, it is available on Research Gate - here
Last edited by pogono; 2018-Feb-07 at 10:29 AM. Reason: link added

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Originally Posted by pogono
That's all folks :-)

How do you like it?
IMO: Not a lot.
You start with flat Minkowski space-time = no interactions at all!
You redefine "without affecting metric tensor" = still no interactions.
You seem to mix classical "action and Lagrangian" with quantum mechanics (de Broglie hypothesis).
A post of symbol manipulation to get a "strong analogy to electromagnetism" in flat spacetime.
"Relativistic Quantum Mechanics" (quantum field theory) is enormously more than the de Broglie hypothesis or wave-particle dualism.
What looks like an irrelevant Frenet–Serret frame section.

And the big problem - no attempt to show that your ATM idea actually contains fundamental interactions.
If the idea contains electromagnetism then where is the derivation of Maxwell's equations? How about applying your idea to textbook examples, e.g. the electric field of a point charge?
Last edited by Reality Check; 2018-Feb-08 at 02:30 AM.

6. Hi Reality Check,
please find below my answers.

Originally Posted by Reality Check
You start with flat Minkowski space-time = no interactions at all!
You redefine "without affecting metric tensor" = still no interactions.
Exactly here ...., tada...., exactly here is the fundamental change of point of view.

Present days we think: naked space-time = no interaction. We have to add interactions artificially or modify metric tensor to obtain any interaction.
But indeed, all known elementary particle with mass (quarks, electrons and its antiparticles) interact electromagnetically.
So on the lowest level, nature, somehow, links mass with electromagnetism.

So my article states:
- Electromagnetism comes directly from space-time definition, and there is no need to add artificially any field.
- Every particle with mass interact electromagnetically, because mass is just the measure of constant angle between two field vectors, what becomes invariant of four-momentum

Originally Posted by Reality Check
A post of symbol manipulation to get a "strong analogy to electromagnetism" in flat spacetime.
(...)
And the big problem - no attempt to show that your ATM idea actually contains fundamental interactions.
If the idea contains electromagnetism then where is the derivation of Maxwell's equations? How about applying your idea to textbook examples, e.g. the electric field of a point charge?
I derive Lorentz force [eq. (38) & (39)] in my article. It is not enough?

Originally Posted by Reality Check
"Relativistic Quantum Mechanics" (quantum field theory) is enormously more than the de Broglie hypothesis or wave-particle dualism.
Yes. But the Broglie hypothesis is the founding, like Heisenberg principle, etc.
So I use on of the main funding of RQM to show, that my work agrees with it.

Originally Posted by Reality Check
You seem to mix classical "action and Lagrangian" with quantum mechanics (de Broglie hypothesis).
We do worse things in RQM :-)

Originally Posted by Reality Check
What looks like an irrelevant Frenet–Serret frame section.
I was thinking over some arguments for you, but after a day of thinking I have to state that here you are probably right. It would be to easy.
I will rewrite this section for tensor based description. So thank you.

7. After short recalculation I exchange chapter 3.4. into below (instead Frenet-Serret frame)

3.4 Chapter. Equations of motion

As we may easy check, four-vector gives following products

(40)

Let us also introduce four-vector defined as

(41)

As we may easy calculate it has following properties

(42)

thus

(43)

and after proper-time derivative

(44)

what reduces to

(45)

Therefore or . Since, as we may easy calculate

(46)

and

(47)

therefore there is no acceleration at all or - after easy transformation of above thanks to (4)

(48)

We know from previous section that acceleration exists, therefore this is the second equation of motion, beside (4). Thus

(49)

As we see fron (48), factor indeed works as the field distributed in space, and we may take gradient of it according to (34).
Last edited by pogono; 2018-Feb-10 at 10:20 AM.

8. Originally Posted by pogono

(48)

As we see fron (48), factor indeed works as the field distributed in space, and we may take gradient of it according to (34).
Maybe some of you remember my first thread "Time dilation as field" on ATM (it was part of BAUT this days) in 2011. As you see, it took me some time, but time dilation indeed seems to be a field ;-)

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Originally Posted by pogono
please find below my answers. ...
No answers in your post - just repeated unsupported assertions.

Let us say that someone manipulates symbols with no mention of any triangles, comes up with the equation "(38) x2 = y2 + z2" and declares this to be the Pythagorean theorem. No one will believe that declaration until they show that x, y and z are the sides of a right triangle. Anything they do based on that declaration is =a waste of everyone's time until they show that x, y and z are the sides of a right angle triangle.

That is what you have done and are doing.

In addition:
Equation 38 is not the "Lorentz law".
Even if you had produced Lorentz's law, it is Maxwell's is that are classical electromagnetism. Thus your conclusion is wrong.
Equation 39 is wrong. The reduced Planck constant is related to the electron charge e, not any charge at all q as in the classical continuous charge from 0 upwards). classical electromagnetism

But just in case:
IF01: Show that equation 38 is the same as the covariant form of the Lorentz force.
IF02: Apply equation 38 to a single particle with a given charge of 3.142 e and show that matches the classical Lorentz force result.

The irrelevant foundation of QM starts well before 1924 when de Broglie wrote his hypothesis. The history of QM starts in 1838 with the pivotal Planck's law in 1900.
RQM is not classical electromagnetism or QFT or QED
In physics, relativistic quantum mechanics (RQM) is any Poincaré covariant formulation of quantum mechanics (QM). This theory is applicable to massive particles propagating at all velocities up to those comparable to the speed of light c, and can accommodate massless particles.

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Originally Posted by pogono
After short recalculation I exchange chapter 3.4. into below (instead Frenet-Serret frame) ...
A waste of our time because the chapter is still based on earlier so far meaningless algebra.

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Originally Posted by pogono
...time dilation indeed seems to be a field ;-)
This is time dilation. This is a field in physics. They are not the same. Thus you are wrong.

12. I am crazy enough to jump where angels feart tread. The maths is too much for me so I ask for an explanation along these lines.
If a particle could hypothetically come to existence its field would expand spherically at c. This introduces a time element into a particle expansion that a distant observer would see not as an inverse square static Gaussian field but a growing field or gravity wave. This under pins general relativity with velocity taking the place of hypothetical coming into existence. is such a time changing field what you are getting at as a new explanation? It seems to be a complicate d way of expressing space time. I guess I missed the pont but. Hope you don't mind me asking.?

13. Originally Posted by Reality Check
Equation 39 is wrong. The reduced Planck constant is related to the electron charge e, not any charge at all q as in the classical continuous charge from 0 upwards). classical electromagnetism
I denoted q as elementary charge and consider interaction between elementary particles with elementary charges.
So, supported with this knowledge, please, compare (39) to this: https://en.wikipedia.org/wiki/Planck_charge

Originally Posted by Reality Check
No answers in your post - just repeated unsupported assertions.
It seems that writing "Equation 39 is wrong" you are the one who just wrote unsupported assertion.

Originally Posted by Reality Check
A waste of our time because the chapter is still based on earlier so far meaningless algebra.
If reading equations is a waste of time for you, it will be hard to convince you to any new knowledge :-(
In typical ATM thread, OP does not like to read equations and gives unsupported assertions. If I understand you well, we have the opposite situation here.

Originally Posted by Reality Check
Equation 38 is not the "Lorentz law".
Really? So, we read the link in wikipedia that you just mentioned and what we see: force =

Next we read (38) and we see: force =

I will help you. Maybe just ?

Originally Posted by Reality Check
Even if you had produced Lorentz's law, it is Maxwell's is that are classical electromagnetism. Thus your conclusion is wrong.
I suppose that my english language is not enough to understand the logic behind the first sentence.
Do I understand correctly, that you just wrote something like this "Even if you have produced electromagnetic tensor and Lorentz force, you must be wrong, because you are not Maxwell"?

Originally Posted by Reality Check
IF01: Show that equation 38 is the same as the covariant form of the Lorentz force.
IF02: Apply equation 38 to a single particle with a given charge of 3.142 e and show that matches the classical Lorentz force result.
I did. However, it will be hard to convince you, since you wrote, that reading equations is "waste of time" :-(

Originally Posted by Reality Check
This is time dilation. This is a field in physics. They are not the same. Thus you are wrong.
Physics moves forward, because from time to time someone destroys such "common knowledge".
I suppose, that you response to A. Einstein Special Relativity Theory would be:

Listen, Albert. This is time: https://en.wikipedia.org/wiki/Time, and this is dimension https://en.wikipedia.org/wiki/Dimension. They are not the same, so you are wrong with your silly space-time idea.

14. Originally Posted by profloater
I am crazy enough to jump where angels feart tread. The maths is too much for me so I ask for an explanation along these lines.
If a particle could hypothetically come to existence its field would expand spherically at c. This introduces a time element into a particle expansion that a distant observer would see not as an inverse square static Gaussian field but a growing field or gravity wave. This under pins general relativity with velocity taking the place of hypothetical coming into existence. is such a time changing field what you are getting at as a new explanation? It seems to be a complicate d way of expressing space time. I guess I missed the pont but. Hope you don't mind me asking.?
Hi, profloater. Nice to meet you. I am glad, you ask your question.

It is really great to talk sometime to someone else than Reality Check :-)

Physical interpretation of "time dilation field" seems to be as follows.

If electric field is indeed related to time dilation factor (as I show in the article), thus light wave would be just disturbance in the space-time structure propagating in the space-time. So, space-time acts as mythical "ether" - the medium for light wave.

So, local increase of time dilation factor must change the path and velocity of the light (time dilation factor acts as refraction index in the lenses).
But local increase of time dilation factor is just local increase of the energy, and changing light velocity and path is a try to "accelerate the light".

So local increase of energy would just make space-time curved (where in such curved space-time light locally has still the velocity of light) - what indeed agrees with General Relativity Theory.

To summarize the picture coming from my work:
Electromagnetism it is not some field in space-time. Space-time it is electromagnetism and gravity is the effect of unevenly distributed electromagnetic field.
Last edited by pogono; 2018-Feb-12 at 02:19 AM.

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Originally Posted by pogono
I denoted q as elementary charge....
Your terminology is still wrong. The symbol q is used for any value of charge in classical electromagnetism which does not contain any "elementary charge". The charge that h bar is related to is the charge of an electron and only the charge of an electron.

Please read what you link to. Planck charge, qp, "is one of the base units in the system of natural units called Planck units", not a definition of h bar.

I never stated that reading equations is useless. It is the equations that you wrote that are useless until you show that they are useful. Writing algebra that results in so far meaningless equations is the problem thus:
IF01: Show that equation 38 is the same as the covariant form of the Lorentz force.
IF02: Apply equation 38 to a single particle with a given charge of 3.142 e and show that matches the classical Lorentz force result.

Sorry but it is a very bad error that
Originally Posted by pogono
(38)
has q. Your equation has an tensor U that you define as a four velocity
Originally Posted by pogono
Using known relations between vectors, we may express four-velocity as

(27)
The Lorentz force has a scalar value q. A velocity tensor is not a scalar charge - you should know the difference! A tensor is not a scalar. A velocity has different units than charge. Equation 38 is not the "Lorentz law".

Irrelevant "Listen Albert" stuff does not make your ATM idea correct. It was Hermann Minkowski who showed that SR could treat space and time as a unified spacetime.
Minkowski is perhaps best known for his work in relativity, in which he showed in 1907 that his former student Albert Einstein's special theory of relativity (1905) could be understood geometrically as a theory of four-dimensional space–time, since known as the "Minkowski spacetime".
ETA: Now we have
IF03: Show that time dilation is a field in physics.
That is not repeating an unsupported assertion. It is taking the definition of a field in physics and showing that time dilation has its properties. This will be a bit hard. This is time dilation
According to the theory of relativity, time dilation is a difference in the elapsed time measured by two observers, either due to a velocity difference relative to each other, or by being differently situated relative to a gravitational field.
Time dilation is a single value that 2 observers can measure.
This is a field in physics
In physics, a field is a physical quantity, represented by a number or tensor, that has a value for each point in space and time.[1][2][3]
As you can read, a field in physics has a value (or tensor) defined for each point in space and time. No velocity mentioned. No gravitational field mentioned.
Last edited by Reality Check; 2018-Feb-12 at 03:03 AM.

16. Originally Posted by Reality Check
Your terminology is still wrong. The symbol q is used for any value of charge in classical electromagnetism. The charge that h bar is related to is the charge of an electron and only the charge of an electron.
We have a freedom in math and physics, to name variables and constants anyhow we want. So I benefit from this freedom, and name elementary charge as "q". So my "q" is related to reduced Planck constant exactly with the relation given in (39) and here https://en.wikipedia.org/wiki/Planck_charge

EQ1:

If you somehow cannot stand, that I use "q" as the symbol for elementary charge, please, be so kind and rewrite above equation using "e" instead of "q" and then compare (39) to https://en.wikipedia.org/wiki/Planck_charge. I hope it helps.

Originally Posted by Reality Check
Please read what you link to. Planck charge, qp, "is one of the base units in the system of natural units called Planck units", not a definition of h bar.
:-)
What can I say. Have you read first equation in wikipedia from the link I provided?

I know it requests some effort, but if you raise to square first equation from Planck charge and take very close look, you will see, that what is exactly the same what says EQ1 above and (39).

But for any case, let me explain.

Step 1.

You raise to square first equation from the article Planck charge to get:

Step 2.

You divide both sides by

Step 3.

You concentrate your eyes on the right side of the equation

P.S. Once again, if you do not like letter "q" to name elementary charge (you are free man, you may hate any letter), so exchange it with "e".
It may help once again.

Originally Posted by Reality Check
I never stated that reading equations is useless. It is the equations that you wrote that are useless until you show that they are useful. Writing algebra that results in so far meaningless equations is the problem
Generally speaking, reading equations I write and links I give, will help you to understand what I say.
If you assume that something is useless, then you will never understand it.

I did. But without reading equations you will not see it.

Originally Posted by Reality Check
IF03: Show that time dilation is a field in physics.
That is not repeating an unsupported assertion. It is taking the definition of a field in physics and showing that time dilation has its properties. This will be a bit hard. This is time dilation

Time dilation is a single value that 2 observers can measure.
This is a field in physics

As you can read, a field in physics has a value (or tensor) defined for each point in space and time. No velocity mentioned. No gravitational field mentioned.
Here we go:
Originally Posted by pogono

(48)

As we see fron (48), time dilation factor indeed works as the field distributed in space, and we may take gradient of it according to (34).
As you see, has a value defined for each point in space and time. No velocity mentioned. No gravitational field mentioned.
Last edited by pogono; 2018-Feb-12 at 04:18 PM.

17. Originally Posted by Reality Check
Sorry but it is a very bad error.

Your equation has an tensor U that you define as a four velocity

The Lorentz force has a scalar value q. A velocity tensor is not a scalar charge - you should know the difference! A tensor is not a scalar. A velocity has different units than charge. Equation 38 is not the "Lorentz law".
So, let us check the dimensions to find out that there is no error and you missed the point once again, because you did not read the equations on confused some symbols I use.

Step 1.

We check dimensions of formula (38)

is the force

is four-velocity

comes from gradients of , thus has the dimension
because

has the dimension of four-momentum
according to def. (19)

Step 2.

We check dimensions in Lorentz force for elementary charge q

where

is the force

is four-velocity

is elementary charge

is electromagnetic tensor

I use letter E, to not to confuse electromagnetic tensor with the force denoted with F. But if you do not like it, you may use some other, e.g. your favorite letter.
If you do not like "q" to denote elementary charge, you may substitute it with "e", as before.

So,

must have dimension

Step 3.

We note Lorentz force as

We see, that has the same dimension as from (38) what is

Step 4. - conclusion

There is no in (38), because has already the dimension of

If this explanation is too complicated for you, let me know. I will try to explain it more simply.
Last edited by pogono; 2018-Feb-12 at 04:23 PM.

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Originally Posted by pogono
We have a freedom in math and physics, to name variables and constants anyhow we want. ...
You are free to use q for the electron charge denoted as e in textbooks. You are not free to state ignorance out physics.
IF04: Cite your sources stating that Planck charge is a definition of Planck's constant in terms of the electron charge e (or q).
Hint: There is one! But it is nothttps://en.wikipedia.org/wiki/Planck_charge
In physics, the Planck charge, denoted by q P {\displaystyle q_{\text{P}}} q_{{\text{P}}}, is one of the base units in the system of natural units called Planck units. It is a quantity of electric charge defined in terms of fundamental physical constants.
As you can read this is a system of units like the SI units. It is a definition of charge in the system of natural units, not Planck's constant.

Unsupported assertions still do not answer
I never stated that reading equations is useless. It is the equations that you wrote that are useless until you show that they are useful. Writing algebra that results in so far meaningless equations is the problem thus:
IF01: Show that equation 38 is the same as the covariant form of the Lorentz force.
IF02: Apply equation 38 to a single particle with a given charge of 3.142 e and show that matches the classical Lorentz force result.

Again: I have no problem with you using q instead of e, so long as you know that means that you are debunking your ATM idea !
IF05: Is the charge q in classical electromagnetism, e.g. the Lorentz law, any charge at all?
Anyone who knows about electromagnetism will answer yes. But then you are not getting electromagnetism and your ATM idea is debunked.

Read what I wrote: That is not repeating an unsupported assertion. I will make the question easier for you:
IF03: Show that time dilation is a field in physics, e.g. take a point in spacetime and give the value of time dilation for that point.
Last edited by Reality Check; 2018-Feb-12 at 09:22 PM.

19. Originally Posted by Reality Check
You are free to use q for the electron charge denoted as e in textbooks. You are not free to state ignorance out physics.
IF04: Cite your sources stating that Planck charge is a definition of Planck's constant in terms of the electron charge e (or q).
Hint: There is one! But it is nothttps://en.wikipedia.org/wiki/Planck_charge
I see you did not follow all the steps I recommended for you.
So let us do it together, step by step, far easier, with confirmation after each step.

We take first equation from wikipedia link https://en.wikipedia.org/wiki/Planck_charge

Here it is to help you to focus on it

where:
e - is elementary charge
- is Planck charge
- is reduced Planck constant
c - is speed of light
- is fine structure constant
- is permittivity of free space

This equation raised to square is equal to:

Do you agree?

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Originally Posted by pogono
...
We read my post and see my actual mistake: I did not notice the U at the and of the covariant form of the Lorentz force

We check the contents of formula (38) and see no charge at all.
We check the contents of covariant form of the Lorentz force and see a charge q that is any charge at all. This is not your charge q which is the charge of an electron.
We conclude that equation 38 is not the Lorentz force.

We also read covariant form of the Lorentz force and see that the left hand side is not a force tensor. The left hand side is the four-momentum differentiated by proper time. is just a contraction of 2 tensors that you selected to write as F (why nor U? or A? or X?). That does not make it a force tensor or related to the Lorentz force.
IF06: Show that your tensor is the same as the LHS of the covariant form of the Lorentz force.
Once again: Do not just repeat your assertion that it is.

Which leads to:
IF07: Show that your is the contravariant electromagnetic tensor in the covariant form of the Lorentz force.

This is to emphasize that just doing algebraic manipulation to get an equation looking mostly like the covariant form of the Lorentz force is not enough (still no q!). There has to be the same q as in the Lorentz force. There has to be electric field components. There have to be magnetic field components.
Originally Posted by Reality Check
Let us say that someone manipulates symbols with no mention of any triangles, comes up with the equation "(38) x2 = y2 + z2" and declares this to be the Pythagorean theorem. No one will believe that declaration until they show that x, y and z are the sides of a right triangle. Anything they do based on that declaration is =a waste of everyone's time until they show that x, y and z are the sides of a right angle triangle.

That is what you have done and are doing.

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Originally Posted by pogono
...Do you agree?
We can square the value of the natural unit of Planck charge. We can also square the SI unit of a metre. Etc. Etc. That has nothing to do with your fundamental error of asserting that an equation 38 is the covariant form of the Lorentz force when anyone who reads that article can see that you are missing q, the classical (not electron) charge.

IF04: Cite your sources stating that Planck charge is a definition of Planck's constant in terms of the electron charge e (or q).
The answer to people who can read Wikipedia is that there are no sources. The Planck charge is a unit in a natural units of measurement called Planck units. Planck units set several physical constants to 1, including the reduced Planck constant, ħ!
Last edited by Reality Check; 2018-Feb-12 at 10:21 PM.

22. Originally Posted by Reality Check
IF07: Show that your is the contravariant electromagnetic tensor in the covariant form of the Lorentz force.
I suppose you ask me to show, that in my article tensor is equal to where

- is electromagnetic field tensor
q - is elementary charge

Your original ask IF07 does not make sense, because even dimensions does not agree.

Yup, I can do it, but first we have to pass easier issue, being the first step to prove anything.
So, let us try to be focused on one thing in one time and please answer to my question in post https://forum.cosmoquest.org/showthr...61#post2439561

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Originally Posted by pogono
I suppose you ask me to show, , ...
The question is clear and now clearer.
IF07: Show that your is the contravariant electromagnetic tensor called ) in the covariant form of the Lorentz force within a factor of q..
The components of the contravariant electromagnetic tensor are stated in the Wikipedia article that you know about. Show that each component of your "" matches the same component in .

I will give an even simpler and clearer alternative.
IF07a: Show that F00 of the contravariant electromagnetic tensor which is 0 is equal to your "F00" within a factor of q.
IF07b: Show that F01 of the contravariant electromagnetic tensor which is -Ex/c is equal to your "F01" within a factor of q.
etc.

I do not need to answer any of your questions. This is the ATM section where it is your task to defend your idea by answering questions.
I was kind enough to answer your irrelevant question: We can square the value of the natural unit of Planck charge. We can also square the SI unit of a metre. Etc. Etc. That has nothing to do with your fundamental error of asserting that an equation 38 ...
Last edited by Reality Check; 2018-Feb-13 at 12:45 AM.

24. Originally Posted by Reality Check
The question is clear and now clearer.
IF07: Show that your is the contravariant electromagnetic tensor called ) in the covariant form of the Lorentz force within a factor of q.
is not equal to electromagnetic tensor
- because even dimensions does not match, what may be spoted by a child
- because

Originally Posted by Reality Check
I do not need to answer any of your questions. This is the ATM section where it is your task to defend your idea by answering questions.
Defending my idea and answering your questions are two different things.

You ask me to compare tensors, that even dimensions does not match.
You seem to have problems with such basic stuff like the fact, that (39) comes out from first eq. in https://en.wikipedia.org/wiki/Planck_charge
You forgot about four-velocity in the Lorentz force formula and accuse me of dramatic mistake
When I start to explain something to you, confirming line by line if we agree, you refuse.

I suppose you are not familiar with basic physics stuff, but believe me, I would really like to explain my article to you.
Maybe you have some friend, who is able to compare physical equations who lives near you and you like him enough to listen to him and read his equations?

I would explain my article to him, then you would meet him every weekend for a next year and he would explain my article to you.
How do you like it? For me it sounds great and maybe could work.

So, do you have a friend Reality Check?
Last edited by pogono; 2018-Feb-13 at 10:38 AM.

25. Originally Posted by pogono
So, do you have a friend Reality Check?
That will earn an infraction. Any more rude comments and this thread is done.

26. Originally Posted by Swift
That will earn an infraction. Any more rude comments and this thread is done.
Hi Swift. I am sorry if it sounds rude.
I would really like to explain this article to Reality Check, however I feel a bit desperate since he is stuck on basic math :-(

I know there are no stupid questions, so I want to answer any question.
But I find it incredibly hard to explain something complex to someone who do not follow equations (to be honest, now I understand how hard is typical discussion with OP on ATM).

What should I do?

27. Originally Posted by pogono
Hi Swift. I am sorry if it sounds rude.
I would really like to explain this article to Reality Check, however I feel a bit desperate since he is stuck on basic math :-(

I know there are no stupid questions, so I want to answer any question.
But I find it incredibly hard to explain something complex to someone who do not follow equations (to be honest, now I understand how hard is typical discussion with OP on ATM).

What should I do?
For starters, you should not be responding back to my moderation instructions in-thread, unless I ask you to (which I did not). If you have such questions, you should Report my post, and express your questions for the moderators there.

From Rule 17

Do not respond to moderation in-thread, unless asked a question by a moderator. If you wish clarification, want to question the moderation, or need to explain your actions, report the post and/or PM a moderator. If you wish to publicly discuss any act of moderation, start a thread in the Feedback forum. You may report the first post of that thread to ensure it is brought to the attention of the moderators.
I also have a very strong suspicion that the problem is not basic math, which I suspect Reality Check is well capable of doing. I suspect the problem is communications and a lack of understanding. If people are not understanding your explanation, maybe you need to do a better job explaining.

And no, do not respond in-thread to this post either.

28. Originally Posted by pogono
Hi, profloater. Nice to meet you. I am glad, you ask your question.

It is really great to talk sometime to someone else than Reality Check :-)

Physical interpretation of "time dilation field" seems to be as follows.

If electric field is indeed related to time dilation factor (as I show in the article), thus light wave would be just disturbance in the space-time structure propagating in the space-time. So, space-time acts as mythical "ether" - the medium for light wave.

So, local increase of time dilation factor must change the path and velocity of the light (time dilation factor acts as refraction index in the lenses).
But local increase of time dilation factor is just local increase of the energy, and changing light velocity and path is a try to "accelerate the light".

So local increase of energy would just make space-time curved (where in such curved space-time light locally has still the velocity of light) - what indeed agrees with General Relativity Theory.

To summarize the picture coming from my work:
Electromagnetism it is not some field in space-time. Space-time it is electromagnetism and gravity is the effect of unevenly distributed electromagnetic field.
Thank you for putting it so simply.
Would we not then expect gravity waves from high energy em events like lightning? Would your proposal make predictions of such waves? There are now exquisite little gravity meters , or would the effect be too small to measure?

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Originally Posted by pogono
is not equal to electromagnetic tensor ...
You need to read my question again which is about the contravariant electromagnetic tensor in the Lorentz force.
The contravariant electromagnetic tensor is not your "E". The contravariant electromagnetic tensor is . The reason that the contravariant electromagnetic tensor is not denoted by E is that E is associated wit the electric field and the contravariant electromagnetic tensor has both the electric and magnetic fields in it.

The units (your "dimensions"?) of the contravariant electromagnetic tensor are a mixture of the units of its components which are those of the electric field, e.g. newtons per coulomb, and the units of the magnetic field, e.g. (newton·second)/(coulomb·metre).

IF01: Show that equation 38 is the same as the covariant form of the Lorentz force.
IF02: Apply equation 38 to a single particle with a given charge of 3.142 e and show that matches the classical Lorentz force result.
IF03: Show that time dilation is a field in physics, e.g. take a point in spacetime and give the value of time dilation for that point.

The Planck charge unit of measurement is a definition assertion pops up again so:
IF04: Cite your sources stating that Planck charge is a definition of Planck's constant in terms of the electron charge e (or q).

IF05: Is the charge q in classical electromagnetism, e.g. the Lorentz law, any charge at all?

IF06: Show that your tensor is the same as the LHS of the covariant form of the Lorentz force (four-momentum differentiated by proper time).

IF07a: Show that F00 of the contravariant electromagnetic tensor which is 0 is equal to your "F00" within a factor of q.
IF07b: Show that F01 of the contravariant electromagnetic tensor which is -Ex/c is equal to your "F01" within a factor of q.
(14 more components to match)
Last edited by Reality Check; 2018-Feb-13 at 09:29 PM.

30. Dear mods.

Writing answer for Reality Check, I have just found some important issue in my work that needs reconsideration. They are two tensor equations that contradict themselves. I will not be able to give any answer before I will not find the explanation.

I kindly ask to suspend this thread until I find the solution.

Thank you all for all your questions.
Thank you Reality Check, since your questions forced me to build gauge transformation for my field what showed my some weakness in my article.

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