Paper: A causal mechanism for gravity

[joigus]

9 minutes ago, Markus Hanke said:

It is not possible to capture all of gravity’s degrees of freedom with a scalar field theory (or even a vector field); you do require at the very least a rank-2 tensor field to do so.

Thank you, Markus. Although you've shot too far ahead for him. I can't +1-you because I've run out of points.

[studiot]

14 hours ago, rjbeery said:

graded time dilation field

What exactly is a 'graded time dilation field' ?

Have you changed your thoughts since this?

https://www.physicsforums.com/threads/gr-as-a-graded-time-dilation-field-in-euclidean-space.742809/

1 hour ago, joigus said:

Thank you, Markus. Although you've shot too far ahead for him. I can't +1-you because I've run out of points.

I'll do it for you.

Marcus has just told the OP what he was told 7 years ago.

[joigus]

2 hours ago, studiot said:

What exactly is a 'graded time dilation field' ?

Have you changed your thoughts since this?

https://www.physicsforums.com/threads/gr-as-a-graded-time-dilation-field-in-euclidean-space.742809/

I'll do it for you.

Marcus has just told the OP what he was told 7 years ago.

Blimey! 7 years! No wonder he's experiencing time dilation.

Thanks a lot, Studiot.

[SergUpstart]

On 5/15/2020 at 2:10 AM, joigus said:

Gravitational fields do not slow down photons, they just-red shift them and make them bend their trajectories. Think again.

The dimension of the gravitational potential is the square of the speed, or m^2/s^2. What is this speed? It is logical to say that the gravitational potential at any point in space is the square of the speed of light at that point.

[joigus]

4 minutes ago, SergUpstart said:

The dimension of the gravitational potential is the square of the speed, or m^2/s^2. What is this speed? It is logical to say that the gravitational potential at any point in space is the square of the speed of light at that point.

So you do dimensional analysis... I'm impressed!

[studiot]

16 minutes ago, SergUpstart said:

The dimension of the gravitational potential is the square of the speed, or m^2/s^2. What is this speed? It is logical to say that the gravitational potential at any point in space is the square of the speed of light at that point.

Really?

What about this?

Quote

Gravitational potential is the potential energy per kilogram at a point in a field. So the units are Jkg^-1, joules per kilogram. r = the distance between the centre of the mass causing the field and the point you are considering.

 

Gravitational Potential | S-cool, the revision website

 

Edited May 16, 2020 by studiot

[Strange]

48 minutes ago, SergUpstart said:

The dimension of the gravitational potential is the square of the speed, or m^2/s^2. What is this speed? It is logical to say that the gravitational potential at any point in space is the square of the speed of light at that point.

I wonder if that relates to Gullstrand-Painlevé coordinates

34 minutes ago, studiot said:

Really?

What about this?

This is another of your "cryptic question, when it might be better to say what you mean" posts, isn't it.

[SergUpstart]

6 hours ago, studiot said:

Gravitational potential is the potential energy per kilogram at a point in a field. So the units are Jkg^-1, joules per kilogram

Yes. J/kg = ( kg * m^2 / s^2 ) / kg = m^2/s^2

[Markus Hanke]

7 hours ago, SergUpstart said:

The dimension of the gravitational potential is the square of the speed, or m^2/s^2. What is this speed? It is logical to say that the gravitational potential at any point in space is the square of the speed of light at that point.

The concept of “gravitational potential” can only be meaningfully defined in some spacetimes with very specific symmetries; it, too, does not generalise. 

[studiot]

3 hours ago, SergUpstart said:

Yes. J/kg = ( kg * m^2 / s^2 ) / kg = m^2/s^2

You're right. Well said. +1

[rjbeery]

On 5/15/2020 at 6:44 PM, swansont said:

Add me to the list. Clock rates are relative to your position in the well. 

Clock A and clock B are in relative motion. A claims that B is clocking slowly, while B claims that A is clocking slowly. Observer C might claim that A or B are clocking more slowly, depending on his frame. All results are relative here.

Now, clock A is beneath clock B in a gravity well. A claims that B is clocking quickly, while B claims that A is clocking slowly. Observer C agrees with A and B that A is clocking more slowly than B, regardless of his frame of reference. The time dilation differential between A and B here is absolute. I'm talking about the specific A-to-B comparison at their established locations. I don't want this discussion to take semantic detours so I'll gladly use something other than "absolute", but it must be a synonym for "absolute" because "relative" does not apply.

On 5/16/2020 at 3:38 AM, joigus said:

'Absorption and instantaneous re-emission' was a colloquial way of saying 'radiation pressure' of the photons on the cavity where you're confining them to make the clock.

That literally leads to a logical contradiction, which I mentioned earlier. The so-called 'radiation pressure' would have to vary by the distance the photon traveled in order for the illusion to be maintained. The re-emission time would have to be delayed by a fraction-of-a-second up to many years, depending on the future path of the emitted photon. A remote variance of c does not suffer that problem.

On 5/16/2020 at 3:44 AM, Markus Hanke said:

It is not possible to capture all of gravity’s degrees of freedom with a scalar field theory (or even a vector field); you do require at the very least a rank-2 tensor field to do so. 

I understand this but...I'm not sure this is a scalar field theory, is it? Just as light isn't refracted within a homogeneous medium, gravitational attraction would not manifest for masses in a homogeneous time dilation field. It's the gradient (i.e. the derivative) that determines the gravitational attraction, and a single point doesn't hold enough information.

I appreciate that the math is terribly complex, but that doesn't make it immutable. Does a unique solution to the Einstein field equations produce a unique time-dilation "field" (in 4 dimensions)?

Anyway, I'm stuck using the tools in my toolbox, and I'm currently I'm looking at how time dilation might affect Mercury's precession. 

[Strange]

10 minutes ago, rjbeery said:

Now, clock A is beneath clock B in a gravity well. A claims that B is clocking quickly, while B claims that A is clocking slowly. Observer C agrees with A and B that A is clocking more slowly than B, regardless of his frame of reference. The time dilation differential between A and B here is absolute. I'm talking about the specific A-to-B comparison at their established locations. I don't want this discussion to take semantic detours so I'll gladly use something other than "absolute", but it must be a synonym for "absolute" because "relative" does not apply.

The difference is relative. It is not symmetrical as in the case of relative velocity. And it is definitely not absolute.

10 minutes ago, rjbeery said:

Anyway, I'm stuck using the tools in my toolbox

When Einstein realised that the tools in his toolbox were inadequate he went and studied differential geometry and tensors. You need better tools.You can't cut fretwork with a mallet.

Apparently people have been explaining this to you for years, with mathematical justification, but you just won't accept it.

[joigus]

58 minutes ago, rjbeery said:

The so-called 'radiation pressure' would have to vary by the distance the photon traveled

And it does. Welcome to our world (the real one.) Radiation pressure is proportional to the number of photons per unit time that hit the mirror and the average energy of the photons, which is,

\[\hbar\omega\]

which is affected by frame-dependence. Inverse time transforms exactly like frequency. In GR is a bit more complicated, but it can be locally understood in terms of inertial frames. So it's not an invariant (or your cryptic "absolute" word.) Radiation pressure is a frame-dependent object as well.

I rest my case.

 

58 minutes ago, rjbeery said:

I appreciate that the math is terribly complex, but that doesn't make it immutable. Does a unique solution to the Einstein field equations produce a unique time-dilation "field" (in 4 dimensions)?

Anyway, I'm stuck using the tools in my toolbox, and I'm currently I'm looking at how time dilation might affect Mercury's precession. 

This is about the first time that you've asked a question. I think you can learn some relativity in a reasonable time (compared to Eddington's years) today thanks to the fact that you've got lots of material, in the form of online courses. Many people here can help you. There are wonderful free e-books out there. You're not dumb, you're just sticking to your guns to the point of nonsense. You can teach yourself relativity by reading good books and following excellent courses, but you've wandered alone for too long. Neither Einstein nor Eddington were lone wanderers.

Every (static) exact solution in GR carries with it what you call an acceleration field. What the meaning of it is is far less clear to me. What's sure is that changing coordinates to locally flat (inertial) takes you to what the free-falling observer sees. But the starting point from the exact solution is far less clear in my opinion. I'm looking forward to what the experts in this community have to say.

Mercury's precession is already a solved problem to 43'' of arc per century. Bettering that is a pretty tall order.

I would start with vector calculus and a relatively simple model of field theory, like Maxwell's equations. When Einstein postulated his equations, he took Maxwell's as a model.

Edited May 17, 2020 by joigus
minor stylistic correction + addition

[swansont]

47 minutes ago, rjbeery said:

Clock A and clock B are in relative motion. A claims that B is clocking slowly, while B claims that A is clocking slowly. Observer C might claim that A or B are clocking more slowly, depending on his frame. All results are relative here.

Yes, that’s what relative means,

47 minutes ago, rjbeery said:

Now, clock A is beneath clock B in a gravity well. A claims that B is clocking quickly, while B claims that A is clocking slowly. Observer C agrees with A and B that A is clocking more slowly than B, regardless of his frame of reference. The time dilation differential between A and B here is absolute. I'm talking about the specific A-to-B comparison at their established locations. I don't want this discussion to take semantic detours so I'll gladly use something other than "absolute", but it must be a synonym for "absolute" because "relative" does not apply.

That specific comparison is not what is meant by absolute. For example, observer C will not get the same answer. When different observers get different results, the results are relative.

So yes, you need to pick a new term.

 

 

[joigus]

32 minutes ago, joigus said:

Every exact solution in GR carries with it what you call an acceleration field.

This is only valid for static solutions!

 

[swansont]

On 5/15/2020 at 5:08 PM, joigus said:

. The bouncing photon clock that you talked about involves photons interacting with matter, which no longer is a photon travelling through the gravitational field. Such system, with two parallel mirrors and a photon bouncing back and forth, doesn't work like you claim it does. If you ever see a radiation pressure fan or radiometer, you will understand what I mean just looking at it. You won't have to think or listen to anybody, or read what they say, which for you is a definite advantage:

photons push against a mirror, you see? That's why your idea didn't work. But I'm starting to lose track of what you're saying. You've talked so much nonsense today I can't keep track.

A radiometer such as the one that was depicted does not work by radiation pressure. It rotates in the opposite direction.

I don’t see that there is a connection here with a light clock, which is an idealized device and shows time dilation’s relationship with length contraction (owing to the invariance of c), rather than any real processes. 

[rjbeery]

9 minutes ago, swansont said:

A radiometer such as the one that was depicted does not work by radiation pressure. It rotates in the opposite direction.

I don’t see that there is a connection here with a light clock, which is an idealized device and shows time dilation’s relationship with length contraction (owing to the invariance of c), rather than any real processes. 

I have personally never heard of gravitational time dilation being explained via "width contraction" to maintain the global invariance of c, but I guess that would work. Varying absorption/emission times does not work.

As an aside, I saw an interesting video about radiometers which claimed that the rotation comes from the edge of the fans. The face color of the fans does not matter, which makes sense if you think about it -- the energy hitting each side of the fan is the same, and the energy being emitted from the black side is the same as the energy being reflected from the white side.

[joigus]

27 minutes ago, swansont said:

A radiometer such as the one that was depicted does not work by radiation pressure. It rotates in the opposite direction.

I don’t see that there is a connection here with a light clock, which is an idealized device and shows time dilation’s relationship with length contraction (owing to the invariance of c), rather than any real processes. 

Right you are. It's absorbing photons. I hadn't noticed. Thank you. But as far as I've been able to read the photon clock made in Caltech does use radiation pressure.

The point I was trying to make is that if you build a periodic system (clock) by having photons bounce back and forth, such photons aren't free-falling anymore; they are interacting by means of non-gravitational forces. What the OP was arguing, at the point that the question surfaced, was that free-falling photons must slow down. The reason being (as I understood the OP) that bouncing photons in a photon clock must slow down too to account for time dilation and length contraction. My argument, IOW: any such clock is not just made of photons bouncing in mid air, so to speak. It involves matter and interactions.

Edited May 17, 2020 by joigus
minor addition

[studiot]

I would just like to point out here that Einstein did not refer to photon's or quantum theory when he introduced relativity and light clocks.
Indeed he carefully avoided the mechanism of light until he had included it in his maths where he always discussed a light pulse.
The light pulse being the instantaneous 'front' of whatever constitutes a travelling light ray.
'Das lichtquant' was another paper, directed at and confined to other effects.

Quote

https://en.wikipedia.org/wiki/Photon

The word quanta (singular quantum, Latin for how much) was used before 1900 to mean particles or amounts of different quantities, including electricity. In 1900, the German physicist Max Planck was studying black-body radiation, and he suggested that the experimental observations, specifically at shorter wavelengths, would be explained if the energy stored within a molecule was a "discrete quantity composed of an integral number of finite equal parts", which he called "energy elements".^[9] In 1905, Albert Einstein published a paper in which he proposed that many light-related phenomena—including black-body radiation and the photoelectric effect—would be better explained by modelling electromagnetic waves as consisting of spatially localized, discrete wave-packets.^[10] He called such a wave-packet the light quantum (German: das Lichtquant).

The name photon derives from the Greek word for light, φῶς (transliterated phôs). Arthur Compton used photon in 1928, referring to Gilbert N. Lewis, who coined the term in a letter to Nature on December 18, 1926.^[6][11] The same name was used earlier but was never widely adopted before Lewis: in 1916 by the American physicist and psychologist Leonard T. Troland, in 1921 by the Irish physicist John Joly, in 1924 by the French physiologist René Wurmser (1890–1993), and in 1926 by the French physicist Frithiof Wolfers (1891–1971).^[8] The name was suggested initially as a unit related to the illumination of the eye and the resulting sensation of light and was used later in a physiological context. Although Wolfers's and Lewis's theories were contradicted by many experiments and never accepted, the new name was adopted very soon by most physicists after Compton used it.^[8][c]

 

[joigus]

1 hour ago, studiot said:

I would just like to point out here that Einstein did not refer to photon's or quantum theory when he introduced relativity and light clocks.

That's very interesting. Thank you. The concept of photons was Einstein's pride and joy, but it took decades for people to buy into it. It's not an easy concept and it remains so to this day. At the time when he published GR's founding papers, the concept hadn't still made it through the barrier of incredulity.

Another thing is the concept of "invariance under general coordinate transformations," which to this day finds physicists discussing as to what it means exactly. In my opinion, it was a simplifying assumption that Einstein took, because he was in direct competition with David Hilbert to be the one to get first at the final form of the field equations.

AAMOF, Einstein made a mistake on the first paper, including a condition that the determinant of minus the metric be 1, which is not an invariant constraint. Hilbert immediately noticed, and so told him. Einstein corrected it, and went on to learn about the Ricci tensor, which gave him the final form of the field equations. So did Hilbert too. Science historians admit today that Einstein got there first.

Edited May 18, 2020 by joigus
changed zero by one. Mistake

[joigus]

59 minutes ago, joigus said:

AAMOF, Einstein made a mistake on the first paper, including a condition that the determinant of minus the metric be 1, which is not an invariant constraint. Hilbert immediately noticed, and so told him. Einstein corrected it, and went on to learn about the Ricci tensor, which gave him the final form of the field equations. So did Hilbert too. Science historians admit today that Einstein got there first.

To be more precise. Einstein demanded,

\[\sqrt{-g}=1\]

with,

\[g=\textrm{det}g_{\mu\nu}\]

which, as Hilbert pointed out, can't be in a diffeomorphism invariant theory.

His first version of field eqs. was,

\[R_{\mu\nu}=8\pi GT_{\mu\nu}\]

which doesn't covariantly conserve matter energy, his goal. As,

\[D_{\mu}R^{\mu\nu}\neq0\]

[Markus Hanke]

11 hours ago, rjbeery said:

It's the gradient (i.e. the derivative) that determines the gravitational attraction, and a single point doesn't hold enough information.

Ok, so the gradient would give you a vector field - which is still insufficient to capture all the necessary degrees of freedom. As I said, at the very least you need a rank-2 tensor field to adequately describe gravity.

11 hours ago, rjbeery said:

Does a unique solution to the Einstein field equations produce a unique time-dilation "field" (in 4 dimensions)?

Time dilation is a relationship between clocks, it’s not a covariant quantity, and it isn’t local either. So, such a thing as a “time dilation field” does not make much physical or mathematical sense.
A solution to the Einstein equations is given by a metric - this is the primary and most fundamental mathematical object in GR. Once you have the metric, you can then calculate the relationship between given clocks in spacetime from this.

[joigus]

2 hours ago, Markus Hanke said:

Ok, so the gradient would give you a vector field - which is still insufficient to capture all the necessary degrees of freedom. As I said, at the very least you need a rank-2 tensor field to adequately describe gravity.

Time dilation is a relationship between clocks, it’s not a covariant quantity, and it isn’t local either. So, such a thing as a “time dilation field” does not make much physical or mathematical sense.
A solution to the Einstein equations is given by a metric - this is the primary and most fundamental mathematical object in GR. Once you have the metric, you can then calculate the relationship between given clocks in spacetime from this.

Only case in which I thought that could make any sense is about static solutions. But not even there. Thank you very much. +1

 

2 hours ago, joigus said:

To be more precise. Einstein demanded,

 

Eqs. rendered badly, prob. because insertion of HTLM tags. Dunno.

Anyway, I meant,

To be more precise. Einstein demanded,

\[ \sqrt{-g}=1\]

with,

\[g=\textrm{det}g_{\mu\nu}\]

which, as Hilbert pointed out, can't be in a diffeomorphism invariant theory.

His first version of field eqs. was,

\[R_{\mu\nu}=\frac{8\pi G}{c^{4}} T_{\mu\nu}\]

which doesn't covariantly conserve matter energy, his goal. As,

\[D_{\mu}R^{\mu\nu}\neq0\]

The moral of all this: Einstein was carefully scanning for mistakes in his proposal. You don't come across like you are, rjbeery.

Edited May 18, 2020 by joigus
addition (moral)

[Strange]

On 5/14/2020 at 10:21 PM, rjbeery said:

The efficacy of the “F=ma optics” is without doubt, however, respective authors on the subject are careful to stress the purely analogous nature of the relationship. We would like to suggest that it isn’t an analogy at all, but rather a literal equivalence.

You still have not shown how this can produce the effects of gravity. Not even the simple Newtonian model. Are you going to do that? Or is this all just guesswork?

Second, you haven't provided a "causal mechanism" because you have simply invoked an analogy. If this process actually happens, then what is the cause? (The theory you reject provides a cause, can you?)

On 5/14/2020 at 10:21 PM, rjbeery said:

In this paper we have shown the connection of optics to the gravitational bending of light in a graded time dilation field. Additionally we have shown that if mass were to possess an electromagnetic nature moving in a cyclic fashion (i.e. “EM mass”) then we are able to precisely predict the gravitational behavior of that mass in the presence of such a time dilation field without invoking any other mechanism related to General Relativity. Lastly, we are able to show that this model may plausibly explain other aspects of Relativity, such as the limiting speed of light and relativistic mass. 

You haven't "shown" any of these things. You are just making baseless assertions.

Unless you can actually show that this analogy reproduces something vaguely similar to gravity, I think this thread has become pointless.

14 hours ago, rjbeery said:

Anyway, I'm stuck using the tools in my toolbox, and I'm currently I'm looking at how time dilation might affect Mercury's precession. 

How about just showing that it can recreate gravity?

Or admit that you can't and then we can all go home.

[SergUpstart]

3 hours ago, Markus Hanke said:

Ok, so the gradient would give you a vector field - which is still insufficient to capture all the necessary degrees of freedom. As I said, at the very least you need a rank-2 tensor field to adequately describe gravity.

 

Three coordinates of the gravitational acceleration vector + three coordinates for the torsion field vector?