# Paper: A causal mechanism for gravity

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9 hours ago, swansont said:

No, it's a claim from GR.

But it isn't. I agree with you that time dilation, and therefore refraction, are correlated with gravitational potential, but a change in gravitational potential requires a change in time dilation. I have given the full GR treatment of velocity and how it relates to a free fall in gravity in equations (1)-(6). I do the same in the second section with refraction.

On 4/16/2021 at 10:31 AM, swansont said:

i.e. that there is no time dilation with constant g. Can you predict the Pound-Rebka experimental results?

Yes, I did this, and we both agree that my math is an exact result, whereas the Newtonian approximation used by Pound-Rebka is just that. It is known to be inexact, and would quickly diverge from reality as the height of the tower increased.

In other words, you're using a known approximation as a proxy for GR when we both know it is not. If you still disagree then I would like to examine a physical scenario where potential increases over a substantial distance of constant gravitational acceleration. The only one I can think of is in the center of a Newton's sphere (where potential remains unchanged).

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1 hour ago, rjbeery said:

But it isn't.

Yes, it is. Do the math.

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I agree with you that time dilation, and therefore refraction, are correlated with gravitational potential, but a change in gravitational potential requires a change in time dilation.

Of course it does. But you previously said that it required a change in g.

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I have given the full GR treatment of velocity and how it relates to a free fall in gravity in equations (1)-(6). I do the same in the second section with refraction.

Yes, I did this, and we both agree that my math is an exact result, whereas the Newtonian approximation used by Pound-Rebka is just that. It is known to be inexact,

You probably shouldn’t tell me what I agree to. I see you used Newtonian physics. Why is that permitted in your treatment? You’re complaining that it gives inexact results.

At what level of precision is Pound-Rebka inexact?

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and would quickly diverge from reality as the height of the tower increased.

Yes, I already pointed this out. “quickly” is quantifiable. The point is, the result obtained is the same as if you did a full GR treatment.

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In other words, you're using a known approximation as a proxy for GR when we both know it is not.

It gives the same answer, because if you expand the GR equation in powers of r, they used the first term, as the others are small and can be ignored.

(Just like 1/2 mv^2 can be extracted from the relativistic KE equation)

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If you still disagree then I would like to examine a physical scenario where potential increases over a substantial distance of constant gravitational acceleration.

I pointed to one already.  I don’t see the point, other than as a distraction from the example I gave.

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The only one I can think of is in the center of a Newton's sphere (where potential remains unchanged).

g=0, so there is no gravitational acceleration, as I mentioned.

So, no comment on Einstein’s elevator?

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1 hour ago, swansont said:

It gives the same answer, because if you expand the GR equation in powers of r, they used the first term, as the others are small and can be ignored.

It doesn't give the same answer. Saying "the other [terms] are small and can be ignored" is like saying that pi is literally 333/106.

1 hour ago, swansont said:

So, no comment on Einstein’s elevator?

If Einstein's elevator is your example of a physical scenario where potential increases over a substantial distance of constant gravitational acceleration, it isn't valid. It too is an approximation.

We can imagine, in our minds, an elevator being accelerated uniformly from top-to-bottom, but the person standing in the elevator could use equipment (available today) to compare the gravitational acceleration at his head vs his feet. If they differ then he knows he is in a gravitational field.

A gravitational field is defined as the negative of the gradient of the gravitational potential. If the gradient is zero, then the gravitational acceleration is zero -- how would you explain that?

Edited by rjbeery
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8 hours ago, rjbeery said:

It doesn't give the same answer. Saying "the other [terms] are small and can be ignored" is like saying that pi is literally 333/106.

Then show the GR calculation and point out the disagreement.

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If Einstein's elevator is your example of a physical scenario where potential increases over a substantial distance of constant gravitational acceleration, it isn't valid. It too is an approximation.

Einstein’s elevator is an example of the equivalence principle, part of GR. It says light bends in an elevator accelerating at 1g, whether due to an external force or due to gravity. You deny this will occur.

8 hours ago, rjbeery said:

We can imagine, in our minds, an elevator being accelerated uniformly from top-to-bottom, but the person standing in the elevator could use equipment (available today) to compare the gravitational acceleration at his head vs his feet. If they differ then he knows he is in a gravitational field.

Incorrect. You are assuming the field is due to a body where the field varies. That’s an additional constraint the you have added.

8 hours ago, rjbeery said:

A gravitational field is defined as the negative of the gradient of the gravitational potential. If the gradient is zero, then the gravitational acceleration is zero -- how would you explain that?

The gradient isn’t zero for constant g. Why do you think that it would be?

Work it the other way. If the field is constant (g), then integrate over a distance (h) to find the potential. It will be gh. The potential energy will be mgh. These equations should look familiar.

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8 hours ago, swansont said:

Einstein’s elevator is an example of the equivalence principle, part of GR. It says light bends in an elevator accelerating at 1g, whether due to an external force or due to gravity. You deny this will occur.

I think it's important that we agree on where we disagree. I don't deny anything about Einstein's elevator, except that it isn't a true equivalence if the acceleration is due to gravity, and that's because I don't believe "constant acceleration due to gravity" is possible, and the Newtonian approximation is obfuscating that fact. Light would obviously bend under acceleration, regardless of the source.

You're asking me to prove that your approximation is an approximation. I may look at doing this, but at this point I don't see much benefit in convincing you as long as you haven't found any objective refutation in the mathematics of my paper.

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4 hours ago, rjbeery said:

I think it's important that we agree on where we disagree. I don't deny anything about Einstein's elevator, except that it isn't a true equivalence if the acceleration is due to gravity, and that's because I don't believe "constant acceleration due to gravity" is possible,

So what?

Physics idealizes all the time. Or have you never taken a physics class? There are no frictionless surfaces and there is always air resistance, in reality. But they don't show up in many problems.

Constant g is a given in the problem. That’s all that matters.

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and the Newtonian approximation is obfuscating that fact. Light would obviously bend under acceleration, regardless of the source.

Earlier you said it wouldn’t (“time dilation would be constant in a field of "constant gravitational acceleration" and therefore would not refract light. If gravitational forces still existed in such a field then equivalence would be broken”). Which is the correct claim?

Let’s try this: What is the GR expression for gravitational potential in a uniform gravitational field?

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You're asking me to prove that your approximation is an approximation. I may look at doing this, but at this point I don't see much benefit in convincing you as long as you haven't found any objective refutation in the mathematics of my paper.

No, you’re hung up on it being an approximation, as if it matters.

I pointed out you use non-relativistic equations. Your problem is set near a black hole, which suggests you need to use relativistic equations. Nothing after that is valid (these are your rules). That’s my refutation.

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19 hours ago, swansont said:

Let’s try this: What is the GR expression for gravitational potential in a uniform gravitational field?

OK, so I've never looked at the derivation of the approximation before. This is a great synopsis: https://campus.mst.edu/physics/courses/409/Assignments/gravitational potential.pdf

I think I understand. The approximation U = mgh has 'g' baked into it; we could rewrite this as g = U/mh, and if we take the derivative with respect to r (or h), the change in g is independent of a change in r (or h) in this form -- so you are right.

However, the true math (sans approximation) is a full Taylor series expansion, with the height variable continuing on indefinitely to higher and higher powers. In other words, the full expression of g = U/mh is infinitely differentiable with respect to r and will always be dependent upon r. There is no scenario where the acceleration can exist in a form that is independent of r.

So, yes, the approximation is exactly the cause of our disagreement.

Edited by rjbeery
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5 hours ago, rjbeery said:

OK, so I've never looked at the derivation of the approximation before.

No, I want the GR equation, so you can’t complain it’s an approximation

5 hours ago, rjbeery said:

However, the true math (sans approximation) is a full Taylor series expansion

Yes. And if the terms you ignore are smaller than your precision, it doesn’t affect the answer. So ignoring them doesn’t change your answer. Meaning the Pound-Rebka result is 2.5 x 10^-15 if you use a full-blown GR calculation or just the leading term of the expansion, because the omitted terms are smaller than 10^-16.

The bottom line is that time dilation happens at different heights for constant g.

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On 4/19/2021 at 5:04 PM, swansont said:

The bottom line is that time dilation happens at different heights for constant g.

No problem. Please provide me with an exact equation showing me this.

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9 hours ago, rjbeery said:

No problem. Please provide me with an exact equation showing me this.

I asked you first, and you're the one making a non-mainstream claim, so it's up to you to support it. My position, and the one that aligns with mainstream physics, is that it's OK to use approximations when it doesn't affect the answer*.

However, by asking this, you are tacitly asserting that the approximation of g is somehow responsible here, even though gravitational potential depends explicitly on r. And yet somehow it would no longer depend on r if the gravitational acceleration were constant.

* and which you are doing in equations (2) and (3) even though the motion is relativistic and these approximations fail

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On 4/19/2021 at 5:04 PM, swansont said:

The bottom line is that time dilation happens at different heights for constant g.

The reason it's difficult to discuss is because "constant g" is unnatural. It's mathematically impossible, so the premise is invalid. You're thinking in terms of "constant acceleration" as somehow adding to a value of velocity, which would increase the time dilation, but gravitational acceleration isn't true acceleration -- free falling objects are unaccelerated by definition.

The bottom line is that there can't be stretches of space where velocity increases but gravitational acceleration remains constant. Potential is defined with r, g is defined with r, so potential cannot be independent of g.

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10 hours ago, rjbeery said:

The reason it's difficult to discuss is because "constant g" is unnatural. It's mathematically impossible,

Not at all. It’s mathematically trivial (or at least easy), and physically impossible. But then, so is the Newton sphere you have invoked a couple of times.

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so the premise is invalid. You're thinking in terms of "constant acceleration" as somehow adding to a value of velocity, which would increase the time dilation, but gravitational acceleration isn't true acceleration -- free falling objects are unaccelerated by definition.

No, that’s not what I’m thinking.

Time dilation in a gravitational field stems from not being in freefall, i.e. you are at some fixed r, like on the surface of a planet.

Thus the gravitational potential at the bottom and top of a tower is different, and thus time runs at a different rate at those points (and all points in between)

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The bottom line is that there can't be stretches of space where velocity increases but gravitational acceleration remains constant.

Velocity is not part of my argument.

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Potential is defined with r, g is defined with r, so potential cannot be independent of g.

I never claimed potential was independent of g.

I said potential still varies with r (or h) when g is constant, which is not the same thing. IOW in the Pound-Rebka experiment, the time dilation, which comes from the change in potential, is dominated by the change in height, and the change in g has a negligible effect, by many, many orders of magnitude. Thus, it is perfectly reasonable to treat this problem as having constant g.

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I'll come back to this. It should be as easy as putting potential in terms of g, although I'm not sure you'll concede the point, regardless.

In an event, have you ever seen gravity's behavior completely described in terms of refraction? Have you actually read the paper? Because that's what it does.

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1 hour ago, rjbeery said:

Have you actually read the paper?

I stopped when I saw you use 1/2mv^2 in a relativistic problem. Beyond that, you claimed that constant g will not cause time dilation or bending of light, which is blatantly wrong, so what would be the point?

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Well, apparently Relativity and gravitational potential don't play nicely; something about being impossible to localize potential energy. It's been a long-standing problem that I'm only just reading about.

In any event, you shouldn't shut yourself off from what you may find to be very interesting:

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On 4/23/2021 at 5:15 PM, swansont said:

I stopped when I saw you use 1/2mv^2 in a relativistic problem.

I've rewritten the first section to derive the relevant equation (eq. 5) without any Newtonian references.

On 4/23/2021 at 5:15 PM, swansont said:

Beyond that, you claimed that constant g will not cause time dilation or bending of light, which is blatantly wrong,

I could rewrite the equations to put the potential in terms of g but, as I said, I suspect you'll be dismissive. Therefore I found a full derivation that I doubt you can object to:

On page 404, equation 54, the author seeks to prove that

Now that these objections are handled, do you have any other feedback? Because I'm going to be submitting this to a journal and I'm largely working in a vacuum.

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If a = d(phi)/dr, we can integrate for a constant a and see that the change in potential is simply ar, or, as I wrote earlier, gh.

So it seems my equation is a GR equation after all.

That would seem to remove your objection to the fact that time dilation will happen in a region of constant g

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2 hours ago, swansont said:

That would seem to remove your objection to the fact that time dilation will happen in a region of constant g

Time dilation would occur for any general form of acceleration, but constant gravitational acceleration is unphysical. The high school shortcut of PE = mgh was superseded with the actual formula. Time dilation (gamma) is literally defined by r I think it's odd that my Newtonian reference offended you enough to not even look at the paper, but you're holding on to what we both know is bad math because you've apparently attached your ego to it.

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9 hours ago, rjbeery said:

Time dilation would occur for any general form of acceleration, but constant gravitational acceleration is unphysical.

So are frictionless surfaces and scenarios that lack air resistance, and Newton spheres, which you have invoked more than once, but that doesn't stop us from doing a gedanken experiment. The physics still works.

9 hours ago, rjbeery said:

The high school shortcut of PE = mgh was superseded with the actual formula. Time dilation (gamma) is literally defined by r

Ah, be careful. Time dilation may be defined this way under a particular set of assumptions such as having a spherical body of mass m, but one can't apply that in a situation where the assumptions don't apply.

9 hours ago, rjbeery said:

I think it's odd that my Newtonian reference offended you enough to not even look at the paper, but you're holding on to what we both know is bad math because you've apparently attached your ego to it.

A. YOU provided the GR equation to me, in the Relativistic Gravitational Potential and its Relation to Mass-Energy link. Don't get pissy because you don't like the answer.

If you think my math is bad, you go ahead and integrate the equation for constant acceleration. Do you get a different answer? (if so, then we can discuss bad math)

B. You have no idea what my motivations are. It is a mistake to think that you do.

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7 hours ago, swansont said:

Time dilation may be defined this way under a particular set of assumptions such as having a spherical body of mass m, but one can't apply that in a situation where the assumptions don't apply.

Then we both agree that the paper is congruous with the implicit assumptions (e.g. spherical body of mass M), and any further objections would have to provide a set of assumptions for which these calculations don't apply.

In other words, we can both agree that the paper is self-consistent, and also that time dilation would occur under constant acceleration (but not vary under constant acceleration).

So, really, the only thing we disagree about is whether constant gravitational acceleration is a physical phenomenon, and I'm fine leaving it at that.

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4 hours ago, rjbeery said:

Then we both agree that the paper is congruous with the implicit assumptions (e.g. spherical body of mass M), and any further objections would have to provide a set of assumptions for which these calculations don't apply.

In other words, we can both agree that the paper is self-consistent,

You know that I have not read the paper, so it is an ill-advised leap to say I agree to anything about it.

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and also that time dilation would occur under constant acceleration (but not vary under constant acceleration).

It would vary with position, because the gravitational potential varies with position.

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So, really, the only thing we disagree about is whether constant gravitational acceleration is a physical phenomenon, and I'm fine leaving it at that.

No, there is no disagreement. You can’t physically realize an actually constant g. My position is that this doesn’t matter, at all, because physics solutions to idealized conditions are legion. Working with models doesn’t require physical realization, just no out-and-out violation of the relevant laws of physics.

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On 4/28/2021 at 3:55 PM, swansont said:

You know that I have not read the paper, so it is an ill-advised leap to say I agree to anything about it.

You've written far more in the discussion of this paper than what exists in the paper itself. I removed the Newtonian reference that offended you. At this point it's pretty suspect that you can't otherwise be bothered, but you've spent weeks explaining that fact.

On 4/28/2021 at 3:55 PM, swansont said:

You can’t physically realize an actually constant g. My position is that this doesn’t matter, at all, because physics solutions to idealized conditions are legion. Working with models doesn’t require physical realization, just no out-and-out violation of the relevant laws of physics.

Imagining a constant g is not the same thing as idealizing a frictionless surface. The former contradicts the theory, whereas the latter is ("merely") a practical impossibility. mgh is a first-order approximation, the same way 1/2 mv^2 is. We can use it for estimates, but we can't use it for making generalizations...particularly when the error in those generalizations is precisely tied to the terms we have excluded in our approximation.

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24 minutes ago, rjbeery said:

You've written far more in the discussion of this paper than what exists in the paper itself. I removed the Newtonian reference that offended you. At this point it's pretty suspect that you can't otherwise be bothered, but you've spent weeks explaining that fact.

What is suspect about someone on a science discussion site wanting to discuss science? Why is it suspect that I don't want to slog through a paper that is obviously wrong, seeing as you stated several conclusions that are in disagreement with GR? Even if I were inclined to find your mistakes, you have fought me at every turn when I have given criticism.

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Imagining a constant g is not the same thing as idealizing a frictionless surface. The former contradicts the theory,

What theory does it contradict? More importantly, how does it contradict that theory?

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whereas the latter is ("merely") a practical impossibility.

They are both practical impossibilities. As is Newton's sphere.

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mgh is a first-order approximation, the same way 1/2 mv^2 is.

You provided a reference which is consistent with mgh being GR. Do you now disagree with your own reference?

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We can use it for estimates, but we can't use it for making generalizations...particularly when the error in those generalizations is precisely tied to the terms we have excluded in our approximation.

I have asked you to do this, and you have thus far declined. And I expect you will decline this invitation as well.

How much error is introduced in the Pound-Rebka experiment by assuming a constant g? Convince me that it matters, with some real justification, rather than a hand-wave.

And yes, you can use it for generalizations, as long as you aren't violating the assumptions you made in the approximation.

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• 3 weeks later...
On 4/30/2021 at 8:33 PM, swansont said:

What is suspect about someone on a science discussion site wanting to discuss science? Why is it suspect that I don't want to slog through a paper that is obviously wrong, seeing as you stated several conclusions that are in disagreement with GR? Even if I were inclined to find your mistakes, you have fought me at every turn when I have given criticism.

Sometimes I have a look on this forum and I occasionally note some kind of discriminations. What kind of discriminations? Threads that normally (according to your sensitivities) should have been shutted down, are kept alive (as this one). And when one (as me) attempts to present a different perspective to a problem then, all of a sudden, the moderators want to close the thread as soon as possible by claiming that "I don't understand physics" and "I don't want to learn", by ignoring the inconsistencies of the participants in the discussion.

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3 hours ago, John2020 said:

Sometimes I have a look on this forum and I occasionally note some kind of discriminations. What kind of discriminations? Threads that normally (according to your sensitivities) should have been shutted down, are kept alive (as this one). And when one (as me) attempts to present a different perspective to a problem then, all of a sudden, the moderators want to close the thread as soon as possible by claiming that "I don't understand physics" and "I don't want to learn", by ignoring the inconsistencies of the participants in the discussion.

And yet we’re 12 pages in and it hasn’t been shut down, so yeah, great example of mods wanting to “close the thread as soon as possible”

I will note that you’ve expended time and effort to complain, but haven’t addressed any of the points I raised. One might think you’re trying to distract from the shortcomings of your position.

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