Paper: A causal mechanism for gravity

[Mordred]

36 minutes ago, Markus Hanke said:

As I have attempted to explain at length, this is true only in Schwarzschild spacetime, since that is a 1-parameter family of metrics. It does not generalise to any other case.

I don’t think you have understood much of what I spent considerable time trying to explain.
Neither time dilation nor gravitational acceleration are variables in the field equation, and for good reason. Gravity, in GR, is geodesic deviation - the failure of initially parallel world lines to remain parallel in the presence of gravitational sources. It’s a geometric property of spacetime. In 4-dimensional spacetime, you cannot describe geodesic deviation by just a scalar quantity, it requires a higher rank object. This is nothing to do with GR specifically, it’s just basic differential geometry.

You can write a scalar field model for the case of Schwarzschild spacetime (simply define a gravitational potential as function of r), but that is only because it is a highly symmetric case - this does not generalise to gravity as an overall concept. So if Schwarzschild spacetime is all you are interested in, then there is not actually an issue; you just can’t claim it is a causal mechanism for gravity in the general case, because it evidently isn’t, for all the many reasons already pointed out in previous posts.

As for your last question, I already gave an example earlier - in FLRW spacetime, you have relative acceleration between test particles due to expansion or contraction of the spatial part of the metric, but no gravitational time dilation between those same test particles. Any metric where the temporal part is constant, but the spatial part is not, will be of that nature.

I'm not sure there is any other way we can explain the above to him. 

 

5 hours ago, rjbeery said:

No, you need to read the words I'm typing. The first equation is the equation for gravitational time dilation. I'm pretty sure the dimensions align without problem.

This is a specific class of solution. For a large non rotating spherical symmetric object. 

[Markus Hanke]

18 hours ago, rjbeery said:

What's wrong with this equation?

Simplify the expression all the way to the end, given the relations you posted earlier:

\[g=\frac{c^{2}}{r}\left( 1-\left(\frac{t_{0}}{t_{f}}\right)^{2}\right) =\frac{c^{2}}{r}\left( 1-\left(\frac{t_{f}\sqrt{1-\frac{2GM}{rc^{2}}}}{t_{f}}\right)^{2}\right) =\frac{2GM}{r^{2}}\]

As r->0, the gravitational acceleration increases without bound, and diverges at r=0. This is clearly not what we physically observe, since a test particle at r=0 experiences no net acceleration at all; yet it is still time dilated wrt to some external reference clock at infinity.

I’ve been thinking about this some more, and I was actually wrong on something, and need to go back on it - even in Schwarzschild spacetime, you cannot specify all aspects of gravity with time dilation alone; you need at least a vector field of some kind. Consider two test particles (with their own gravitational influence being negligible) which fall freely side by side, but separated by some distance, towards a central mass. They fall at the same rate, so at every point their radial distance to the central mass is the same, hence they experience no gravitational time dilation with respect to each other. However, as they fall, their trajectories will start to converge, i.e. they approach each other as they fall towards the central mass, and eventually collide near r=0. There will be relative acceleration between the test particles perpendicular to their radial in-fall, even though they are not time dilated wrt to one another. This is because even in Schwarzschild spacetime there is tidal gravity - all radial free fall geodesics converge at r=0. You can capture purely radial in-fall via time dilation alone, but not these tidal effects. So even in simple Schwarzschild spacetime this idea ultimately fails; if you use a single scalar field to model gravity, you do not obtain the correct free-fall geodesics which we observe in the real world (unless the free fall is purely radial, which is trivial anyway). In fact, if you write the proper equations of motion for light using only a scalar model, you will find that there is no gravitational bending of light around massive objects, which is of course contrary to observational evidence (see Misner/Thorne/Wheeler, Gravitation, §7.1).

[Mordred]

Accurate post well described. 

[rjbeery]

Markus, I understand your position and I appreciate your input. You're correct that I keep referring to the simpler Schwarzschild spacetime solution but that was to illustrate the theoretical connection to others who can't see it at all. I'm "facing many fronts" in this thread. I just spent 6 hours convincing another poster that the gravitational time dilation equation is mathematically valid.

You might be right that the connection doesn't generalize, but I remain unconvinced. The FLRW spacetime example doesn't work, for example - the reason we know about cosmological expansion in the first place is due to time dilation (red-shifting of the distant stars). In fact, when people present me with apparent counter-examples that I can explain it does nothing but strengthen my resolve. If that's frustrating, I'm sorry.

4 hours ago, Markus Hanke said:

As r->0, the gravitational acceleration increases without bound, and diverges at r=0. This is clearly not what we physically observe, since a test particle at r=0 experiences no net acceleration at all; yet it is still time dilated wrt to some external reference clock at infinity.

4 hours ago, Markus Hanke said:

I’ve been thinking about this some more, and I was actually wrong on something, and need to go back on it - even in Schwarzschild spacetime, you cannot specify all aspects of gravity with time dilation alone; you need at least a vector field of some kind.

This is right but we've already covered it. It's the local time dilation gradient that determines gravitational movement. Remember discussing Newton's shell?

 

 

[Ghideon]

I have passively followed this from the sidelines due to limited knowledge in the area but I've learned a few things*.

22 hours ago, rjbeery said:

I'm trying to understand where my model would have problems generalizing.

Are you sure? There are now 10 pages of excellent examples and objections from several experts in the field, none of which seems to bring you closer to the desired understanding. I've browsed through the thread again, each time a critical argument is added the standard type of response is:

22 hours ago, rjbeery said:

You give good explanations, but your answers don't bring clarity to me.

What prevents you from understanding the objections related to your idea while at the same time you seem capable to understand several other complex concepts of physics**? What prevents required new tools from being added? 

On 5/18/2020 at 12:11 AM, rjbeery said:

I'm stuck using the tools in my toolbox

I may have some ideas about (over-)simplified analogies as a complement to the expert explanations given so far but at this time I'm not sure if that is what you are looking for?

 

 

*) @Mordred's "What curves is the principle of least action" certainly trigger some thoughts, I'll try to study that, check if my intuitive understanding of that single line matches the mainstream science.   

**) I lack your level insight into GR but I can still understand much of the discussion. 

[rjbeery]

26 minutes ago, Ghideon said:

I may have some ideas about (over-)simplified analogies as a complement to the expert explanations given so far but at this time I'm not sure if that is what you are looking for?

Feel free to throw out thoughts, I love hearing other perspectives. Dispersion and FLRW are things I had never considered, and I appreciated their mention. 

[Mordred]

3 hours ago, Ghideon said:

 

*) @Mordred's "What curves is the principle of least action" certainly trigger some thoughts, I'll try to study that, check if my intuitive understanding of that single line matches the mainstream science.   

**) I lack your level insight into GR but I can still understand much of the discussion. 

Here is an Caltech lecture note on the Langrangian formalism of GR.

https://www.google.com/url?sa=t&source=web&rct=j&url=http://www.tapir.caltech.edu/~chirata/ph236/2011-12/lec33.pdf&ved=2ahUKEwjQn_i52tnpAhW1MX0KHcR9BAwQFjAAegQIBBAB&usg=AOvVaw0FPL8yDcjn0EG4tH5W8eZ5

Now a better way to learn this is through the Einstein Hilbert action which is mentioned in the above link however here is the MIT lecture note.

https://www.google.com/url?sa=t&source=web&rct=j&url=http://web.mit.edu/edbert/GR/gr5.pdf&ved=2ahUKEwiH7vDZ29npAhUWIDQIHda1D54QFjAAegQICBAB&usg=AOvVaw0WRK38p_2yCObL796dRDk5

[Markus Hanke]

On 5/29/2020 at 3:56 PM, rjbeery said:

This is right but we've already covered it. It's the local time dilation gradient that determines gravitational movement. Remember discussing Newton's shell?

This is irrelevant, as it still cannot model tidal effects, for reasons already explained numerous times. The necessary information content just isn’t there in a scalar field, and it won’t magically appear by taking the gradient.

On 5/29/2020 at 3:56 PM, rjbeery said:

The FLRW spacetime example doesn't work, for example - the reason we know about cosmological expansion in the first place is due to time dilation (red-shifting of the distant stars).

I didn’t mention anything about cosmology, the FLRW metric describes the interior of any matter distribution that is homogenous, isotropic, and only gravitationally interacting. Of course it is most often used as a cosmological model, but doesn’t have to be.

On 5/29/2020 at 3:56 PM, rjbeery said:

In fact, when people present me with apparent counter-examples that I can explain it does nothing but strengthen my resolve. If that's frustrating, I'm sorry.

The frustrating part about this is that you are simply ignoring most of the things we say to you, which makes me feel like I’m wasting my time with this. Also, claiming that you have “explained” something when in fact you haven’t, is also really frustrating.
The other thing is that you still haven’t presented an actual model, you just keep verbally describing an idea in your head - there is nothing wrong with that in itself, it is in fact commendable that you spend time thinking about these issues. Nonetheless, until you write down a mathematical model, you can’t be sure just what the implications are - you obviously think you are right, but you won’t know either way until you actually run some numbers.

On 5/29/2020 at 3:56 PM, rjbeery said:

You might be right that the connection doesn't generalize, but I remain unconvinced.

Then I don’t think you really understand what the term “gravity” actually means, because if you did, you would immediately see yourself that this idea of yours cannot work in the general case, and why. Just this one point is already enough; gravity is geodesic deviation. I’ll write it down formally for you:

\[\xi {^{\alpha }}{_{||\tau }} =-R{^{\alpha }}{_{\beta \gamma \delta }} \thinspace x{^{\beta }}{_{|\tau }} \thinspace \xi ^{\gamma } \thinspace x{^{\delta }}{_{|\tau }}\]

wherein \(\xi^{\alpha}\) is the separation vector between geodesics, and \(x^{\alpha}\) is the unit tangent vector on your fiducial geodesic. Can you find a way to replace the dependence on the metric tensor in these equations with a dependence on just a scalar field and its derivatives, in such a way that the same physical information is captured? If, and only if, you can do so, then you might be onto something with your idea. 

Edited May 31, 2020 by Markus Hanke

[Markus Hanke]

Apologies, I need to correct myself, I omitted an index. This should have been

\[\xi {^{\alpha }}{_{||\tau \tau}} =-R{^{\alpha }}{_{\beta \gamma \delta }} \thinspace x{^{\beta }}{_{|\tau }} \thinspace \xi ^{\gamma } \thinspace x{^{\delta }}{_{|\tau }}\]

[rjbeery]

On 5/31/2020 at 4:40 AM, Markus Hanke said:

Nonetheless, until you write down a mathematical model, you can’t be sure just what the implications are - you obviously think you are right, but you won’t know either way until you actually run some numbers.

Have you actually read the OP? Or its references?

On 5/14/2020 at 3:21 PM, rjbeery said:

[1]The optical-mechanical analogy for stationary metrics in general relativity; Paul M. Alsing; American Journal of Physics 66, 779 (1998); https://doi.org/10.1119/1.18957

[2] The optical-mechanical analogy in general relativity: Exact Newtonian forms for the equations of motion of particles and photons; James Evans, Kamal K. Nandi & Anwarul Islam; General Relativity and Gravitation volume 28, pages 413–439(1996)

[3] ‘‘F=ma’’ optics; James Evans and Mark Rosenquist; American Journal of Physics 54, 876 (1986); https://doi.org/10.1119/1.14861

[4] Space, Time and Gravitation; Sir Arthur Eddington; http://www.gutenberg.org/files/29782/29782-pdf.pdf

Did you look at the numeric analysis I posted? I shared the spreadsheet so you can see that there are no fudge factors involved. The math works.

That being said, I understand the tensor objection, which is why I'm asking for real-world examples where spacetime curvature and time dilation diverge.

On 5/31/2020 at 4:40 AM, Markus Hanke said:

Can you find a way to replace the dependence on the metric tensor in these equations with a dependence on just a scalar field and its derivatives, in such a way that the same physical information is captured?

Maybe the full time dilation field requires more information than I'm presuming; maybe GR has redundancies in distinguishing mass/momentum and other forms of energy (IOW, two different systems could produce the same result); maybe there's more information in the EFEs than mere spacetime curvature; maybe this connection doesn't generalize and is only useful in limited analyses. I think about all of these things.

But insisting that either this idea can either immediately and completely replace all of GR, or else it's worthless, seems premature.

 

[Markus Hanke]

14 hours ago, rjbeery said:

Have you actually read the OP? Or its references?

Yes, and as it happens I am already familiar with some of these sources from my own studies. All of these papers work with highly symmetric, static and stationary spacetimes, mostly Schwarzschild. None of them makes any claim to the effect that the metric can be replaced with a scalar field, in the general case.

14 hours ago, rjbeery said:

That being said, I understand the tensor objection, which is why I'm asking for real-world examples where spacetime curvature and time dilation diverge.

If you are asking if you can have scenarios where there are gravitational effects without gravitational time dilation being present between reference clocks, then we have already given you several examples. A lot of interior solutions are of this kind, as are some pp-wave vacuum metrics. You can also set up such scenarios in symmetric spacetimes such as Schwarzschild, by looking at geodesics that are not purely radial. Plus many more.

The point is simply this - on a 4-dimensional spacetime manifold, you can have ‘curvature in time’ (gravitational time dilation), and ‘curvature in space’ (tidal gravity). Crucially, both of these can (but don’t necessarily have to) be present simultaneously and be mutually dependent in complicated ways - for example, tidal effects don’t need to be static, they can be time-dependent and propagate, and the time dependence can itself by non-trivial. A real-world example would be spacetime in and around a binary star system. It’s due to this inherent complexity and nonlinearity that the 2-body problem does not have a closed analytical “on paper” solution.

Thus, in the general case you will need more than a single number to accurately model the situation. That this is so - i.e. that geodesic deviation on this kind of manifold requires a rank-2 tensor - is not specifically linked to GR, it’s just basic differential geometry.

14 hours ago, rjbeery said:

Did you look at the numeric analysis I posted? I shared the spreadsheet so you can see that there are no fudge factors involved. The math works.

As I have pointed out several times already - yes, you can make this work for certain sets of limited and restricted circumstances. The issue is, though, that it doesn’t generalise, so it’s not a “causal mechanism for gravity”, to quote the title of this thread.

14 hours ago, rjbeery said:

Maybe the full time dilation field requires more information than I'm presuming; maybe GR has redundancies in distinguishing mass/momentum and other forms of energy (IOW, two different systems could produce the same result); maybe there's more information in the EFEs than mere spacetime curvature; maybe this connection doesn't generalize and is only useful in limited analyses. I think about all of these things.

The only way for you to know for sure is to write down a mathematical model for your idea, and then investigate what kind of predictions it makes in cases other than purely radial in-fall in Schwarzschild spacetime, and comparing those to available data. I can’t stress this enough, and it is the best advice I can give you. I could keep trying to explain things until the cows come home (as they say here where I am), but until you see things with your own eyes in your own mathematical model, you won’t be able to make progress either way. 

At this point in time, I do not feel I really have anything further of value to add to this discussion.

Edited June 2, 2020 by Markus Hanke

[rjbeery]

8 hours ago, Markus Hanke said:

At this point in time, I do not feel I really have anything further of value to add to this discussion.

Agreed. I'll post to the forum if and when I find or produce a new analytic solution. Thanks so much for the patient and mature discussion.

[joigus]

On 6/1/2020 at 6:17 PM, rjbeery said:

But insisting that either this idea can either immediately and completely replace all of GR, or else it's worthless, seems premature.

Nothing is pre-nothing here. It's gone full circle a few times already.

But please keep going. I'm planning on getting myself a really good GR monograph by copying and pasting Markus' detailed explanations.

[SergUpstart]

On 5/17/2020 at 1:31 AM, Strange said:

I wonder if that relates to Gullstrand-Painlevé coordinates

 

I don't know about the Gulstand-penlevet coordinates, but if we assume that c^2= - Phi (Phi is the gravitational potential), then the formula E=mc^2 transforms into E= - m*Phi with an understandable physical meaning, a body of mass m has energy that must be applied to move it to infinity, where the gravitational potential is 0.

This is just information to think about

[Markus Hanke]

2 hours ago, SergUpstart said:

I don't know about the Gulstand-penlevet coordinates, but if we assume that c^2= - Phi (Phi is the gravitational potential), then the formula E=mc^2 transforms into E= - m*Phi with an understandable physical meaning, a body of mass m has energy that must be applied to move it to infinity, where the gravitational potential is 0.

This is just information to think about

As has been mentioned earlier on this thread, the concept of ‘gravitational potential’ can only be meaningfully defined in spacetimes that admit a time-like Killing vector field, which is only a small subset of solutions to the field equations - it does not generalise to arbitrary spacetimes.

[rjbeery]

6 hours ago, Markus Hanke said:

As has been mentioned earlier on this thread, the concept of ‘gravitational potential’ can only be meaningfully defined in spacetimes that admit a time-like Killing vector field, which is only a small subset of solutions to the field equations - it does not generalise to arbitrary spacetimes.

Markus, may I ask your profession?

[SergUpstart]

6 hours ago, Markus Hanke said:

As has been mentioned earlier on this thread, the concept of ‘gravitational potential’ can only be meaningfully defined in spacetimes that admit a time-like Killing vector field, which is only a small subset of solutions to the field equations - it does not generalise to arbitrary spacetimes.

Does this mean that if in a static gravitational field you move a body in space from point A to point B along different paths or at different times, the amount of work against the force of gravity can be different?

[joigus]

28 minutes ago, rjbeery said:

Markus, may I ask your profession?

My guess would be cerebrorum malleus.

 

[Markus Hanke]

20 hours ago, rjbeery said:

Markus, may I ask your profession?

I don’t really have one, as I have chosen to live in unconventional ways. Currently I am resident in a monastery, and preparing to ordain as a monk in a contemplative tradition, which should happen sometime next year, all going well. I also freelance as an online translator (I speak several languages) on an as-needed basis, to cover the very few expenses I have.

In case you meant academic qualifications - I don’t have any, since I never went to university. The things I say here in these discussions reflect my own understanding of the subject matter; it is always up to the reader to verify any information given by consulting established textbooks, before taking them as fact. Online forums in themselves are never valid sources of scientific information.

Edited June 11, 2020 by Markus Hanke

[SergUpstart]

On 6/10/2020 at 12:30 PM, Markus Hanke said:

As has been mentioned earlier on this thread, the concept of ‘gravitational potential’ can only be meaningfully defined in spacetimes that admit a time-like Killing vector field, which is only a small subset of solutions to the field equations - it does not generalise to arbitrary spacetimes.

I expressed this idea ( that the square of the speed of light is equal to the gravitational potential) on another forum and received the answer "This idea is not new, on its basis V. Yanchinin developed the quantum theory of gravity". You wrote that you know several languages, including Russian? If so, here is a link where you can read this theory. http://www.vixri.com/d/Janchilin V.L. _Kvantovaja teorija gravitacii.pdf the Theory is very interesting and very likely correct.

[Markus Hanke]

7 hours ago, SergUpstart said:

You wrote that you know several languages, including Russian?

No, not including Russian.

[joigus]

9 hours ago, SergUpstart said:

I expressed this idea ( that the square of the speed of light is equal to the gravitational potential) on another forum and received the answer "This idea is not new, on its basis V. Yanchinin developed the quantum theory of gravity".

Google search:

Did you mean: "V. Yanchi In" "quantum theory of gravity"

 

No results containing all your search terms were found.

Your search - "V. Yanchinin" "quantum theory of gravity" - did not match any documents.

Suggestions:

• Make sure that all words are spelled correctly.
• Try different keywords.
• Try more general keywords.
• Try fewer keywords.

[Dord]

 

1 hour ago, joigus said:

Google search:

Did you mean: "V. Yanchi In" "quantum theory of gravity"

 

No results containing all your search terms were found.

Your search - "V. Yanchinin" "quantum theory of gravity" - did not match any documents.

Suggestions:

• Make sure that all words are spelled correctly.
• Try different keywords.
• Try more general keywords.
• Try fewer keywords.

Yanchinin looks like typo as the title of the pdf posted by @SergUpstart includes Janchilin V.L.

Does this help..?

https://www.google.co.uk/url?sa=t&source=web&rct=j&url=http://www.pirt.info/files/documents/proceedings_PIRT_2015.pdf&ved=2ahUKEwi7_aWduv7pAhVxsHEKHRFdBcoQFjAAegQIARAB&usg=AOvVaw3v6BAYpo9xPt503b_96TEq

The name Janchilin only appears twice, most notably as Reference 21,on page 298.

It may be worth a look...?

Edited June 13, 2020 by Dord

[joigus]

52 minutes ago, Dord said:

The name Janchilin only appears twice, most notably as Reference 21,on page 298.

It may be worth a look...?

Thank you. Well, I was just pointing out some mistyping. With a new theory, it's never just "a look." That's one problem. You must monitor the time you spend on ideas, own or from others. The premises alone tell me it's not gonna be worth my time.  

[SergUpstart]

5 hours ago, Dord said:

 

Yanchinin looks like typo as the title of the pdf posted by @SergUpstart includes Janchilin V.L.

Does this help..?

https://www.google.co.uk/url?sa=t&source=web&rct=j&url=http://www.pirt.info/files/documents/proceedings_PIRT_2015.pdf&ved=2ahUKEwi7_aWduv7pAhVxsHEKHRFdBcoQFjAAegQIARAB&usg=AOvVaw3v6BAYpo9xPt503b_96TEq

The name Janchilin only appears twice, most notably as Reference 21,on page 298.

It may be worth a look...?

Yes, you are right, not Yanchinin but Yanchilin. Briefly, the essence of his theory, as it explains the mechanism of gravitational attraction.

The square of the speed of light is equal to the gravitational potential with a minus sign

Planck's constant and the speed of light are related by the ratio

 

 

Thus

Therefore, the gravitational potential determines not only the speed of light, but also the value of the Planck constant. the greater the absolute value of the gravitational potential, the smaller the value of the Planck constant. This means that at a point with a higher absolute value of the gravitational potential, the quantum uncertainty value is less, and this in turn means that the probability of a particle's transition from a point with a lower gravitational potential is greater than the probability of a particle's transition from a point with a higher gravitational potential to a point with a lower absolute value of the gravitational potential.

 

Edited June 13, 2020 by SergUpstart