Paper: A causal mechanism for gravity

[rjbeery]

37 minutes ago, Strange said:

But the usual meaning of gravitational attraction is the "force of gravity" (the acceleration due to gravity, g here on Earth). In which case, there is direct relationship between the two. You can have two places with the same value of g but different time dilation. (Or the same time dilation but very different values of g.)

You're saying that there is a direct relationship between the variables, and also that they are not dependent. Please provide examples where their dependence breaks down (if you have any).

[Strange]

4 minutes ago, rjbeery said:

You're saying that there is a direct relationship between the variables, and also that they are not dependent. Please provide examples where their dependence breaks down (if you have any).

No, I’m saying there is a relationship but not a direct or necessarily simple one. I’ll work out an example...

Imagine two planets with exactly the same surface gravity but where one is 10% heavier and has a 5% larger radius. There will be a slight difference in gravitational time dilation: clocks on the larger one will run about 3 billionths of a percent(*) slower (I think I've got that the right way round). 

So gravity and time dilation are related but not directly.

(*) I really should have chosen a more extreme example, but I can't be bothered to go through it again.

[rjbeery]

4 hours ago, Strange said:

No, I’m saying there is a relationship but not a direct or necessarily simple one. I’ll work out an example...

If we take

g = GM/r² and

t₀ = t_f * sqrt(1 - (2GM/rc²))

The equations rely on the same parameters -- we can equate them. Back of the napkin shows:

g = (c²/r)(1-(t₀/t_f)²)

where t₀ is proper time between two events under the gravitational acceleration of g, and t_f is the coordinate time of those same events for a distant observer. It's interesting to note that (t₀/t_f) is simply the analog of the refraction index of the material which would cause light to behave as if it were near such a gravitational influence.

[joigus]

"Occasionally, an obsession does turn out to be something good."

Chen Ning Yang

The key word here is "occasionally."

"It was a crazy idea, I grabbed the back of a napkin and did the necessary calculations."

Murray Gell-Mann

The key words here are "necessary calculations."

[Strange]

9 hours ago, rjbeery said:

If we take

g = GM/r² and

t₀ = t_f * sqrt(1 - (2GM/rc²))

The equations rely on the same parameters -- we can equate them. Back of the napkin shows:

g = (c²/r)(1-(t₀/t_f)²)

where t₀ is proper time between two events under the gravitational acceleration of g, and t_f is the coordinate time of those same events for a distant observer. It's interesting to note that (t₀/t_f) is simply the analog of the refraction index of the material which would cause light to behave as if it were near such a gravitational influence.

That loud noise you can hear is my head hitting the table repeatedly.

I give up. Have it your own way,. You are a genius. Einstein was wrong. Everyone else is blind to the simple truth.

I think this thread has run its course.

[Markus Hanke]

19 hours ago, rjbeery said:

Honestly, that's pretty surprising -- two massive bodies passing each other at great speeds seems to be a pretty fundamental physics problem.

Just to be extra clear - the scenario can of course be treated via GR, it’s just that it’s not possible to do so via pen-and-paper methods. You would need to feed this into specialised software, and let a computer run the numbers. I do not have access to such software, so I can’t give you an outright answer to your original question. You are right, it is a pretty fundamental problem - but many fundamental problems in physics can only be solved numerically. Even in simple Newtonian gravity, if there are more than 2 gravitating bodies, the system can only be treated numerically.

It is actually not surprising to me at all that this can’t be done on paper, given that the Einstein equations are a system of 16 highly nonlinear, coupled, partial differential equations. It’s more surprising to me that it can be done if one of the two masses is negligible, giving the Aichlburg-Sexl ultraboost solutions. 

19 hours ago, rjbeery said:

Do you believe that time dilation and the so-called "gravitational attraction" (i.e. spacetime curvature) are independent variables in GR?

Spacetime curvature overall is a rank-4 tensorial quantity, the Riemann curvature tensor - it describes how geodesics deviate in any arbitrary 4-dimensional spacetime. Time dilation is only a subset of that geometrical information; essentially, you can think of time dilation as ‘curved time’, and tidal gravity as ‘curved space’. Unless you have very special, highly symmetric circumstances (as e.g. in Schwarzschild spacetime), you cannot separate these two aspects - which is why, after taking account of all the various index symmetries, there are a total of 20 functionally independent components in the Riemann tensor, and you need them all to uniquely determine all aspects of a spacetime’s geometry in the general case. Time dilation alone is not enough, i.e. you can’t replace a rank-4 object that has 20 functionally independent components with just one scalar quantity, and expect to be able to capture the same information.

So the answer is no, for the general case you cannot separate time dilation from the rest of your spacetime’s geometry in any meaningful way. 

This being said, as you introduce symmetries into your spacetime, the amount of information required to uniquely determine its geometry decreases. For Schwarzschild spacetime, you are dealing with a highly special case that is spherically symmetric, static, stationary, a vacuum, and asymptotically flat. Because it admits a time-like Killing vector field, you are able to define the notion of ‘gravitational potential’ here - the Schwarzschild geometry then simply is a family of nested surfaces (spheres) of gravitational equipotential. So for this special case, you can in fact write down a scalar field that is simply a gravitational potential with respect to some reference point (usually the center of the gravitating mass). But this is only possible because Schwarzschild spacetime is so highly symmetric - this does not generalise to more general spacetime, and most certainly not to the set of all possible spacetimes. And even then, the simple-looking form of the Schwarzschild metric is somewhat deceptive, because once you do actual calculations with it (e.g. how long it takes for a test particle to fall along a certain trajectory), things can become fairly complicated fairly quickly, since you need to integrate the relevant parts of the line element.

[MigL]

Nice explain, Markus.

Reminds me of QM, where one can take advantage of symmetry in the Hydrogen atom, in spherical polar co-ordinates to reduce the 2nd order partial differential equation and get exact answers. But as soon as asymmetries are included, like you get with multi-electron systems of Helium and higher, the equations become intractable, and must be handled by numerical methods.

with the number of EFEs the situation is probably a few orders of magnitude harder in GR.

On the 'bright side' ...

, the OP's stubbornness to abandon his simplistic idea, has allowed for a lot of these teaching/learning opportunities.
And the rest of us who choose to seriously consider the information presented by you, Mordred, and others, are 'richer' for it.

[rjbeery]

6 hours ago, Strange said:

I give up. Have it your own way,. You are a genius. Einstein was wrong. Everyone else is blind to the simple truth.

I'm not arguing against Einstein in any way, I'm trying to understand where my model would have problems generalizing. I certainly am stubborn, but only to the extent that I will keep asking questions until I understand something. And your desire to close the thread is curious - the conversation is civil, people are learning, and this is the Alternative Theories channel.

3 hours ago, Markus Hanke said:

Spacetime curvature overall is a rank-4 tensorial quantity, the Riemann curvature tensor - it describes how geodesics deviate in any arbitrary 4-dimensional spacetime. Time dilation is only a subset of that geometrical information; essentially, you can think of time dilation as ‘curved time’, and tidal gravity as ‘curved space’.

You give good explanations, but your answers don't bring clarity to me. Gravitational acceleration is determined by G, M, c, and r. Time dilation is determined by the same parameters. As written earlier, we can equate the variables to get:

g = (c²/r)(1-(t₀/t_f)²)

What's wrong with this equation? If time dilation and "gravitational acceleration" are independent variables perhaps you could describe an extreme scenario, in layman's terms, where "gravitational acceleration" exists but time dilation does not.

 

 

[swansont]

50 minutes ago, rjbeery said:

I'm not arguing against Einstein in any way, I'm trying to understand where my model would have problems generalizing. I certainly am stubborn, but only to the extent that I will keep asking questions until I understand something. And your desire to close the thread is curious - the conversation is civil, people are learning, and this is the Alternative Theories channel.

Gravity isn’t the only effect of GR. How does an “index” give rise to e.g. frame dragging? Or other effects of GR?

[rjbeery]

6 minutes ago, swansont said:

Gravity isn’t the only effect of GR. How does an “index” give rise to e.g. frame dragging? Or other effects of GR?

Exactly. Folks seem to think that I'm trying to replace GR or, bizarrely, claim that Einstein was wrong about something. Please re-read the OP. I'm proposing a causal mechanism for gravity.

[swansont]

13 minutes ago, rjbeery said:

Exactly. Folks seem to think that I'm trying to replace GR or, bizarrely, claim that Einstein was wrong about something. Please re-read the OP. I'm proposing a causal mechanism for gravity.

Can/will you answer my question?

And make no mistake, if you are proposing this mechanism, you are replacing GR. 

[rjbeery]

3 minutes ago, swansont said:

Can/will you answer my question?

And make no mistake, if you are proposing this mechanism, you are replacing GR.

No I can't answer your question; I'd have to think about it but I'm currently thinking about perihelion precession. I don't aspire to replace GR, but it's pretty simple -- if all of GR can be described in terms of spacetime curvature, and we can equate spacetime curvature to time dilation, then we can describe all of GR with time dilation.

[Mordred]

19 hours ago, rjbeery said:

 

t₀ = t_f * sqrt(1 - (2GM/rc²))

 

g = (c²/r)(1-(t₀/t_f)²)

 

These equations are invalid. If you perform a dimensional analysis you will find the LHS and RHS do not match.

 

[Strange]

17 minutes ago, rjbeery said:

I don't aspire to replace GR, but it's pretty simple -- if all of GR can be described in terms of spacetime curvature, and we can equate spacetime curvature to time dilation, then we can describe all of GR with time dilation.

You cannot equate spacetime curvature with time dilation. For all the reasons that have been explained to you repeatedly and in great detail by many people over many years.

As you desire to replace the Einstein Field Equations with some simplistic model based on a refractive aether, you very obviously do want to replace GR.

"I don't want to replace GR, I just want it to be completely different. And give the wrong results."

[rjbeery]

17 minutes ago, Mordred said:

These equations are invalid. If you perform a dimensional analysis you will find the LHS and RHS do not match.

 

Both sides are L / t^2.

11 minutes ago, Strange said:

You cannot equate spacetime curvature with time dilation. For all the reasons that have been explained to you repeatedly and in great detail by many people over many years.

I think it's great that you understand why, and I appreciate your patience while I try to get there myself.

[Mordred]

No how are you cancelling for example Kg in the first equation. You have no kg on the LHS. That's just one of the terms.

Follow the procedures as per

https://www.google.com/url?sa=t&source=web&rct=j&url=http://web.mit.edu/2.25/www/pdf/DA_unified.pdf&ved=2ahUKEwi6ybXastfpAhWTsJ4KHVrVCP8QFjAAegQIChAB&usg=AOvVaw3hTYBubBOwEQX7596gEKFR

Easiest to convert to SI units.

Edited May 28, 2020 by Mordred

[rjbeery]

2 hours ago, Mordred said:

No how are you cancelling for example Kg in the first equation. You have no kg on the LHS. That's just one of the terms.

The first equation is for gravitational time dilation. GM/c^2 is the Schwarzschild radius of a mass, and the additional radius term in the denominator makes the entire square root a dimensionless scalar.

[Mordred]

Sigh no the SI units for G is [math] m^3\cdot kg^{-1}\cdot s^{-2}[/math]

The SI unit for mass is kg. Radius obviously has units of length

Those threeunits are on the RHS of the equal sign in formula one. 

On the left hand side you have the SI unit for time. Guess what it's seconds.( A single unit)

So how can the left hand as side equal the right hand side when the units do not match regardless of value ? I have kg on the right hand side and units of length 

Yet on the left hand side I only have units of time. The right hand side does not cancel our the kg of meter units to leave only seconds.

Please study the link I posted on dimensional analysis.

Edited May 29, 2020 by Mordred

[rjbeery]

50 minutes ago, Mordred said:

Sigh no the SI units for G is [math] m^3\cdot kg^{-1}\cdot s^{-2}[math]

The SI unit for mass is kg.

Those two units are on the RHS of the equal sign in formula one. 

On the left hand side you have the SI unit for time. Guess what it's seconds.

So how can the left hand as side equal the right hand side when the units do not match regardless of value ? I have kg on the right hand side and units of length 

Yet on the left hand side I only have units of time. The right hand side does not cancel our the kg of meter units to leave only seconds.

Please study the link I posted on dimensional analysis.

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.

Edited May 29, 2020 by rjbeery

[Mordred]

Sigh no have you never done dimensional analysis on an equation ? 

Do you understand what I mean when I state the word " unit"

On the left hand side your unit is seconds in SI units.

How many units are on the right hand side of the equal sign in the first equation ?

This is a basic mathematics skill to ensure the units on the left hand or right side of an equal sign match up in the same equation.

Let's put it bluntly you cannot claim 

Seconds= kg times meters times seconds

as an example your first equation does something highly similar .

You have seconds on the left hand side but on the right hand side you have meters and kg along with seconds.

Invalid

The first equation is fine little g is equivalent to force which has SI units . Kg time mass/seconds^2 Those units are on the right hand side of the equal sign. Please identify them.

[math] F=\frac{GM}{r^2}[/math]

Edited May 29, 2020 by Mordred

[rjbeery]

On 5/18/2020 at 12:00 PM, Mordred said:

(Lol a little side note I had the opportunity to prove a peer reviewed article wrong on applying Snell's law to describe gravitational lensing to a PH.D in astrophysics. He pulled his article off Arxiv)

Mordred...you're peer reviewing PhD astrophysics articles and you've never seen or dealt with the gravitational time dilation equation?

Look at the numerator of the fraction under the square root: 2GM. This has units of m^3 * kg^-1 * s^-2 * kg. This simplifies to m^3 * s^-2

Look at the denominator of the fraction under the square root: rc^2. This has units of m * (m/s)^2. This simplifies to m^3 * s^-2

They cancel. It's a dimensionless scalar, as I've said multiple times. It's OK to miss a mass term in the numerator, or whatever you seem to be doing, but I don't understand how you aren't reading the words that I'm typing, explaining what the equation is, telling you exactly what you're looking at. If you don't like the equation, your problem is not with me but with the entire astrophysics community.

[Mordred]

Lol honestly  ? It's not ok to ignore units in an equation. They are a fundamental part of any equation. For example time is not dimensionless which your LHS  of your equation. Neither mass nor radius. So go ahead try to prove a cancellation of your equation to end up with units on the RHS to equal the unit of seconds on the LHS. Impress me with your math.

It literally makes no sense to state time is a dimensionless unit. Time has SI units of seconds end of discussion.

However all that aside the Schwartzchild metric is only one class of solutions. As others has told you. 

The most common class of solutions is the weak field approximations. Which applies around the average star or planet.

The Schwartzchild only applies to a static non rotating black hole. If you have rotation you need the Kerr metric. However in this case you have four event horizons and nearly BH observed in nature is rotating.

Quite frankly this is getting pointless.

 

Edited May 29, 2020 by Mordred

[rjbeery]

51 minutes ago, Mordred said:

Lol honestly  ? It's not ok to ignore units in an equation.

I'm ignoring nothing. There are time units on the LHS (t₀), and time units on the RHS (t_f). The remaining units under the square root all cancel out. I literally did the math for you.

Numerator units: GM = m^3/s^2

Denominator units: rc^2 = m^3/s^2

They are the same units. Meters cubed over seconds squared. What are you missing?

[Mordred]

Nevermind figured it out. I will stand corrected on that. Missed a - sign on one of the SI unit powers.

(14 hour work day so stupid mistake)

Edited May 29, 2020 by Mordred

[Markus Hanke]

12 hours ago, rjbeery said:

Gravitational acceleration is determined by G, M, c, and r.

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.

12 hours ago, rjbeery said:

If time dilation and "gravitational acceleration" are independent variables perhaps you could describe an extreme scenario, in layman's terms, where "gravitational acceleration" exists but time dilation does not.

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.