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?

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.

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.

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.

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.

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.

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.

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.

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.

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).

1 hour ago, Markus Hanke said:

What you are describing here is a relativistic 2-body problem, for which there is no closed analytical solution to the field equations; you can only treat this case via numerical methods.

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

Let me ask you a question, Markus. Do you believe that time dilation and the so-called "gravitational attraction" (i.e. spacetime curvature) are independent variables in GR?

2 hours ago, MigL said:

If you consider the TWO masses as parts of the system, then the energy of the system is increased, and so the contribution to the energy density of the system is increased.
The system, as a whole, will have a larger gravitational potential, but I don't think the 'attraction' between the individual members of the system will change.
( I could be wrong, but if Markus says the calculations are not trivial, don't expect me to do them )

Yeah I'm not asking for calculations, just a qualitative description. It's a pretty simple question: does GR predict that momentum energy of a mass increases gravitational attraction towards that mass?

40 minutes ago, MigL said:

Seemed simple enough to follow...

I'm glad you thought so. Maybe you can answer my question:

If massive objects, A and B, are moving in opposite directions at a substantial speed and pass near each other, will the gravitational attraction between them be more than what is calculated by their rest masses?

4 hours ago, Markus Hanke said:

If there is any kind of momentum present in a gravitational source, then it will contribute to one or both of the aforementioned quantities, but the way it does so is not always trivial; in fact, finding the energy-momentum tensor for a given distribution of matter-energy can be a very difficult task, particularly if the distribution is not static or stationary.

It's confusing to me that you claim momentum isn't a source of gravity, but that it "contributes to energy flux" which is a source of gravity. If massive objects, A and B, are moving in opposite directions at a substantial speed and pass near each other, will the gravitational attraction between them be more than what is calculated by their rest masses?

5 hours ago, swansont said:

Can you transform into a frame where angular momentum goes to zero, the way you can with linear momentum?

This is now a moot point. GR predicts that linear velocity is in fact a source of gravity.

3 hours ago, Markus Hanke said:

Gravitation in GR is geodesic deviation, and thus a geometric property of spacetime; all free-falling test particles experience gravity (they must follow geodesics in spacetime), regardless of whether they have mass or not, and regardless of their internal composition or size.
Remember also that within the Standard Model, all fundamental particles are point-like, i.e. any mass distribution is simply a collection of point particles.

Yeah my "point particle" objection is philosophical. To me, it's obvious that a point particle is unphysical but that doesn't mean it isn't useful in modeling.

3 hours ago, Markus Hanke said:

Relative motion is not a source of gravity; the source term in the field equations is the stress-energy-momentum tensor, which, as being a tensor, is covariant under Lorentz transformations. If that were not so, the theory would not be internally self-consistent.

This isn't the first time, or even the first forum, where this has been discussed. The covariance of the tensor has also been mentioned in the past, and I understand the thought process -- "if the tensor is zero in one frame then it's zero in all frames." If objects A and B are in relative motion, where does the energy "between" A and B exist? I can't answer this. This enters the realm of philosophy, because we suspect that it exists...but neither at A nor B.

Why would angular momentum cause additional gravity but not linear momentum? Why would photons be affected by other photons traveling in opposite directions...but the same isn't true for massive particles? Those were my initial thoughts, but the fact is that GR does claim that kinetic energy increases gravitational attraction. Not easy to find discussion on the topic, but it does exist.

 https://cds.cern.ch/record/398687/files/9909014.pdf

Quote

According to the general theory of relativity, kinetic energy contributes to gravitational mass. Surprisingly, the observational evidence for this prediction does not seem to be discussed in the literature.

Maybe it would be constructive to explicitly identify topics. I think I've fielded a few objections, and the latest one is whether or not gravitational attraction and time dilation are dependent variables. I don't believe we've produced a counter-example, yet.

19 minutes ago, swansont said:

Are you arguing philosophy or physics? Last I checked, gravity was in the realm if science. IOW, what evidence do you have that e.g.an electron doesn’t experience gravity?

I didn't know we were arguing anything. If my model can't withstand scrutiny then I'll adjust or abandon it. And I do believe that an electron experiences gravity, I just don't believe that it is a point particle (i.e. "EM mass") -- that fact is discussed in the OP, with references, if you're truly interested.

On 5/23/2020 at 4:16 AM, Markus Hanke said:

I am honestly not sure if I follow your thought process correctly, since such a notion as “time dilation gradient” does not make much sense to me. But nonetheless, the aforementioned case of an orbit around a rotating mass should be an example. Another scenario that immediately comes to mind would be two parallel beams of light (or any other pp-wave spacetime, for that matter) - if you fire two parallel beams of light in the same direction, there will be no gravitational attraction between them, even though they carry energy. But if you fire the same two beams of light so that they are initially parallel, but travel in opposite directions (i.e. you let emitter and receiver trade places for one of the beams), then they will indeed experience a gravitational attraction.

I'm a visual thinker, so when I say "time dilation gradient" I'm describing a picture which may be using poorly chosen mathematical language. Philosophically, to me, a point mass cannot be affected by gravitation; only masses of non-zero volume can. The volume of a given mass can be viewed as a 3-dimensional time dilation field. In this model, the mass will gravitate in the direction of highest dilation. Two masses moving in the same direction would not detect or consider the other to be experiencing time dilation (beyond the negligible dilation caused by their respective masses). However, if they are moving very quickly in opposite directions, they each calculate (and observe) that the other is experiencing a large amount of time dilation, and there is in fact additional gravitational attraction between the masses.

Producing scenarios where dilation clearly exists but gravitational attraction does not will not suffice. In the dust cloud, and inside Newton's shell, all particles are in uniform time dilation, and therefore experience no gravity. The distant observer is obviously experiencing a different rate of time passage and will, in fact, be drawn toward the cloud or shell, subject to his distance from them. However, that attraction isn't technically due to the time dilation differential between the masses in the shell (for example) and his watch in this model, but rather between the areas of the field comprising his own volume facing the shell and the areas of the field of his own mass further away from the shell. The gradient of the volume.

On 5/23/2020 at 4:16 AM, Markus Hanke said:

However, if we allow the manifold to not be flat, then the situation changes; following the standard prescription for this (refer to any textbook on differential geometry), we must now replace ordinary with covariant derivatives, which do not in general commute. The degree to which they fail to commute is (I use double bars “||” to denote covariant derivatives):

Like I said, I'm a visual thinker. What's the "gradient" of the center of a saddle point? Well...it's zero, or it depends on the direction that you're wanting to move. I think this is saying the same thing that you're saying above. Your solution (and GR's solution) to this is to say that a rank-2 tensor is required for all points; my method for this would be to demand the volume in question be established a priori. Once you know the volume comprising a mass you can determine the direction of gravitational attraction.

On 5/23/2020 at 10:16 AM, studiot said:

I don't know if anyone has considered time dilation at lagrange points and lines where there are at least two such potentials.

Thank-you for the book reference, Studiot, that looks great. After talking things out, I'm starting to wonder if we're talking about 2 sides of the same coin. In order to determine the direction of gravitational attraction for a given point, we need a second point of reference (i.e. a direction) to determine the gradient. I think, mathematically, this is the same thing as demanding a rank-2 tensor a for point if we want to calculate gravity in arbitrary directions.

I really appreciate the back-and-forth on this.

8 minutes ago, swansont said:

That's not enough. This is physics; we quantify things. Is the amount of dilation from the momentum equal to the amount you'd get from gravitation?

(AFAICT the answer is trivially no, BTW)

If you have a trivial counter-example, please share it. If you don't, then how do you draw the above conclusion?

9 hours ago, Markus Hanke said:

Well, you can consider a hollow sphere made from a thin shell of matter. The exterior of the shell looks like any other spherically symmetric body, so it is described by the usual Schwarzschild metric. The hollow interior of the shell however is a different story - no tidal gravity is detected therein, meaning a test particle placed anywhere into the interior remains at rest.

Ahh yes, I'm familiar with the shell theorem. I misspoke when I said "find a scenario where gravity "exists" but time dilation does not (OR time dilation exists but gravity does not)" because I've already mentioned that it's the gradient that determines gravitational attraction (in this model). Maybe a better way to say it is that I need to "find a scenario where the time dilation gradient and gravitational attraction differ"?

10 hours ago, Markus Hanke said:

A real-world example of a case where you have tidal gravity in the spatial part of the metric, but no time dilation, would be a region of spacetime that is uniformly filled with dust, in a way that ensures homogeneity and isotropy. The FLRW metric - on which our current understanding of cosmology, the Lambda-CDM model, is based - is an example of this. In this metric the temporal part is constant, but the spatial part is not.

I don't understand this description but I'll look into it. I can't picture in my mind's eye how a cloud of dust would create tidal gravity but no time dilation. A volume of dust has mass, and mass causes time dilation.

10 hours ago, Markus Hanke said:

I think you are beginning to see now that the dynamics of spacetime are very rich and varied - they can’t be captured by just assigning some scalar field. I actually seem to remember having once seen a formal proof that a rank-2 tensor is the lowest rank object required to capture all dynamics of GR, I just can’t remember where I have seen it. If I come across it, I will post it here.

I would be very interested in seeing this. How certain are we that there are no redundancies in GR? As an off-the-cuff example, we know of the mass-energy equivalence but we still account for mass separately in the equations.

In the end, obviously, no amount of abstract discussion is going to sway any opinions. If and when I discover more analytic proof I'll share it here.

9 minutes ago, MigL said:

Well, there is time dilation due to relative motion...

1 minute ago, Ghideon said:

Does the time dilation for observers in relative motion in a flat Minkowski spacetime count as an example?

It's a good thought, but I believe in this very thread we've had links showing that linear momentum is a source of gravitational attraction.

Fair point, *I* will work on an analytic proof. In the mean time, if Markus can think of a scenario where gravity and time dilation are independent of one another in GR I would be very interested to learn about it.

OK I've given this more thought. I think until we can come up with an analytic proof (or disproof) we are left trying to find a scenario where gravity "exists" but time dilation does not (OR time dilation exists but gravity does not). Frame-dragging around a rotating object does cause both gravity and time dilation effects depending on direction of orbit.

6 hours ago, Markus Hanke said:

How would you capture all this by assigning a single value to point P, as you seem to want to do with your “time dilation field” idea? 

Your example is well described, thank-you. The proper time of any object would still depend on its path through the field, so the point P wouldn't be expected to hold all relevant information. Regardless, if clock A went East and clock B went West they would still move through equivalent scalar fields of equal length. I'll have to think about it. I suspect it's related to the gradient of the field.

11 minutes ago, joigus said:

Don't put words in my keyboard. The only one who believes in remote dilation as a frame-independent phenomenon here is you! That remote dilation is only in your mind. You don't even understand that, which says all about you as a "thinker." The fact of whether something suffers frame-dependent dilation or not does involve having things other than photons in it. In fact, in order to write down the geodesic equation for photons you must do an affine transformation, because their proper time is identically zero, so no common-sense clocking will help you describe their histories. But what am I telling you; you know next to nothing about relativity, that not being the worst. The worst being that you don't bother to examine your own assumptions, or anybody's criticism. Can you imagine Einstein telling Hilbert "please consider my silly mistake as a valid assumption"? Einstein quickly re-wrote his paper. Learnt much from Hilbert, and went on to publish one of the most important papers in the history of physics.

I will pop up every now and then to see what experts and other serious thinkers have to say. Your post is only valuable in that sense. The only trouble is I will have to check for you twisting everything I or anybody else has said, just because you don't understand the first thing about relativity, you don't read what you write, let alone others, and you stubbornly stick to a bunch of silly pseudo-scientific propositions to no end.

If I've mischaracterized your position on this then I apologize. I guess I don't know what your position is, at all.

18 minutes ago, Strange said:

I shall suggest that this thread is closed.

18 minutes ago, MigL said:

And there is no point keeping this thread open if we aren't welcome to discuss its merits.

I'm not opposed to discussing merits. What I'm saying is that, once both sides understand each other and acknowledge an impasse, further discussion is a waste of time. Joigus believes that cavity interaction explains remote dilation. I explained why I disagree. MigL believes that time dilation can be explained by adjusting both frequency and wavelength such that c remains constant, globally. I explained why I disagree. Strange demands things and then is unusually dismissive when they are provided. I explained why that discourages me from doing it again. There is literally no benefit to me to attempt to change minds here; I'm here for criticisms. Mordred demands that spacetime would disperse light if it had a refractive index, for example. That's a valid point, and I dealt with it to my satisfaction.

To be honest, someone from another forum asked if I knew Markus Hanke from here. I did not know him, but he is why I started a couple of threads here, and his responses so far have been the most interesting to me.

Anyway, there is still an active discussion going on so I think closing the thread is premature.