rjbeery

I'm ignoring nothing. There are time units on the LHS (t0), and time units on the RHS (tf). 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...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.

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.

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.

Both sides are L / t^2. I think it's great that you understand why, and I appreciate your patience while I try to get there myself.

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.

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.

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. 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/tf)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.

If we take g = GM/r2 and t0 = tf * 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/tf)2) where t0 is proper time between two events under the gravitational acceleration of g, and tf is the coordinate time of those same events for a distant observer. It's interesting to note that (t0/tf) 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.

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).

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?

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?

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?

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?

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

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. 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 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. 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.

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. 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. 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.

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

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"? 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. 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.

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.

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.

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

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.