More on gravitational time dilation and escape velocity.

[Shaw]

First, thanks for all the replies to the first post. I was able to predict this result (an engineer did the proof) using an analogy for gravitation I worked out to replace the standard marble rolling on a rubber sheet analogy used to show the effect of curved space time, which is useless on a number of levels. The analogy is extremely effective and highly predictive, so is there any advice as to how I would go about getting the predictions checked?

 

[pellman]

You'll need to link to the other post or provide more details. Not enough info here.

 

[Shaw]

I'm rather loathe to give more details because its part of my essay on mass, which I would like to present as a whole in some way. What I can say is that this new analogy for mass and gravitational attraction can be used to explain 'Dark Energy.' Dark Matter makes sense. There's other mass in the universe, invisible to us, that affects the behavior of the stars and galaxies, but Dark Energy is bizarre. The stars and galaxies on the outer reaches of the universe are accelerating away from the center of the big bang at a greater rate than the ones closer in. The universe is mysterious, not crazy. There is no Dark Energy, it's just an illusion. Physicists are sampling the velocity of the objects at various distances, so notice we would get the same result if the outer, faster objects were just decelerating more slowly due to that velocity. My analogy requires Newtonian gravitational calculations to have an added variable that would cause this. For someone with skills in orbital mechanics, there's a relatively easy way to check on this. This variable will affect the orbit of Mercury, so it's a matter of seeing if the result agrees with GR.

 

[PeterDonis]

Dark Energy is bizarre. The stars and galaxies on the outer reaches of the universe are accelerating away from the center of the big bang at a greater rate than the ones closer in.

No, that's not what's happening.

First, there is no "center of the big bang". The big bang did not happen at some particular place in our universe. If it happened in any "place", it happened everywhere in our universe. We see differences in the recession velocities of galaxies from us, as a function of distance, because the distance affects how long it takes light to get to us from those galaxies (see below), not because we occupy any special place in the universe. An observer in some other galaxy billions of light years from us would see recession velocities of galaxies from *him* varying with distance from *him*.

Second, the "acceleration" caused (according to our best current theory) by dark energy is a change in the way the entire universe is expanding. Up until a few billion years ago, the expansion was slowing down; now it's speeding up. We observe this as an increase in the expansion rate of galaxies *closer* to us, relative to galaxies further away (i.e., the opposite of what you claim)--the increase being relative to what we would have seen in the galaxies closer to us if the expansion had continued to slow down. We see it in the closer galaxies because the light we're seeing from them now was emitted more recently, during the accelerating phase of the universe's expansion; the light we're seeing now from further galaxies was emitted a longer time ago, when the expansion was still slowing down.

There is no Dark Energy, it's just an illusion. Physicists are sampling the velocity of the objects at various distances, so notice we would get the same result if the outer, faster objects were just decelerating more slowly due to that velocity. My analogy requires Newtonian gravitational calculations to have an added variable that would cause this. For someone with skills in orbital mechanics, there's a relatively easy way to check on this. This variable will affect the orbit of Mercury, so it's a matter of seeing if the result agrees with GR.

This looks like your personal speculation, and this forum is not for discussing personal speculations.

 

[Shaw]

Thanks for this. I appreciate the time you took to explain this to me. Shows what kind of trouble you can get into when you're miles out of your depth. However, I'm still stuck with an analogy that appears to be more useful than the rubber sheet analogy, and it did predict correctly (the sheet predicts nothing), that gravitational time dilation would equal the time dilation at the escape velocity in deep space. GR obviously gives the same answer, but it did not make it a requirement prior to the calculations. This prediction could be just a fluke, but it doesn't seem likely. Since it also predicts some kind of affect on the orbit of Mercury (I should not have tried to extrapolate to Dark Energy), I 'm very curious to know what really happens.

 

[PeterDonis]

gravitational time dilation would equal the time dilation at the escape velocity in deep space.

As was discussed in the previous thread, as far as GR is concerned this is just a coincidence. That is, the fact that $v_{escape} = \sqrt{2GM / r}$, so that the time dilation factor $\sqrt{1 - 2GM / c^2 r} = \sqrt{1 - v_{escape}^2 / c^2}$, has no deeper meaning in GR that I'm aware of. If you think there ought to be some deeper meaning, rather than looking for some analogy to "explain" why, I would suggest looking for some physical reason why time dilation due to rapid motion should be connected to time dilation from being in a gravity well. (I'm not aware of any such reason.)

 

[PAllen]

Also, note that gravitational time dilation is only defined in special situations in GR (stationary spacetime, or region that can be approximately treated as such). In more general situations it cannot even be defined. Meanwhile, reciprocal time dilation between nearby observers in relative motion is universal. This underscores the point Peter made that your observation is coincidence rather than a general feature of either GR or our universe.

 

[Shaw]

Thanks for your reply. I do indeed have a reason to connect the two; it's central to the analogy.
The logical development of the analogy leads to the conclusion that mass, time, gravity and velocity are intimately entwined, and mass should be referred to as masstime to be accurate. It was after I was able to see this, that I worked out that the time dilation on the surface of a planet should equal the time dilation at its escape velocity. It was a guess, but it had to be right, or my entire scheme would've been rubbish.

I know the rules. You have to show proof, and in physics that proof must be mathematical. The escape velocity conclusion was a nice start, but obviously not nearly good enough. The only way left to see if my ideas are correct, is to apply them to the behavior of Mercury as it goes around the Sun. If this gives the same result as GR, then I've got something to talk about. I have no idea how I'll get a physicist to do that calculation for me, for reasons that are all too obvious.

 

[PeterDonis]

I do indeed have a reason to connect the two; it's central to the analogy.

A *physical* reason? If so, it should be something that has some force independently of the theory you're constructing based on this analogy.

I know the rules. You have to show proof, and in physics that proof must be mathematical.

No, you have to show predictions that match the results of experiments. Math is the best way we know of to demonstrate how your theory does that, but the predictions are more important than the math.

But you have to match *all* the experiments. If you want your theory to compete with GR, you have to be able to match experimental predictions for *all* the planets, not just Mercury, plus all the other measurements of the behavior of gravity--rocks falling, satellites orbiting Earth, GPS clocks, light bending as it goes past the Sun, time delay of radar signals passing the Sun, binary pulsar orbits, the expansion of the universe...

 

[Shaw]

Thanks for this. It was never my intention to compete with GR, but if Mercury's orbit is affected by what the analogy suggests, to the same degree as GR, that would be something - never been done before as far as I know. This 'scheme' does make experimental predictions, so if the orbit calculations proved out, the experiments might be of interest. I guess I've said all I can on the matter. I've appreciated the time you've taken with my submissions.

 

[PeterDonis]

It was never my intention to compete with GR

Then I'm not sure what your objective is. Is it to "explain" phenomena associated with gravity? Or just to find a handy visualization tool? The rubber sheet analogy doesn't explain anything; it's just a visualization tool that helps for some people (and creates confusion for many others, which is why many people, including me, think it does more harm than good). There's certainly nothing wrong with looking for better visualization tools.

But if you really want to explain the phenomena associated with gravity, an analogy won't cut it. You have to have a theory, and the theory has to cover *all* the phenomena. An analogy that gives the right answer for some phenomena, but the wrong answer (or no answer) for others, can't be used to explain anything.

 

[Shaw]

Well, thanks again for more input. I guess ultimately my goal was to represent curved space time in a simpler way, so the results would not contradict GR, to the degree I was able to examine them. The mathematics of GR are brutally formidable, very difficult even for many physicists. I've read that mathematical solutions can be likened to climbing a mountain. There can be many routes to the top, but instead of slogging up the slope, the ideal is to get in a mathematical helicopter, and just fly straight to the top. No one argues that GR is incorrect, but that doesn't mean there isn't a simpler mathematical route to the same answers.

My analogy is certainly better than the rubber sheet analogy (its prediction alone trumps the sheet), and I would be pleased to make that small contribution, but to accept the analogy, one has to accept its consequences, and they're, at least, interesting, so I want to explore them if I can. Let me know if you have any advice as to how I might be able to get a physicist to do an orbital calculation. Paying a consultant for the privilege would be fine.

One last thing, the analogy defines the maximum possible velocity for mass as when time goes to zero. I can see that it would have to be the speed of light, so if you show that the time dilation on the surface of the Earth is equal to the time dilation at the Earth's escape velocity, do we then have enough information to calculate the speed when time goes to zero. I assume not.

 

[WannabeNewton]

The mathematics of GR is actually very simple when compared to the mathematics of other advanced physical theories. QFT, rigorous QM, and rigorous statistical mechanics make the mathematics of GR look like a joke. You're going to have a very hard time coming up with a correct mathematical description of GR that is simpler than the one offered by semi-Riemannian geometry. The union of gravitation with semi-Riemannian geometry is one of the most elegant things about GR.

 

[PeterDonis]

Let me know if you have any advice as to how I might be able to get a physicist to do an orbital calculation.

I have no experience in this area so I can't really give any advice. My only comment is that I think you would first have to get a physicist interested in your analogy at all. Either that or figure out how to develop the mathematical machinery of your theory yourself, at least enough to calculate Mercury's orbit in it. (Which invites the obvious comment that if you can't do this, does your theory really provide a mathematical framework that's any simpler than GR?)

the time dilation on the surface of the Earth is equal to the time dilation at the Earth's escape velocity

You realize, don't you, that this isn't just true at the surface of the Earth--it's true at *any* radius in a spherically symmetric, asymptotically flat spacetime. Look at the formula I wrote earlier in this thread: the $r$ in it can be *any* radius at all; there's nothing in the argument I gave that restricts it to the Earth's surface radius only.

 

[Shaw]

Thanks again. I think it's clear that I can't develop the mathematical machinery myself, simple though it may be from your point of view, or I wouldn't be posting on the forum like this; so the only alternative is to get a physicist interested in the analogy. I'll try my best. I understood your point in the second comment; the Earth was just an example. If I ever get interesting results I'll post them on the forum.

 

[Mentz114]

It seems it is possible to derive GR from horizons. T. Padmanabhan has written a paper Gravity: the inside story where this is explained. The abstract is

It is well known that one could determine the kinematics of gravity by
using the Principle of Equivalence and local inertial frames. I describe how the dynamics
of gravity can be similarly understood by suitable thought experiments in a local
Rindler frame. This approach puts in proper context several unexplained features of
gravity and describes the dynamics of spacetime in a broader setting than in Einstein’s
theory.

The full reference is
Gen Relativ Gravit (2008) 40:2031–2036
DOI 10.1007/s10714-008-0669-6

but there is a copy in the arXiv.

 

[Shaw]

Thanks for this. I'll give it a try, but I fear it will be too complicated for me. He does mention the Principle of Equivalence. Consider that if we do a free fall experiment on Earth, the Earth's velocity is irrelevant. We will always get the same result. But at higher velocities, clocks on Earth will slow down. If the free fall rate doesn't slow down with it, we will see objects fall faster.

 

[PAllen]

It seems it is possible to derive GR from horizons. T. Padmanabhan has written a paper Gravity: the inside story where this is explained. The abstract is



The full reference is
Gen Relativ Gravit (2008) 40:2031–2036
DOI 10.1007/s10714-008-0669-6

but there is a copy in the arXiv.

I can't find it in the arxiv, but here is a link:

http://www.gravityresearchfoundation.org/pdf/awarded/2008/Padmanabhan_2008.pdf

On a quick read, I don't think it says much about the issues under discussion in this thread. To wit: For SC geometry, is there some deeper meaning to the equality of time dilation factor of a static clock observed from infinity, and time dilation factor in an inertial frame of clock moving at the escape velocity corresponding to said static observer. The majority view expressed here is: probably not, because this fact is true for exactly one ideal, unrealistic solution in GR (perfect spherical symmetry, no rotation of body; only one body in isolation. Change any of these, the idea fails).

 

[A.T.]

The majority view expressed here is: probably not, because this fact is true for exactly one ideal, unrealistic solution in GR (perfect spherical symmetry, no rotation of body; only one body in isolation. Change any of these, the idea fails).

The idea fails, because escape velocity cannot be defined, right? Or is there a case where escape velocity can be defined, but the time dilations don't match?

 

[WannabeNewton]

Well one cannot define gravitational time dilation for arbitrary space-times as it only makes sense in stationary space-times.

 

[PAllen]

The idea fails, because escape velocity cannot be defined, right? Or is there a case where escape velocity can be defined, but the time dilations don't match?

It would be interesting to check for the next simplest case - the Kerr metric. I started to check this, but got bogged down a bit in the calculation and don't have time to complete it. My 'intuition' says they would not match, but don't put any stock in this unless a calculation is displayed.