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nikko lyng
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Im curious what is it about space-time or Einsteins field equations which explains Mercurys precession correct while Newton's formula doesn't? So exactly what difference causes GR to explain it that Newton could not?
nikko lyng said:Im curious what is it about space-time or Einsteins field equations which explains Mercurys precession correct while Newton's formula doesn't?
The extra terms (compared with Newtonian theory) appear in the solution, which in this case is based on the Schwarzschild solution for a static central mass.nikko lyng said:Thanks, where in the field equations can I find this extra term?
Jonathan Scott said:The extra terms (compared with Newtonian theory) appear in the solution, which in this case is based on the Schwarzschild solution for a static central mass.
If you have access to Misner, Thorne and Wheeler "Gravitation", section 40.5 gives the perihelion shift to post-Newtonian accuracy in terms of a more generalised "PPN" (parameterised post-Newtonian) metric, and then when the specific parameter values are plugged in for General Relativity, the result matches that observed for Mercury.
The overall effect for a more general theory is ##(2 - \beta + 2\gamma)/3## times the observed result for Mercury. For GR, ##\beta## and ##\gamma## are both equal to 1. (For Newtonian theory, ##\beta## is 0 and ##\gamma## is effectively -1, from the assumption that coordinate ##c## is constant, so there is no perihelion precession).
The ##\gamma## parameter describes the curvature of space. The ##\beta## parameter relates to the second-order term in the time dilation, i.e. the value of ##\beta## in the following formula for the gravitational time factor in isotropic coordinates:
$$\sqrt{1 - 2\frac{GM}{rc^2} + 2 \beta \left ( \frac{GM}{rc^2} \right ) ^2}$$
[Edited to correct typos and add brackets for clarity]
nikko lyng said:I suppose all this information came from Einstein assuming that the total momentum and its direction which defines mass equals to how coordinates of space relates to coordinates of time beyond the mass in itself?
nikko lyng said:So this curvature can be interpreted as what coordinates of space relates to what coordinates of time indicating that it could be possible to take new perspectives in order to model the theory with a different ontology than "space-time" or time as a dimension and in a way which is more compatible with quantum mechanics and the rest of physics?
PeterDonis said:I'm not sure what you mean by this, but in general the properties of a given spacetime, i.e., a given solution of the Einstein Field Equation (which is what we are talking about when we talk about how to apply GR to calculating planetary orbits--we are using the Schwarzschild solution of the EFE), are not "assumed", they are calculated from the solution.
Any more fundamental theory, even if it had a different "ontology" underneath (such as string theory, or loop quantum gravity, or whatever), would still have to have GR emerge from it in the appropriate limit; otherwise such a more fundamental theory could not explain why GR is so successful within its domain of validity. So I would not expect a more fundamental theory to involve "new perspectives" on solutions to problems like planetary motion, which are well within GR's proven domain of validity. Certainly neither of the ones I mentioned (string theory and LQG) do that; they explain planetary motion by having GR emerge from them in the appropriate limit, and within that domain, GR is not changed at all.
nikko lyng said:would time as a dimension be a necessity
nikko lyng said:could it be substituted by "how coordinates of space relates to coordinates of time" where time is not a dimension?
nikko lyng said:If you are bored enough you can check my fundamental attempt of explaining physics in terms of properties of consciousness.
PeterDonis said:Spacetime as a 4-dimensional manifold would be a necessity. Whether you call the fourth dimension "time" is a matter of words, not physics.
If this is just an alternate way of choosing coordinates in 4-dimensional spacetime, then yes. (There are plenty of cases of coordinate charts with no timelike coordinate.) If it's a way of trying to get by with only 3 dimensions instead of 4, then no.
Off topic for this thread. Also quite possibly off topic for PF in general, since PF is not intended for discussion of speculative theories or for discussion of philosophy.
nikko lyng said:maybe one could assume that there are 4 dimensions but that the fourth isn't time?
nikko lyng said:a 4th dimension implies that it has similar properties to the other three.
nikko lyng said:Are you sure it is not possible that something which is still different could appear to have the properties of a 4th dimension?
PeterDonis said:What would this mean? Remember that, as I said above, it's perfectly possible to construct coordinate charts on 4-D spacetime in which none of the coordinates are timelike. But that doesn't mean there are no timelike curves in that spacetime; there are timelike curves in every spacetime.
PeterDonis said:Why?
PeterDonis said:This looks like just empty speculation to me. There's no point in discussing empty speculation.
PeterDonis said:In any case, the statement that spacetime is a 4-dimensional manifold has a perfectly definite physical meaning. So does the statement that there are timelike curves in spacetime. These are not hypotheses; they are physical facts that are reflected in the models we use in GR. Any alternate model would also have to account for the same physical facts, so any alternate model would also have to accommodate the existence of a 4-D spacetime with timelike curves in it.
nikko lyng said:For example there could be a fourth dimension which is not time, but which the other three dimensions curve relative to?
nikko lyng said:Because if it does not have any similar properties it would not be logical to name it similar as well i suppose.
nikko lyng said:I would call it a fruitful question though.
nikko lyng said:I am curious of how necessary is it that time is a dimension instead of for example that time is a by product of causation itself.
PeterDonis said:You're still missing the point. What does it mean to say the fourth dimension "is not time"? If you try to actually give this a precise meaning, I think you will find you can't. "Time" is not a property of one specific dimension. It's just a property of spacetime as a whole that it has four dimensions and that it contains timelike curves.
PeterDonis said:"I suppose" is not an argument.
PeterDonis said:There are plenty of people working on possible more fundamental models that would have GR emerge from them in the appropriate limit. I've already mentioned two, string theory and loop quantum gravity. So in that sense the idea is certainly fruitful, yes.
PeterDonis said:What is not fruitful, IMO, is your particular approach to this idea, which is to throw out vague ordinary language statements instead of trying to construct precise models with precise consequences.
PeterDonis said:See my comments above about dimensions; "time" is not a dimension, nor is it a property that can be assigned to one particular dimension.
PeterDonis said:As for time being a "by product of causation", I think the statement "spacetime contains timelike curves" basically captures that. So I don't think the redundancy you are describing is actually there in GR.
nikko lyng said:I cannot really make more sense of what you're saying here than that.
nikko lyng said:As far as I've heard they failed to
nikko lyng said:I have modeled all the laws of physics in the link to my article.
nikko lyng said:All the experts who explain general relativity seem to call time the fourth dimension.
nikko lyng said:What do you mean by that space-time has timelike curves?
GR, or General Relativity, is a theory of gravity developed by Albert Einstein in the early 20th century. It differs from other theories of gravity, such as Newton's theory of gravity, in that it describes gravity as the curvature of spacetime rather than a force between masses.
The precession of Mercury's orbit refers to the gradual change in the orientation of Mercury's orbit around the Sun. GR explains this phenomenon by predicting that the curvature of spacetime around the massive Sun causes the orbit of Mercury to deviate from the expected path predicted by Newton's theory of gravity.
GR not only explains the precession of Mercury's orbit, but also the precession of other planets in our solar system. This is because all massive objects, not just the Sun, cause a curvature of spacetime, which affects the motion of other objects around them. Therefore, GR can accurately predict the precession of all planets in our solar system.
No, there is a wealth of evidence supporting GR, including the bending of light by massive objects, the gravitational time dilation, and the expansion of the universe. The precession of Mercury's orbit is just one of the many phenomena that GR explains.
While GR has been extremely successful in explaining the precession of Mercury's orbit, there are still some small discrepancies between the predicted and observed values. These discrepancies could be due to other factors, such as the influence of other planets or measurement errors, but they continue to be studied and refined in order to further improve our understanding of gravity and the universe.