Why special relativity is unsuitable to describe gravity

[PeterDonis]

I want to understand the claimed instability!

The simplest way to describe it is that, if we take Newtonian gravity and just put in a light-speed propagation delay with nothing else changed, then, for example, the force on the Earth due to the Sun no longer points towards the Sun's position "now"--it points towards the Sun's position one light-travel time ago (i.e., about 500 seconds in a frame in which the Sun is at rest). But this means the force is no longer pointing in the right direction to keep Earth's orbit a stable, closed ellipse--since the standard Newtonian direction is the only possible direction that does that.

 

[FactChecker]

The simplest way to describe it is that, if we take Newtonian gravity and just put in a light-speed propagation delay with nothing else changed, then, for example, the force on the Earth due to the Sun no longer points towards the Sun's position "now"--it points towards the Sun's position one light-travel time ago (i.e., about 500 seconds in a frame in which the Sun is at rest). But this means the force is no longer pointing in the right direction to keep Earth's orbit a stable, closed ellipse--since the standard Newtonian direction is the only possible direction that does that.

Wouldn't that be mathematically identical to the problem of standard Newtonian orbit around the Sun's position 500 seconds ago? Both in direction and magnitude of force. I would think that the stability of the orbit would be identical in the two approaches to a solution.

 

[PAllen]

Wouldn't that be mathematically identical to the problem of standard Newtonian orbit around the Sun's position 500 seconds ago? Both in direction and magnitude of force. I would think that the stability of the orbit would be identical in the two approaches to a solution.

Think of it this way. What is the direction of Newtonian gravity? The vector from Earth to sun now, one or 500 seconds ago? This gets rid the question do whose point of view. If you use a time retarded vector, you get highly unstable orbits. Newton was amazingly well aware of this issue, and reluctantly proposed the instantantaneous vector direction because that was necessary for orbital stability as had been observed.

 

[FactChecker]

Think of it this way. What is the direction of Newtonian gravity? The vector from Earth to sun now, one or 500 seconds ago? This gets rid the question do whose point of view. If you use a time retarded vector, you get highly unstable orbits. Newton was amazingly well aware of this issue, and reluctantly proposed the instantantaneous vector direction because that was necessary for orbital stability as had been observed.

At first I didn't see why the current relative position of the Sun mattered at all since the only interaction is with a "mythical" Sun positioned 500 seconds ago. I couldn't see why a planet wouldn't have just as good an orbit (although different) around the mythical Sun position as it would around the actual current Sun position. I suppose that there must be some immediate interaction with the current Sun position that is mixed in with the delayed gravitational force that would cause the situation to be essentially different.

 

[PAllen]

At first I didn't see why the current relative position of the Sun mattered at all since the only interaction is with a "mythical" Sun positioned 500 seconds ago. I couldn't see why a planet wouldn't have just as good an orbit (although different) around the mythical Sun position as it would around the actual current Sun position. I suppose that there must be some immediate interaction with the current Sun position that is mixed in with the delayed gravitational force that would cause the situation to be essentially different.

Just consider that for a circular orbit, the acceleration must in the direction of the center. The direction from prior position to the center as a current acceleration direction cannot possibly produce a circular orbit. A slight generalization establishes that an elliptical orbit is impossible. The deviations are large, not on the scale of perihelion advance. Physicists in the 1800s had even calculated that a propagation delay of ten billion times light speed would still be inconsistent with observations.

 

[FactChecker]

Just consider that for a circular orbit, the acceleration must in the direction of the center. The direction from prior position to the center as a current acceleration direction cannot possibly produce a circular orbit. A slight generalization establishes that an elliptical orbit is impossible. The deviations are large, not on the scale of perihelion advance. Physicists in the 1800s had even calculated that a propagation delay of ten billion times light speed would still be inconsistent with observations.

Thanks. I'll have to think about it. I believe you. I certainly see that the delay would change the orbit. I also see that a delay in what is essentially a feedback system could change the stability of the orbit. Still, I have a hard time seeing how the actual orbit with the delay would be different from a theoretical orbit with no delay around a theoretical Sun at the position of the real Sun 500 seconds ago and why that theoretical orbit would have different stability properties.

 

[PeterDonis]

Wouldn't that be mathematically identical to the problem of standard Newtonian orbit around the Sun's position 500 seconds ago?

No, because the Earth is not in the same position now as it was 500 seconds ago, and the force is acting on the Earth now.

 

[FactChecker]

No, because the Earth is not in the same position now as it was 500 seconds ago, and the force is acting on the Earth now.

Oh! Thanks! I think I see. The velocities and behavior of the planet does not match the actual current distance from the Sun, it matches the gravity from the earlier distance. So the current velocities and distances do not indicate that the orbit would be stable. Only by considering the delay would a stable orbit with that behavior make sense.

PS. Sorry if I have hijacked this thread. I will bud out.

 

[PeterDonis]

The velocities and behavior of the planet does not match the actual current distance from the Sun, it matches the gravity from the earlier distance.

Yes, you've got it.

 

[Adel Makram]

How if instead of the sun, there is a magical structure pulls the Earth with a long rope and rotates it. Still the pulling force has to propagate with some propagation speed due to the electromagnetic force at the rope's mollecular level. Will be any instability in the rotating Earth orbit? In general will a rotating disc be unstable because the direction of the force acting on the edge is not on the same direction of the force a moment ago?

 

[FactChecker]

The physical situation may have stable orbits with or without delays in gravity. It's just that the actual stable orbit will not exactly match a calculated stable orbit unless the calculations include the correct delays. The observed orbit of a planet will not match the zero-delay Newtonian calculations of a stable orbit because the delays used in the calculations are not correct. But that does not mean that there would be no stable orbit if there were no delay in gravity -- just that the stable orbit would be different.

PS. I am probably using the term "stable" incorrectly. If the orbit is not an exact repeating ellipse, but rather a rotating rosette, I think of that as stable.

 

[Vanadium 50]

This thread is really messy. If one is talking about Newtonian gravity - or for that matter, SR - one should not muddy the waters discussing spacetime curvature. The nit that the sun's mass is not exactly constant is singularly unhelpful. It's also negligible, as it is less than a part per trillion per decade.

Ibix answer is right - you cannot take Newtonian gravity, make it travel at c rather than instantaneously, and match observations. However, this is not (directly) due to "the position of the sun in the sky 8 minutes ago". First, that's dominated by the Earth's rotation. Second, as pointed out, insofar as the sun is stationary, the gravitational field at point X is the same as it was 8 minutes ago, so the field the Earth traverses is the same as it was 8 minutes ago, so how can the orbit be different?

The answer to this apparent paradox is that the sun is not exactly stationary. Even in a one-planet solar system, the Earth and Sun revolve around their common center of mass. If you put in a propagation delay, the Earth sees its own gravity through the Sun's (small) motion with a 16 minute delay. This tends to perturb the orbit, and as described earlier, results in an instability over many millions of years. When you add the other 8 - sorry, 7 - planets, this instability just gets worse.

GR doesn't actually have to fix this up. There's no reason to demand that it give you stable orbits (although if you want to consider it as a viable description of nature you do, but the theory itself doesn't have to). It does and it doesn't - orbits in GR are not ellipses but rosettes, but these rosettes are stable over long time scales. It is a success of GR that it matches the data, both the long-term stability and the rosette nature of the orbits.

 

[Adel Makram]

This thread is really messy. If one is talking about Newtonian gravity - or for that matter, SR - one should not muddy the waters discussing spacetime curvature. The nit that the sun's mass is not exactly constant is singularly unhelpful. It's also negligible, as it is less than a part per trillion per decade.

Ibix answer is right - you cannot take Newtonian gravity, make it travel at c rather than instantaneously, and match observations. However, this is not (directly) due to "the position of the sun in the sky 8 minutes ago". First, that's dominated by the Earth's rotation. Second, as pointed out, insofar as the sun is stationary, the gravitational field at point X is the same as it was 8 minutes ago, so the field the Earth traverses is the same as it was 8 minutes ago, so how can the orbit be different?

The answer to this apparent paradox is that the sun is not exactly stationary. Even in a one-planet solar system, the Earth and Sun revolve around their common center of mass. If you put in a propagation delay, the Earth sees its own gravity through the Sun's (small) motion with a 16 minute delay. This tends to perturb the orbit, and as described earlier, results in an instability over many millions of years. When you add the other 8 - sorry, 7 - planets, this instability just gets worse.

GR doesn't actually have to fix this up. There's no reason to demand that it give you stable orbits (although if you want to consider it as a viable description of nature you do, but the theory itself doesn't have to). It does and it doesn't - orbits in GR are not ellipses but rosettes, but these rosettes are stable over long time scales. It is a success of GR that it matches the data, both the long-term stability and the rosette nature of the orbits.

I agree with FactChecker. To see this in a simple way, imagine we are dealing with 1-D force acting on an object moving along x-axis back and forth around the center. If the force is instantenous, the object will continue moving to the right side of the axis to some point and then back in the opposite direction to the negative side of x-axis and so on. If there is a propagation delay, again the particle will continue moving to the positve direction until the force catches it and pulls it back but it may take it further to the right this time compared with the first case. In both cases, the conservation of the energy holds the particle in stable motion.

 

[Vanadium 50]

You should do the math, then. There's a famous paper by I.J. Good in the 70's that works this all out.

The problem shows up in the calculation very quickly. If A and B are in orbit around a common center of mass, and the force between A and B is not aligned with the present positions of A and B, there is a torque on the system. That torque is destabilizing.

 

[FactChecker]

You should do the math, then. There's a famous paper by I.J. Good in the 70's that works this all out.

The problem shows up in the calculation very quickly. If A and B are in orbit around a common center of mass, and the force between A and B is not aligned with the present positions of A and B, there is a torque on the system. That torque is destabilizing.

In this context, does the term "unstable" mean that the radius of the orbit changes or does it also include a constant radius rosette pattern? I can easily understand a torque causing the rosette pattern. Does it also imply an unstable radius?

 

[Vanadium 50]

There is a torque through an angle, and that means work is done. This work expands the radius of the orbit and separates the bodies.

 

[FactChecker]

There is a torque through an angle, and that means work is done. This work expands the radius of the orbit and separates the bodies.

Ha! That is a very straightforward and, I think, intuitively convincing argument. Thanks.

 

[jk22]

Formally the problem becomes an iterative functional equation :

$$\ddot{\vec{r}}(t+\frac{2r(t)}{c})=-\frac{Gm\vec{e_r}(t)}{(2r(t))^2}$$

This has memory properties so that for example the initial condition is given by $$\{\vec{r}(t)|t\in [-\infty;0]\}$$

I didn't find a documentation about how to solve this exactly or even with a first order term which gives a component of the force along the jerk.

We could write the special relativistic dynamics in the same way but general relativity solves this time delay in a completely different way getting rid of higher derivatives and memory.

 

[MikeGomez]

Hi. Fake gravitation such as motions of constant acceleration or rotation can be fully understood by applying SR. Real gravity seems to have similar behaviour with fake ones thus introduced GR. Best.

There is no such thing as "fake" gravity, is there?

 

[Ibix]

There is no such thing as "fake" gravity, is there?

I think the distinction being made is between non-inertial frames in flat spacetime (e.g. rotating sections on spacecraft to provide "artificial gravity") which can be handled in special relativity, and curved spacetime which cannot. Whether you regard non-inertial effects in flat spacetime as "fake gravity" is up to you. I'm pretty sure it's not a standard term.

 

[MikeGomez]

I think the distinction being made is between non-inertial frames in flat spacetime (e.g. rotating sections on spacecraft to provide "artificial gravity") which can be handled in special relativity, and curved spacetime which cannot.

Yes, but it really needs to be said that way so that people who read it don't think that there are different kinds of gravity..

Whether you regard non-inertial effects in flat spacetime as "fake gravity" is up to you..

The term "fake gravity" makes my head explode, and I think it should be banished from the face of the earth.

The thing is, I think even "artificial" gravity, although not as bad, should not be used. Inertia and gravity are phenomenon identical in nature. Maybe "induced" gravity would be a good way to describe space-station gravity.

PeterDonis wrote up an excellent description of the situation from another post here recently.

...There is a common confusion here which is worth going into. When we speak of "tidal forces", or for that matter when we speak of a "fictitious" force such as centrifugal force or the force of gravity, we are really being sloppy. Consider the following three cases:

(1) A person standing at rest on the surface of the Earth.

(2) A person pressed against the wall of a rotating cylindrical chamber (like those amusement park rides where you stand against the wall, the chamber starts rotating, and then the floor drops out from under your feet but you stay pressed to the wall and don't fall).

(3) An extended object free-falling radially towards Earth and being stretched by tidal gravity, setting up stresses (i.e., internal forces) inside the object.

In all three of these cases, there are forces present, but they are not, according to GR, properly described as "the force of gravity", "centrifugal force", or "tidal force". They are, respectively:

(1) The force of the Earth's surface pushing up on the person's feet, keeping them from following a geodesic path (which would be free fall towards the center of the Earth).

(2) The force of the chamber wall pushing on the person's back, keeping them from following a geodesic path (which, if we imagine the chamber far out in deep space, so there is no large gravitating mass present, would be to fly off in a straight line tangent to the chamber wall).

(3) The force of the internal bonds in the material that makes up the object, keeping its parts from following geodesic paths (which would be for the parts of the object to diverge from each other).

In that thread PeterDonis has accepted the statement that "all three cases are different manifestations of the same underlying phenomenon".

 

[sweet springs]

The term "fake gravity" makes my head explode, and I think it should be banished from the face of the earth.

I am not confident of rightness in my terminology so you can invent more appropriate one.

What I would like to stress is that coordinate systems are classified in

Type A : There exists a global coordinate transformation that reduces the system to a global IFR. Energy momentum tensor that appears in Einstein equation does not play a role.
The examples include rotation system and Rindler system

Type B: Energy momentum tensor works in Einstein equation. There does not exist a global coordinate transformation as mentioned above.
The examples include Schwatzshild metric. There are complex hybrid-like coordinates in B, for example, the system on the spinning Earth that revolve around the Sun by universal gravitation.

 

[PAllen]

Yes, but it really needs to be said that way so that people who read it don't think that there are different kinds of gravity..

The term "fake gravity" makes my head explode, and I think it should be banished from the face of the earth.

The thing is, I think even "artificial" gravity, although not as bad, should not be used. Inertia and gravity are phenomenon identical in nature. Maybe "induced" gravity would be a good way to describe space-station gravity.

PeterDonis wrote up an excellent description of the situation from another post here recently.
In that thread PeterDonis has accepted the statement that "all three cases are different manifestations of the same underlying phenomenon".

What you describe is a valid way of looking at SR/GR, that is consistent with how Einstein looked at it. However, it is hardly the only valid or useful way. Another major alternative is to consider gravity like all other interactions. Then, gravity is what is mediated by gravitons. The effects of noninertial motion are then part of mechanics, while curvature that results from self interaction of gravitions is a distinguishing feature of gravity. The geometric description of GR is then the classical limit of the yet to be determined QG theory, though already you can do a lot with effective field theory approach without knowledge of the full theory.

 

[PeterDonis]

coordinate systems are classified

What you call Type A coordinate systems are only possible in flat spacetime. So I'm not sure how useful this classification is if you think of it as classifying coordinate systems.

 

[PeterDonis]

Another major alternative is to consider gravity like all other interactions. Then, gravity is what is mediated by gravitons. The effects of noninertial motion are then part of mechanics, while curvature that results from self interaction of gravitions is a distinguishing feature of gravity.

This isn't really a different viewpoint from the one I was describing. I was simply pointing out that, regardless of what fundamental view you take about "gravity" (the "curved spacetime" view or the "field on flat spacetime as a limit of some underlying quantum gravity theory" view), you have to be careful not to misidentify non-gravitational forces as "gravity". All three of the examples I gave were of non-gravitational forces; they would be described the same on either view of what "gravity" is at a fundamental level.

 

[jk22]

Btw I don't understand why the metric is time independent regarding the aequivalence principle. My reasoning is wrong :

-the gravity is locally equivalent to phenomena in an accelerated frame
-since from SR the lorentz factor depends on v and here v depends on t
-then the contraction is at each point dependent on t
-so g should be a function of space and time too ?

 

[PeterDonis]

I don't understand why the metric is time independent regarding the aequivalence principle.

The equivalence principle doesn't have anything to do with the time independence (or lack thereof) of the metric.

gravity is locally equivalent to phenomena in an accelerated frame

That's not what the equivalence principle says. You need to be more careful in stating it.

from SR the lorentz factor depends on v and here v depends on t

This is irrelevant to the equivalence principle because the EP only applies in a small patch of spacetime, small enough that tidal gravity is negligible. Lorentz transformations simply switch between different inertial coordinate systems in that small patch of spacetime, which can be considered flat. There is no sense in which "v depends on t" in any of this.

the contraction is at each point dependent on t

No, it isn't. See above.

so g should be a function of space and time too ?

No. See above.

 

[MikeGomez]

What you describe is a valid way of looking at SR/GR, that is consistent with how Einstein looked at it. However, it is hardly the only valid or useful way. Another major alternative is to consider gravity like all other interactions. Then, gravity is what is mediated by gravitons.

Are you saying that it is more valid or useful to think of gravity as a “real” force and gravitons the force carrier? That doesn’t seem to make sense to me for the SR/GR forum, where gravitational forces are considered as inertial forces.

The effects of noninertial motion are then part of mechanics, while curvature that results from self interaction of gravitions is a distinguishing feature of gravity.

Then gravitons are excluded from the rotating cylinder and accelerating rocket?

Disclaimer: Gravitons are theoretical. I am merely responding to comments by others. Personally I have no opinion one way other the other as to the existence or non-existence of gravitons.

 

[PAllen]

Are you saying that it is more valid or useful to think of gravity as a “real” force and gravitons the force carrier? That doesn’t seem to make sense to me for the SR/GR forum, where gravitational forces are considered as inertial forces.

I said nothing about more valid. I said just as valid. Treating gravity as a force mediated by gravitons indeed means the tendency of initially parallel geodesics to converge or diverge is attributed to this force which happens to have a geometric description.

Then gravitons are excluded from the rotating cylinder and accelerating rocket?

Disclaimer: Gravitons are theoretical. I am merely responding to comments by others. Personally I have no opinion one way other the other as to the existence or non-existence of gravitons.

Yes, gravitons are not involved in inertial forces, which are simply whatever nongravitational forces are required to achieve some specific noninertial motion. They are instead involved in what causes geodesic motion to be not described by flat spacetime

 

[Ibix]

PeterDonis wrote up an excellent description of the situation from another post here recently.

Just a note - the little up arrow in the quote header links to the post you quoted. In this case, that suggests you just quoted Peter's #39 from this thread and pasted in his words from #27 in the Local meaning of the equivalence principle thread.

In that thread PeterDonis has accepted the statement that "all three cases are different manifestations of the same underlying phenomenon".

I don't disagree with Peter, but I do think there's a distinction he wasn't making in that thread. As Peter says, the truth in all three cases is that the cannot-be-transformed-away forces in play are all electromagnetic forces between atoms and molecules, which are driving something out of the geodesic path it would take if those forces weren't present. I feel heavy, in the GR view, because the sofa is pushing up on me, not because I'm being pulled down. The same would be true if I were in a rocket.

However, the reason for feeling these forces is quite different, and the consequences can be quite different. For example, if you drill into the "floor" (and fill in behind you) in each case you'll get very different behaviour. On Earth, the force on your feet will first increase then decrease as you drill down (density isn't constant) until you reach the centre, then reverse until it you reach the surface again. In a rotating cylinder, the force will increase (in principle without bound, although material science may have a thing or two to say about that) until you drill through the outer wall, where it falls abruptly to zero. In the third case, the "floor" will smoothly shift to "ceiling" as you move around, and drilling into it will see a very slow change in force which again drops abruptly to zero once you're through.

So I agree that all possible gravity, artificial or natural, is actually electromagnetic forces making the locally obvious choice of "not moving" frame a non-inertial one. But as soon as you step out of that local paradigm, they can be quite different phenomena.