Does Special Relativity Predict Zero Acceleration in Free Fall?

[harrylin]

[..] what is an accelerometer, or actually more importantly, what is free fall? That last bit might have us ask what is gravity, or maybe more generally what is a force field (no, not the star trek kind). [..]

Commonly (and also what I had in mind), an accelerometer is a mechanical device such as described here:
http://en.wikipedia.org/wiki/Accelerometer#Structure
However, also optical accelerometers are possible, and that made for an interesting twist in the discussion. And concerning gravity, SR doesn't propose a conceptually new theory of gravity; thus in SR gravity is a force which accelerates all matter equally. You also bring up details about SR corrections which I expect to all zero out for an accelerometer in free fall. Apparently some people don't believe that and so they want to see that.

If the question was about the Newtonian case, I would answer accelerometers will read zero. In the simple Newtonian case, any global uniform force is undetectable in a closed experiment. Accelerometers will not detect uniform forces, which gravity can be considered to be... approximately.[..] ... but I don't think this is relevant to the question. I assume the non-uniformity should be considered small enough to be disregarded. Somehow intuitively, I'd expect the same answer for SR, by extension. [..]

Yes, tidal effects aren't the topic here.

The problem is the definition of a global uniform force in that context, though.

The transformation of forces is well defined in SR.

 

[harrylin]

[..] I haven't made any such claim, and I don't think anyone else has either.

To the contrary, such repeated claims were the reason for this thread; see post #1 (which is non-exhaustive).

I agree, and I suspect all the others here do too, that SR predicts zero accelerometer reading in free fall.
[SNIP off-topic misunderstanding]

OK. That was what I tried to make clear, when thinking of standard accelerometers.

However, there is another issue that was next brought up in this thread concerning optical accelerometers (using light instead of a mass); that's still interesting to discuss.

I don't understand the contrast you're trying to make here. Doesn't "freely moving" mean the same thing as "inertial"?

I meant it in the sense of unobstructed; motion in under influence of gravity is not "inertial" in SR. See also posts #26 and #28.

 

[Fredrik]

SR is based on Maxwell's electrodynamics as well as Newton's mechanics, but makes well known corrections to Newton''s mechanics.

It was certainly inspired by those things, but I wouldn't say that it's "based" on either of them.

Please explain how you think that gravitational attraction of matter but not of EM waves can violate the first postulate.

The inverse square law clearly implies instantaneous transfer of information, which is problematic (to say the least) in Minkowski spacetime. See e.g. this post.

After short consideration I expect SR to predict that an optical accelerometer will indicate acceleration in a gravitational field.

A term like "gravitational field" must be defined by a theory of gravity. There are only two relevant theories of gravity here: Newton's and Einstein's. The former is a theory of gravitational interactions in Galilean spacetime, and the latter is about geometrical properties of a curved Lorentzian manifold. So neither of them says anything about Minkowski spacetime.

 

[harrylin]

It was certainly inspired by those things, but I wouldn't say that it's "based" on either of them. [..]

Ok, it's definitely based on Maxwell's electrodynamics, and it does make known corrections to Newton's mechanics. One correction is indeed that the speed of light is the maximum speed.

A term like "gravitational field" must be defined by a theory of gravity. There are only two relevant theories of gravity here: Newton's and Einstein's. [..]

SR corrects Newton's mechanics but does not introduce Einstein's theory of gravity.

 

[Fredrik]

Ok, it's definitely based on Maxwell's electrodynamics, and it does make known corrections to Newton's mechanics. One correction is indeed that the speed of light is the maximum speed.

Pre-relativistic physics is about theories of matter in Galilean spacetime. SR is about theories of matter in Minkowski spacetime. Maxwell's equations inspired the definition of Minkowski spacetime. To me that's not a reason to say that SR is based on Maxwell's equations, but perhaps "based on" means to you what "inspired by" means to me.

SR corrects Newton's mechanics; GR includes Einstein's theory of gravity.

GR is Einstein's theory of gravity.

SR certainly doesn't correct Newtonian mechanics on anything that involves gravity. Theories of matter in Minkowski spacetime are more accurate than theories of matter in Galilean spacetime when high speeds are involved, but not when gravity is involved. Minkowski spacetime is simply incompatible with both Newtonian gravity (because of the problem with instantaneous messages) and Einsteinian gravity (because matter has no effect on spacetime geometry in SR).

People often say that experiments favor SR over pre-relativistic physics, but the fact is, it's far easier to rule out SR by experiment than to rule out pre-relativistic physics, since there's no gravity in a special relativistic universe.

 

[harrylin]

Pre-relativistic physics is about theories of matter in Galilean spacetime. SR is about theories of matter in Minkowski spacetime. Maxwell's equations inspired the definition of Minkowski spacetime. To me that's not a reason to say that SR is based on Maxwell's equations, but perhaps "based on" means to you what "inspired by" means to me. [..] there's no gravity in a special relativistic universe.

Sorry you really have it upside down, but that discussion is mostly off-topic. Minkowski spacetime was developed based on SR, and SR is based on Maxwell's theory - in contrast to ballistic emission theories. Moreover, SR doesn't deny the existence of gravity; that wouldn't make any sense.
- http://www.fourmilab.ch/etexts/einstein/specrel/www/

 

[dx]

Einstein came to SR by looking at the symmetry of Maxwell's theory, but you don't need electrodynamics to formulate SR.

 

[Fredrik]

Sorry you really have it upside down, but that discussion is mostly off-topic. Minkowski spacetime was developed based on SR, and SR is based on Maxwell's theory - in contrast to ballistic emission theories. Moreover, SR doesn't deny the existence of gravity; that wouldn't make any sense.
- http://www.fourmilab.ch/etexts/einstein/specrel/www/

That article doesn't support any of your claims. If you want to continue the "based on" discussion, I think you need to define what you mean by "based on", and in particular how the meaning of those words differs from the meaning of "inspired by".

You are wrong about gravity. SR describes a world without gravity.

 

[harrylin]

That article doesn't support any of your claims. If you want to continue the "based on" discussion, I think you need to define what you mean by "based on", and in particular how the meaning of those words differs from the meaning of "inspired by". [..]

I don't want to continue an off-topic discussion in my thread, and you're of course free to disagree with Einstein's formulation of SR.

 

[Fredrik]

you're of course free to disagree with Einstein's formulation of SR.

The first statement of a theory is never the best. We can certainly do better 108 years later.

 

[georgir]

The transformation of forces is well defined in SR.

Well defined, but not well understood by me :p
I already wrote that a uniform force in one reference frame will not seem uniform in another, but I realize that I was wrong in my train example now. Yes there will be non-uniform motion of different parts of the train in a different reference frame, but it will not appear as a result of the applied force.

thus in SR gravity is a force which accelerates all matter equally

Well, I guess you mean 4-acceleration. And that is lorentz-invariant, so a uniform 4-acceleration field will remain uniform under SR transforms. This clears up the matter of definitions to me. It is so obvious now, but I guess I needed a little nudge. Thanks for that.

Now I have no doubt that we get the same thing as in the Newtonian model. Namely, a global uniform 4-acceleration force field is not detectable in any experiment. Or in other words, your accelerometer will read zero.

 

[georgir]

A term like "gravitational field" must be defined by a theory of gravity. There are only two relevant theories of gravity here.

A theory of gravity will define how such a field is caused and how its magnitude or other properties are determined. But a complete such theory is not needed to answer the question in the original post of the thread. We need to take into account only a single property of gravity, namely "gravity is a force field causing (approximately) uniform 4-acceleration" and now the problem is completely well defined within SR.

Just SR+that gravity property.

Edit: Well, I guess we also need to add a clear definition about what gravity does to light, if we're to cover light-based accelerometers. I don't know how that works at all, but I expect the end result to still be the same, zero reading.

 

[harrylin]

The first statement of a theory is never the best. We can certainly do better 108 years later.

That's OK; however as a result the topic at hand doesn't match your thinking.

 

[harrylin]

Well defined, but not well understood by me :p
I already wrote that a uniform force in one reference frame will not seem uniform in another, but I realize that I was wrong in my train example now. Yes there will be non-uniform motion of different parts of the train in a different reference frame, but it will not appear as a result of the applied force.

You may be on to something, but I don't see it yet. The standard way of addressing such problems is to first examine them in the rest frame of the gravitational field (the case is relatively simple thanks to the approximation of a small mass in the field of a large mass).

[..] Now I have no doubt that we get the same thing as in the Newtonian model. Namely, a global uniform 4-acceleration force field is not detectable in any experiment. Or in other words, your accelerometer will read zero.

In fact I simply meant 3-acceleration, as we only need to examine the problem in a single frame; but it boils down to the same for the prediction.

 

[harrylin]

[..] Well, I guess we also need to add a clear definition about what gravity does to light, if we're to cover light-based accelerometers. I don't know how that works at all, but I expect the end result to still be the same, zero reading.

Here's my argument to the contrary: the second postulate + Huygen's principle => no light bending possible in free space according to SR. Compare: The equivalence principle + Huygen's principle => Einstein's GR prediction of light bending.

 

[georgir]

In fact I simply meant 3-acceleration, as we only need to examine the problem in a single frame; but it boils down to the same for the prediction.

Well, 3-acceleration due to gravity can not be the same for all objects. It has to depend on their velocity... otherwise we may get to accelerate something above c by accident ;)
Edit: you could say that the "proper acceleration" caused by gravity is the same, but that's just saying 4-acceleration is the same.

 

[Dale]

Neither of us knows such a reference

I am glad that you realize that you are just making stuff up. I would remind you about the rule against speculation and personal theories.

but we made contrary claims about what we think SR predicts for that case.

The difference between your claim and mine is that mine represents the mainstream understanding of SR and yours is unsupported speculation. They are not just two claims with equal validity.

 

[Dale]

Somehow intuitively, I'd expect the same answer for SR, by extension. The problem is the definition of a global uniform force in that context, though.

The problem is that there is no SR theory of gravity. All you can do in SR is neglect gravity.

Please, do not post speculations on what a SR theory of gravity would be like, unless you can produce a mainstream reference for such a theory. This forum is for discussion of mainstream scientific theories only, not development of new ones.

 

[Dale]

in SR gravity is a force which accelerates all matter equally.

No, gravity is not a force which can be treated in SR. Please provide your reference, if you cannot then stop speculating.

 

[georgir]

The equivalence principle + Huygen's principle

I'm sure in freefall light rays will seem to be straight, so then from a static external view point light rays should appear curved. How exactly we can get that in SR though... no clue.

I don't think Huygen's principle is any use though... "its like every point that a wave reaches becumes like a new wave source"... doesn't tell you anything really. Not about how exactly the wave "reaches" any new points from any "source".

In the presence of gravity, or maybe any uniform force field (if we ever discover other kinds at all) it could be like the wave is in a flowing medium instead of a fixed one.

 

[georgir]

No, gravity is not a force which can be treated in SR. Please provide your reference, if you cannot then stop speculating.

ok... change
in SR gravity is a force which accelerates all matter equally.
to
in Classical Physics gravity is a force which accelerates all matter equally.

And just extend that to SR in the most natural way you can.

 

[Dale]

ok... change
in SR gravity is a force which accelerates all matter equally.
to
in Classical Physics gravity is a force which accelerates all matter equally.

And just extend that to SR in the most natural way you can.

If it were that easy then it would have been done more than a century ago, before the development of GR.

Again, stop speculating about gravity in SR and provide any references if you are not speculating.

 

[Fredrik]

ok... change
in SR gravity is a force which accelerates all matter equally.
to
in Classical Physics gravity is a force which accelerates all matter equally.

And just extend that to SR in the most natural way you can.

I think the only way to discuss something that resembles gravity in the context of SR is to consider a uniformly accelerating reference frame. For example, there was recently a thread that discussed the question of what happens to a submarine moving at a relativistic speed under the influence of gravity. The only way to even begin the discussion was to interpret the question as "what happens to a submarine that's moving at a relativistic speed in a huge water tank that's being uniformly accelerated".

 

[georgir]

Ok, DaleSpam, now you are arguing that SR does not and can not say anything about gravity or freefall...
How does that fit with your words quoted in the original post?

SR predicts a very large accelerometer reading during the turnaround

 

[Dale]

Ok, DaleSpam, now you are arguing that SR does not and can not say anything about gravity or freefall...
How does that fit with your words quoted in the original post?

Good question. I have maintained from the beginning that SR cannot model gravity. All you can do is neglect it. So, when you neglect gravity (as you must in SR) and apply the proper SR formula to the Langevin scenario you get an erroneously high accelerometer reading during the turnaround. Indicating that the Langevin scenario is outside the domain of applicability of SR.

 

[georgir]

I think the only way to discuss something that resembles gravity in the context of SR is to consider a uniformly accelerating reference frame. For example, there was recently a thread that discussed the question of what happens to a submarine moving at a relativistic speed under the influence of gravity. The only way to even begin the discussion was to interpret the question as "what happens to a submarine that's moving at a relativistic speed in a huge water tank that's being uniformly accelerated".

When you say "uniformly accelerating reference frame" it is not quite obvious what you mean. Do you mean the actual objects are being accelerated, or just the imaginary measurement reference frame... The two are actually related, I guess. In an accelerated reference frame it would appear that there is a force accelerating the objects.

Yes, when I (and from what I gather, harrylin too) think of Gravity (or a sufficient approximation) in SR, this is pretty much the kind of force I think of.

 

[georgir]

Good question. I have maintained from the beginning that SR cannot model gravity. All you can do is neglect it. So, when you neglect gravity (as you must in SR) and apply the proper SR formula to the Langevin scenario you get an erroneously high accelerometer reading during the turnaround. Indicating that the Langevin scenario is outside the domain of applicability of SR.

Apologies, I do not know the context of that original discussion. Nor do I know what that Langevin scenario is all about. But what happens if instead of neglecting gravity, you replace it with a force field producing locally uniform 4-acceleration?

EDIT: Nevermind, I actually know what happens. What happens is you derive GR, as this is how Einstein came up with it. And get the same 0 predicted reading.

 

[harrylin]

I am glad that you realize that you are just making stuff up. I would remind you about the rule against speculation and personal theories. [..]

No, and I was talking about us, not about only me. Do you claim that you were just speculating and presenting your personal theories?

 

[Dale]

Do you claim that you were just speculating and presenting your personal theories?

I am not speculating. I have references to support my formula; you have none to support yours. My forumla is the correct and well-recognized one; yours is simply made up. I am glad that you recognize that yours is speculative, even if you don't realize yet that mine is not.

 

[Dale]

Apologies, I do not know the context of that original discussion. Nor do I know what that Langevin scenario is all about.

No worries. In short, the Langevin scenario is a standard twins-paradox scenario except that instead of firing a rocket to turn around the traveling twin swings around a star using the star's gravity for the turnaround.

But what happens if instead of neglecting gravity, you replace it with a force field producing locally uniform 4-acceleration?

If you do that you wind up with a theory of gravity without tidal effects.

 

[georgir]

DaleSpam, are you perhaps confusing
"SR predicts a very large accelerometer reading during the turnaround"
with
"SR predicts a very large acceleration of the accelerometer during the turnaround"
?

The two are not the same. The accelerometer may be accelerating and read 0, because all of its components are accelerating completely uniformly.
Anyway... enough with me posting without the full context. I'll be silent until I get more info.
[edit: posted before seeing your last reply, feel free to disregard]

 

[georgir]

If you do that you wind up with a theory of gravity without tidal effects.

Bingo. This is the key to it... tidal effects can always be neglected in a small enough locality, and if we do neglect them, we all agree... zero reading.

The only way an "accelerometer" would detect a freefall is if it was large enough to detect tidal effects. I'd not even call that freefall though.
[edit: the same applies to the classical Newtonian case too, btw]

edit 2: your quote again:

[..] SR predicts a very large accelerometer reading during the turnaround, and real free falling accelerometers read 0.

If there were noticeable tidal forces, then a real free falling accelerometer would also not read 0.

 

[Fredrik]

When you say "uniformly accelerating reference frame" it is not quite obvious what you mean. Do you mean the actual objects are being accelerated, or just the imaginary measurement reference frame... The two are actually related, I guess. In an accelerated reference frame it would appear that there is a force accelerating the objects.

Yes, when I (and from what I gather, harrylin too) think of Gravity (or a sufficient approximation) in SR, this is pretty much the kind of force I think of.

I mean that the coordinate system is accelerated, so that the coordinate acceleration (d²x/dt²) of an objectively non-accelerating object is non-zero. You could then define the "force" in this coordinate system by F=mx''(t). Note however that if you make the same definition in an inertial coordinate system, the "force" will be 0.

It seems pointless to even mention a "force" in this scenario. Why not just let S be a Rindler coordinate system and describe the motion of some other object in terms of the S coordinates?

To call this force "gravity" is pretty odd in my opinion. It's like using the term "gravity" for the force you feel when you slam the breaks of your car.

 

[georgir]

To call this force "gravity" is pretty odd in my opinion. It's like using the term "gravity" for the force you feel when you slam the breaks of your car.

We don't call that force Gravity. We do the opposite, we claim that Gravity can be viewed as such a force, at least in a small enough locality where it appears uniform
[edit: by "we", I refer to me, myself and Einstein, in his equivalence principle ;)]

 

[harrylin]

I am not speculating. I have references to support my formula; you have none to support yours. My forumla is the correct and well-recognized one; yours is simply made up. I am glad that you recognize that yours is speculative, even if you don't realize yet that mine is not.

Instead, your formula for what according to SR an accelerometer in free fall will read was not supported by your references and as for me, I will need some time to search more specific references myself. I won't respond anymore to such personal attacks but discuss such references and basic derivations. Meanwhile I think that the participants to this thread are not a bad sample of "mainstream" opinion, and the opinions are divided.