Does Special Relativity Predict Zero Acceleration in Free Fall?

[PeterDonis]

SR merely makes predictions.

Fine, s/explain/predict/ in what I wrote; it's still true.

This thread examines the repeated claim elsewhere that SR predicts a large accelerometer reading in free fall

I haven't made any such claim, and I don't think anyone else has either. I agree, and I suspect all the others here do too, that SR predicts zero accelerometer reading in free fall. What SR doesn't predict is that a worldline curving around a star the way the turnaround worldline of the traveling twin has to will be in free fall. You need GR to predict that.

Similarly, Langevin's example could be analyzed within one, resp. two universal inertial frames (the ones of SR) because the turn-around was supposed to happen so fast and over such a short time span compared to the duration of the trip that this should be irrelevant for the calculation

For the calculation of total proper time, yes. But not for the calculation of what an accelerometer will read during the turnaround. There's no way to do such a calculation in a single local inertial frame.

however both for CERN as well as Langevin we can only be certain if we do a GR estimation

But what you will be "certain" of is two very different things:

In the CERN case, you'll just be confirming that any single CERN experiment can be analyzed in a single local inertial frame: the corrections from spacetime curvature are too small to matter. So you'll just be confirming that the SR calculation you do in a single local inertial frame is valid to within a good enough approximation.

In the Langevin case, you'll be actually doing a calculation (of the accelerometer reading during the turnaround) that can't be done at all with SR, because it can't be done within a single local inertial frame.

 

[PeterDonis]

With "fall" I mean the standard meaning of "falling" in SR and English, of a freely moving object in a gravitational field. That is in contrast to "inertial".

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

 

[Dale]

I think this is a matter of semantics. Einstein defined an "inertial frame" (or rather, an inertial coordinate system) to be one where Newton's laws held (approximately, anyway). You get a different answer as to "what frames are inertial" depending on whether you consider gravity to be a "force" or not.

I thought more about this until I got tired. Then I realized that it doesn't matter. There is no theory of gravity which is compatible with SR, so the question never comes up if it is considered a force or not. You have to go to GR for a relativistic theory of gravity. All you can do in SR is to neglect gravity. The validity of neglecting gravity depends on how large the resulting errors are.

 

[georgir]

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.
It is not completely uniform, as it is directed towards a point and dependent on the distance, and this slight non-uniformity might be possible to detect, i.e. we might be able to build some kind of "accelerometer" (gravitymeter?) based on that... 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. The problem is the definition of a global uniform force in that context, though.

 

[harrylin]

[..] Specifically, there is no way to calculate g in SR.
Please provide a reference for this formula. [.] Or, at a minimum, a reference for g in SR.

Neither of us knows such a reference, but we made contrary claims about what we think SR predicts for that case. The purpose of this thread is to find out what SR predicts, based on the foundations. SR is based on Maxwell's electrodynamics as well as Newton's mechanics, but makes well known corrections to Newton''s mechanics. I think that it's easy to show that my interpretation is correct, by making those corrections to the standard classical equations.

[..] then mechanical systems and optical systems would have different sets of inertial frames. Which would violate the first postulate.

I think that you misapply a GR definition to SR. The postulates are defined wrt the reference systems of Newton's mechanics and gravity is a force in SR. Please explain how you think that gravitational attraction of matter but not of EM waves can violate the first postulate.

 

[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.