Can You Truly Achieve No Motion in Space?

[AlanC]

In theory, Is it possible to have no motion at all in relative to all of space? A point in-between galaxies perhaps?
Or, given enough energy, to suspend motion in absolute? If this were possible would everything rush away? We are moving through space at approx. 830 km/s.

 

[Dale]

There is no such thing as velocity relative to space or absolute velocity. Or at least, our most sophisticated attempts to detect it have all failed.

 

[Alan McIntire]

New question. Years ago I was posting on an alt.sci.relativity thread. The postulates were given that
1. The speed of light is constant,
2. All motion is relative

And Einstein's special theory can be derived just using those two postulates.
I thought {1} could be reduced to the weaker
1. The speed of light is finite, but someone else pointed out that in that case light could act like particles in Newtonian mechanics, with velocities additive.
CAN Einsteins's theory be deduced from
1. The speed of light is finite
2. All motion is relative
or do you need the more restrictive postulate
1. The speed of light is constant,

 

[SlowThinker]

CAN Einsteins's theory be deduced from
1. The speed of light is finite
2. All motion is relative
or do you need the more restrictive postulate
1. The speed of light is constant,

Einstein's theory of relativity is BASED on (1) (the lower one).
If the speed of light varied from one place to another, and was different today from yesterday, the world would be a very different place.

 

[PeterDonis]

CAN Einsteins's theory be deduced from
1. The speed of light is finite
2. All motion is relative
or do you need the more restrictive postulate
1. The speed of light is constant

The short answer is, you need the more restrictive postulate.

The somewhat longer answer is, if you just take the principle of relativity ("all motion is relative" is a bit skimpy as a statement of this principle, btw; a better statement would be "the laws of physics are the same in all inertial frames"), then you have two possibilities: there is no finite invariant speed, or there is. The former possibility leads to Newtonian mechanics; the latter leads to SR, with the finite invariant speed being the speed of light. So just postulating that the speed of light is finite, combined with the principle of relativity; isn't enough to get you SR; you could, as the person you referred to in your post said, be in a Newtonian universe with no finite invariant speed. The speed of light has to be constant (or better, invariant, meaning it is the same in all inertial frames) to pin down the theory to SR.

 

[Herman Trivilino]

The somewhat longer answer is, if you just take the principle of relativity ("all motion is relative" is a bit skimpy as a statement of this principle, btw; a better statement would be "the laws of physics are the same in all inertial frames"), then you have two possibilities: there is no finite invariant speed, or there is. The former possibility leads to Newtonian mechanics; the latter leads to SR, with the finite invariant speed being the speed of light.

But if you include, among the laws of physics that are the same in all inertial reference frames, the laws embodied in Maxwell's equations, you have special relativity as the only possibility. In this sense, couldn't you say that all you need to get SR is the Principle of Relativity?

 

[PeterDonis]

But if you include, among the laws of physics that are the same in all inertial reference frames, the laws embodied in Maxwell's equations, you have special relativity as the only possibility. In this sense, couldn't you say that all you need to get SR is the Principle of Relativity?

The principle of relativity in itself doesn't tell you what the laws of physics are; it just tells you that, whatever they are, they must be the same in all inertial frames. So there has to be at least one additional assumption, namely, something specific about what counts as "the laws of physics". Assuming that Maxwell's Equations fall in that category is equivalent to assuming that there is a finite invariant speed, so in that sense, you can substitute the assumption of Maxwell's Equations for the assumption of the finite invariant speed of light. But you're still making an assumption that isn't contained within the principle of relativity by itself.

Another way of looking at this is from the standpoint of a late 19th century physicist, who was looking at two sets of "laws of physics" that looked contradictory, namely, Maxwell's Equations and Newton's Laws. The former indicated a finite invariant speed, while the latter indicated no finite invariant speed. Picking which choice was right was not, I would say, a slam dunk either way based on the evidence available that the time. It could very well have been, at that time, that Newton's Laws were exactly right, and that there were small corrections to Maxwell's Equations that only came into play in contexts that hadn't yet been tested experimentally. It's only from the standpoint of today, where we have so much more experimental evidence that clearly tells us that Newton's Laws are only approximations and Maxwell's Equations are exactly right, that we can say it's "obvious" that Maxwell's Equations are what should combine with the principle of relativity and give us a finite invariant speed.

 

[Herman Trivilino]

The principle of relativity in itself doesn't tell you what the laws of physics are; it just tells you that, whatever they are, they must be the same in all inertial frames. So there has to be at least one additional assumption, namely, something specific about what counts as "the laws of physics".

Saying "all" the laws of physics doesn't preclude mentioning which specific ones you're talking about?! Is it just semantics?

Another way of looking at this is from the standpoint of a late 19th century physicist, who was looking at two sets of "laws of physics" that looked contradictory, namely, Maxwell's Equations and Newton's Laws. The former indicated a finite invariant speed, while the latter indicated no finite invariant speed. Picking which choice was right was not, I would say, a slam dunk either way based on the evidence available that the time.

I will have to think about this some more. It seems there's something more to it than just the experimental evidence. The symmetry between electricity and magnetism present in, but not satisfactorily explained by, Maxwell's theory guided the choice?

 

[PeterDonis]

Saying "all" the laws of physics doesn't preclude mentioning which specific ones you're talking about?! Is it just semantics?

No, it's the fact that the principle of relativity is equally compatible with different laws of physics. The principle of relativity, as a recognized physical theory, predates the theory of Special Relativity by several centuries. Galileo stated the principle of relativity in the early 1600's, even before Newton; and Newtonian mechanics is consistent with the principle of relativity. So the principle of relativity by itself can't possibly pin you down to one specific set of laws of physics.

The symmetry between electricity and magnetism present in, but not satisfactorily explained by, Maxwell's theory guided the choice?

Symmetry is nice, but Newton's Laws have symmetry too. As I said, the problem was that there were two sets of physical laws, with different symmetries, and they weren't compatible. Today it seems obvious to us that the symmetry of Maxwell's Equations is the "right" one, and that the symmetry of Newton's Laws is only approximate. But that wasn't obvious in the late 19th century; it is obvious now because of lots of experimental evidence that we have now that they didn't have then.

 

[Nugatory]

But if you include, among the laws of physics that are the same in all inertial reference frames, the laws embodied in Maxwell's equations, you have special relativity as the only possibility. In this sense, couldn't you say that all you need to get SR is the Principle of Relativity?

It didn't seem that way to two entire generations of physicists between 1861 and 1905...

I have suggested (with tongue firmly in cheek and the full benefit of hindsight) that Einstein's second postulate could have been worded differently - "And I really mean the first postulate, especially when it comes to electrodynamics" or "And we don't need no stinkin' aether!" - but it's still needed in some form. Had experiments shown that the speed of light was finite but not the same in all inertial frames (and presumably obeying the Galilean velocity addition rule) we'd postulate a luminiferous aether instead, we'd still have a consistent physics that respected the principle of relativity, and no nineteenth-century physicist would have been in the least surprised.

 

[russ_watters]

Saying "all" the laws of physics doesn't preclude mentioning which specific ones you're talking about?! Is it just semantics?

I don't think you quite absorbed what he said: the other postulate establishes a new "law of physics". That new law of physics (and of course the implications) is the entirety of what makes SR different from the previously established principle of relativity. Since it is what's new, it absolutely cannot be excluded!

 

[Herman Trivilino]

the other postulate establishes a new "law of physics".

I was under the impression that the second postulate follows from Maxwell's electrodynamics, given the Principle of Relativity (first postulate).

I do take the other points made in this thread about the necessity of a second postulate, though.

 

[Herman Trivilino]

Had experiments shown that the speed of light was finite but not the same in all inertial frames (and presumably obeying the Galilean velocity addition rule) we'd postulate a luminiferous aether instead, we'd still have a consistent physics that respected the principle of relativity, and no nineteenth-century physicist would have been in the least surprised.

Wouldn't the presence of an aether present a way to distinguish one inertial reference frame from another? All you'd have to do is measure the speed of light to determine how fast your reference frame is moving?

 

[russ_watters]

I was under the impression that the second postulate follows from Maxwell's electrodynamics, given the Principle of Relativity (first postulate).

Not exactly. Maxwell's equations were interpreted at the time to imply a speed of light that is constant but frame dependent, not unlike the speed of sound. The second postulate says it is constant and frame independent.

Wouldn't the presence of an aether present a way to distinguish one inertial reference frame from another? All you'd have to do is measure the speed of light to determine how fast your reference frame is moving?

Right. That's what the Michelson Morley experiment attempted to do.

 

[Nugatory]

Wouldn't the presence of an aether present a way to distinguish one inertial reference frame from another? All you'd have to do is measure the speed of light to determine how fast your reference frame is moving?

Yes, but that doesn't have to violate Galilean relativity. We can propose laws of physics that predict that the speed of light is different for observers moving at different velocities relative to the aether (that is pretty much the hypothesis that Maxwell and an entire generation of 19th-century physicists adopted) so that we can detect motion relative to the aether, but we still don't have absolute motion.

The only flaw in this approach is that it is falsified by Michelson-Morley and similar experiments.

 

[Alan McIntire]

When I posted my question, I was thinking of something like the doppler shft, which in the case of sound waves, gives different results depending on whether
the source or observer is moving with respect to the air, or eather, or whatever.

 

[Janus]

When I posted my question, I was thinking of something like the doppler shft, which in the case of sound waves, gives different results depending on whether
the source or observer is moving with respect to the air, or eather, or whatever.

That doesn't happen with light in a vacuum. For it the Doppler shift has the relationship of

$$\sqrt{\frac{1-\frac{v}{c}}{1+\frac{v}{c}}}$$

Where v is the relative velocity between source and receiver (positive when they are receding from each other) and c is the speed of light in a vacuum. There is no distinction between source or receiver motion.

 

[Nugatory]

When I posted my question, I was thinking of something like the doppler shft, which in the case of sound waves, gives different results depending on whether
the source or observer is moving with respect to the air, or eather, or whatever.

That's a fair question, and it turns out that light doesn't behave that way; as long as we're in a vacuum it moves at $c$ relative to all observers regardless of their relative velocity.

There is a Doppler effect. If you and I are both observing light from the same source and I am moving towards it relative to you, I will measure a higher frequency and shorter wavelength (the light is blue-shifted) than you do. We will both agree that the light is propagating at speed $c$. The precise amount of blueshift is different than classical Doppler and is as described by Janus above.

 

[Herman Trivilino]

Yes, but that doesn't have to violate Galilean relativity. We can propose laws of physics that predict that the speed of light is different for observers moving at different velocities relative to the aether (that is pretty much the hypothesis that Maxwell and an entire generation of 19th-century physicists adopted) so that we can detect motion relative to the aether, but we still don't have absolute motion.

The only flaw in this approach is that it is falsified by Michelson-Morley and similar experiments.

The notion that the presence of an aether wouldn't constitute a preferred frame of reference is not something I recall ever having thought about. It may be one of those things that some authors of textbooks get wrong. Or it may be that I've been misinterpreting their comments.

For example, from Spacetime and Gravitation by Ohanian and Ruffini:

Einstein had a strong conviction that Maxwell's equations should not permit any intrinsic distinction between two inertial reference frames

So even if Maxwell's equations did present a way to distinguish between inertial reference frames, it would still be possible to retain the equivalence of inertial reference frames. That seems to be what you're saying. I could imagine, for example, that old idea of aether drag, permitting the notion that parts of the aether themselves could be in motion relative to each other. Maxwell's equations would not provide a way to determine an absolute motion of anyone patch of aether.

Am I understanding this correctly?