Why is light speed constant in all reference frames?

[John232]

It is interesting to note, that one can derive the "equations of special relativity" (i.e. the Lorentz transformations) without requiring that the speed of light is constant. The principle of causality (i.e. that an event cannot be caused by a future event), is enough to impose a maximum speed of transmission of information. It turns out that this coincides with the speed of light.

I don't see how this is possible. From my understanding, the derivation itself comes from the fact that the speed of light is constant. If d = c t and c is constant then only d and t can change when compared to another distance c t. Then d and t have to be assigned as d' and t' from the frame of reference of another observer where the constant c wouldn't allow for the same d and t value. (d' and t' can not equal d and t) If you where to say there was instead a c and a c' to make the equations valid with each other you would get completely different equations. It would be like solving for the speed of an object seen from two different point of views.

Why, 300,000 km/s? Why is the sky blue? It just is. I think it is amazing with spacetime dilation that we can even observe an object traveling at a limited constant speed that is so fast that spacetime itself approuches zero for an object at that speed.

 

[harrylin]

Thanks again for the comments and reference. The reference you gave may not have been the one you were remembering. There are only 16 pages in this reference.

Scientia 10 p.31-54, http://en.wikisource.org/wiki/The_Evolution_of_Space_and_Time - the page numbers are indicated on the left.

Although he did use an illustration analogous to the twin scenario, he did not actually present the twin paradox in this paper.
Also, there was no discussion of the interpretation of special relativity.

As far as I know that was the first full presentation of the twin scenario (viewed from both perspectives) - but indeed he did not call them "twins". He did not at all present it as something paradoxical but as another illustration of his physical interpretation of the theory (p.47):

"We therefore have hold on the ether through accelerations, and acceleration has an absolute sense as determining the production of waves from matter that has undergone a change in velocity, and the aether manifests its reality as the vehicle, as the carrier of energy transported by these waves."

Evidently he would have fully agreed with Einstein's citation by you here under:

From what you say, I assume he takes the position of logical positivists, wherein physics should no longer be concerned with external objective reality--or models of an assumed external material world. This is in contrast to Einstein's comment,

"The belief in an external world independent of the perceiving subject is the basis of all natural science." (from "Clerk Maxwell's Influence on the Evolution of the Idea of Physical Reality", from Einstein's "The World As I See It").

Einstein himself was careful to not force such a model on his audience [..]

As SR does not directly depend on a physical model, it united people with such different interpretations as Lorentz and Minkowski. However, in his Leyden inauguration speech of 1920 Einstein did indicate that SR corresponds to the Lorentzian ether.

But my primary point here is, again, that a physicist chooses one of three stances: 1) physics pursues the comprehension of an external physical world (which from special relativity directly implies a a 4-dimensional world), 2) the logical positivist or operational view, in which physics should only be interested in predicting the outcome of experiments, making measurements and advancing mathematical models that agree with experiments (the models are mathematically symbolic only and have no implications about an actual external physical reality), or finally 3) One may simply take the stance of no committment to either 1) or 2).

Nearly so. I cannot follow that exact separation of options, and I'd say that it already doesn't match such individuals as Einstein and Langevin. My variant on your statement:

A physicist chooses one of three stances (or flip-flops between them!):
1) physics pursues the comprehension of an external (or "real") physical world. Special relativity seems to imply either a Lorentzian ether (3D ether) or a physical Minkowski Spacetime (a 4D block universe, not just the "world of events");
2) the logical positivist or operational view, in which physics should only be interested in predicting the outcome of experiments, making measurements and advancing mathematical models that agree with experiments. The formulation of SR by Einstein in 1905 reflects that operational view.
3) One may simply take the stance of no commitment to either 1) or 2).

Mathematical models do certainly not imply the actual physical reality; however linking that argument to the above numbering requires an additional sub division.

 

[harrylin]

I don't see how this is possible. From my understanding, the derivation itself comes from the fact that the speed of light is constant. [..].

It is possible to derive the same based on the assumption that there is a limit speed, and that was also understood in 1905. It just happened that the speed of light was an easy boundary condition for the derivation; it was known to correspond (at least to very good approximation) to that limit speed.

 

[bobc2]

Scientia 10 p.31-54, http://en.wikisource.org/wiki/The_Evolution_of_Space_and_Time - the page numbers are indicated on the left.

As far as I know that was the first full presentation of the twin scenario (viewed from both perspectives) - but indeed he did not call them "twins". He did not at all present it as something paradoxical but as another illustration of his physical interpretation of the theory (p.47):

"We therefore have hold on the ether through accelerations, and acceleration has an absolute sense as determining the production of waves from matter that has undergone a change in velocity, and the aether manifests its reality as the vehicle, as the carrier of energy transported by these waves."

Evidently he would have fully agreed with Einstein's citation by you here under:


As SR does not directly depend on a physical model, it united people with such different interpretations as Lorentz and Minkowski. However, in his Leyden inauguration speech of 1920 Einstein did indicate that SR corresponds to the Lorentzian ether.

Nearly so. I cannot follow that exact separation of options, and I'd say that it already doesn't match such individuals as Einstein and Langevin. My variant on your statement:

A physicist chooses one of three stances (or flip-flops between them!):
1) physics pursues the comprehension of an external (or "real") physical world. Special relativity seems to imply either a Lorentzian ether (3D ether) or a physical Minkowski Spacetime (a 4D block universe, not just the "world of events");
2) the logical positivist or operational view, in which physics should only be interested in predicting the outcome of experiments, making measurements and advancing mathematical models that agree with experiments. The formulation of SR by Einstein in 1905 reflects that operational view.
3) One may simply take the stance of no commitment to either 1) or 2).

Mathematical models do certainly not imply the actual physical reality; however linking that argument to the above numbering requires an additional sub division.

Good job, as usual, Harrylin.

I'm afraid I'm the hopeless pursuer of the external reality (although I'm still repulsed by some of the implications of the "block universe"). I would embrace Einstein's comment, "The belief in an external world independent of the perceiving subject is the basis of all natural science." And I would embrace it without Einstein's follow-up apologetics.

I wish I could rediscover the reference in which Einstein once expressed the sentiment (and I could be wrong) that to pursue something other than the external physical continuum world is to leave one vulnerable to solipsism. I do remember vividly his statement that included the phrase, "...there is no escape from solipsism."

I'm not sure of the logic, but it may have been something to the effect that if your reality is not that of an external world, then you evidently have an internal reality in mind ("inside the mind"). But then all of these other observers in your world are in your mind and that's getting dangerously close to solipsism.

Some may claim their reality is external--it's just of an ethereal sort--not physical or material. But, now we leave physics. The external 4-dimensional space is physics (it is directly described by special and general relativity); the other stuff is philosophy and metaphysics--unless considered strictly from the standpoint of mathematical modeling (with no implications about reality--as you clarified in your post).

[edit] Post-Script: If I cannot have an external physical world, then I would rather take the fall-back position of just not pursuing reality at all. Just make predictions about the outcome of experiments and then do the measurements--and you can do the math modeling if don't take the models literally. As Dalespam put it, "...time is the t in the equations of physics." (or something to that effect).

 

[harrylin]

[..]
Some may claim their reality is external--it's just of an ethereal sort--not physical or material. But, now we leave physics. The external 4-dimensional space is physics (it is directly described by special and general relativity); the other stuff is philosophy and metaphysics--unless considered strictly from the standpoint of mathematical modeling (with no implications about reality--as you clarified in your post).

[edit] Post-Script: If I cannot have an external physical world, then I would rather take the fall-back position of just not pursuing reality at all. Just make predictions about the outcome of experiments and then do the measurements--and you can do the math modeling if don't take the models literally. As Dalespam put it, "...time is the t in the equations of physics." (or something to that effect).

I'm afraid that I didn't express myself very well (by mistake I omitted the word "directly"). I did not mean that mathematical models have no implications at all about reality, but I meant that there doesn't need to be a 1-to-1 correspondence to what physically "really" happens. Mathematical models help us to imagine possible physical models of nature, but often there are several proposed explanations that perfectly match the same mathematical predictions.

Perhaps it's better to clarify this with an example - here is a rather silly one:
When we bring two equal volumes of gas of different temperatures together, the standard mathematical model for predicting the resulting temperature is T=(T1+T2)/2. But the equation does not reflect what really happens: nature doesn't add the two temperatures and then cuts that temperature in half. :tongue2: In reality the temperature evolves from the extremes to the average and that's not at all what the (simplest) standard mathematical model appears to suggest.