Why does light have invarient speed?

lightarrow

Quote by mdeng

[tex]tangh\ R\ =\ \frac{v_1/c+v_2/c}{1+v_1v_2/c^2}\ =\ \frac{tangh\ R_1+tangh\ R_2}{1+tangh\ R_1\ tangh\ R_2}\ =\ tangh(R_1+R_2)[/tex]

Thanks for the math. Regarding the deductions, does the final result hold for v1 = -v2? It would make the denominator equal 0.

If

[tex]v_1 = -v_2[/tex]

the denominator is not zero but

[tex]1 - v_1^2/c^2.[/tex]

mdeng

Quote by lightarrow

If

[tex]v_1 = -v_2[/tex]

the denominator is not zero but

[tex]1 - v_1^2/c^2.[/tex]

I meant v_1=-v_2 and |v_1| = c. I guess it still holds.

mdeng

Hi rbj,

Many thanks for all the effort to answer my question.

I think the disconnection between your reasoning and my question is about the understanding of what role the light speed constancy plays in SR. It seems to me that you think that’s implied by the principle of relativity. However, this would mean that Einstein could do away one of the two of his postulates. Since Einstein did not do that, it then follows (blindly, or out of my laziness) that light speed constancy must be independent of and thus can’t be explained by the principle of relativity. But I am having a second thought.

I am not exactly sure why Einstein had to postulate light speed constancy. One explanation is as stated at http://en.wikipedia.org/wiki/Introdu...ial_relativity that the postulate is needed to establish Maxwell’s equation in the time-space 4D space. For the lack of knowledge on Minkowski's formula and my rusty math, I don’t know how this point worked out or what Minkowski’s equation postulates.
---
Therefore, by assuming that the universe has four dimensions that are related by Minkowski's formula the speed of light appears as a constant and it does not need to be assumed to be constant as in Einstein's original approach to special relativity. Notice that c is not explicitly required to be the speed of light. It is a consequence of Maxwell's electrodynamics that light travels with c. There is no such requirement inherent in special relativity.
---
Another explanation may have to do with “dependence on definition of units” as stated below from http://en.wikipedia.org/wiki/Status_...ial_relativity. But I am not sure where “but then the invariance of c is non-trivial” would come from.
---
Because of the freedom one has to select how one defines units of length and time in physics, it is possible to make one of the two postulates of relativity a tautological consequence of the definitions, but one cannot do this for both postulates simultaneously because when combined they have consequences which are independent of one's choice of definition of length and time. For instance, if one defines units of length and time in terms of a physical object (e.g. by defining units of time in terms of transitions of a caesium atom, or length in terms of wavelengths of a krypton atom) then it becomes tautological that the law determining that unit of length or time will be the same in all reference frames, but then the invariance of c is non-trivial. Conversely, if one defines units of length and time in such a way that c is necessarily constant, then the second postulate becomes tautological, but the first one does not; for instance, if the length unit is defined in terms of the time unit and a predetermined fixed value of c, then there is no a priori reason why the number of wavelengths of krypton in a unit of length will be the same in all reference frames (or even in all orientations).
---
There is yet another possible explanation at http://en.wikipedia.org/wiki/Status_...ial_relativity.
---
In fact Maxwell's equations combined with the first postulate of special relativity can be used to deduce the second postulate. Actually electromagnetism is greatly simplified by relativity, as magnetism is simply the relativistic effect obtained when the simple law of electrostatics is put into a relativistic Universe.
---
Perhaps Einstein did not want SR to depend on Maxwell’s equation and as such he would be able to show that Maxwell’s equation is a logical consequence of SR. But again, I don’t know how one would come to conclude “magnetism is simply the relativistic effect obtained when the simple law of electrostatics is put into a relativistic Universe.”
So it seems that we are very close to an agreement. Nevertheless, in addition to the mathematical consequence of Maxwell equation plus the principle of relativity, I’d like to know what mechanics is behind light to allow it travel that way, or “how does light travel at an invariant speed to anyone and everyone”? :)

EDIT: Just noticed that the last "explanation" actually is problematic given that Minkowski's formula is needed in addition to SR's 1st postulate to derive 'c' in SR.

Mentz114

Ming,

thus can’t be explained by the principle of relativity.

You've got completely the wrong way round. It is a postulate of relativity that everyone measures the same speed for light.

The postulate is supported by the fact that the laws of physics require it to avoid contradictions.

Also, is the Wiki really the best source you have ? I must say I find your arguments incomprehensible but I don't think you understand relativity at all.

DaleSpam

Quote by mdeng

I hope/think you are not referring to the question of mine about why light has a constant speed c to anyone and everyone.

As you noted in other posts the more scientific question is "how". Science answers "how" questions much better than "why" questions. However, that was not what I was refering to in this case.

What I am talking about is this:

Quote by mdeng

Well, it's not a proof, is it? "Proof by example" is not a proof

If you refuse to allow experimental evidence in the answer then you are rejecting the scientific method and therefore you are not asking a scientific question. In fact, your question of this thread appears to be a philosophical or mathematical question.

DaleSpam

Quote by rbj

i fail to see how mdeng can accept the broader postulate of relativity, that "any law of nature should be the same at all times; and scientific investigations generally assume that laws of nature are the same regardless of the person measuring them", yet insist that a quantitative parameter of some of those laws can vary and, for some reason, needs yet another postulate to tie it down to a fixed value (at least between inertial observers). i don't get it, and i doubt that mdeng will convince me that i'm the one that's missing something in the logic here.

I tend to agree with you on this point. I have often thought that the first postulate was sufficient and that the second postulate is simply a corolary to the first one. But I have been told by rather reliable sources that I was wrong, they were actually two separate postulates, and I didn't feel strongly enough about it to argue. I have a similar "wrong but not strong" opinion about Newton's first and second laws.

phyti

If the theory is based on the first and second postulates, then the speed of light 'c' is guaranteed, but the abstract mathematical manipulations will not reveal the 'how' or 'why'. The purpose of the theory is to produce numbers that agree with measurements/perceptions by the observer. To explain 'why', you have to analyze the behaviour in terms of physical processes. There is an answer to this, just as there is for time dilation.

mdeng

Quote by DaleSpam

As you noted in other posts the more scientific question is "how". Science answers "how" questions much better than "why" questions. However, that was not what I was refering to in this case.

:) And in the sense of the article I quoted, I agree with you about 'why' vs. 'how'.

Quote by DaleSpam

What I am talking about is this:If you refuse to allow experimental evidence in the answer then you are rejecting the scientific method and therefore you are not asking a scientific question. In fact, your question of this thread appears to be a philosophical or mathematical question.

My statement was actually meant to refer to my misconception of rbj's reasoning as proving one postulate by another or using SR as an absolute truth. I don't refuse experimental evidence at all. That's what physics and all empirical science are about when seeking truth (or "how" :-).

My original question is about the (physical) mechanism/process, not philosophy/abstract-math.

mdeng

Quote by DaleSpam

I tend to agree with you on this point. I have often thought that the first postulate was sufficient and that the second postulate is simply a corolary to the first one. But I have been told by rather reliable sources that I was wrong, they were actually two separate postulates, and I didn't feel strongly enough about it to argue. I have a similar "wrong but not strong" opinion about Newton's first and second laws.

I don't know what your reliable sources are, but what they told you appears to be consistent with what I have read so far (except for some loose introductory articles).

mdeng

Quote by phyti

If the theory is based on the first and second postulates, then the speed of light 'c' is guaranteed, but the abstract mathematical manipulations will not reveal the 'how' or 'why'. The purpose of the theory is to produce numbers that agree with measurements/perceptions by the observer. To explain 'why', you have to analyze the behaviour in terms of physical processes. There is an answer to this, just as there is for time dilation.

Right, I have no issues with the revealing math results or their accuracy, but I am curious about any insights on how nature does 'c' and what this insight may tell us over and above SR. BTW, did you mean "there will be an answer" or there is one already?

rbj

Quote by DaleSpam

I tend to agree with you on this point. I have often thought that the first postulate was sufficient and that the second postulate is simply a corolary to the first one.

i'm glad to think it wasn't just i that was going crazy. like we're in Opposite World where we get to switch who is in a subset of what. are the quantitative parameters of a law part of the law?

I have a similar "wrong but not strong" opinion about Newton's first and second laws.

as if an acceleration rate of zero is a subset of the second law. why would you think such an heretical thing?

lightarrow

Quote by mdeng

I meant v_1=-v_2 and |v_1| = c. I guess it still holds.

In that case R itself is not defined because artgh(1) is not defined.
Note that the case v1 = c cannot however studied in SR because v1 is the speed of the moving ref. frame S' with respect to the stationary ref. frame S (v2 is the speed of the object with respect to S') and we know that no ref. frame with that speed can exist.

*Xeinstein*

Quote by mdeng

What is the physics answer to the question of why light has an invariant speed
to anyone and everyone, other than this is what light is? There must be a
reason why light behaves this way (or perhaps not necessarily this way
always). I'd think something must have happened external to the light to give
it this peculiar property. Put it in another way, what's wrong with the
classical physics where velocity would follow the law of vector arithmetics,
when applied to light?

Thanks,
- Ming

It's a matter of time.
The solution, Einstein explained, lay in a reconception of the idea of time.

Einstein lifted the idea that the speed of light is constant intact from electromagnetic theory, devised forty years earlier by the Scottish-born physicist James Clerk Maxwell. Part of Einstein's larger ambition was to reconcile electromagnetism with Galilean relativity. Then one night in May 1905, after discussing the problem with his longtime friend Michele Besso, Einstein saw how to do so.

Thank you!" Einstein greeted Besso the following morning. I have completely solved the problem."

The solution, he explained, lay in a reconception of the idea of time. Any velocity is simply distance divided by time. In the case of light, though, the velocity isn't just 186,282 miles per second; according to Einstein's postulate, it's always 186,282 miles per second. It's a constant. It's on one side of the equal sign, humming along at its imperturbable rate. On the other side of the equal sign are distance and time, which become, by default, variables. They can undergo as many changes in value as you can imagine, as long as they continue to divide in such a way that the result is 186,282 miles per second. Change the distance, and you have to change the time.

You can solve the problem too.

*Xeinstein*

Quote by belliott4488

I would say that historically we first discovered that the speed of light is invariant and then from that learned the properties of space and time (as described by Special Relativity). Now that we know those properties, however, I would venture to say that it is a property of space and time that massless particles always move at the maximum speed that any object can obtain, which is also invariant for different observers. Light happens to be an example but is otherwise not special.

In other words, I'd say the invariance of the speed of light is a by-product of the underlying properties of space-time, so the question becomes, why are space and time the way they are? I doubt there's a definitive answer for that yet.

I disagree.
I'd say the underlying properties of space-time is a by-product of the invariance of the speed of light which is a postulate of SR

Doc Al

Quote by Xeinstein

I disagree.
I'd say the underlying properties of space-time is a by-product of the invariance of the speed of light which is a postulate of SR

Don't confuse how we deduce the consequences of relativity from the usual postulates with how we interpret "why" things are the way they are. I'd agree with belliott4488 that it's space and time itself that is structured in such a way as to make anything moving with speed c have an invariant speed with respect to any frame. It's interesting that light has such a property, but not fundamental.

*Xeinstein*

Quote by Doc Al

Don't confuse how we deduce the consequences of relativity from the usual postulates with how we interpret "why" things are the way they are. I'd agree with belliott4488 that it's space and time itself that is structured in such a way as to make anything moving with speed c have an invariant speed with respect to any frame. It's interesting that light has such a property, but not fundamental.

I would say Einstein postulated the invariant speed of light in his 1905 paper first.
It was Minkowski who pointed out how important the geometry of spacetime was.
Einstein himself did not at first seem to think geometrically about spacetime.

Doc Al

Einstein used the invariant speed of light to deduce how space and time behaved. (It's not just a "trick of light".) That's his huge contribution. True, the full modern view of the geometry of spacetime came later.

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