Why is c invariant for all FORs? Special R took it as a postulate but it did not explain it,,,
That is correct, no theory can explain its postulates. You would have to look to another theory, however AFAIK all modern theories have the invariance of c as a postulate.
You could use QFT to explain why light travels at c (because photons are massless). But that is not quite the same question as why c is invariant.
EDIT: I forgot to post a link to the FAQ
Because that's the way the cookie crumbles!
That's the way nature works, why does gravity attract rather than repel?
I believe the whole c thing historically came from the study of EM but I could be wrong, history has a wierd way of doing things.
It's a bit chicken and egg-ish. Einstien believed that c had to be constant for all observers and in exploring this turned to time dilation and length contraction. Experiment has demonstrated time dilation - more so than length contraction. However, both are necessary since the observed time dilation isn't enough by itself to keep c constant.
Time dilation and length contraction are therefore fundamental properties of the universe resulting in the invariance of c to all observers. The real question is why does velocity or gravity cause time dilation and length contraction? The answer to this might also explain why light, or rather, massless particles, have a speed limit at all.
Before Einstein, Lorentz and others took the view that length contraction and time dilation of objects moving through an aether explained the invariance of the speed of light.
Einstein took the opposite view that the invariance of the speed of light explained length contraction and time dilation. Under that view, there is no explanation for the invariance of the speed of light, that's just a fundamental symmetry of the universe we happen to live in.
Physicists quite like explanations in terms of symmetry.
That view seems backward. In the current model spacetime predates matter. And the invariance of c is only possible due to time dilation and length contraction. Eesh, anyone know a shorthand for that? How about "the phenomenon"?
If A logically implies B and B logically implies A, then you can choose to say "A causes B" or "B causes A".
So I could just as easily say "time dilation and length contraction are only possible due to the invariance of c."
It's a postulate, so it would be easy (and unhelpful) to say that it doesn't have to be explained. You choose a postulate, you apply some logic, you get some results that are valid assuming the postulate is valid, and you're done.
But in fact there are three good reasons, two before the fact and one after, why Einstein chose this particular postulate.
1) The principle of relativity says that we don't expect the laws of physics to change with motion. An experiment performed in a windowless and sealed laboratory in December can be expected to produce the same results in June as in December, even though (because of the Earth's motion about the sun) the laboratory is moving in a different direction at many miles a second in June and in December. The speed of light can be calculated from Maxwell's equations of electricity and magnetism, the principle of relativity says that we all use the same equations of electricity and magnetism, so we all get the same speed of light if the world really works that way.
2) There is much experimental evidence, starting with the MM experiment, that suggests that the world really does work those way.
So this looks like a good postulate to start with. And if you do start with it, you end up with special relativity and we come to the third good reason to like this postulate:
3) There is an enormous amount of experimental evidence to support the conclusions of special relativity.
Thanks. Bit of a fingerful to type.
That's a big leap from implications to suggesting either can cause the other... How exactly do you suggest a photon might cause time dilation? Special Relativity, on the otherhand, well covers how time dilation... Lorentz symmety causes invariant c. And the experimental evidence would seem to take us beyond stating time dilation is an implication.
It may not be entirely related to the thread, but I just want to ask a question:
Is it the speed of all massless particles that are invariant, or is it just the speed of light itself that is invariant in all reference frames? If I were to observe the velocity of another massless object, such as a gauge boson, would it also remain constant.
All massless particles move at the invariant speed c.
This how the logical theory works. But in physics we always looking for a theory to explain things in a more fundamental base not just to use a chain of logical statements to reach a result!. Therefore, it is important to know how to start a good start in order to have a beautiful theory not just a logic theory. I can build up a new theory started from " the rate of heat dissipation from a hot body is directly proportional to its total surface area" but that would be a weak theory because we still have more facts to even explain that statement from a more basic logic such as the first law of thermodynamics,,, I feel that " Not all postulates can be stated in an equal Degree of Freedom"
The invariance of c needs to be explained, not on basis of length contraction & time dilatation, but on a mere basic theory possibly involving the electrodynamics
Most of these 'Why?' questions cannot be answered, other than to say, 'That's the way the universe is.'. You might find it instructive to watch Feynman's brief lecture on the difficulty of answering 'Why?'
In regards to the main question, it depends on what you mean by "why". If you are asking for some philosophical reason, then the question is the same as asking "why is there gravity", for which the answer for a physicist would probably be "it just is". Science does not have an answer to those questions, but then again, it does not deal with "why", but with "how".
Good question, beacause Einstein does not mention it in his paper http://www.fourmilab.ch/etexts/einstein/specrel/www/ when he arrives at the transformation of coordinates.
SR took the invariance of the speed of light as a an assumption, though Einstein did not explain why he singled out light as a special case (Probably because electromagnetism was the only known field at the time).
See post #3 in this thread for a better explanation:
In a standford lecture on SR by Leonard Susskind, he explained it that Einstien chose to assume Maxwell was right about the speed of light being a fundamental part of the EM equations and therefore Galilean additive velocities needed to be modified.
c is invariant for all Frames Of Reference because of the way the 4-dimensional universe is structured:
1) All observers move along their 4-dimensional world lines
2) The continuous sequence of 3-dimensional worlds that an observer lives in is associated with a space-like coordinate that is rotated symmetrically with respect to the rotation of the observer's world line.
3) Any photon world line always bisects the angle between the world line and space-like coordinate for all observers, regardless of the slope of the world line (regardless of velocity). Notice how, resulting from the 4-dimensional universe structure shown below for observers with different velocities, every observer will find that the ratio of distance along the X1 dimension to the distance along the X4 dimension is unity (X1/X4 = 1), i.e., speed of light is invariant among all observers. This will be the case for only objects having a world line that bisects the angle between X1 and X4 (massless bosons).
So, perhaps a more fundamental question is, "Why is the universe structured with the observers' coordinates oriented the way they are?"
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