Second postulate of Special theory of relativity-help

[ravisastry]

Hi,

Pls help me understand the reason for 2nd postulate of special theory of relativity. why is the speed of light independent of the source ? after reading some of the threads, i got to know that there is no mathematical basis for this constancy.
I thought deep into this and figured out that electron movement across the different states in an atom is independent of the motion of atom. Electrons orbit in fixed states & when they jump across these states(higher or lower energy), it happens with a fixed velocity...which is the reason why photons are emitted at C, irrespective of the motion of the source. This can also be calculated mathematically (im a novice in this field :) ) pls let me know if this argument can be considered ?

thanks
Ravi

 

[Dale]

Pls help me understand the reason for 2nd postulate of special theory of relativity. why is the speed of light independent of the source ? after reading some of the threads, i got to know that there is no mathematical basis for this constancy.

The reason is simply because it fits the data.

 

[jtbell]

Exactly. It's a postulate, so it's a starting point for the theory which cannot be deduced from anything else in the theory. To attempt to do so would be circular logic, because everything else in the theory is derived from its postulates. One gains confidence in a postulate by testing it experimentally, and by testing other predictions of the theory that is derived from it.

 

[ravisastry]

Exactly. It's a postulate, so it's a starting point for the theory which cannot be deduced from anything else in the theory. To attempt to do so would be circular logic, because everything else in the theory is derived from its postulates. One gains confidence in a postulate by testing it experimentally, and by testing other predictions of the theory that is derived from it.

well,there has to be an explanation... even though its an observed phenomena, i believe there is a reason behind it. will try to come up with a mathematical reasoning for the same

 

[Dale]

If you come up with some mathematical proof then you will have started from some initial set of axioms. Then we will be able to ask "why those axioms", and all you will be able to respond is "because it fits the data".

You may choose to axiomatize a physical theory in a variety of different ways, changing which parts of the theory are considered underived postulates and which are considered derived consequences. But in the end you can never have a better reason for the postulates of any physical theory than "because it fits the data".

 

[HallsofIvy]

The speed of light is "postulated" to be constant from all frames because of the basic reason for any "postulate" or other basic fact of physics: experimental evidence. The entire structure of relativity is then intended to extend, illuminate, and, hopefully, explain, those experimental results.

 

[Austin0]

The speed of light is "postulated" to be constant from all frames because of the basic reason for any "postulate" or other basic fact of physics: experimental evidence. The entire structure of relativity is then intended to extend, illuminate, and, hopefully, explain, those experimental results.

I thought it was theoretically neccessitated by the Maxwell electrodynamic maths?
I assumed without being familiar with the math, that the math itself both indicated that c would be constant and demanded it to be, to maintain invariance of electrodynamics between frames.
AM I totally misunderstanding the origen of SR ? I thought the experimental evidence was electrodynamic rather than the limited measurement of the speed of light available at the time.

 

[Dale]

I thought it was theoretically neccessitated by the Maxwell electrodynamic maths?

Sure. If you assume Maxwell's equations and assume the first postulate then you can derive the second postulate. But then why do you assume Maxwell and the first postulate? Because it fits the data.

 

[bcrowell]

FAQ: Why is the speed of light the same in all frames of reference?

The first thing to worry about here is that when you ask someone for a satisfying answer to a "why" question, you have to define what you think would be satisfying. If you ask Euclid why the Pythagorean theorem is true, he'll show you a proof based on his five postulates. But it's also possible to form a logically equivalent system by replacing his parallel postulate with one that asserts the Pythagorean theorem to be true; in this case, we would say that the reason the "parallel theorem" is true is that we can prove it based on the "Pythagorean postulate."

Einstein's original 1905 postulates for special relativity went like this:

P1 - "The laws by which the states of physical systems undergo change are not affected, whether these changes of state be referred to the one or the other of two systems of co-ordinates in uniform translatory motion."

P2 - "Any ray of light moves in the 'stationary' system of co-ordinates with the determined velocity c, whether the ray be emitted by a stationary or by a moving body."

From the modern point of view, it was a mistake for Einstein to single out light for special treatment, and we imagine that the mistake was made because in 1905 the electromagnetic field was the only known fundamental field. Really, relativity is about space and time, not light. We could therefore replace P2 with:

P2* - "There exists a velocity c such that when something has that velocity, all observers agree on it."

And finally, there are completely different systems of axioms that are logically equivalent to Einstein's, and that do not take the frame-independence of c as a postulate (Rindler 1979).

For someone who likes axioms P1+P2, the frame-independence of the speed of light is a postulate, so it can't be proved. The reason we pick it as a postulate is that it appears to be true based on observations such as the Michelson-Morley experiment.

If we prefer P1+P2* instead, then we actually don't know whether the speed of light is frame-independent. What we do know is that the empirical upper bound on the mass of the photon is extremely small (Lakes 1998), and we can prove that massless particles must move at the universal velocity c.

In a system such as Rindler's, the existence of a universal velocity c is proved rather than assumed, and the behavior of photons is related empirically to c in the same way as for P1+P2*. We then have a satisfying answer to the "why" question, which is that existence of a universal speed c is a property of spacetime that must exist because spacetime has certain other properties (basically, it has some symmetries, and it doesn't have universal simultaneity).

Rindler, Essential Relativity: Special, General, and Cosmological, 1979, p. 51

R.S. Lakes, "Experimental limits on the photon mass and cosmic magnetic vector potential", Physical Review Letters 80 (1998) 1826, http://silver.neep.wisc.edu/~lakes/mu.html

 

[starthaus]

.

In a system such as Rindler's, the existence of a universal velocity c is proved rather than assumed, and the behavior of photons is related empirically to c in the same way as for P1+P2*. We then have a satisfying answer to the "why" question, which is that existence of a universal speed c is a property of spacetime that must exist because spacetime has certain other properties (basically, it has some symmetries, and it doesn't have universal simultaneity).

Rindler, Essential Relativity: Special, General, and Cosmological, 1979, p. 51

Rindler took out this from his 2006 edition

 

[ravisastry]

Thanks for the discussion, I'm learning here. I have few doubts, pls clarify them. consider a hydrogen atom. The setup of electron or electron wave revolving around proton is fixed and this forms a closed body. Any amount of shaking the H atom won't disturb this electron-proton distance and even when an excited electron falls back to its ground state, it does with a fixed speed, which is immaterial of the motion of H atom as a whole. now because of this fixed speed with which the electrons jumps across states in any atom, the photons speed is always C(in vacuum). Can this be the reason of constant C in an apparatus which emits photons or captures photons to measure its speed ?

 

[bcrowell]

Any amount of shaking the H atom won't disturb this electron-proton distance and even when an excited electron falls back to its ground state, it does with a fixed speed, which is immaterial of the motion of H atom as a whole.

It doesn't do it with a fixed speed. It doesn't do it with any speed. Speed isn't a concept that applies to this atomic transition.

now because of this fixed speed with which the electrons jumps across states in any atom, the photons speed is always C(in vacuum). Can this be the reason of constant C in an apparatus which emits photons or captures photons to measure its speed ?

No.

 

[Meir Achuz]

"why is the speed of light independent of the source ?"
That is a poor way to put it, although it is what Einstein said in his first paper.
The speed of light independent of the source for sound and in the aether theory.

A better way to put it is that light has the same speed in any Lorentz frame.
The second postulate is not necessary if the first is interpreted to include electrodynamics, which is only Lorentz covariant if the speed of light is the same in all Lorentz systems.

 

[Austin0]

Originally Posted by ravisastry
Any amount of shaking the H atom won't disturb this electron-proton distance and even when an excited electron falls back to its ground state, it does with a fixed speed, which is immaterial of the motion of H atom as a whole.

It doesn't do it with a fixed speed. It doesn't do it with any speed. Speed isn't a concept that applies to this atomic transition.

Is this statement in the context of non-locality of electrons and the assumption of instantaneous transitions as it appears is the interpretation with tunneling?

Originally Posted by ravisastry
now because of this fixed speed with which the electrons jumps across states in any atom, the photons speed is always C(in vacuum). Can this be the reason of constant C in an apparatus which emits photons or captures photons to measure its speed ?

No.

Isn't an assumptionn of c part of the electrostatic interactions between charged particles though?

 

[HallsofIvy]

Thanks for the discussion, I'm learning here. I have few doubts, pls clarify them. consider a hydrogen atom. The setup of electron or electron wave revolving around proton is fixed and this forms a closed body. Any amount of shaking the H atom won't disturb this electron-proton distance and even when an excited electron falls back to its ground state, it does with a fixed speed, which is immaterial of the motion of H atom as a whole. now because of this fixed speed with which the electrons jumps across states in any atom, the photons speed is always C(in vacuum). Can this be the reason of constant C in an apparatus which emits photons or captures photons to measure its speed ?

Pretty much nothing you say here is actually true. This is the old "planetary" model of the atom which does not fit quantum mechanics. A more modern (and hopefully more accurate) model of the atom is that the electron exists in various "clouds" around the nucleus, the specific nature of the cloud depending on the energy. When an electron loses energy by emitting a photon, it does not "move" at any constant speed from one orbit to another. The nature of the cloud changes.

And, in any case, I think you have a misunderstanding of what is mean by the "constant speed of light". If you throw a baseball to another person, with, say, a velocity of 50 mph, it will have, pretty closely, a "constant speed" (yes, it loses energy and speed slightly but ignore that). Now suppose you are standing on the back of a truck, moving at 50 mph relative to the road, to a person standing on the side of the road. If you throw that baseball at a speed of 50 mph relative to you, then, classically, it will reach the other person with a speed of 50+ 50= 100 mph relative to the other person.

Light is not like that. If one person, standing on the side of the road, and another person, standing in the truck going 50 mph, shine flashlights at a third person standing on the side of the road, the two light beams will NOT reach the third person at speeds of "c" and "c+ 50" mph. They will both reach the third person at speeds of "c". The speed of light is constant no matter how fast the source is moving relative to you. That is the key point of special relativity.

 

[ravisastry]

Pretty much nothing you say here is actually true. This is the old "planetary" model of the atom which does not fit quantum mechanics. A more modern (and hopefully more accurate) model of the atom is that the electron exists in various "clouds" around the nucleus, the specific nature of the cloud depending on the energy. When an electron loses energy by emitting a photon, it does not "move" at any constant speed from one orbit to another. The nature of the cloud changes.

And, in any case, I think you have a misunderstanding of what is mean by the "constant speed of light". If you throw a baseball to another person, with, say, a velocity of 50 mph, it will have, pretty closely, a "constant speed" (yes, it loses energy and speed slightly but ignore that). Now suppose you are standing on the back of a truck, moving at 50 mph relative to the road, to a person standing on the side of the road. If you throw that baseball at a speed of 50 mph relative to you, then, classically, it will reach the other person with a speed of 50+ 50= 100 mph relative to the other person.

Light is not like that. If one person, standing on the side of the road, and another person, standing in the truck going 50 mph, shine flashlights at a third person standing on the side of the road, the two light beams will NOT reach the third person at speeds of "c" and "c+ 50" mph. They will both reach the third person at speeds of "c". The speed of light is constant no matter how fast the source is moving relative to you. That is the key point of special relativity.

Be it the planetary model or the cloud stuff, the change in electron cloud orientation happens in a finite and systematic manner (i believe, since electron has mass). Also, in the last example which you gave about 50mph...people end up with saying the speed of light is measured. I'm interested in knowing how it is measured. when the photon strikes the apparatus with + or -C, the change in atomic configuration(electron cloud) of the apparatus again happens in a fixed manner. my doubt is...what if a photon actually hits the atom or molecule with >c, but due to the finite speed of cloud reconfiguration(not sure how ?) we 'may' measure it as c ? this may be a dumb doubt, but certainly didnt want to ignore this possibility.

 

[Dale]

I am not sure which measuring device for the speed of light has a "cloud reconfiguration". Why don't you briefly go through the measurements of the speed of light listed below and tell us which experiments you think may have the "cloud reconfiguration" delay.

http://www.edu-observatory.org/phys...iments.html#Tests_of_Einsteins_two_postulates

 

[Austin0]

Be it the planetary model or the cloud stuff, the change in electron cloud orientation happens in a finite and systematic manner (i believe, since electron has mass). Also, in the last example which you gave about 50mph...people end up with saying the speed of light is measured. I'm interested in knowing how it is measured. when the photon strikes the apparatus with + or -C, the change in atomic configuration(electron cloud) of the apparatus again happens in a fixed manner. my doubt is...what if a photon actually hits the atom or molecule with >c, but due to the finite speed of cloud reconfiguration(not sure how ?) we 'may' measure it as c ? this may be a dumb doubt, but certainly didnt want to ignore this possibility.

Consider this: Whatever the electron reaction time is, it will be consistent.
The speed of light is consistent as measured in an inertial frame over any distance.
SO if the electron reaction is the same when registering a photon over a long distance as over a short distance it could not be a factor in the invariant measurements in these two cases,,,,, Yes?