High School Constancy of the speed of light

[dayalanand roy]

It's an experimental fact that the principle of relativity is applicable to light. So ignoring this fact doesn't make much sense.
Michelson–Morley experiment
Kennedy–Thorndike experiment
de Sitter double star experiment
Absence of vacuum dispersion and birefringence of light

Probably i was unable to express myself. The above experiments are the bases to theory of relativity. I was talking about principle of relativity (Galilean) - that is physical observations are invariant to frames of reference.t

But I was talking about consequences of the two postulates, not the consequences of the Lorentz transformations.
There definitely is no upper limit on the energy. This is why you see more and more energetic particle accelerators being created.
I don't think justify is the best word here, perhaps it should be explain. And there are other ways to explain it, but none of them are satisfactory either because they imply the existence of an ether or don't provide an explanation that matches what's observed.
You want to suppose that the laws of physics don't properly describe the behavior of Nature when it's been demonstrated that these particular laws do indeed describe it?!

That's a rabbit hole you can go down, I suppose, but I can't imagine why you'd want to do that. The goal is to provide descriptions that match observation.[/QUOT

But I was talking about consequences of the two postulates, not the consequences of the Lorentz transformations.
There definitely is no upper limit on the energy. This is why you see more and more energetic particle accelerators being created.
I don't think justify is the best word here, perhaps it should be explain. And there are other ways to explain it, but none of them are satisfactory either because they imply the existence of an ether or don't provide an explanation that matches what's observed.
You want to suppose that the laws of physics don't properly describe the behavior of Nature when it's been demonstrated that these particular laws do indeed describe it?!

That's a rabbit hole you can go down, I suppose, but I can't imagine why you'd want to do that. The goal is to provide descriptions that match observation.

Thanks a lot.
I don't suppose that the laws of physics do not describe the behaviour of nature. I have full faith in them.
I was reading Einstein's "Theory of relativity- special and general". What I could follow from this book is this-
There are two laws of physics. One is the principle of relativity that has its origin from Galeleo. According to it, physical observations are independent of the frame of reference. All measurements done in a rest frame should give the same results when performed in a moving frame. Probably this principle was initially proposed for material objects only.
The second law was about the constancy of the speed of light, which was also proved by many experiments.
But this second law was probably not agreeing with the first law. To remove this disagreement, Einstein created the STR, which perfectly explained it.
I am not sure if I have properly understood the above case. But if I have understood it, I only want to ask that the principle of relativity was mainly about material objects, and electromagnetic radiations behave differently from matter (have no rest mass, always travel at speed c), so naturally they may not agree with all the laws shown by material objects.
After all, in order to remove that disagreement, Einstein had to propose laws like time dilation and length contraction, the physical bases of which we are yet to appreciate.
Anyway, I thank everyone who participated in this discussion. I have learned a lot.

 

[dayalanand roy]

Relativity doesn't justify that the speed of light is invariant. The entire thing is simply the logical consequences of assuming that the speed of light is invariant - so justifications based on the maths of relativity are circular (although they do reassure us that relativity is not self-contradictory). The only thing we can do is convert those consequences into testable predictions, work out the predictions of Newton, and compare to experiment.
Not really. Maxwell's equations do predict an invariant speed of light which is inconsistent with Newtonian physics, that is true. Einstein was the first person to realize that the problem was with Newton not Maxwell, and he simply took the invariant speed of light at face value and worked out the implications.

But this still isn't a justification for an invariant speed of light, since Maxwell's equations assume the theory of relativity. That's not completely obvious, but it turns out that the first and second equations combine to form a single equation operating on a tensor, as do the third and fourth. That makes no sense unless you assume a Minkowski spacetime. Maxwell, of course, had no idea that was assuming any such thing. He simply described what he saw.

So in summary, you cannot justify the existence of an invariant speed on theoretical grounds (so far, anyway - who knows what the future may bring). All such arguments are circular. You can only test the implications empirically - and that last step is what separates science from philosophy.
...then we are not describing anything like our universe. What would be the point?

Thanks. It is highly illuminating.

 

[Herman Trivilino]

All measurements done in a rest frame should give the same results when performed in a moving frame. Probably this principle was initially proposed for material objects only. The second law was about the constancy of the speed of light, which was also proved by many experiments. But this second law was probably not agreeing with the first law. To remove this disagreement, Einstein created the STR, which perfectly explained it. I am not sure if I have properly understood the above case. But if I have understood it, I only want to ask that the principle of relativity was mainly about material objects, and electromagnetic radiations behave differently from matter (have no rest mass, always travel at speed c), so naturally they may not agree with all the laws shown by material objects.

The goal is to create laws of physics that are more general. Galilean relativity, when applied to light, doesn't work. Einsteinian relativity does. It works for both light and for what you are calling material objects. Galilean relativity works for neither of those. It seems to work at low speeds, so it seems to work for what you are calling material objects but only when they move at low speeds.

After all, in order to remove that disagreement, Einstein had to propose laws like time dilation and length contraction,

He did not propose them. He showed that they are consequences of the two postulates.

 

[Sorcerer]

Probably i was unable to express myself. The above experiments are the bases to theory of relativity. I was talking about principle of relativity (Galilean) - that is physical observations are invariant to frames of reference.t

But that is exactly what the Einstein’s relativity says. The principle of relativity applies in both Galileo and Einstein, but Galileo’s spacetime laws were incompatable with Maxwell’s equations. Einstein fixed that problem, so that the principle of relativity didn’t hold for just mechanics (like Galileo’s did).

 

[Ibix]

One is the principle of relativity that has its origin from Galeleo. According to it, physical observations are independent of the frame of reference. All measurements done in a rest frame should give the same results when performed in a moving frame. Probably this principle was initially proposed for material objects only.

I'm not sure this makes sense. I can imagine a universe where the principle of relativity applies, and I can imagine one where it doesn't apply. I have trouble with one where the principle applies to some things and not others. What about interactions between members of the two classes? Would they respect the principle of relativity and violate the rules for the no-relativity particles? Or vice versa? Either way, something ends up behaving in a way it can't behave.

The idea of the ether respected relativity. The laws of physics would be the same in all frames, but the physical situation picked out an interesting frame for electromagnetism - the rest frame of the ether. Once we'd found that, more sensitive experiments would be expected to show electromagnetic phenomena deviating from Maxwell in other frames, and we could fix his equations so that they respected Galilean relativity. Of course, it didn't work out that way.

The second law was about the constancy of the speed of light, which was also proved by many experiments.

Although you are correct that we had quite a lot of evidence of the invariance of light speed before 1905, I don't think anyone had recognised that this was what we had. We just had a lot of inexplicanle experimental results. (In a way, this is the exact opposite of what we have now, where we know we have theoretical problems but the experiments keep stubbornly matching the theories...)

 

[dayalanand roy]

The goal is to create laws of physics that are more general. Galilean relativity, when applied to light, doesn't work. Einsteinian relativity does. It works for both light and for what you are calling material objects. Galilean relativity works for neither of those. It seems to work at low speeds, so it seems to work for what you are calling material objects but only when they move at low speeds.
He did not propose them. He showed that they are consequences of the two postulates.

Thanks a lot. I am gaining.

 

[dayalanand roy]

I'm not sure this makes sense. I can imagine a universe where the principle of relativity applies, and I can imagine one where it doesn't apply. I have trouble with one where the principle applies to some things and not others. What about interactions between members of the two classes? Would they respect the principle of relativity and violate the rules for the no-relativity particles? Or vice versa? Either way, something ends up behaving in a way it can't behave.

The idea of the ether respected relativity. The laws of physics would be the same in all frames, but the physical situation picked out an interesting frame for electromagnetism - the rest frame of the ether. Once we'd found that, more sensitive experiments would be expected to show electromagnetic phenomena deviating from Maxwell in other frames, and we could fix his equations so that they respected Galilean relativity. Of course, it didn't work out that way.

Although you are correct that we had quite a lot of evidence of the invariance of light speed before 1905, I don't think anyone had recognised that this was what we had. We just had a lot of inexplicanle experimental results. (In a way, this is the exact opposite of what we have now, where we know we have theoretical problems but the experiments keep stubbornly matching the theories...)

Thanks and regards.

 

[dayalanand roy]

But that is exactly what the Einstein’s relativity says. The principle of relativity applies in both Galileo and Einstein, but Galileo’s spacetime laws were incompatable with Maxwell’s equations. Einstein fixed that problem, so that the principle of relativity didn’t hold for just mechanics (like Galileo’s did).

Thanks and regards.

 

[Sorcerer]

Thanks and regards.

Just for a quick little history nugget, in Einstein's first major paper on relativity he highlighted the issue. For example, it was believed that the following two situations were two different phenomena:

(1) If you move a magnet near a conductor at rest, it produces an electric current.
(2) If you move a conductor near a magnet at rest, it also produces an electric current.​

Einstein recognized that they were the same phenomenon, and in fact, were manifestations of the principle of relativity. The key question is, of course, which one is "really" moving and which one is "really" at rest? Here is a PDF of his paper. The very first paragraph discusses this:

http://hermes.ffn.ub.es/luisnavarro/nuevo_maletin/Einstein_1905_relativity.pdf

Here is the relevant quote:

"It is known that Maxwell’s electrodynamics—as usually understood at the
present time—when applied to moving bodies, leads to asymmetries which do
not appear to be inherent in the phenomena. Take, for example, the recipro-
cal electrodynamic action of a magnet and a conductor. The observable phe-
nomenon here depends only on the relative motion of the conductor and the
magnet, whereas the customary view draws a sharp distinction between the two
cases in which either the one or the other of these bodies is in motion. For if the
magnet is in motion and the conductor at rest, there arises in the neighbour-
hood of the magnet an electric field with a certain definite energy, producing
a current at the places where parts of the conductor are situated. But if the
magnet is stationary and the conductor in motion, no electric field arises in the
neighbourhood of the magnet. In the conductor, however, we find an electro-
motive force, to which in itself there is no corresponding energy, but which gives
rise—assuming equality of relative motion in the two cases discussed—to elec-
tric currents of the same path and intensity as those produced by the electric
forces in the former case."​

 

[dayalanand roy]

Just for a quick little history nugget, in Einstein's first major paper on relativity he highlighted the issue. For example, it was believed that the following two situations were two different phenomena:

(1) If you move a magnet near a conductor at rest, it produces an electric current.
(2) If you move a conductor near a magnet at rest, it also produces an electric current.​

Einstein recognized that they were the same phenomenon, and in fact, were manifestations of the principle of relativity. The key question is, of course, which one is "really" moving and which one is "really" at rest? Here is a PDF of his paper. The very first paragraph discusses this:

http://hermes.ffn.ub.es/luisnavarro/nuevo_maletin/Einstein_1905_relativity.pdf

Here is the relevant quote:

"It is known that Maxwell’s electrodynamics—as usually understood at the
present time—when applied to moving bodies, leads to asymmetries which do
not appear to be inherent in the phenomena. Take, for example, the recipro-
cal electrodynamic action of a magnet and a conductor. The observable phe-
nomenon here depends only on the relative motion of the conductor and the
magnet, whereas the customary view draws a sharp distinction between the two
cases in which either the one or the other of these bodies is in motion. For if the
magnet is in motion and the conductor at rest, there arises in the neighbour-
hood of the magnet an electric field with a certain definite energy, producing
a current at the places where parts of the conductor are situated. But if the
magnet is stationary and the conductor in motion, no electric field arises in the
neighbourhood of the magnet. In the conductor, however, we find an electro-
motive force, to which in itself there is no corresponding energy, but which gives
rise—assuming equality of relative motion in the two cases discussed—to elec-
tric currents of the same path and intensity as those produced by the electric
forces in the former case."​

Thank u so much sir.
I have read this paper. I do have a copy of the book that compiles his papers.
But as the papers are highly technical, his book, Relativity: special and general theory helps me better. And more helpful is the book, The universe and Mr Einstein by Lincoln Barnette, to which Einstein himself wrote a preface. Barnette has given some hint towards the physical meaning of time dilation, and as Einstein has wrote its preface, I shall presume that he might not be against Barnette's views.
But sir, my limited thinking capacity can appreciate the above case of relative motion only for limted contexts, for calculation of distance and relative speeds ect. I am unable to treat the photons and the stationary torch that is emitting them on equal footing. This needs a higher thinking capacity that I do not have.
My intention behind starting this thread was only to know one thing- why cannot we accept that Maxwell's theory of electrodynamics (about constancy of light speed) is itself a law and we do not need any other law to explain it?
And I have gained a lot from the discussions done here.
Thanks and regards.

 

[Sorcerer]

Thank u so much sir.
I have read this paper. I do have a copy of the book that compiles his papers.
But as the papers are highly technical, his book, Relativity: special and general theory helps me better. And more helpful is the book, The universe and Mr Einstein by Lincoln Barnette, to which Einstein himself wrote a preface. Barnette has given some hint towards the physical meaning of time dilation, and as Einstein has wrote its preface, I shall presume that he might not be against Barnette's views.
But sir, my limited thinking capacity can appreciate the above case of relative motion only for limted contexts, for calculation of distance and relative speeds ect. I am unable to treat the photons and the stationary torch that is emitting them on equal footing. This needs a higher thinking capacity that I do not have.
My intention behind starting this thread was only to know one thing- why cannot we accept that Maxwell's theory of electrodynamics (about constancy of light speed) is itself a law and we do not need any other law to explain it?
And I have gained a lot from the discussions done here.
Thanks and regards.

Based on my limited knowledge of Maxwell’s equations, they come with special relativity already built in. I would say special relativity isn’t any new laws, but is rather the logical consequence of Maxwell’s equations applying to both electromagnetism and mechanics.But if you are looking for something that appears a bit more fundamental, look up the fine structure constant, something I’ve learned a little bit about since being here.

 

[dayalanand roy]

Based on my limited knowledge of Maxwell’s equations, they come with special relativity already built in. I would say special relativity isn’t any new laws, but is rather the logical consequence of Maxwell’s equations applying to both electromagnetism and mechanics.But if you are looking for something that appears a bit more fundamental, look up the fine structure constant, something I’ve learned a little bit about since being here.

Thanks sir.
This is what i have thinking about- Special relativity is just a logical consequence of Maxwell's law and Lorentz transformation, not a new law.
But i am unable to follow what you mean by "fine structure constsnt". I shall be obliged to have it more clarified..
Regards.

 

[PeterDonis]

i am unable to follow what you mean by "fine structure constant"

Have you tried Google?

 

[Ibix]

Special relativity is just a logical consequence of Maxwell's law and Lorentz transformation, not a new law.

Special relativity is the Lorentz transforms. Everything follows from them.

But if you want to regard relativity as a consequence of electromagnetism then you should also argue that it is (independently) a consequence of the strong force, the weak force, and gravity, since all of those are also relativistic theories.

 

[dayalanand roy]

Have you tried Google?

I am trying.
Thanks

 

[dayalanand roy]

Special relativity is the Lorentz transforms. Everything follows from them.

But if you want to regard relativity as a consequence of electromagnetism then you should also argue that it is (independently) a consequence of the strong force, the weak force, and gravity, since all of those are also relativistic theories.

Thanks.
I agree.

 

[Ziang]

Time dilation and length contraction are actually logical consequences of the speed of light (really, electromagnetic waves) being independent of its source of motion.

They are logical or not depends on how light propagates in a vacuum.
If light travels like a particle then they are logical.
If light travels like waves then they might not be logical.

 

[PeterDonis]

If light travels like a particle then they are logical.
If light travels like waves then they might not be logical.

No, this makes no difference. Maxwell's Equations are Lorentz invariant, and they describe the propagation of electromagnetic waves.

 

[Sorcerer]

They are logical or not depends on how light propagates in a vacuum.
If light travels like a particle then they are logical.
If light travels like waves then they might not be logical.

Are you aware that Maxwell’s equations, which are built inherently with the rules of special relativity, describe electromagnetic propagation as a wave? This can be relatively easily derived from Maxwell’s equations with undergraduate math (“easily” if you’ve taken two semesters of differential equations and three or four of calculus). You get a second order partial differential equation - in particular, a WAVE equation - with a phase velocity that “just so happens” to be the speed of light.

As has already been stated, Maxwell’s equations are Lorentz invariant (that is, they are built with special relativity already in them), AND they describe light as a wave.

So basically, and sorry if this comes as rudeness, but your claim is simply false.Edited to add:

More information: https://en.m.wikipedia.org/wiki/Electromagnetic_wave_equation

 

[Ziang]

Let us see the following picture

Light is a transverse wave. In the spaceship the light path is vertical. So the oscillations (blue waves) are horizontal as shown in section a.
According to SR, the diagonal red line in section b is a light path with respect to a stationary observer (who is standing on the ground).

Argument
Physics laws are the same to all observers. Light must be a transverse wave to all observers.
When the spaceship is moving at a constant velocity v, the blue waves would appear as shown in section b, with respect to the stationary observer. These blue waves are not perpendicular to the diagonal red line. So the diagonal red line is not a light path with respect to the stationary observer.

 

[Ibix]

Let us see the following picture

View attachment 223357Light is a transverse wave. In the spaceship the light path is vertical. So the oscillations (blue waves) are horizontal as shown in section a.
According to SR, the diagonal red line in section b is a light path with respect to a stationary observer (who is standing on the ground).

Argument
Physics laws are the same to all observers. Light must be a transverse wave to all observers.
When the spaceship is moving at a constant velocity v, the blue waves would appear as shown in section b, with respect to the stationary observer. These blue waves are not perpendicular to the diagonal red line. So the diagonal red line is not a light path with respect to the stationary observer.

This argument is based on a misconception. Light is not a mechanical wave. There is nothing moving transversely in an EM wave. The electric and magnetic field vectors at a point change in a sinusoidal way, but nothing moves. Transforming the electromagnetic field tensor will give you a transverse electromagnetic wave in both frames, qualitatively because there's cross talk between the electric field as measured in one frame and the magnetic field in the other.

Furthermore your argument is obviously wrong, since you are arguing that light waves aren't light waves in another frame.

 

[PeterDonis]

Light is a transverse wave.

Not in the sense you mean. @Ibix's response is correct. Please do not post further on this without taking the time to learn the correct model of light.

 

[Dale]

Light is a transverse wave.

You clearly don’t know what this means. It does not mean that light wiggles back and forth as you show in your diagram, it means that light can be polarized.

Write the equation for a plane wave, propagating along z and polarized along x. Transform it and you have a polarized plane wave. Similarly for a plane wave propagating along z and polarized along y.

 

[Sorcerer]

I believe this link covers most of the bases here. It is extremely informative about why electromagnetic phenomena are waves AND why they are inherently Lorentz invariant. It also points out the similar relation ship the E and B fields have with the space and time interval. Very interesting read for those interested in learning.

http://www.mathpages.com/rr/s2-02/2-02.htm

 

[JulianM]

You clearly don’t know what this means. It does not mean that light wiggles back and forth as you show in your diagram, it means that light can be polarized.

Write the equation for a plane wave, propagating along z and polarized along x. Transform it and you have a polarized plane wave. Similarly for a plane wave propagating along z and polarized along y.

What then is the meaning of a polarized wave? It is created by placing a slit in the light beam so that only waves which are aligned with the slit pass through.

I don't see how the equations help one to visualize this.

 

[Nugatory]

What then is the meaning of a polarized wave? It is created by placing a slit in the light beam so that only waves which are aligned with the slit pass through.

Nothing is wiggling though. At every point in space there is an electrical field, and at every moment that field points in some direction. If the direction is always the same (so only the amplitude of the field is changing with time - written as a vector we have $\vec{E}=(A\sin{\omega}t)\hat{x}$ where $\hat{x}$ is a fixed unit vector in the direction of polarization), then we say that the wave is linearly polarized.

 

[JulianM]

Nothing is wiggling though. At every point in space there is an electrical field, and at every moment that field points in some direction. If the direction is always the same (so only the amplitude of the field is changing with time - written as a vector we have $\vec{E}=(A\sin{\omega}t)\hat{x}$ where $\hat{x}$ is a fixed unit vector in the direction of polarization), then we say that the wave is linearly polarized.

If that were true then surely a light beam could be polarized by a pinhole and a slit would not be necessary.

 

[Nugatory]

If that were true then surely a light beam could be polarized by a pinhole and a slit would not be necessary.

The direction of polarization (the direction that vector $\hat{x}$ points) is necessarily perpendicular to the direction of propagation of the light.

A linear polarizer doesn't really use a slit - that's just the way the illustrations are drawn. For an easy-to-understand example of how a polarizer might really work, you might try the Wikipedia description of a wire-grid polarizer.

 

[Ibix]

If that were true then surely a light beam could be polarized by a pinhole and a slit would not be necessary.

A polariser (or, at least, one kind of polariser) works by letting electrons flow in the x direction but not the y direction. So an incident EM wave with an electric field in the x direction starts electrons wiggling in the x direction, and one with its electric field in the y direction does not excite electrons. But nothing about the wave itself is moving in the x direction; the field is time varying, that's all.

A pinhole does not have a preferred direction for electron motion, so is not a polariser.

 

[JulianM]

A polariser (or, at least, one kind of polariser) works by letting electrons flow in the x direction but not the y direction. So an incident EM wave with an electric field in the x direction starts electrons wiggling in the x direction, and one with its electric field in the y direction does not excite electrons. But nothing about the wave itself is moving in the x direction; the field is time varying, that's all.

A pinhole does not have a preferred direction for electron motion, so is not a polariser.

Nugatory said nothing is wiggling. Your opinion is electrons are wigling.

The OP was talking about light so presumably photons. What are the opinions on light?

As far as I am aware a wire grid is just a matrix of slits and is quite similar to the lines in polarizing sun glasses.