Exploring the Constancy of Light in Vacuum: Einstein vs Maxwell's Equations

In summary: Although Lorentz had not explicitly formulated the transformation laws in the form in which they are now known, it was clear that he had done so, and that they were equivalent to the laws of special relativity.Einstein postulated that Maxwell's equations remain unmodified regardless of the velocity of the rest frame.Also that the group of linear transformations that leave Maxwell's Equations unchanged also leave the rest of physics unchanged, including mechanics. Maxwell's equations were in a form that Einstein felt was equivalent to the laws of special relativity.
  • #36
Devils said:
So, as a newbie, is this saying Lorenz transforms form a group? [..]
I did not understand the part that I left out, but yes, Poincare (who was first of all a mathematician) emphasized that these transformations form a group.
- https://en.wikisource.org/wiki/On_the_Dynamics_of_the_Electron_%28June%29
 
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  • #37


"It is, in fact, possible to derive the Lorentz transformations from the principle of relativity alone and obtain the constancy of the speed of light as a consequence."
http://en.wikipedia.org/wiki/Principle_of_relativity

This is interesting. Can somebody point me to a proof?
 
  • #38


Devils said:
"It is, in fact, possible to derive the Lorentz transformations from the principle of relativity alone and obtain the constancy of the speed of light as a consequence."
http://en.wikipedia.org/wiki/Principle_of_relativity

This is interesting. Can somebody point me to a proof?

The statement in WP is footnoted to a 2004 paper by Friedman, which I don't have access to. But I think they are probably referring to an argument that, in various forms, dates back to 1911:

W.v.Ignatowsky, Phys. Zeits. 11 (1911) 972
Rindler, Essential Relativity: Special, General, and Cosmological, 1979, p. 51
Morin, Introduction to Classical Mechanics, Cambridge, 1st ed., 2008, Appendix I
Palash B. Pal, "Nothing but Relativity," http://arxiv.org/abs/physics/0302045v1
http://www.lightandmatter.com/html_books/0sn/ch07/ch07.html [Broken] (my own presentation)
 
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  • #39


OK I can see that there has to be a universal speed limit, but why does this have to be the speed of light (or other electromagnetic waves)? What implies that light must travel at a constant speed anyway (waves in water can have various speeds)?
 
  • #40


Devils said:
OK I can see that there has to be a universal speed limit, but why does this have to be the speed of light (or other electromagnetic waves)? What implies that light must travel at a constant speed anyway (waves in water can have various speeds)?

Water waves have a speed relative to the water. The speed of light in a vacuum can't be relative to anything, because there isn't any medium for it to be relative to.
 
  • #41


Devils said:
"It is, in fact, possible to derive the Lorentz transformations from the principle of relativity alone and obtain the constancy of the speed of light as a consequence."
http://en.wikipedia.org/wiki/Principle_of_relativity

This is interesting. Can somebody point me to a proof?
Instead I can point to a counter claim in that same encyclopedia:
http://en.wikipedia.org/wiki/Histor...rentz_transformation_without_second_postulate
In fact, that should be obvious: Classical mechanics has the PoR but with the Galilean transformations.
 
  • #42


Devils said:
OK I can see that there has to be a universal speed limit, but why does this have to be the speed of light (or other electromagnetic waves)? What implies that light must travel at a constant speed anyway (waves in water can have various speeds)?
That was based on observation combined with Maxwell's theory which models light as a wave with constant speed, similar to the speed of sound in a homogeneous medium.
 
  • #43


bcrowell said:
Water waves have a speed relative to the water. The speed of light in a vacuum can't be relative to anything, because there isn't any medium for it to be relative to.

harrylin said:
Instead I can point to a counter claim in that same encyclopedia:
http://en.wikipedia.org/wiki/Histor...rentz_transformation_without_second_postulate
In fact, that should be obvious: Classical mechanics has the PoR but with the Galilean transformations.
So the implication here is that if we have 'something' that doesn't travel relative to anything, this 'something' has to travel at the 'universal speed limit' (this is probably provable). Light in a vacuum is an example of this 'something'; are there any others (gravitons?)

Also the speed of light in a vacuum is an axiom, rather than being able to be derivable; even Pauli thought so.
 
  • #44


Devils said:
So the implication here is that if we have 'something' that doesn't travel relative to anything [..]
Instead, and sticking with the topic, the model that is used is that of Maxwell, according to which light propagates at speed c relative to a "stationary" frame, or "space":

"light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body"
"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."

- Einstein 1905

"We [..] assume that the clocks can be adjusted in such a way that the propagation velocity of every light ray in vacuum - measured by means of these clocks - becomes everywhere equal to a universal constant c, provided that the coordinate system is not accelerated.
- Einstein 1907

Einstein explained it as follows in 1907:

" It is by no means self-evident that the assumption made here, which we will call the "principle of the constancy of the velocity of light", is actually realized in nature, but - at least for a coordinate system in a certain state of motion - it is made plausible by the confirmation of the Lorentz theory [1895], which is based on the assumption of an ether that is absolutely at rest, through experiment". [footnote refers to Fizeau's experiment]

And with the PoR this model can be used for any inertial frame:
"the phenomena of electrodynamics as well as of mechanics possesses no properties corresponding to the idea of absolute rest"
- Einstein 1905
 
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  • #45


Devils said:
Also the speed of light in a vacuum is an axiom, rather than being able to be derivable; even Pauli thought so.

Whether it's a postulate or a theorem depends on what system of axioms you pick. We have a FAQ about this: https://www.physicsforums.com/showthread.php?t=534862 [Broken]
 
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  • #46


(Sorry to derail this thread).

So to summarise
- we start with a Euclidean space
- we introduce a "speed limit", which is light, which leads to hyperbolic functions (and hyperbolic identities), which leads to the Lorenz transform
- normally distance = speed * time, but the speed limit distorts this as well, to dilate time

So special relativity is a dressed-up version of hyperbolic algebra. I think it really is that simple, I don't know why people want to make it so complicated.
 
<h2>What is the constancy of light in vacuum?</h2><p>The constancy of light in vacuum refers to the fact that the speed of light in a vacuum is constant and does not change regardless of the observer's frame of reference. This concept is a fundamental principle in physics and was first described by Albert Einstein in his theory of special relativity.</p><h2>What are Einstein's equations?</h2><p>Einstein's equations, also known as the special theory of relativity, are a set of mathematical equations that describe the relationship between space and time. They were developed by Albert Einstein in 1905 and are based on the principle of the constancy of the speed of light in a vacuum.</p><h2>What are Maxwell's equations?</h2><p>Maxwell's equations are a set of four equations that describe the behavior of electric and magnetic fields. They were developed by James Clerk Maxwell in the 19th century and are considered one of the cornerstones of modern physics. These equations also predict the existence of electromagnetic waves, which include light.</p><h2>What is the difference between Einstein's equations and Maxwell's equations?</h2><p>The main difference between Einstein's equations and Maxwell's equations is that Einstein's equations describe the relationship between space and time, while Maxwell's equations describe the behavior of electric and magnetic fields. However, both sets of equations are interconnected and together they provide a deeper understanding of the nature of light and its behavior in a vacuum.</p><h2>Why is it important to explore the constancy of light in vacuum?</h2><p>Exploring the constancy of light in vacuum is important because it helps us understand the fundamental nature of our universe. It also has practical applications in fields such as telecommunications, where the constancy of light in a vacuum is crucial for the transmission of information. Additionally, this concept has played a significant role in the development of modern physics and has led to groundbreaking discoveries such as the theory of special relativity and the existence of electromagnetic waves.</p>

What is the constancy of light in vacuum?

The constancy of light in vacuum refers to the fact that the speed of light in a vacuum is constant and does not change regardless of the observer's frame of reference. This concept is a fundamental principle in physics and was first described by Albert Einstein in his theory of special relativity.

What are Einstein's equations?

Einstein's equations, also known as the special theory of relativity, are a set of mathematical equations that describe the relationship between space and time. They were developed by Albert Einstein in 1905 and are based on the principle of the constancy of the speed of light in a vacuum.

What are Maxwell's equations?

Maxwell's equations are a set of four equations that describe the behavior of electric and magnetic fields. They were developed by James Clerk Maxwell in the 19th century and are considered one of the cornerstones of modern physics. These equations also predict the existence of electromagnetic waves, which include light.

What is the difference between Einstein's equations and Maxwell's equations?

The main difference between Einstein's equations and Maxwell's equations is that Einstein's equations describe the relationship between space and time, while Maxwell's equations describe the behavior of electric and magnetic fields. However, both sets of equations are interconnected and together they provide a deeper understanding of the nature of light and its behavior in a vacuum.

Why is it important to explore the constancy of light in vacuum?

Exploring the constancy of light in vacuum is important because it helps us understand the fundamental nature of our universe. It also has practical applications in fields such as telecommunications, where the constancy of light in a vacuum is crucial for the transmission of information. Additionally, this concept has played a significant role in the development of modern physics and has led to groundbreaking discoveries such as the theory of special relativity and the existence of electromagnetic waves.

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