Can the Speed of Light be derived?

In summary: Correct me if I'm wrong, but as I understand it, μ0 and ε0 are entities of the EM field only. This does not leave much room for confidence that other fields would propagate at a maximum speed of light.Yes, that is correct. The speed of light is constrained by the speed of the EM waves.
  • #1
friend
1,452
9
Einstein postulated that the speed of light is the same for all observers. But it seems that this speed limit applies to more than just photons. It also applies to any massless particle. So I have to wonder if there is some way of deriving the speed of light from more general principles that applies to all massless particles. For example, could more general principles hide a maximum speed of information? Any thoughts are welcome.
 
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  • #2
It doesn't make much sense to derive a non-dimensionless constant. We _define_ the value of the speed of light. We don't derive it. Historically, it made sense to derive it, because we had a conventional standard for the meter. But we abandoned that standard and just define the meter based on the speed of light.
 
  • #3
Khashishi said:
It doesn't make much sense to derive a non-dimensionless constant. We _define_ the value of the speed of light. We don't derive it. Historically, it made sense to derive it, because we had a conventional standard for the meter. But we abandoned that standard and just define the meter based on the speed of light.

Yes, I'm sure a derivation would be in terms of other dimensionful constants like h-bar, charge of the electron, etc. So my question is whether there is some means of deriving the speed of light within the formulism that does contain other dimensionful constants.

PS. I'm not sure this thread belongs to SR&GR forum since the speed of light is assumed constant there in ALL there calculations. It seems actually deriving "c" would require a much broader theory that includes SR and GR and so would be beyond the standard model.
 
  • #4
Well, historically Maxwell used his newly-corrected Ampere law to get an electromagnetic wave equation. When solving this equation, he found that EM waves travel at a speed given by:

[itex]v=\frac{1}{\sqrt{\mu_0 \epsilon _0}}[/itex]

, where μ0 and ε0 are the magnetic and electric constants. When he calculated this value, he found that it was the same speed that light was known to travel at, suggesting that light consisted of EM waves.
 
  • #5
Starting from certain symmetry principles, it is possible to prove that there is a universal speed which also acts as a speed limit: http://www.lightandmatter.com/html_books/0sn/ch07/ch07.html [Broken]
 
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  • #6
bcrowell said:
Starting from certain symmetry principles, it is possible to prove that there is a universal speed which also acts as a speed limit:
http://www.lightandmatter.com/html_books/0sn/ch07/ch07.html [Broken]
But even Newton would have accepted the existence of a universal speed limit, he just thought its value would be infinite in all inertial reference frames.
 
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  • #7
lugita15 said:
But even Newton would have accepted the existence of a universal speed limit, he just thought its value would be infinite in all inertial reference frames.

Yes, you can consider Galilean/Newtonian spacetime as the limit of Einstein's spacetime as [itex]c\rightarrow\infty[/itex].
 
  • #8
bcrowell said:
Starting from certain symmetry principles, it is possible to prove that there is a universal speed which also acts as a speed limit: http://www.lightandmatter.com/html_books/0sn/ch07/ch07.html [Broken]

It would help if you could give a reference to where to find these "symmetry principles" in the long article that you link to.
 
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  • #9
friend said:
it would help if you could give a reference to where to find these "symmetry principles" in the long article that you link to.

7.2.1
 
  • #10
elfmotat said:
When solving this equation, he found that EM waves travel at a speed given by:

[itex]v=\frac{1}{\sqrt{\mu_0 \epsilon _0}}[/itex]

, where μ0 and ε0 are the magnetic and electric constants.

Correct me if I'm wrong, but as I understand it, μ0 and ε0 are entities of the EM field only. This does not leave much room for confidence that other fields would propagate at a maximum speed of light.
 

1. Can the speed of light be derived from first principles?

Yes, the speed of light can be derived from first principles through the use of Maxwell's equations, which describe the relationship between electric and magnetic fields. These equations, along with other fundamental constants such as the permittivity and permeability of free space, can be used to calculate the speed of light.

2. How was the speed of light first calculated?

The speed of light was first calculated by the Danish astronomer Ole Rømer in 1676. He observed the eclipses of Jupiter's moon Io and noticed that the timing of these eclipses varied depending on the distance between Earth and Jupiter. By measuring this variation and knowing the distance between Earth and Jupiter, Rømer was able to calculate the speed of light to be about 220,000 kilometers per second.

3. Can the speed of light be measured exactly?

No, the speed of light cannot be measured exactly due to various factors such as experimental error and the uncertainty principle in quantum mechanics. However, with advancements in technology and precision, scientists have been able to measure the speed of light to a high degree of accuracy, currently accepted as 299,792,458 meters per second.

4. Has the speed of light always been constant?

According to Einstein's theory of relativity, the speed of light is a constant in all inertial frames of reference. This means that the speed of light has always been constant and does not change based on the observer's perspective or the relative speed between the observer and the source of light.

5. Can the speed of light be exceeded?

Based on our current understanding of physics, the speed of light is considered to be the fastest speed possible. Nothing with mass can travel at or faster than the speed of light, as it would require infinite energy. Some theories, such as the concept of wormholes, suggest the possibility of traveling faster than light, but these are still hypothetical and have not been proven.

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