The Speed of Light: A Constant Mystery

[benzun_1999]

Why is the speed of light a constant?

 

[StarThrower]

Your question is meaningless.

According to the theory of relativity, the speed of light is c in any inertial frame. Suppose that is true. There are still reference frames in which the speed of light is not c, however those frames are non inertial.

The theory of relativity does not assert that the speed of light is c in any frame.

Let me ask and answer another question.

"Why is the speed of light c in any inertial frame?"

Well it isn't clear that the speed of light is c in any inertial frame. Einstein postulated that the speed of light is c in any inertial frame, but that doesn't make it so. All that has to be true for the postulate of relativity to be false, is for the speed of light to not equal c in at least one inertial reference frame.

So the question, "Why is the speed of light c in any inertial frame?" is begging the question.

A few words on electrodynamics

The formula for the electric field is:

$$\vec E = \frac{1}{4\pi \epsilon_0} \int \rho d\tau \frac{\vec r}{r^3}$$

The formula for the magnetic field is

$$\vec B = \frac{\mu_0}{4\pi} \int \vec J \times \frac{\vec r}{r^3} d\tau$$

Now, by design the permittivity of free space $$\epsilon_0$$ amd the permeability of free space $$\mu_0$$ are constants, whose value are determined by experiment.

Once you accept that they are true constants of nature, it isn't hard to realize that the following quantity is also a constant of nature:

$$\frac{1}{\sqrt{\epsilon_0 \mu_0}}$$

The units of the above quantity are meters per second, which are units of speed, and in the 19th century, this quantity computed to about 3 x 10^8 meters per second, which was roughly equal to the speed of light as measured earlier. Let us define c as follows:

$$c = \frac{1}{\sqrt{\epsilon_0 \mu_0}}$$

It now follows that c is a constant, and so any derivative of it with respect to time must equal zero, that is, dc/dt=0. But, the speed of anything only makes sense after one chooses a reference frame in which that speed is defined in. It is not clear from electromagnetic theory in what frames the speed of light actually is c, although Einstein postulated that it is c in any inertial frame.

An alternative postulate, is that the speed of a photon is c relative to that which emits the photon.

 

[mormonator_rm]

Excellecnt reply by StarThrower. Also keep in mind that $\epsilon_0$ is possibly determined by the charge density of the universe according to some cosmological models, and hence it changes as the volume of the universe expands. Additionally, there is a theory of Doubly Special Relativity (DSR) that may be worth looking into; in addressing the problem of high-energy cosmic rays exceeding Plank-energy, energy-dependent reference frames are the basis there, and lead to an interesting wavelength and velocity dependence of light as one of the biproduct predictions. I wouldn't put too much stock in DSR just yet, though, so be careful when looking into that stuff.

In any case, we cannot definitively say that the speed of light is absolutely constant with regards to any inertial reference frame, although I would like to agree with StarThrower and say it is to the best of our knowledge.

 

[NateTG]

This doesn't answer the question you asked, but it might help with the question you wanted to ask.

In the 19th century Maxwell developed a theory that unified electricity and magentism. A surprising prediction that this theory made is that the speed of light is constant in all inertial reference frames. Previously it was thought that light was transmitted through some sort of 'ether' the same way that sound is transmitted through matter.

Once this, at the time incredulus, prediction came to light, Michelson and Morely created a device for testing it. Michelson and Morely tested at different lattitutes, in different seasons, on hot air baloons. Their testing was extremely thorough, and esentially destroyed and theory of 'ether wind', indicating that Maxwell's predicition was indeed correct.

Finally, Einstein applied this prediction to create a theory of mechanics we call Special Relativity, which has made some successful predictions of its own.

 

[speso72]

In mathematics they use the speed of light (186,271.6 miles per second) as a constant in order to prove theorums and equations, just as they often use Earth to equal 1 (i.e. 3.4 AU's). However, in reality the speed at which light travels is not constant and the speed of light can be altered. As light passes through window glass, the speed slows.

 

[benzun_1999]

This is what I read regarding speed of light in a book in my school library.
This is what it said (in my own words).
In the morning when the light having a constant speed of c strikes the Earth which is at a speed of x in the opposite direction.
The speed that a possible detector would record will be c+x. but even at condition the speed of light remains the same c. (this is the explanation given by the book.)

Now here is my question is this explanation correct?

-Benzun.
All for God

 

[Adrian Baker]

Originally posted by benzun_1999
This is what I read regarding speed of light in a book in my school library.
This is what it said (in my own words).
In the morning when the light having a constant speed of c strikes the Earth which is at a speed of x in the opposite direction.
The speed that a possible detector would record will be c+x. but even at condition the speed of light remains the same c. (this is the explanation given by the book.)

Now here is my question is this explanation correct?

-Benzun.
All for God

A detector would NOT record a speed as c+x. It is a constant, c, for every observer in the Universe no matter what speed or direction they are traveling in. Re-read the excellent answers above.

 

[Integral]

One more piece of the puzzle that has not been explicitly stated. In 1867 when Maxwell cast his equations into the form of a Wave equation the expression

$$\frac{1}{\sqrt{\epsilon_0 \mu_0}}$$


appeared as the velocity of electo magnetic waves. This was the first indication that electro magnetic waves existed, 20 yrs later based on this prediction Hertz was able to produce and detect these waves. When Maxwell evaluated the above expression for the speed of electro magnetic waves he found that it was the same as the then best known value for the speed of light, this was the first true indication that light was electro magnetic in nature. The fact that it was a constant based on fundamental electro magnetic properties of space caused a rift in Physics that lasted until Einstein's papers in 1905.

This is not a Quantum Mechanics problem so I have moved the topic to General Physics.

 

[Integral]

Originally posted by speso72
In mathematics they use the speed of light (186,271.6 miles per second) as a constant in order to prove theorems and equations, just as they often use Earth to equal 1 (i.e. 3.4 AU's). However, in reality the speed at which light travels is not constant and the speed of light can be altered. As light passes through window glass, the speed slows.

Actually the speed of propagation does not change. As light is passing through a medium it is adsorbed by the atomic structure, then after a brief pause it is re-emitted, then travels at c until it is adsorbed by the next atom. Thus the light speed is not changed but simply delayed by the atomic structure.

 

[way2go]

Originally posted by Integral
Actually the speed of propagation does not change. As light is passing through a medium it is adsorbed by the atomic structure, then after a brief pause it is re-emitted, then travels at c until it is adsorbed by the next atom. Thus the light speed is not changed but simply delayed by the atomic structure.

This is not true. Recent research by Harvard University has shown that light can be stopped and restarted again! Here's the article:

Harvard researchers stop, restart, light
Einstein would be surprised
Albert Einstein theorized that light cannot travel faster than 186,282 miles per second. But he never said it couldn't go slower.

Lene Hau, a physics professor in the Faculty of Arts and Sciences at Harvard University, says Einstein would "probably be stunned" at the results of her recent experiments. Working in her laboratory at the Rowland Institute for Science, she and her colleagues slowed light 20 million-fold in 1999, to an incredible 38 miles an hour. They did it by passing a beam of light through a small cloud of atoms cooled to temperatures a billion times colder than those in the spaces between stars. Just recently, they were able to stop light completely.

"In this odd state, light takes on a more human dimension; you can almost touch it," Hau says.

Inspired by Hau's success at slowing light, researchers at the Harvard-Smithsonian Center for Astrophysics (CfA) used a similar technique to stop, then restart, a light beam.



Here's a link to the full story:
http://www.news.harvard.edu/gazette/2001/01.24/01-stoplight.html

 

[sharpstones]

I am by no means an expert on this subject, but from reading the article it seems that it does not go against what Integral said at all. I think it's just a confusing matter of semantics since the article uses terms like "slow down," but in one of the paragraphs it says that, "Hau explains that light entering the atomic entanglement transfers its energy to the atoms. Light energy raises the atoms to higher energy levels in ways that depend on the frequency and intensity of the light." This seems to imply that the light is actually being absorbed into the atom. Somebody please correct me if I'm wrong.

 

[russ_watters]

Originally posted by sharpstones
I am by no means an expert on this subject, but from reading the article it seems that it does not go against what Integral said at all. I think it's just a confusing matter of semantics since the article uses terms like "slow down," but in one of the paragraphs it says that, "Hau explains that light entering the atomic entanglement transfers its energy to the atoms. Light energy raises the atoms to higher energy levels in ways that depend on the frequency and intensity of the light." This seems to imply that the light is actually being absorbed into the atom. Somebody please correct me if I'm wrong.

No, you look right to me - this is just a material with a very high index of refraction.

 

[Integral]

The "news" in this type of experiment is that the after material adsorps the photon, the reemission event can be triggered. It is this type of contol of quantum events which will make Quantum computers possible.

 

[god]

If light is stopped does that not create an event horizon?

 

[Adrian Baker]

Originally posted by god
If light is stopped does that not create an event horizon?

No.
Light hits surfaces and is absorbed all of the time. You are probably thinking about gravitational forces preventing photons from escaping from an area of space, which is very different.

 

[The_Brain]

I will give an example to help show you what your book is saying although I don't think it's explaining what you think it is. Imagine you have a ball and a "moving wall" that has a detector implanted in it. Now start moving the two towards each other, the ball with speed c and the wall with speed x. When the two collide, the detector will read the velocity as c+x because it was also moving but my friend, the velocity of the ball was still c, it didn't matter that the wall was moving thus picking up a larger velocity. However, your book is flawed in the sense that c will read the same for every observer no matter what their frame of reference is.

Originally posted by benzun_1999
This is what I read regarding speed of light in a book in my school library.
This is what it said (in my own words).
In the morning when the light having a constant speed of c strikes the Earth which is at a speed of x in the opposite direction.
The speed that a possible detector would record will be c+x. but even at condition the speed of light remains the same c. (this is the explanation given by the book.)

Now here is my question is this explanation correct?

-Benzun.
All for God

 

[pallidin]

The speed of light is a constant because it's speed has never been observed to change under any verifiable experimental circumstances of propagation, transference or reflectance.
As pointed out, the "slowing" down of light while passing through a dense medium is a complete myth. The photon itself, regardless of environmental conditions, will always propagate at C.
And, curiously enough, while many atomic and sub-atomic movement ceases at 0-degrees Kelvin, light traveling through a 0-degree Kelvin free-space area is completely unaffected.
Even over long distances, or under intense gravitational influences, the original frequency of the photon may decrease or be otherwise changed, but it's speed remains at C.

 

[Genesis]

This might be a bit off-topic, but... Is light a particle or a wave?

 

[mormonator_rm]

If you leave light alone it acts very clearly as a wave, as in diffraction and interference experiments. But as soon as you do something to detect or deflect it, it makes a decided choice on its quantum state, and acts like a particle. This is clearly demonstrated in diffraction experiments where the photons passing through a grating trigger a detector; resulting in the total breakdown of the diffraction pattern (as if it were no longer a wave).

 

[Adrian Baker]

Originally posted by mormonator_rm
If you leave light alone it acts very clearly as a wave

Your example is a good one, but the wording quoted above is a little imprecise. For example, the Photoelectric effect can ONLY be explained by considering light as a particle. It does not need to be 'left alone' to do this.
It is perhaps best to say that light can ACT like a particle, or like a wave but is neither.

Benzun_1999 - if this leaves you asking, "How is it possible to visualise this?" then join the queue with the rest of us...

 

[mormonator_rm]

"Detected or deflected". If a photon is deflected, then it is clearly NOT left alone (though the experimenter has done nothing directly, an interaction has). "Deflected" includes the Photoelectric effect. If a photon strikes something, such as an electron on the surface of a metal, then it is forced to chose a quantum state, and hence act as a particle. Until it strikes the object, though, it is still in wonderful wavefunction limbo-land.