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Sunday, November 11, 2012

What stops light from going faster?

So, lets approach this a few different ways. First with the simplest, and then to increasingly more accurate descriptions.

So, as theduffer said, according to the laws of electricity and magnetism, the speed of light is related to these two variables, permeability and permativity of the material its going through. Now, why is that? That is because following the classical derivation of electricity and magnetism, we come up with some differential equations which describe the proegation of a wave. This wave is what we call light. This light is self perpetuating, just the same as a pendulum is self perpetuating. A pendulum will continue to swing forever as long as there is no friction or drag. This is also in the same way the fact that earth is self preptuating around the sun, it is in an orbit. In the same way, as light is traveling, the electric and magnetic fields are oscillating back and forth, necessitating that the light continues flowing forward. A good way to understand that light is just due to this oscillation, we can just look at a radio antenna. Radio waves are light, as is all electromagnetic radiation. We make radio waves by literally pushing and pulling electrons to one end of the antenna, and then back to the first end Doing this creates an electric field which is oscillating, this in turn creates a magnetic field that is oscillating, which makes an electric field that is oscillating, each one extended in space a little, creating a wave that physically moves and travels.

So, what describes the speed of that light? Well, we have equations which describe if you put an electron at point A, and another electron at point B, and we can measure how strong those two things pull on each-other. Likewise we can do this with spin and magnets. With these measurements, we find out that nature itself has a fundamental strength when it comes to electric and magnetic fields. And, there is a physical response of the universe to these things, that just always is the same no matter where and how we measure it. We have overtime determined that this fundamental and universal thing we keep seeing is also the same limit of the speed of light.

So now, we have determined that the fundamental speed of light is due to the medium through which it travels, and in a vacuum, it still has a characteristic speed that is not infinite. This is to say, space itself and electric and magnetic fields in space cannot respond instantaneously. Then we must ask, why not? What is physically stopping us here. And this is where we must get into relativity.

As it turns out, the universe itself has some fundamental relation between the dimension of time and the dimension of space. This is to say, space and time can be turned into each other (in a sense). If you were to start moving very very fast the distances you are traveling and the time you experience will be different from someone who is stationary. This ability for us to transform from time to space is contained within the math of "Lorentz Transformations"

So, this is to say, nature has a specific way for us to change physical dimension, length into time. These things as it turns out are necessarily directly related. These things are two heads to the same coin, except that time itself is always propagating in one direction, and the spatial dimensions are things we are free to roam around in. (That is a much harder question and concept to try to tackle, and up to much debate)

So! Now we have made mention that space and time are actually connected, they are actually fundamentally related somehow. Well, we measure time by counting essentially. We find a pendulum and count how many times it has ticked. We assign an arbitrary number to that and say "15 ticks have passed, and it ticks once every millisecond, therefore 15 milliseconds have passed" That is how a second is defined. And now, we have space, how is space defined? Well, we used to have a stick on the ground and said, this stick is "1 unit" length, and people called it a foot, a meter, whatever they wanted. And with these two variables, we are able to measure what the speed of light is, as a length over time. Some 3*10^8 meters per second. However, as it turns out, due to relativity, meters and second should be the same thing in some way. They are both measurements of length in their dimension. So, we could have just as easily stopped at the definition of 1 second, and then said that c is the speed of light, and called that "1" At this point, we would say that the stick you placed on the ground is actually 3 nanoseconds long. In this sense, nature actually specifically relates these two dimensions and defines C in such a way that that is how the two dimensions talk to each other.

So now, I have two last points to make.

One: That in fact, speed of light is less of a "speed" and more of a conversion factor between time and space. For this reason, when we are wondering why you cannot go faster than the speed of light, why isn't speed of light higher, etc. what we are really asking is why is the ratio of time to space defined as is? Why can space not be longer for the same amount of time? Now that is the hardest question to answer, as we are getting deep into the fundamentals of general relativity, and the limits of modern physics. As it stands right now, its almost taken for granted, that... space itself is all wibbly-wobbly, and the amount of bounce and shape and cushion that space itself has fundamentally is described by some physical _constants_ and in that sense, the speed of light is one of them. In some way, space itself has some built in number that explains this, and all we can do is measure it. This is the same way as asking about the other fundamental constants, which as it is understood are fundamental descriptions of the universe. One possible interpretation is that there is some symmetry group which describes the universe, and under this symmetry there are constants, and from these constants come other constants such as the speed of light. (Noether's theorem)

And Two: just a small side comment / joke: When I saw your question about "c+1" I actually read that as is twice as fast. It turns out, when you write down the math, if you measure length in seconds, and time in seconds (or length in meters and time in meters. (I'm 7 parsecs old!)) then c is just equal to 1 exactly. In this sense our notion of "3*10^8" is almost arbitrary. And that is why we have defined it precisely (for the sake of the definition of the meter) as being: 299,792,458 meters per second _exactly_. But we could have just as well defined it as 17 potatoes per hour. And then measured our lengths in potatoes.

So... **TL;DR**: Sorry for just going on for so long, but I felt like a lot of background is needed for this unsatisfactory sounding answer... As far as we know, light goes as fast as it does because it simply is the constant in the universe that is the "fastest" anything can go. And therefore, it cannot go faster because the concept of moving faster than that simply does not exist. Also, yes, light is truly self perpetuating.
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Wiki articles that are worth looking at:
http://en.wikipedia.org/wiki/Permittivity
http://en.wikipedia.org/wiki/Vacuum_permittivity
http://en.wikipedia.org/wiki/Permeability_(electromagnetism)
http://en.wikipedia.org/wiki/Vacuum_permeability
http://en.wikipedia.org/wiki/Maxwell's_equations
http://en.wikipedia.org/wiki/Speed_of_light
http://en.wikipedia.org/wiki/Lorentz_transformation
http://en.wikipedia.org/wiki/Noether's_theorem

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