As the title says - Why does the speed of light have a maximum speed limit? In the outer space the medium that transmits lights is as close as possible to what we call "nothing", though not really nothing in the physicists sense. The nature of space should determine the rate of transmission through it, right? Does empty space being close to a perfect vacuum limit the speed of light? Objects exist in space, so space must also be an object, and it must in some measureable way excert influence on the speed of light. Is there a hypothesis on the reason why the speed of light has an end limit to its speed and what limits it? Or is its speed considered a "given" for now?
The constancy of the speed of light in a vacuum is one of the postulates of SR. As a postulate, it's not proven from something more basic (think of a math postulate). This postulate has been confirmed time and again by experiments, however. So well has this fact been proven, that the SI unit of meter has been redefined to be the distance light travels in 1/299792458 seconds.
So there is no meaningful answer why the speed of light is close to 300 000km/sec^2 in vacuum or what limits it to that speed?
Well, in physics we can always go around and "explain" things like this, but in the end you have to take some things as postulates and let the experimental evidence show you that they are true. I mean, I could say that light travels at 300,000km/s because the permittivity and permeability of free space take on specific values, but you can always just ask me "why are they these values?"...and then we just go on a loop.
There's a point here with which the OP may not be entirely familiar. From Maxwell's equations of classical electrodynamics, one can derive a wave equation that the electric and magnetic fields in a vacuum satisfy. From this equation you can read off the velocity of the waves; it turns out to be related to two constants of nature- the permittivity and permeability of the vacuum. This then implies that the speed of light is itself a constant, upon which all observers in all reference frames agree- SR takes that ball and runs with it. So the important fact that light travels at a fixed velocity is derivable from known theory, which is how Einstein saw it; his 1905 E=mc^2 paper contains a footnote: "The principle of the constancy of the velocity of light is of course contained in Maxwellâ€™s equations". The specific value of this constant is what then isn't really derivable from anything without reference to some experimental input.
Yes, but then I can equally well ask "why are those two constants the way they are?". I think whether we take the permittivity and permeability or the speed of light to be what they are depends on which theory or which way we construct the model. Whatever model we choose to use must be based on several postulates from which all the deductions can be made. Those postulates can then only be verified by experiment. We can take different postulates and derive each other (like Newtonian F=ma to Lagrangian principle of least action), but in the end experimental evidence reigns king over physics. But I guess my point is more on the side of the philosophy of science than science itself. All I'm trying to say is that eventually one just needs to take the experimental evidence as the "proof" of the pudding. Not everything can be derived from something else without eventually going in a loop.
Light travels at the speed it does because that is that rate at which energy is exchanged between the electric field and magnetic field. Or stated alternately, that is the rate polarization takes place in a vacuum. Specifically it is determined by the constants: vacuum permittivity and vacuum permeability expressed as: [tex]c = \frac{1}{\sqrt{\varepsilon \mu}}[/tex] All else regarding speed limits is pure conjecture.
There's more than one way to skin a cat. We can also say that light travels at the speed it does because it has zero rest mass, and particles with zero rest mass have to travel at c.
So back to the original question, the reason light has an end limit has more to do with the "shape" of space. If space-time were a simple euclidean 4D geometry then yes, things could go as fast as they wanted. But our universe is a Minkowski space-time. So technically things can still go as fast as they want but only from their own perspective. A stationary observer is going to see this thing approach some limit. Asking if something can go faster than light is like asking if it can go faster than infinity, which doesn't make any sense. Light doesn't experience time, a photon will go through its entire life in zero seconds from its perspective. But then something has to give right? Yes that is correct. From our perspective an object may not look like it is going faster and faster as it approaches c but we will see its mass increase. From the objects perspective it does not see its mass increasing but it does see itself going faster and faster. I can take a spaceship going very close to c and go from one end of the galaxy to the other in a few seconds. The galaxy will have aged many years in the process though. That limit is some totally random constant, trying to understand why it is this constant as apposed to another is pointless. The important thing is this constant's relation to other physical constants. Certain relations may provide a universe that can sustain life while other relations won't. Everything clear now?
That's odd. It makes sense though, now that you mention it. Given the measurement properties of space-time called the metric, you can obtain one unique velocity that is non-zero. If you follow paths where parts of the path have a velocity over the unique velocity, you get all kinds of physically questionable things happening. You could go back and meet yourself in the past. You could have perpetual motion machines. You could cool water down by boiling it. Stuff like that. The speed c is just a property of spacetime geometry.
But there is also the very real possibility that "spacetime geometry" arises purely because it is a by-product of EM interactions. I believe that can be proven mathematically.