The Special theory of relativity postulates the existence of a speed (let that be denoted by "c") whose value is independent of any inertial reference frame it's being measured in. Why "c" is the velocity of an electromagnetic wave in vacuum should be clear from classical electrodynamics, i guess...And one more thing: why "c" in the postulates coincides with the "c" in the Maxwell equtions: the latter are invariant under the Lorentzian boosts (which are transformations of coordinates on [itex] \mathbb{M}_{4} [/itex] whose existence is implied by the 2 Einsteinian postulates), iff the "c" from the boosts expression is the "c" from Maxwell's equations. Why is this "c" maximum ? Well, if we think of particles that move faster than "c", then they should have an imaginary invariant/proper mass. Fortunately, we haven't seen any of the latter, so we're convinced, for the moment, that "c" cannot be exceeded. Daniel.
Is there a lay version of that, particularly of Einstein's part? So I take it that there is some equation that relates inertia to speed (to mass?), and at light speed one of those values becomes infinite, which indicates that faster speeds aren't possible?
In chronological order: They calculated and measured light speed to be the same for all observers, even when they are moving relative to the light source. Einstein showed that the existence of such a constant speed leads to the conclusion that this speed is the highest possible speed. And why is it exacly lightÂ´s speed? Because light (a photon) has no mass; no matter how small the amount of energy you give it, it will run away as fast as possible.
An oversimplified answer: We have found that time is not an independent factor in our universe; it is inextricably tied up with space. It can be loosely thought of as a direction of travel, like the three we are familiar with. The faster you go in the spatial directions, the slower you'll go in the time direction. When you are travelling at the speed of light in the spatial directions, you are not travelling at all in the time direction. Since 'speed = distance divided by time', and time is zero, there is simply no way of going any faster than that.
I prefer to think of it the other way around... First we calculate that there IS a fastest speed. THEN we say that anything that travels at this speed IS "light".
Daniel, and many (but not all) other scientists are convinced. Lately a few scientists---such as Laurent Freidel, Joao Magueijo,...---have been considering the possibility that Special Rel is slightly (ever so slightly) wrong and needs to be corrected. A test has been proposed using a satellite scheduled for launch next year (2007) In the modified theory not all light travels the same speed in vacuum. Very energetic gammaray photons are predicted to go just a wee bit faster. (think of the slight differences in speed as a "quantum correction" that could be just barely measurable using the GLAST satellite: "gammaray large array space telescope") the idea is to examine very powerful brief GRB "gammary bursts" that have been traveling on the order of a billion years, and look at brief millisecond spikes containing some photons that are very much more energetic than the rest. If the more energetic photons have crept out in front, during the billion years of flight, so they arrive just a fraction of a second earlier than the rest, this will be evidence suggesting a slight difference in speed. Too small to detect in ordinary earth circumstances (where the time of flight is not long enough for a small difference in speed to take effect) Daniel's explanation is correct----the theory of a clearcut max is based on the POSTULATES of Special Rel. there is no ultimate certainty that Special Rel is absolutely correct and will never be improved on by some small adjustment like this. so my advice is not to believe Special Rel too strongly. keep a corner of the mind open. more information here: http://arxiv.org/abs/hep-th/0501091 Note: this has nothing to do with "imaginary mass"
Well, first you have the Maxwell equations, which say that the speed of EM waves depends on the properties of space, not on the speed of the emitter or absorber. Then you have the Lorentz transformations, which are a consequence of that. Then you have relativity, which implements the Lorentz transformations. Einstein was not concerned to prove that lightspeed was the fastest speed, but that it was the same for all inertial observers. The "fastest" property then follows.
Einstein ASSUMED (hypothesized) the speed of light in vacuum was constant. It was a good assumption because Michelson & Morley kept trying and failing to measure a difference between the speed of light 1) in the direction of the Earth's motion round the sun and 2) a direction perpendicular to that motion. They (M&M) expected to see a difference because all known waves obeyed Gallilean invariance: if they move at c_m in their medium, and the medium is moving at v wrt to an observer, then the observer will see the wave move at c_m+v. Light was known to be a wave, so shouldn't it behave the same way? The reason Einstein chose the speed of light is because...drum roll...that's what they were measuring! The rest is history, Maxwell's equations, some algebra and a few Taylor expansions. Notably, Einstein did not assume that there was some constant speed that just happens to turn out to be the speed of light, nor did he assume that nothing could travel faster than light.
I'll take a crack at this but I'll probably be repeating what is posted above. First we start of with Maxwell's equations and use those to derive a wave equation for an electromagnetic wave. See derivation at http://www.geocities.com/physics_world/em/mawell_eq.htm Prior to 1905 it was universally asssumed that this held only in an "absolute frame of reference" where the EM field traveled as a disturbance in the ether (postulated back in ancient times as that which is there when nothing else is - :yuck:). So this wave equation in above link held in the rest frame of the ether. Then came Einstein and made two postulates 1) The laws of physics are the same in all inertial frames of reference 2) The speed of light has the value c independant of the speed of the source, i.e. has the same numerical value in all inertial frames. With this the ether was of no use for the propagation of EM waves. No inertial frame is distiguishable experimentally than any other inertial frame. Thus Maxwell's equations are covariant i.e. have the same form in all frames. It is not yet know for certain if this is the greatest speed. Someone has postulated a class of particles called Tachyon's. To be a tachyon the particle must always move at speeds v > c. What can't be done is take a normal particle like a proton, which can move at v<c (i.e. tardyons) and then prove that it would take an infinite amount of energy to accelerate the particle to a speed of c. So therefore tardyons must always move at speeds less than c. Particles with zero proper mass (a luxon) always moves at v = c. Pete
Here's an interesting talk (in RealPlayer format) on this subject vmsstreamer1.fnal.gov/VMS_Site_03/Lectures/Colloquium/041201Geroch/index.htm