grounded said:
I keep hearing that the relative speed of light remains constant because time and lengths change with speed, what I believe is called the Lorentz factor. At slow speeds the Lorentz factor is extremely small, so what do people believe accounts for the rest of the change?
If I travel towards a source of light at 55 miles per hour, then relative to me, the speed of light will have to be reduced 55 miles per hour for the speed to remain constant. The Lorentz factor is so small at this speed that it can be ignored, so what is currently believed to account for the 55 miles per hour change?
There is not cause that physics can answer. It's just the way the universe is. But maybe a
reason can be given for you? What follows is a overly simplistic historical retracing of some of the events and reasoning that led to this realization, and hopefully some understanding.
(1) Galileo realized (with Newton eventually filling in all the fine details derived from this) that if you are moving smoothly, there is no experiment you can perform that will determine exactly how fast you are moving, or if you are even moving at all. His quintessential example of being inside the cargo hold of a smoothly sailing ship* illustrates this: water dripping from a bucket does not suddenly fly to the back of the ship as you go forward; butterflies still fly the same; etc. You can see this yourself in an airplane once you reach cruising altitude and there is no turbulence. Simply flip a coin. If it flies to the back of the airplane, Galileo is wrong (Hint: it doesn't. It does up and down, just like on the surface). In physics parlance, the laws of physics are the same for all inertial reference frames. This is the
principle of relativity, and it leads to the assertion that all speeds are meaningless unless specified what the speed is relative to (e.g., 30 MPH is meaningless, but 30 MPH with respect to the Eiffel Tower means something).
*What Galileo actually wrote (not really needed but it provides some historical enrichment):
Shut yourself up with some friend in the main cabin below decks on some large ship, and have with you there some flies, butterflies, and other small flying animals. Have a large bowl of water with some fish in it; hang up a bottle that empties drop by drop into a wide vessel beneath it. With the ship standing still, observe carefully how the little animals fly with equal speed to all sides of the cabin. The fish swim indifferently in all directions; the drops fall into the vessel beneath; and, in throwing something to your friend, you need throw it no more strongly in one direction than another, the distances being equal; jumping with your feet together, you pass equal spaces in every direction. When you have observed all these things carefully (though doubtless when the ship is standing still everything must happen in this way), have the ship proceed with any speed you like, so long as the motion is uniform and not fluctuating this way and that. You will discover not the least change in all the effects named, nor could you tell from any of them whether the ship was moving or standing still. In jumping, you will pass on the floor the same spaces as before, nor will you make larger jumps toward the
stern than toward the
prow even though the ship is moving quite rapidly, despite the fact that during the time that you are in the air the floor under you will be going in a direction opposite to your jump. In throwing something to your companion, you will need no more force to get it to him whether he is in the direction of the
bow or the stern, with yourself situated opposite. The droplets will fall as before into the vessel beneath without dropping toward the stern, although while the drops are in the air the ship runs many spans. The fish in their water will swim toward the front of their bowl with no more effort than toward the back, and will go with equal ease to bait placed anywhere around the edges of the bowl. Finally the butterflies and flies will continue their flights indifferently toward every side, nor will it ever happen that they are concentrated toward the stern, as if tired out from keeping up with the course of the ship, from which they will have been separated during long intervals by keeping themselves in the air. And if smoke is made by burning some incense, it will be seen going up in the form of a little cloud, remaining still and moving no more toward one side than the other. The cause of all these correspondences of effects is the fact that the ship's motion is common to all the things contained in it, and to the air also. That is why I said you should be below decks; for if this took place above in the open air, which would not follow the course of the ship, more or less noticeable differences would be seen in some of the effects noted.
Hundreds of years of experiments with electricity and magnetism led to four crucial equations called
Maxwell's equations (you will recognize some of the names that contributed: Faraday- of the unit for capacitance, the "farad"; Volta- of the unit for electric potential, the "volt"; Ohm of "Ohm's law" and the unit of resistance, the "ohm"; Ampère, who's name is used for the unit of electrical current the "almpere," usually shortened to "amp"; Joule (you guessed it- the unit of energy, the "joule," is named after him); Galvani (of "galvanization" and "galvanometer"); Gauss (even if you don't take physics, if you take calculus you'll hear of him); and countless others (I could make an entire thread full of these guys).
These equations happened to combine into a wave equation. This wave equation describes the electromagnetic wave (and shows that light is part of this wave). This wave also has a characteristic speed- but one that is not described as being with respect to anything.
(3) Physicists assumed this speed was with respect to the medium through which the electromagnetic wave traveled. After all, all waves need a medium, right? Except experiments failed to find this medium. Experiments suggested that this speed was with respect to everything, not just some medium. Of course,
this directly contradicted (1), the principle of relativity. This was a big problem, because the principle of relativity was experimentally true, but so were Maxwell's equations AND the medium through which the electromagnetic wave traveled was undetectable.
(4) Einstein realized the two ideas were not mutually exclusive. All that had to change was the way in which the results from the principle of relativity were formulated- specifically, the way coordinates are transformed from one inertial frame to another (some have already posted the addition of velocity formula. That is derived from the corrected transformation equations). Fortunately, the math was already there (in part thanks to Lorentz, of the Lorentz factor). Einstein simply realized what that math really meant: that our instinctual notions about how velocities add, how coordinates transform, how time and space "behave," and that simultaneity is absolute, were all mistaken. With this also died the theoretical need for a medium for light to move through.
(5) Then comes the special theory of relativity, which puts it all together, unifying the
principle of relativity (and mechanics along with it) with
Maxwell's equations. The way this was done by Einstein was he took the experiments at face value, and from them made two assumptions:
I - The laws of physics are the same for all inertial reference frames (the principle of relativity)
II- The speed of light in a vacuum is the same for all inertial reference frames, regardless of the speed of the source of the light (with respect to anything. That is, the speed of light on an airplane going 500 mph is the same as the speed of light on the ground, and anyone on the ground will measure a beam of light coming from the airplane moving at c, not 500+c).
And that is a brief summary of the reason as it is usually presented (historically). The tl;dr version is this: We observe both the principle of relativity to be true AND that the speed of light is the same regardless of its source. The logical (mathematical) conclusion of those two things is that the correct transformation between reference frames is the Lorentz transformation (which includes the Lorentz factor), and from that comes all the interesting things of special relativity.
