 # How Did Einstein Discover Near-Light Velocity's Affect on Other Things?

As anyone who has ever taken a high school physics class knows, the closer you go to the speed of light, the slower time goes for you in relation to the things around you not going that speed. This is called time dilation, and Albert Einstein is usually credited with discovering it. But that supposedly isn’t the only thing that happens when you approach the speed of light. Length shortens, and the object approaching the speed of light gets heavier.

This is what I don’t understand. When I took high school physics, it was explained time dilation was discovered accidentally by doing experiments with light early on in the 20th century. That makes sense I guess. When you are doing experiments, variables like time are easy to determine (I guess again). But how did scientists determine the length and weight thing? How could they possibly observe such a phenomenon? And if they didn’t observe it, how did they determine it? From the link you gave (and from what I recall) it is clear that the effect of time dilation can be inferred from the postulate that light speed is constant. In fact, I know that this effect of time dilation was predicted long before is was actually confirmed in an experiment.
As for space dilation (the effect that length shortens at high speed), this is a direct result of time dilation. Since (light) speed is length divided by time, any changes done to time must induce appropriate changes to length (again using the postulate that light speed is constant).

What was discovered experimentally, or at least very strongly indicated (through the Michaelson-Morely experiments, IIRC) is that the speed is the same in all frames of reference. This means that while the light coming out of the flashlight in my hands is moving at c (3x10[sup]8[/sup]m/s), the light coming out of the front of the train moving at 50 m/s is not moving at c + 50, as classical physics would tell you it is. It’s moving at c, just like the light from my stationary (relative to me) flashlight.

What Einstein did was start from the assumption that the speed of light was always constant, and then look at how it affected the rest of the physics.

Time dilation was needed to explain how I can see my relatively stationary light moving at c, but the light on the speeding train also moving at c.

The mass effects come into play when you start calculating the momentum and acceleration of fast-moving objects. If you keep expending force into an object but it can’t accelerate past c, then the object’s mass must somehow be increasing.

I don’t remember the reasoning behind the length effects, but I do remember a neat problem I was given to solve in a history of science class: you have a train 200m long, moving at such a speed that relativistic effects cause it to appear 100m long. It passes through a barn 100m long. After it enters, the farmer at the front door and the farmer at the back door both quickly shut and then reopen their doors. Has a 200m train been completely enclosed within a 100m barn? Explain how this is or isn’t possible.

My mass explanation isn’t very good, let me try that again.

If you (in your spaceship) observe Cecil (in his) to be moving near the speed of light, time for him will appear to be slowed down. At the same time, Cecil will be observing you moving near the speed of light, and so to him it will appear that time is slowed down for you.

Cecil drops a rock (your ships have artificial gravity or something), which lands on his foot and breaks his toe. To him, the rock behaves normally for its mass. To you (because you observe Cecil’s time to be slowed down), the rock has fallen very slowly but has still managed to break his toe, which means it must have become much more massive. This causes you so much surprise that you drop the rock you’re holding. It falls normally and breaks your toe. Cecil now observes exactly the same thing happening to you that you saw happen to him, including the slow moving rock that behaves as though it were much more massive.

Remember of course that these effects occur in things moving relative to the observer. To the thing (or person) that’s moving, everything appears to be completely normal.

Einstein didn’t discover things like time dilation experimentally. He made a couple of assumptions based on the experiments of others and deduced what the world would be like if these assumptions were true.

Before Einstein, most physicists believed light was a wave, and like most waves, it had to have a medium. For example, the medium for sound waves is air, and the medium for ocean waves is sea water. They assumed that light waves traveled in a medium they called the “ether.” The ether, if it existed, would have provided an absolute frame of reference for all motion.

In the late 19th century, a couple of physicists decided to measure how quickly the earth was traveling through the ether. They set up a sophisticated experiment using an interferometer - there’s a pretty good description here. The experiment depended on measuring differences in the speed of light relative to the earth’s motion - light going the same direction of the earth through the ether would look slower than light going perpendicular to the earth’s motion through the ether.

They found that they couldn’t measure the speed of the earth going through the ether. The measured speed of light was always the same, regardless of the direction of the light relative to the earth’s motion. No one knew how to explain these results.

Einstein solved the problem by assuming the speed of light in a vacuum is a universal constant - that a beam of light will have the same speed relative to an observer no matter how the observer is moving. For example, if an observer is moving in the same direction as the light, the light will appear to have the same speed as if the observer is moving in the opposite direction. This assumption means there is no absolute frame of reference. Einstein figured out the implications of the assumption and published it as his special theory of relativity. Physicists validated the theory with experiments over a period of years.

I remember that NASA tested time dilation by putting a very accurate clock aboard a space flight, while an identical clock remained on earth. Einstein’s theory predicted that less time would pass on board the space flight than on earth, because of the acceleration of the flight. Indeed, when the flight returned to earth, the clock aboard the flight was slightly behind the one that had been left on earth. The difference in the clocks’ times was close to what NASA scientists had predicted.

Jeff do you have a cite for that last point?

alterego, I think Jeff was referring to the Hydrogen Maser Clock Project

or possibly to a shuttle experiment experiment in 1985

The Michelson-Morley Experiment performed in 1887 in order to try and detect the ether, produced an unexpected null result. Lorentz in order to try and preserve the ether and explain the result of the experiment came up with the ideas of length contraction and time dialtion. Lorentz transformations form the basis of Einstein’s 1905 theory of special relativity from which from more basic principles was able to derive Lorentz’s equations which had been criticized as too ad hoc.

The different Lorentz transformations can be shown to be results of each other with simple thought experiments.

IIRC length contraction though it is a real enough physical phenoumna is not directly observed as objects travelling at relativistic speeds do not actually appear to be contracted, but it is easily proved that it is a necessary result of a speed of light that is constant in all inertial reference frames.

So what’s the answer to this question then? Will the train fit in the barn or not?

As already mentioned, Einstein deduced time dilation and length contraction from his assumptions. Experimental confirmation came later.

One of the most striking demonstrations of time dilation comes from elementary particle experiments. A muon at rest lives about 2 microseconds (on average). A cosmic ray muon travels 99.999% of the speed of light, and so lives almost 200 times longer. If not for the time dilation effect, we wouldn’t detect any cosmic ray muons at all, as explained here:
http://www.prestoncoll.ac.uk/cosmic/muoncalctext.htm

AFAIK, length contraction has never been directly measured. Some related properties, like the distortion of the electric fields of moving particles, can be tested, though.

The fact that we see more muons than would be expected can also be put down to length contaction as for a muon the Earth’s atmosphere contracts meaning it has a shorter distance to travel than a non-relativistic muon.

failure of simultaneity at distance means that though for the farmer the doors will close at the same time, but for the train the doors will not close at the same time.

The signal that tells the farmer at the far end of the barn could not travel faster than the train, therefore the train and the signal would arrive at the same time but the train would be through the barn door before the farmers reaction could occur.

Epimetheus: You don’t need to resort to “reaction time”, and unless the train is travelling at the speed of light a signal could travel faster than the train.

MCMoC’s explanation is correct, but let me elaborate on it a little. When we ask, “Is the train in the barn?”, we’re really asking, “Does the front end of the train leave the barn after the rear end enters?” (The answers to these questions should be the same.) The problem is hidden in the word “before”: two events can appear to occur in different orders to different observers, i.e. even though I see event A happen before event B, my friend zooming by at half the speed of light might equally well say that event B preceeded event A.

In general, this kind of strangeness won’t occur if a signal travelling at the speed of light (or slower) could have travelled between event A at time A and event B at time B; we say that such events are causally related. However, if event A is the front end of the train leaving the barn and event B is the rear end entering the barn, these two events are not causally related, since a light pulse couldn’t travel between event A and event B. (This may have been what Epimetheus was driving at.) Thus, two different observers (say, the farmer and the conductor) may disagree on their order.

Hope this helps.

While we’re at it, the usual interpretation (among physicists, at least) is not that mass increases near the speed of light, but that the formula for momentum is no longer p = mv near the speed of light. Mass is generally considered to be synonomous with “rest mass”, which is the mass an object would have if you were moving along with it (in other words, if it’s not moving in your reference frame).

The relativistic equation for momentum is actually just as simple as it is in the non-relativistic case: Instead of p = mv, we have p = mu, where p is the “four-momentum”, a four-dimensional vector, and u is the “four-velocity”. The three space dimensions of the four-velocity are approximately equal to the three-velocity, at low speeds, so the Newtonian equation p = mv is approximately valid at low speeds, but as v approaches c, u grows without bound, so any object can have arbitrarily large momentum, if it’s going close enough to c.

This definition of four-velocity is also useful in other contexts. For instance, the acceleration felt by a person in a spaceship, and in Newton’s law F = ma is the change in four-velocity, not the change in three-velocity. So when you accelerate, your four-velocity can always increase, and get arbitrarily large, but your three-velocity will never exceed c.

While we’re at it, the usual interpretation (among physicists, at least) is not that mass increases near the speed of light, but that the formula for momentum is no longer p = mv near the speed of light. Mass is generally considered to be synonomous with “rest mass”, which is the mass an object would have if you were moving along with it (in other words, if it’s not moving in your reference frame).

The relativistic equation for momentum is actually just as simple as it is in the non-relativistic case: Instead of p = mv, we have p = mu, where p is the “four-momentum”, a four-dimensional vector, and u is the “four-velocity”. The three space dimensions of the four-velocity are approximately equal to the three-velocity, at low speeds, so the Newtonian equation p = mv is approximately valid at low speeds, but as v approaches c, u grows without bound, so any object can have arbitrarily large momentum, if it’s going close enough to c.

This definition of four-velocity is also useful in other contexts. For instance, the acceleration felt by a person in a spaceship, and in Newton’s law F = ma is the change in four-velocity, not the change in three-velocity. So when you accelerate, your four-velocity can always increase, and get arbitrarily large, but your three-velocity will never exceed c.

While we’re at it, the usual interpretation (among physicists, at least) is not that mass increases near the speed of light, but that the formula for momentum is no longer p = mv near the speed of light. Mass is generally considered to be synonomous with “rest mass”, which is the mass an object would have if you were moving along with it (in other words, if it’s not moving in your reference frame).

The relativistic equation for momentum is actually just as simple as it is in the non-relativistic case: Instead of p = mv, we have p = mu, where p is the “four-momentum”, a four-dimensional vector, and u is the “four-velocity”. The three space dimensions of the four-velocity are approximately equal to the three-velocity, at low speeds, so the Newtonian equation p = mv is approximately valid at low speeds, but as v approaches c, u grows without bound, so any object can have arbitrarily large momentum, if it’s going close enough to c.

This definition of four-velocity is also useful in other contexts. For instance, the acceleration felt by a person in a spaceship, and in Newton’s law F = ma is the change in four-velocity, not the change in three-velocity. So when you accelerate, your four-velocity can always increase, and get arbitrarily large, but your three-velocity will never exceed c.

It probably helps some people but my dim mind is balking.

Why is the front of the train not causally related to the back of the train? They are attached to each other and moving at the same speed. Slow the front down and you slow the back down…it is essentially a single object.

Further, I have a problem with defining who sees what and when. Lets take observation/reaction out of the equation (if this is ok to do). Say we time this experiemtn very well and set a computer at either end of the barn to shut the doors at a predetermined time. We will be sure to have the Relativity Express Train in the barn at that time. Our 200m long train is passing through the barn and the doors slam shut (I guess for this experiment we can ignore the time it takes to close the doors and just assume they do so really fast). Is the train in the building or not?

You may not have been around trains much. As the engine starts moving the slack comes out of the first coupling before the second car moves, then the next coupling before the thirsd car moves etc. It may be some time before the caboose moves.

You may think that is irrelevant but it’s not. Say we make the entire train out of a single block of steel. It’s not one object but a whole bunch of atoms joined together by finite forces. The connection between each atom is kind of like the slack train coupling. This accounts for eleasticity in metal. If there were no elasticity there would be no such thing as a springs and the speed of sound in metal would be faster than the speed of light.