ajm51987

I had a look at howstuffworks.com and am really confused. What the heck is Relaitivity?

Baptist Vine

Here is my crack at an explanation. There is the 'special theory' and the 'general theory'.

There are two postulates to Special Relativity: (1) ALL the laws of physics are the same in any inertial reference frame, and; (2) the speed of light is the same for all observers.

Number (1) requires some history and backgound explanation - not so much mathematical explanation. Number (2) is more easily grasped, and really follows directly from (1).

Number (1) postulate really deals with applying the old Galilean relativity to ALL the laws of physics, including the electromagnetic phenomenon. What is meant by this? This requires some history and background. Postulate 2 is probably easier to grasp.

Think about this. What is amazing about the speed of light is not that it is so really fast (which it actually is really fast); but what is really amazing is that IT IS THE SAME SPEED FOR ALL OBSERVERS!!

Now the speed of most things we are familiar with should never be the same for all observers, but should depend on the motion of the observer making the measurements.

For example, if I am travelling in a car on a highway at 100 miles per hour and you are in a car parallel to me travelling at 100 miles per hour in the same direction, and you point your radar gun at my car (assuming your radar gun doesn't take into account your actual motion), well you will measure my speed as zero. If you are travelling in the same direction as me but only at 50 miles per hour, your radar gun will measure my speed as only 50 miles per hour. And so on and so on; you could invent more simple examples like this. You get the idea. The speed of things is supposed to depend on the motion of the observer taking the measurements. This seems to be intuitive.

But with light, no matter how you move, no matter how fast or how slow or in what direction, you will always measure the same speed for light! This is something that really should not be! But it turns out it really is! This is like pointing your radar gun at a particular car and always measuring a consant value for it's speed no matter what speed or direction you are travelling in.

Now speed is distance divided by time. In the case of light, no matter how you move or with what speed, distance and time themselves, space and time, or 'spacetime', will 'conspire' against you and always adjust themselves in exactly the right amounts so as to ensure that you always measure one single constant value for the speed of light.

Instead of distance, or space, and time being absolute, and speed the variable, is SR, the speed of light is the absolute, and space and time are what is variable.

The speed of light being constant has some peculiar and amazing consequences. Moving objects are actually measured as contracted in their direction of motion. For all but extremely high speeds the measured contraction is never noticeable. At high speeds approaching an appreciable fraction of the speed of light, the effect kicks in more noticeably.

The measurement of time is not absolute because of the constancy of the speed of light.

Before and just prior to Einstein, people thought the speed of light should behave like the measurement of other speeds of ordinary objects we are familiar with, ie the speed should depend upon the motion of the observer. After all this is what experience and familiarity tell us.

But Maxwell's theory of electormagnetism, which seemed to be accepted and adequately account for and describe electromagnetic phenomenon including light only had one speed for light. So the question was asked, in what particular reference frame does this speed arise? Like the moving cars on the highway, Maxwell's particular value for the speed of light had to be due to a certain and particular relational juxtaposition of certain reference frames to get a certain value. The value for light's speed should also be subjet to change; if you moved differently, as in the moving cars example, then you should be able to measure a different value for the speed of light.

But this turned out not to be the case. Different values for the light speed in Maxwell's equations gave rise to electromagnetic phenomenon that were not observed. Moreover, nobody could actually detect a different value for the speed of light in experiments designed to attempt to measure a different speed by varying the motion as in our car example.

The fact that the speed of light seemed to be constant looked like the speed of light was not simply a value to be measured, but was actually a physical law in itself. The speed of light had only one measureable value, and this constituted a physical law. But scientists of the time thought the law had to have a special reference frame to give rise to the particular value - like the car example; saying the car is moving at 50 miles per hour describes a particular reference frame.

Before Einstein, it was already well known that the laws of mechnaics, Newton's laws, were the same in all inertial reference frames. But it seemed that the laws of electromagnetisim had to have a special frame, one that gave rise to a particular value for the speed of light.

What Einstein did in SR was to say no; ALL the laws of physics, including electromagnetism, are the same in all inertial reference frames. So if the speed of light is a law, then it is the same for all observers, and if this changes notions of the absoluteness of space and time, then so be it. Einstein then worked out the perculiar effects this had on absolute space and time notions.

This is just 'Special Relativity'. General relativity extends the relativity of physical law to accelerated reference frames where it really becomes a theory of gravity.

Friar Bellows

Baptist Vine's explanation was excellent.

I just wanted to point out that one shouldn't be mistaken into thinking that special relativity (SR) is a theory about light, even though it always seems to be going on about "the speed of light this", "the speed of light that". The speed of any massless particle in SR is the same for all inertial observers. I suppose it's just easier to say "speed of light", and devise thought experiments involving the propagation of light, a phenomenon with which we are familiar in everyday life.

A nice not-very-technical introduction to special relativity can be found here:

http://www.lassp.cornell.edu/~cew2/P209/P209_home.html

A set of lecture notes from David Mermin.

Undercurrent

Just to add to BV and FB's response, SR includes not just the bahviour of light or massless particles, but all velocities of any objects.

For example, if you are standing at the edge of a straight road with a radar gun and clock a police car moving at 50 mph, while at the same time the police car, using a radar gun not compensating for his velocity, clocks a speeder at 50 mph, one would imagine that if you (at the edge of the road) were to try and clock the speeder, you would measure 100mph.

In general, if you measure the cop at speed u, and the cop meaures the speeder at speed v, then you would measure the speeder at speed u + v. This is so obvious that it is taken for granted in Newtonian mechanics, but it is wrong.

In reality, with a sufficiently accurrate radar gun, you would measure the speeder's speed as (u+v)/(1+u*v/c^2), where c is the speed of light. If u and v are both very small compared to c, then u*v/c^2 is almost zero, and the formula gives results not very different than the Newtonian u + v. This is why nobody noticed this for a couple of centuries.

If either u or v is large compared to the speed of light, the denominator gives a significant discrepency from the Netwtonian results. If, in the extreme case, v=c, then:

(u+c)/(1+u*c/c^2) = (u+c)/(1+u/c) = c*(u+c)/(c+u) = c

Indicating that if the cop sees the speeder going at c, you also see the speeder going at c, no matter what speed the cop is going.

DNAunion

DNAunion: Undercurrent surely knows this, but for those who don't.

What Undercurrent posted deals with the relativistic addition of velocities. Here's an important consequence of that.

Why can't any thing go faster than c? It sounds simple to beat c. Build a small spaceship that can go at 0.6c and put it intside a larger spaceship that can also go at 0.6c. Now have the large one hit its 0.6c and then launch the smaller one. The bigger one will be going at 0.6c and the smaller one will be going at 0.6c relative to the bigger one. So surely the smaller one would be going at 0.6c + 0.6c = 1.2c.

And it would, if velocities added in the simple manner we are taught in school. But as Undercurrent pointed out, that is not exactly correct. The closer one gets to c, the farther away from the simple 4 + 6 = 10 the true result is, and it turns out that you cannot add two, or three, or four, or ..., velocities and end up with a final result that is greater than c. So one can't "leap frog" to beat c.