Relativity - General Example?

[AceofSpades]

Can someone give me a layman's overview of A.E.'s theory of relativity and an example/proof/thought experiment that shows it to be true?

[MrMon]

You're gonna have to work harder than that. Try reading this:

http://images.amazon.com/images/P/0375708111.01._AA240_SCLZZZZZZZ_.jpg

It's about as laymans terms as you're going to get and still be thorough.

[chrisnice]

Id suggest "Fabric of the Cosmos" by the same author.

[MrMon]

"Fabric" does not explain relativity in nearly the same manner as "Elegant". Start with "Elegant", then do "Fabric".

[chrisnice]

[ QUOTE ]
"Fabric" does not explain relativity in nearly the same manner as "Elegant". Start with "Elegant", then do "Fabric".

[/ QUOTE ]

After reading your post I went and skimmed both and I must concede that you are correct sir. I got them both for Christmas and the info tends to smear I guess. But to the OP, read them both, theyre excellent reads.

[AceofSpades]

thanks

.....

[ffredd]

The special theory of relativity (1905) deals with the consequences of the fact that the speed of light is independent of the speed of the light source. (It may seem impossible, but it's a proven fact). The general theory of relativity (1915) is a theory of gravitation. SR is included in GR in the sense that GR describes many possible universes, one of which is a universe where there is no gravity at all. This universe is identical in every way to the one that SR describes.

The standard model of elementary particles is based on quantum mechanics and SR. It has been tested with enormous accuracy and has passed every test so far. One example is the measurement of the magnetic moment of an electron. The experimental result is a number with about 9 decimals (I don't remember exactly) and it's in complete agreement with the theoretical calculation. This is conclusive proof that the special relativistic description of space and time is much more accurate than the old Newtonian description. The famous equation E=mc^2 is also a prediction of SR.

GR is all about one equation, Einstein's equation, that describes the relationship between the geometry of spacetime and its content of matter and energy. "Matter tells space how to curve. Space tells matter how to move". GR has also been tested with enourmous accuracy. One famous example involves astronomical observations of two neutron stars in orbit around their common center of gravity. GR says they will lose energy due to emission of gravitational waves ("ripples" in spacetime), and therefore need slighly more time to complete each new orbit, while Newtonian gravity says that no such thing will happen. The time delay was measured with even greater accuracy than the magnetic moment I mentioned earlier, and the result was in complete agreement with the theoretical prediction of GR. This is conclusive proof that the general relativistic description of spacetime is much more accurate than the special relativistic description.

There is actually at least one kind of technology that uses the predictions of GR. GPS satellites have to compensate for the gravitational time shift that causes clocks to run more slowly when gravity is weaker.

I agree with the other guys that The Elegant Universe by Brian Greene is a very good place to start reading more about this.

[Mik1w]

basic solid overview:
special relativity is based on two postulates:
1. the physics of ANY two inertial frames is the same
this is basically saying if you're on a train and on a platform in a closed box, there's nothing you can do to determine whether you're on the train or platform. basically, there is no absolute velocity wth which things can be measured against. (an inertial frame is basically specified by a velocity... eg. the frame of the train, the platform are both inertial frames. intertial frames do not accelerate)
2. the speed of light is the same in all inertial frames
this is the weird thing - no matter what speed you travel at, no matter if you move towards or away from light, you will measure it to be the same speed. very weird, but apparently true.

from these two basic postulates the whole of SR can be derived. the famous thought experiment is the light clock, bsaically a setup consisting of two facing mirrors with a single photon bouncing between them, and each tick is the time taken for a photon to travel from one mirror to the other. From the maths of this, it can be shown that the time of a tick measured by an observer moving at speed v relative to he clock is dilated by a factor of gamma, where gamma is a function of the velocity (gamma = 1/sqrt(1-vv/cc)). So if a car moves towards you at speed 0.8c, then the gamma factor is about 1.7; what takes a second to you appears to take 1.7 seconds in the car. By symmetry (the first postulate, that no inertial frame is favoured), the driver of the car observes the same thing of you.

It can also be derived that lengths are contracted by the same factor, that is, the car will appear to be 1.7 times shorter, although its width will not be affected (the contraction is only in the direction parallel to motion).

The lorentz transformations (which were proposed before SR to solve some problems in the area of electromagnetism)can be derived from this; they basically summarise motion in special relativity by relating five quantities: the position and time of an event in frame one, the position and time of the event in frame two, and the velocity between the frames, in four equations.

But that isn't all. What if v=c? You get an infinite factor gamma, suggesting that photons don't observe time and they see the entire universe contracted into a plane perpendicular to their direction. But anything with a mass cannot move at the speed of light.

The momentum of an object was first thought to be the product of that object's mass and velocity. in special relativity, it is the product of the object's mass, velocity AND gamma factor, which depends on the velcoity between the object and the observer - the momentum of a train when measured on board is different to that when measured at the station.

To accelerate something, you must provide a force. Newton's defenition of force is the rate of change of momentum of the body; to make something speed up, you have to add to its momentum. Before special relativity, this would mean you can just keep pushing it; its mass isn't going to change, so the velocity is "forced up" to greater than the speed of light. (Einstein actually first considered special relativity when he was 16, when he thought what you'd see when you did this). With the extra gamma factor in momentum, now you can keep adding to the momentum, as you could always do, but the velocity will not increase proportionally, it will tend towards a limit, as the gamma factor increases. That limit is the speed of light. Essentially, the amount of energy you require to accelerate an object to the speed of light is not finite.

The famous equation E=mc^2 is also not exactly accurate. It does relate the total energy E of an object and the mass of that object, but it is only valid when the object is stationary. When moving, you have to add the kinetic energy it has. When you use a binomial expansion to find an approximation to the kinetic energy, K=(gamma-1)*mc^2, the first three terms come to 0.5*mv^2, the non-SR kinetic energy. But there are more factors that become important at large velocities, I think the next one is 3mv^4/8c^2.

Thats pretty much a university course on special relativity summarised without the equations. If you want the interesting stuff and nothing more then read Brian Greene, but its much better I think if you know the maths behind it. It isn't very hard maths, its just quite a conceptual leap to solve some problems, but its well worth it to get a deeper understanding.

If you want that, then I recommend going to the library, University Physics has a solid chapter about it and the maths, and Leo Sattori (sp?) has a good dedicated book which is about £18 I think.