Relativity and Such
Most recent answer: 10/22/2007
Q:
What in god’s name is relativity? (without the "in god’s name" part...)
What in the hell is: E=MC^2? (without the "in the hell" thing...)
- Anonymous
- Anonymous
A:
Everybody knows that some of the properties of anything you look at
depend on how you look at it. For example, wheter a box is wide and
shallow or deep and narrow depends on what direction you look at it
from. many properties also depend on your state of motion. For example,
whether a coffee cup is staionary or zipping by depends on whether it’s
described by the person holding it on a train or a person standing on
the ground.
Despite such differences in how particular things look, Galileo noticed that the laws of nature (or at least most of them- he wasn’t always consistent)look exactly the same from the point of view of someone who is ’at rest’ and one who is moving steadily. Actually, that means that there’s no real meaning to who is moving and who isn’t. They can use exactly the same laws, treating themselves as stationary, so there is no test as to who is ’really’ stationary, so we might as well quit thinking that concept has any meaning.
When Maxwell developed the laws of electromagnetism, it became apparent that they were in conflict with our ideas Galilean invariance. If you just add velocities when looking at things in different reference frames, as Galileo told us, then light should travel at a speed that varies with how fast the observer is moving. In fact, sound waves do exactly this -- you can catch up with one if you go fast enough. Maxwell’s theory predicted that the speed of light didn’t depend on the observer’s motion.
Einstein noticed that Maxwell’s laws would work for different observers, but only if the things which look different depending on your state of motion included some very surprising features. These include the lengths of objects and the duration of time intervals between events! He developed a complete mathematical theory, Special Relativity, to describe how space and time and other properties depend on the reference frame in which they are described. When people started to say that he’d showen that ’everything is relative’ he attempted to change the name of the theory to ’invariants theory’, since what he’d really done was to show that the invariants, the things that come out the same regardless of how you look, were different from the ones you initially guess. The speed of light is the most obvious of these surprising new invariants.
Einstein went on to develop a more general set of ways to change coordinate systems, General Relativity, in which gravity appears as an aspect of the geometry of space and time. It still has invariants.
As for E=mc^2, I’m sure we have other answers on that, which you can find with a search. It’s one of the many consequences of Special Relativity which can be obtained by very simple arguments using only elementary math.
Mike W.
p.s. In this 100th anniversary of Special Relativity, I’m starting to feel pretty silly filing this answer under ’new and exciting physics.’.
Well hey, it’s still pretty exciting. But all the other categories are exciting too, in their own ways -- Tom
Despite such differences in how particular things look, Galileo noticed that the laws of nature (or at least most of them- he wasn’t always consistent)look exactly the same from the point of view of someone who is ’at rest’ and one who is moving steadily. Actually, that means that there’s no real meaning to who is moving and who isn’t. They can use exactly the same laws, treating themselves as stationary, so there is no test as to who is ’really’ stationary, so we might as well quit thinking that concept has any meaning.
When Maxwell developed the laws of electromagnetism, it became apparent that they were in conflict with our ideas Galilean invariance. If you just add velocities when looking at things in different reference frames, as Galileo told us, then light should travel at a speed that varies with how fast the observer is moving. In fact, sound waves do exactly this -- you can catch up with one if you go fast enough. Maxwell’s theory predicted that the speed of light didn’t depend on the observer’s motion.
Einstein noticed that Maxwell’s laws would work for different observers, but only if the things which look different depending on your state of motion included some very surprising features. These include the lengths of objects and the duration of time intervals between events! He developed a complete mathematical theory, Special Relativity, to describe how space and time and other properties depend on the reference frame in which they are described. When people started to say that he’d showen that ’everything is relative’ he attempted to change the name of the theory to ’invariants theory’, since what he’d really done was to show that the invariants, the things that come out the same regardless of how you look, were different from the ones you initially guess. The speed of light is the most obvious of these surprising new invariants.
Einstein went on to develop a more general set of ways to change coordinate systems, General Relativity, in which gravity appears as an aspect of the geometry of space and time. It still has invariants.
As for E=mc^2, I’m sure we have other answers on that, which you can find with a search. It’s one of the many consequences of Special Relativity which can be obtained by very simple arguments using only elementary math.
Mike W.
p.s. In this 100th anniversary of Special Relativity, I’m starting to feel pretty silly filing this answer under ’new and exciting physics.’.
Well hey, it’s still pretty exciting. But all the other categories are exciting too, in their own ways -- Tom
(published on 10/22/2007)