狭义相对论评论.pptx

In the absence of the aether there is no natural preferred reference frame for ic theory. We still conclude that all inertial reference frames are equally valid and hence the wave equations must have the same form in all inertial reference frames. However, it is straightforward to show that the wave equation does not satisfy Galilean relativity. Consider the transformation of the wave equation for a one dimensional wave V(x,t). In the O system,
We will use eqns 1 to transform this into the O’ system.
In general the transformation from one coordinate system to another is given by,
3
库文档分享
(4a) , 4(b)
Applying eqns 4 a second time gives
(5)
So we see from eqn (5) that the wave equation is not a Galilean invariant. Equations 1 must be modified so that the wave equation is invariant in transforming from one inertial frame to another. The coordinates (y,z) perpendicular to v do not change. We must consider a more general transformation for the x and t coordinates. It makes sense to try a symmetrical representation of the transformation.
In eqns 6 we choose coefficients a’s and b’s to be dimensionless.
We now use equations 6 in equations 3 and derive for the wave equation
4
库文档分享
(7)
In order to ensure invariance . coordinate transformation we need
We can try to find a solution to 7 that is symmetric, namely try a1=b1 , and a0=b0. Both 7a and 7b give the same result.
5
库文档分享
The counterpart to the Galilean transformations ( eqns 1), which makes the wave equation invariant is called the Lorentz transformation.
Inherent in this derivation are two assumptions.
The first is that the speed of light, c, is the same in the O’ and O reference frames. This is actually an experimental fact.
The second is that the laws of physics have the same form in all inertial reference frames.
There is, in fact, nothing special about ism other than in the vacuum the waves propagate at a universal speed, c. Any wave disturbance that travels at this speed will also requir