Re: THE COVARIANCE OF THE GENERAL LAWS OF THE NATURE
- From: "Bill Hobba" <rubbish@xxxxxxxx>
- Date: Fri, 17 Aug 2007 01:49:05 GMT
"Stamenin" <tasko.s@xxxxxxxxxxx> wrote in message
news:1187297354.569845.147800@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
THE COVARIANCE OF THE GENERAL LAWS OF THE NATURE
Einstein in his book "Relativity" in page 44, writes: "Every general
law of nature must be so constituted that it is transformed into a law
of exactly the same form when, instead of the space-time variables x,
y, z, t of the original coordinate system K, we introduce new space-
time variables x', y', z', t' of a coordinate system K'. In this
connection the relation between the ordinary and the accented
magnitudes is given by the Lorentz transformation. Or in brief:
General laws of the nature are co-variant with respect to Lorentz
transformation.
This is a definite mathematical condition that the theory of
relativity demands of a natural law and in virtue of this, the theory
becomes a valuable heuristic aid in the search for general laws of
nature. If a general law of nature were to be found which did not
satisfy this condition, then at least one of the two fundamental
assumptions of the theory would have been disproved".
In this direction let us take as an example the second law of the
mechanics to see how this law fulfils this condition with the Galilei
transformation and with the Lorentz transformation.
The second law of the mechanics can be written in this form:
In the system K, we can have:
F=a.m=m.(d^2.x/dt^2).
1) With the Galilei transformation for K': x'=x-v.t.
We can have the form of this law in K':
F'=m.d^2/dt2(x-v.t)=m(a-0)=m.a.
F'=ma=F....(1)
2) With the Lorentz transformation: x'=(1/R)(x-v.t).
We can have the form of this law in K':
F'=m.(d^2.x'/d^2.t')(d^2.t'/d^2.t)=m[(d^2.x'/d^t.2)]=(d^2/d^t)(1/R)(x-
v.t)]
=m.1/R(a-0)=(ma)/R
Or, F'=ma/R=F/R.....(2)
3) If we try to repeat the calculus with this result to find F in the
system K, when we know The force F'=F/R in K' the result should be:
F=(F'/R)/R=F'/R^2 .....(3), and not the initial form F=ma.
When proper acceleration is used the force is a 4 tensor
Bill
If we reaped the passing from K to K' and inverse there will appear
errors every time with the square tooth R.
So the conclusion is that the Lorentz transformation does not satisfy
the covariance for this general law of the nature, while the Galilei
transformation satisfies it.
This is one additional evidence about the mistaken Lorentz
transformation.
.
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