Re: Special Relativity is saved from collapse by means of silly algebraic tricks
- From: Albertito <albertito1992@xxxxxxxxx>
- Date: Fri, 1 Feb 2008 05:37:52 -0800 (PST)
On 1 feb, 12:10, "Jeckyl" <no...@xxxxxxxxxxx> wrote:
"Albertito" <albertito1...@xxxxxxxxx> wrote in message
news:5bca1e95-17b9-43ef-89e0-10564a05c20b@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
On 31 ene, 22:55, "Jeckyl" <no...@xxxxxxxxxxx> wrote:
"Albertito" <albertito1...@xxxxxxxxx> wrote in message
news:062b4778-d7cc-445d-8cc9-8c764f309b69@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Here we go .. more criticism from ignorance. Why do you keep doing this
..
you know it makes you look foolish
[snip a load of nonsense]
Consider now that set S as the set of all possible relativistic
velocities under Special relativity, where the operator * is for
Einstein's addition of velocities.
And it works just fine .. do you really think that a*b <> b*a for
velocity
composition in SR?
It is not what I may think, it results that a*b <> b*a
for some cases in SR
OK .. my apologies .. when we are talking about general vectors, rather the
colinear ones, you get a*b <> b*a.
That then begs the question .. is that a problem?
This issue may be a problem if three observers are involved,
There might be cases where they wouldn't agree in their
relative velocities. Three observers involved would mean
associativity doesn't hold, either,
v_AB = velocity of observer A wrt observer B,
v_BC = velocity of observer B wrt observer C,
v_CA = velocity of observer C wrt observer A,
v_BA = velocity of observer B wrt observer A = - v_AB,
v_CB = velocity of observer C wrt observer B = - v_BC,
v_AC = velocity of observer A wrt observer C = - v_CA,
v_CA = v_BA*v_CB, [1]
v_CB = v_AB*v_CA, [2]
v_AC = v_BC*v_AB, [3]
v_AB = v_CB*v_AC, [4]
v_BA = v_CA*v_BC, [5]
v_BC = v_AC*v_BA, [6]
Let's take eq. [1], and multiply both sides by v_BC for the right,
v_CA*v_BC = v_BA*v_CB*v_BC,
now, associate as
v_CA*v_BC = (v_BA*v_CB)*v_BC,
v_CA*v_BC = v_BA*(v_CB*v_BC),
Associativity doesn't hold, in general, for Einstein addition
of velocities.
From eq. [5], you get
v_CA*v_BC = v_BA, so you are left to test
v_BA = (v_BA*v_CB)*v_BC, [7]
v_BA = v_BA*(v_CB*v_BC), [8]
Eq. [7] holds, because v_BA*v_CB = v_CA , but
Eq. [8] has v_CB*v_BC = e, with 'e' the identity element ,
so
v_BA = v_BA*e = v_BA ???
It should be v_BA = - v_AB. Have I made something wrong? :-(
.
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