Re: Teaching logic is urgent

[Bob LaMontagne <rlamont@POSTOFFICE.PROVIDENCE.EDU>]

Pentcho Valev wrote:

> Some time ago I showed that special relativity is based on inconsistent premises.
> Now I am giving another example. In  thermodynamics, .............. (Snip)

I've been away for a while and am catching up on postings to the list. I was curious
about one of your previous postings related to the statement above. I assumed there
would be some responses, but for some reason I can't find a thread that continues your
subject heading "a Relativity Problem". I'm a little hesitant to reply, because I find
all the treads related to your postings end after one response. I hope I'm not about
to post something that no one else on the list is interested in.

Anyway - your previous post stated (I'll put it in quotes and separate it by a  dashed
line since it runs a few paragraphs)

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"The following problem could be given to students. For the derivation
of Lorentz transformations, Einstein introduced

(A)  x' = 0  <->  x = vt

He should have introduced, or WE now introduce, in accordance with
the special relativity principle, a premise symmetrical to (A):

(B) x = 0  <->  x' = -vt'

Einstein also introduced, for a beam moving along the x-axis,

(C) x = ct  <->  x' = ct'

Now the problem is that (A), (B) and (C) are incompatible. (A) and
(C) are compatible and lead to Lorentz transformations but it is easy
to see that one cannot deduce (B) from Lorentz transformations. (A)
and (B) are also compatible and lead to transformations different
from Lorentz transformations. (B) and (C) are also compatible and
lead to transformations insignificantly different from Lorentz
transformations. So, in order to be able to proceed, we must declare
either (A) or (B) or (C) as false. Which one is false?"
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You say (A) and (C) are compatible and lead to the Lorentz transformations. If I take
one of those transformations, namely

x = (x' + vt')/sqrt(1-v^2/c^2)

and substitute x' = -vt', I get x=0, which is your statement (B).

In like manner, Starting with (B) and (C) and applying the Lorentz transformations,
(A) appears as a result. Also, (C) itself is just a trivial result of applying the
same transformations. What's always surprising is how easily the standard Lorentz
transformations tie (A), (B), and (C) together so well.

 From past discussions on this list, I know there are differences of opinion as to
whether (A), (B) and (C) all by themselves are sufficient to produce the Lorentz
transformations, but the transformations (once proposed) certainly make (A), (B) and
(C) consistent.

Also, while I'm catching up, I don't quite follow why non-conservative bulk dielectric
effects in the capacitor problem require a revision of the fundamentals of electricity
and magnetism. Non-conservative tidal effects between gravitating objects don't demand
a revision of the conservative gravitational force - or a rejection of the Second Law
of thermodynamics.

Bob at PC