Re: Should math be held to be literally the 'language of physics'?
From: Eugene Shubert (http://www.everythingimportant.org)
Date: 11/03/04
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Date: Wed, 3 Nov 2004 16:37:14 -0600
"Eric Gisse" <fsegg@uaf.edu> wrote in message
news:fd0fc2fa.0411022356.7d8b0e3f@posting.google.com...
> "Eugene Shubert" <http://www.everythingimportant.org> wrote
http://groups.google.com/groups?&selm=4187dc55@sys13.hou.wt.net
>
>> Eric Gisse wrote:
>> > you make huge gaping errors in mathematical logic.
>>
>> What error did I make using the principle called, change
>> of variables? What assumption is made in the substitution,
>> u=v/sqrt(1 -v^2/c^2)?
>> http://www.everythingimportant.org/relativity/special.pdf
>> http://groups.google.com/groups?&selm=418524d7@sys13.hou.wt.net
>
> Read the following for comprehension:
>
> Your math is fine. Technically it is correct, but it is not a proper
> derivation in any sense of the word.
You're not qualified to make that judgment. You're a beginning
physics student, not a math major. Isn't that right?
> The assumption you make in the substitution is that the proper
> form of the equation is v/sqrt(1-v^2/c^2). You do not derive
> gamma anywhere, you assume it.
>
> Do you understand what I said? You do not derive gamma,
> you assume it.
I understand your claim. You don't understand my assertion. You also
lack experience with mathematical proofs to know that mathematicians
command great power and often pull things out of the air. You also
don't see that my official derivation on pages 4 to 6 doesn't depend
on this little tidbit that you're objecting to on page 2. You also
failed to notice my insistence that my definition of v and gamma works
perfectly well in a Galilean universe. You seem to believe that I
assumed something Einsteinian. If so, then construct a gedanken
experiment in a Galilean universe and reach a contradiction.
"The justification of page 2 and 3 is extraordinarily easy. Let 1/c be
any real number. Try to argue how the substitution
u=v/sqrt(1 -v^2/c^2) could be invalid in a Galilean universe or in any
other universe that begins with an undeclared symbol v. Understand
that I started my paper by defining u, not v. I never gave v a
physical meaning. So where's the contradiction? Devise a gedanken
experiment in a Galilean universe to prove that this substitution
leads to contradictory results. It's impossible. Inconceivable! It
can't even be imagined to be false. So it's true without any effort.
It's just one step in a powerful magic trick."
http://www.everythingimportant.org/relativity/special.pdf
> If you truly have a [degree] in mathematics, this would
> be patently obvious to you.
It's improper for you to speak for mathematicians.
> Why should u = v/sqrt(1-v^2/c^2)?
Because it's vacuously true in every conceivable universe.
> You assume what you wish to derive!
Since there is no conceivable universe where that substitution is
false, it is then always true, even in a Galilean universe.
> But you ASSUME u=v/sqrt(1-v^2/c^2)!
> You ASSUME u=v/sqrt(1-v^2/c^2)!
You have no proof that my change of variables is a physical
assumption. You are merely arguing out of blind and bigoted ignorance.
The onus is on you. Magicians aren't expected to justify waving their
magic wands or their use of the word, abracadabra. Those are just
props used to invoke a sense of mystery in some and to entertain
others. The challenge is for you to prove that my steps violate some
law of physics in some conceivable universe. Suppose universe X and
real numbers u and 1/c. How does writing u=v/sqrt(1 -v^2/c^2) violate
the laws of physics in that universe?
Eugene Shubert
http://www.everythingimportant.org/relativity/special.pdf
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