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Relativity and Quantum Theory


Date: 03/15/2002 at 05:15:14
From: nabi dhanoya
Subject: Relativity and Quantum theory

What is the problem between relativity and quantum theory that 
scientists are trying to solve? I hear so much about it, but have not 
been able to truly understand it. 

Nabi


Date: 03/15/2002 at 09:08:18
From: Doctor Mitteldorf
Subject: Re: Relativity and Quantum theory

Dear Nabi,

This is a fascinating area to want to know more about, but I'm afraid 
it really does require a lot of background before you can appreciate 
the problem. 

Quantum mechanics is about lumpiness. You'd think that the energy of 
a particle can be any real number - if its energy starts out equal to 
1 erg, you can give it a tiny push and bring its energy to 1.00001 or 
even 1.0000000001 ergs.  But it turns out that small systems don't 
work this way - they might have an energy of 1 or 2 or 3 units, but 
never 1.5 or 1.00001. (These units aren't ergs, but "natural units" 
for the system, depending on the mass of the particles, the strength 
of the force holding it together, and Planck's constant h.)

Quantum mechanics was invented around 1923, and already by 1929 there 
were some good candidates for ways to combine QM with Einstein's 
Special Theory of relativity. This work was spearheaded by Dirac.

It's General Relativity that has been difficult to combine with 
quantum mechanics. This is because GR is a theory that relates space 
and time to energy. If energy is quantized, then space and time must 
be lumpy, too. No one has been able to imagine a consistent system 
where there is a time=1 and a time=2, but it's meaningless to talk 
about time=1.00000001 unit. A "consistent" system has to be not only 
logically consistent with itself, but it also has to be one that 
predicts answers on a large scale consistent with QM and with GR, so 
that "we wouldn't know the difference."

There's a new book out on the subject that might be at just the right 
level for you. I recommend "Three Roads to Quantum Gravity" by Lee 
Smolin:

http://www.amazon.com/exec/obidos/ASIN/0465078354/qid=1016201223/sr=2-3/102-6258870-4532957   

- Doctor Mitteldorf, The Math Forum
  http://mathforum.org/dr.math/   
    
Associated Topics:
High School Physics/Chemistry

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