[extropy-chat] still no biscuit!

[Robin Hanson]

At 05:55 PM 1/19/2005, Eliezer S. Yudkowsky wrote:
>>>the hypothesis of conservation of momentum is not that momentum is 
>>>conserved 90% of the time or even 99.9999% of the time.  The hypothesis 
>>>of conservation of momentum is that momentum is conserved 100.00000% of 
>>>the time.  We may be uncertain, but the hypothesis of "conservation of 
>>>momentum" hypothesizes a state of affairs in which reality is *not* 
>>>uncertain; a reality in which it is *absolutely certain* that momentum 
>>>will be conserved on each and every occasion.
>>It's true that physicists thought so 100 years ago. Then they found that 
>>with the conjugate properties position and momentum, 100% accuracy in 
>>measuring position meant momentum went all over the ship. Bugger, eh?
>>Granted, `reality' as Eliezer is using it refers to immense ensembles of 
>>individually uncertain events, so that by and large observed macroscopic 
>>momentum is pretty robust, even if its substrate is only statistical. But 
>>let's not go all 19th century on Brett's ass.
>
>I don't understand exactly why, but I was under the impression that 
>conservation of momentum remains exact.  Do any local physicists care to 
>speak up?

Momentum conservation is usually derived from a spatial translation 
invariance of the basic mechanics, just as energy conservation is derived 
from a temporal translation invariance.

In general relativity, spatial and temporal translation invariances lose 
some of their meaning - there are local versions but not global 
versions.  So one usually says that neither energy nor momentum is 
conserved at a global level.

In quantum mechanics, measurements are usually viewed as non-deterministic 
stochastic events, wherein given an initial state which is not an 
eigenstate of a momentum operator and a final state which is an eigenstate, 
one cannot predict which final eigenstate will result.  In this sense the 
only things which can be conserved have what are called superselection 
rules, that forbid certain kinds of states.



Robin Hanson  rhanson at gmu.edu  http://hanson.gmu.edu
Assistant Professor of Economics, George Mason University
MSN 1D3, Carow Hall, Fairfax VA 22030-4444
703-993-2326  FAX: 703-993-2323