science sense and common sense, was Intelligent Design Invading Liberal Classrooms

On 2005-11-26, Brian Tung wrote:
[re Big Bang thermodynamics, omitting other good stuff]
What's more, the laws of thermodynamics are not the absolutes you seem
to suggest they are. For one thing, energy is not even well-defined
for strongly curved pieces of spacetime, so that the first law of
thermodynamics cannot be exactly applied except for closed systems in
asymptotically flat pieces of spacetime. There's no such thing, though
very good approximations exist in laboratories. But certainly the
initial conditions at the Big Bang are too curved to expect energy to
behave the way "common sense" predicts it to.

There are ways around this, using what are called pseudo-tensors, but as
I understand it, their use is somewhat controversial because they don't
transform like tensors (as their name suggests), which violates one of
the principles of general relativity--that the laws of physics are the
same in all reference frames. They *almost* transform like tensors...
but not quite. So it is far from certain that we can count on the
conservation of energy at the Big Bang; in fact, it seems almost
certain that we cannot.

Hey, this all sounds pretty neat. I'd never heard of pseudotensors,
or the notion that energy might not be well-defined in curved spacetime.
Do you know of references, books or web pages, that might say more about
either, for a reader with some physics background but only a little GR?

Cheers

Stuart Levy

In article ,
Stuart Levy wrote:
On 2005-11-26, Brian Tung wrote:

[re Big Bang thermodynamics, omitting other good stuff]
What's more, the laws of thermodynamics are not the absolutes you seem
to suggest they are. For one thing, energy is not even well-defined
for strongly curved pieces of spacetime, so that the first law of
thermodynamics cannot be exactly applied except for closed systems in
asymptotically flat pieces of spacetime. There's no such thing, though
very good approximations exist in laboratories. But certainly the
initial conditions at the Big Bang are too curved to expect energy to
behave the way "common sense" predicts it to.

There are ways around this, using what are called pseudo-tensors, but as
I understand it, their use is somewhat controversial because they don't
transform like tensors (as their name suggests), which violates one of
the principles of general relativity--that the laws of physics are the
same in all reference frames. They *almost* transform like tensors...
but not quite. So it is far from certain that we can count on the
conservation of energy at the Big Bang; in fact, it seems almost
certain that we cannot.

Hey, this all sounds pretty neat. I'd never heard of pseudotensors,
or the notion that energy might not be well-defined in curved spacetime.
Do you know of references, books or web pages, that might say more about
either, for a reader with some physics background but only a little GR?

See http://math.ucr.edu/home/baez/physic...energy_gr.html
for an intro.

The crux is that energy certainly _is_ conserved in GR, for infinitesimal
regions. The problem comes in when you try to speak about finite regions.
The pseudo-tensors, used correctly, can let you evaluate integral energy
conservation over a finite region, at least some of the time.

When you get to trying to evaluate the energy content of the whole
universe, or the entropy, such as you would want to for doing things
with thermodynamic laws, you are way, way up the proverbial creek without
much by way of either canoe or paddle. With the return of the cosmological
constant, this is even worse.

See the page for some of the details, and for references for the
real guts.

--
Robert Grumbine http://www.radix.net/~bobg/ Science faqs and amateur activities notes and links.
Sagredo (Galileo Galilei) "You present these recondite matters with too much
evidence and ease; this great facility makes them less appreciated than they
would be had they been presented in a more abstruse manner." Two New Sciences