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Registered Member #29
Joined: Fri Feb 03 2006, 09:00AM
Location: Hasselt, Belgium
Posts: 500
Symmetry breaking....
Take the time reversal symmetry of so-called Hamiltonian systems (systems that conserve energy). This means that if you run them forward or revrese, they are indistiguishable from each other. Imagine a lossless spring-mass system oscillating. It looks the same whether time runs forward or reverse. It oscillates the same way... This is time-reversal symmetry. The electromagnetic wave equation also exhibits this symmetry.
Now imagine the same oscillating system with some loss... The oscillations die away if time runs forward, but grow exponentially if time is run in reverse. The time reversal symmetry has been broken. All diffusive systems break time symmetry.
There are many symmetries in physics (spatial, parity, time-reversal, etc.) Symmetries usually indicate some form of conservation law is at work, that is why they are so important to theoreticians and why experimentalists look for them. All study of symmetries starts with the study of classical mechanics. It's mathematical framework formed the basis for both modern relativity theory as well as quantum mechanics....
EDIT: Symmetry breaking is important in this discussion because the "particles in a box" model of a gas are an example of a system that obeys Newton's laws and should exhibit time reversal symmetry. Moreover, being a closed, non-dissipative system, it should exhibit periodic behaviour, i.e. should return to its initial state in some long, but finite time. This violates both common sense as well as the second-law. We know that real systems do not behave like this. The Boltzmann equation is not time reversible, even though it is based on Newtonian mechanical description of the particles. This causes a contradiction. Boltzmann invented his scattering function to destroy the correlation between the particle momenta before and after collisions. This breaks time reversal symmetry as well as any periodicity. However, it had no theoretical basis. It just seems to work. Quantum uncertainty may be a way out of this conundrum......
Registered Member #27
Joined: Fri Feb 03 2006, 02:20AM
Location: Hyperborea
Posts: 2058
This example requires a lot of assumptions and fine tuning and there are probably many reasons for why it can't work. It is just to show it is possible to imagine the existence of a working demon process.
Imagine a perfect mirror box with particles of some average energy. Then we insert a small black hole with a higher average temperature. It will absorb all the cool particles and emit hotter ones in return.
Inside the singularity all newtonian and other senses of reality will break down and be replaced with some sort of entangeled quantum gravity. So laws as we know it will not apply and if they do they will not apply in the sense we are used to so the common arguments against Maxwell's demon are not valid.
That the old arguments does not apply is not important for this idea, The important reason why the common arguments fail is that the black hole does not observe the particles in the traditional sense but processes them all equally, so it will not use any energy in processing the particles. It just pools their energy and a separate process generates new particles of a higher energy from the pool. The new temperature depends on the size of the pool and not the properties of the individual particles that went into the pool.
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Maxwell's demon
