Conservation of Matter/Energy Question (from a student)

[Molyneux]

This query is actually something that occurred to me while reading Magnetic's post regarding reincarnation and quantum physics...

Energy is an invariant of an isolated system in question, not an indestructible stuff in that system. It is deeply related (through Noether's theorem) to the fact that physical laws are symmetrical with respect to time translations (the physical laws today are the same as the laws yesterday).

If conservation of energy is based on the physical laws being symmetrical with respect to time...then does that mean that energy or matter COULD be created, so long as it is later destroyed, so in the long run it remains constant?

[SeeingRed]

Not sure if this is a valid response, but consider this line of reasoning:

Reversible processes must proceed through a series of equilibrium states; this is a fact of thermodynamics. Let's split up your proposal into two phases, the creation of energy phase and the destruction of energy phase. Considering the creation phase first, this is clearly not at all a series of equilibrium states, so therefore the process would have to occur irreversibly, a premise that is negated by the proposition that the energy is going to be destroyed.

So, it isn't possible? Though I'm not 100% confident of this argument...

[Kuroneko]

Classically, no. In terms of the Lagrangian, the symmetry being reffered to is about every point in time, i.e., the Lagrangian is completely time-independent for an isolated system. In terms of the spacetime manifold of the GTR, it usually refers to the presense of a timelike Killing vector field, which is a generator of an isometry and thus can be loosely considered to be a symmetry. Energy is always conserved locally, in the sense that for any 'sufficiently small' piece of spacetime, as much energy 'flows in' as 'flows out' (think ∇·B = 0 of electromagnetism), but without a Killing vector, it is not globally definable except in some particularly nice cases. Quantum-mechanically, it's a matter of interpretation. There are some effects in quantum field theory which can be viewed as temporary fluctuations in the energy of the system, but they can also be interpreted in other ways.

[Molyneux]

Ah...fair enough, then.

I'm not quite sure that I understood all of Kuroneko's post, but what I do understand makes sense...I'll just bow to the judgement of those who've actually studied this other than in their spare time.

[SyntaxVorlon]

Actually there is something in quantum physics that might be a good parallel to this. Because of the Uncertainty principle having an Energy and time formula (the normal form is prob(x)*prob(p)>= h/PI, with those being probabilities(well not really, more bell curves), there are ways to turn this inequality from x and p to time and Energy) there can be a very large amount of energy present given an increasingly small period of time.

The result of this is that particle-antiparticle pairs can quickly appear and disappear anywhere in space spontaneously. This is actually how Hawking Radiation works, so you can look that up for a better description.

[drachefly]

A better way of looking at that for most purposes is that the 'listed' mass of a particle is a target, and if the particle exists only briefly, it can 'miss', and bring a different amount of energy.

As for background particles... so, the ground state, with its distinctly defined energy, has a nonzero density of certain particles and their antimatter counterparts, which are in creation/annihilation equilibrium.

In this way total energy never fluctuates at all.

[SpacedTeddyBear]

You also have to consider entropy as well when you talk about the conservation of energy. The entropy of an isolated system can only increase in time. So if you were to throw a glass cup at wall and time reverse it, the laws of physics still apply in the time reversed system, but since entropy is increasing, we never observe the time reversal.