Is the law of the conservation of energy always true?

[vincent 1st]

Is the law of the conservation of energy always true? (Energy cannot be created/destroyed)
Thanks in advance

 

[mgb_phys]

Under reasonable conditions yes.
Under some circumstances (extreme conditions, nuclear reactions) you have to expand it to say that energy + mass-energy (by E=mc^2) is conserved.

Actually it's better to say that the rule "energy + mass-energy" is conserved is always true - it's just that in every day situations the mass-energy change is too small to be noticed.

 

[TVP45]

Not to be coy, but in reference to what? Are you talking about classical physics? Are you including mass-energy equivalence?

Sorry mgb. Ya got ahead of my 1 finger typing.

 

[rbj]

the other thing that bothers me about the newly discovered (a decade ago) accelerated expansion of the universe is that this surely appears to me to violate the conservation of energy. it's like i throw a ball up into the air and it accelerates upward even faster as it gets higher.

 

[vincent 1st]

thanks for the help

 

[Loren Booda]

Fluctuations within time interval t - where Et<hbar/2, E is the corresponding energy interval and hbar is Planck's constant - do allow for directly immeasurable (yet statistically accountable) violations of energy conservation.

Who knows what mechanics lie beyond outward universal acceleration or the microscopic Planck region; maybe the above E interval over all spacetime makes up for the energy of cosmological thrust?

 

[mjsd]

conservation of energy is simply a statement or expectation that physics don't change over time. And if we believe that invariance in time is a good symmetry then conservation of energy would follow.

 

[Stingray]

the other thing that bothers me about the newly discovered (a decade ago) accelerated expansion of the universe is that this surely appears to me to violate the conservation of energy. it's like i throw a ball up into the air and it accelerates upward even faster as it gets higher.

Energy conservation is violated (or more precisely, concepts become ill-defined) in general relativity. There are situations where it can be recovered exactly or very nearly so, but they are not completely general. Of course the circumstances where these effects are significant do not occur in everyday life.

 

[Loren Booda]

Can you give us a simple example, Stingray? Is it due to nonlinearity of GR?

 

[Stingray]

Can you give us a simple example, Stingray? Is it due to nonlinearity of GR?

It is not related to the nonlinearity of GR. As others have said, energy conservation follows from a certain temporal symmetry. If you have a highly dynamic spacetime, you lose that symmetry. You therefore lose energy conservation. Examples are the universe as a whole, coalescing black holes, etc.

Another issue is that you might want to write down an energy as one component of a 4-momentum (as in special relativity). That's ok in a very small volume, but becomes problematic over large scales. The basic idea is that a vector is technically something which is attached to a specific point. This is usually glossed over in elementary physics because there's a natural and trivial way to transport vectors from point to point in Euclidean or Minkowski geometry. That disappears if the spacetime is curved, so it's not even clear what type of mathematical object the momentum of a finite system should be.

There's much more to say about these and other issues. The problems can be solved in some special cases, but nobody knows any way of recovering energy conservation in a form as useful as what's found in Newtonian mechanics.