Henry Cobb wrote:
> On Fri, Jul 10, 2009 at 12:18 AM, Erik Max Francis<max@...
> <mailto:max%40alcyone.com>> wrote:
> >
> >
> > Henry Cobb wrote:
> >> Nope, gravity works just fine. Objects that fall into a gravity field
> >> "lose time" to make up for the potential energy they give up.
> >
> > Huh? If you're referring to gravitational time dilation, then the fact
> > that clocks run more slowly in a gravitational field has to do with
> > length of paths through curved spacetime, not potential energy.
> >
> > After all, you hardly need general relativity to explain why being able
> > to pull a body out of a gravitational field doesn't violation
> > conservation of energy; it's because you're supplying the energy by
> > pulling it out, doing work against the force of gravity.
>
> Take a certain amount of energy and create an electron-positron pair
> in deep space.
>
> Then move this pair to the surface of the moon and turn them back into
> a pair of gamma rays and measure them locally and you will see the
> same amount of energy as before.
>
> But if you send these gamma rays out into deep space you will find
> there that you don't have quite enough energy to remake the
> electron-positron pair because of the gravitational red shift than
> manifests as a difference in time rates.

Yes, that's a feature of general relativity (and, as I said, the cause
is the curvature of spacetime, not gravitational time dilation;
gravitational redshift and time dilation are both caused by spacetime,
one doesn't cause the other). But you don't need general relativity to
see why nothing special in terms of conservation of energy is going on
here, as I showed.

But let's take your example at face value. An electron-positron pair
annihilating in a gravitational field creates photons that may rise up
in the gravitational field, and must lose energy according to
conservation of energy. This is indeed the correct results of a simple
thought experiment that doesn't require full general relativity or even
the weak equivalence principle to demonstrate; all you need is Newtonian
gravity plus the notion of mass-energy.

But you're again missing the point: How did the electron-positron pair
get where it is before it annihilated? If it fell under the force of
gravity, it gained energy. So when it's converted to energy and
emitted, the total energy before and after is exactly the same.

To get two plates to experience the Casimir force, you had to bring them
close enough together so that it could come into effect. To test their
masses afterwards, you had to pull them apart. You're the one providing
the energy, and then pulling it out again (or even vice versa for
opposite potentials), but nothing is violating conservation of energy here.

> > Same thing for your Casimir plates. The scales don't balance because
> > you're ignoring one end of them.
>
> No, the Casimir effect is purely potential energy and so is taken out
> of the mass of the local objects instead of coming out of the vacuum
> energy.

No. And, once again, vacuum energy doesn't have jack to do with the
Casimir force.

> Virtual particles have no net mass or energy to give.

They can change potentials, which is what's happening here. The
potential function is modified with the introduction of a Casimir force,
but the principle of conservation of energy doesn't change. dU/dx = -F
and path independence tells you that.

--
Erik Max Francis && max@... && http://www.alcyone.com/max/
San Jose, CA, USA && 37 18 N 121 57 W && AIM/Y!M/Skype erikmaxfrancis
Convictions are more dangerous enemies of truth than lies.
-- Friedrich Nietzsche