Re: A small conservation of energy puzzle
sal wrote:
> On Tue, 31 Jan 2006 20:59:07 -0700, N:dlzc D:aol T:com (dlzc) wrote:
>
> > Dear sal:
> >
> > "sal" <pragmatist@xxxxxxxxxx> wrote in message
> > news:pan.2006.02.01.03.34.14.556985@xxxxxxxxxxxxx
> >> Here's a little problem in conservation of energy which I found rather
> >> puzzling. For your amusement...
> >>
> >> (C=1 throughout, and so E=M throughout. It's a simple problem but a
> >> precise statement takes about a page; bear with me...)
> >>
> >> We have two frames of reference, a spaceship's frame, "M", and an
> >> Observer's frame, called "O".
> >>
> >> On a spaceship, an astronaut converts a small mass, "dM",
> > ...
> >> Where did that energy go?
> >
> > The energy went here. The energy produced is "dM", not dM * g.
>
> <g>
>
> It's not that simple. The mass which was converted had energy dM*g
> in the observer's frame, just as I said -- I mean, really, think about it.
> That's the rest mass, plus the energy which had to be pumped into that
> bit of mass to get it going at its observed velocity, right?
>
> In any case that doesn't answer the question, because the energy which
> comes back out is just dM/g due to the redshift of the photon. So the
> books still wouldn't balance, even if you were correct; you'd just have a
> smaller quantity of "lost mass" to account for.
>
> It doesn't have to be an exotic "magic conversion" of mass into energy,
> either. It can be as simple as a flashlight beam. When you turn on a
> flashlight, the batteries get ever so slightly lighter as they run down.
> In the observer's frame, the batteries have had extra energy pumped into
> them to get them going at velocity "v", and the mass change as they
> discharge is hence larger by a factor of gamma. Where's that extra energy
> go?
>
> For about two days this one drove me nuts...
The mass which was converted had energy dM*g -- wrong.
The mass which was converted had energy dM -- right.
http://www.androcles01.pwp.blueyonder.co.uk/E^2/EnergySquare.htm
What do you mean, "drove"?
You ARE nuts. You've always been nuts.
Androcles
.
Relevant Pages
- Re: .Re: Why all the fascination with E = mc^2 ??
... The *correct* expression for the kinetic energy ... frame of the mass). ... > velocity v, and being relativists, we immediately invoke the Lorentz ... > relativistic mass but such does not exist). ...
(sci.physics) - Re: .Re: Why all the fascination with E = mc^2 ??
... I have total energy totally analyzed and explicated in Fig. 6 in Ch. ... That's right it is in the rest frame, Pardin knew it, I knew it now ... >> relativistic mass but such does not exist). ...
(sci.physics) - Re: .Re: Why all the fascination with E = mc^2 ??
... The *correct* expression for the kinetic energy ... frame of the mass). ... > velocity v, and being relativists, we immediately invoke the Lorentz ... > relativistic mass but such does not exist). ...
(sci.physics.relativity) - Re: .Re: Why all the fascination with E = mc^2 ??
... I have total energy totally analyzed and explicated in Fig. 6 in Ch. ... That's right it is in the rest frame, Pardin knew it, I knew it now ... >> relativistic mass but such does not exist). ...
(sci.physics.relativity) - Re: Nobel Prize for David Thomson?!
... force will invariably stress the aether to ... >> having zero mass, no electric charge, and an indefinitely long lifetime. ... So indeed, a photon IS energy. ...
(sci.physics.particle) |
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