```ReplyTo   : Kevin and Kelly
Subject   : Infinite energy?

> > I have a lot of problem bying the idea that the light bouncing
> > off a sail doesn't lose energy proportional to the kinetic or
> > heat energy gain of the ship.  Th power has to be coming from
> > somewhere.
>
>If the sail is reflective to the incident photon, then the photon
>doesn't lose energy as a result of reflection.  The ship changes
>velocity because the photon changes direction.  That's where the
>"power" comes from.

I think I can't agree with that Steve, when the photon enters the first
stage of the reflection, i.e. absorption, it adds some momentum to the ship.
So the velocity of the ship increases. Now we enter the second stage of
reflection, re-transmission. Relative to the ship the outgoing wavelength of
the photon is the same as the incoming photon (because of invariance). But
the observer at rest sees that that transmitted photon has dopplershifted
(nice verb) and thus lost some energy.

This is the same principle the police uses to measure speeding cars with radar.

>What happens to the mirrors?  What happens to the light pulse?
>An answer describing the limit state of the mirrors and light
>pulse is acceptable; you don't have to perform a step-by-step
>analysis of each reflection.

Assuming these mirrors have mass, they indeed will get some velocity that
correspondends to the same momentum as the photon. By each reflection the
photon will loose some momentum and lower its wavelength.

>I agree that we are stuck without a new power source.  Kevins microwave
>system or my Externally fueled system are at best theoretical possibilities,
>with no real credible way to build them.

Externally fueled did that mean scooping? I'm not sure anymore, please tell
me if my assumption is right.

Subject  : Relativistic mass increase

>>>I say that "relativistic mass increase" is a misnomer and that
>>>you are better off treating mass as invariant.

>> I've always looked at is as follows: When you move faster and faster, part
>> of the energy is transformed into mass, the other part is used to get the
>> extra momentum.
>
>I used to look at it this way, but Taylor and Wheeler talked me
>out of it (see chapter 8 of _Spacetime Physics_ for a lengthy,
>careful discussion on "Use and Abuse of the Concept of Mass").
>The problem here is that relative velocity or acceleration do not
>cause any fundamental changes in the structure of the moving
>object.  Where is this extra mass?  If it's really stashed on the
>ship somewhere then the people on the ship could measure it.  But
>they don't feel the ship getting heavier or see any increase in
>the mass of the ship in their frame.

I wrote it wrong the first time, indeed then the mass must be somewhere on
the ship. But look at it this way: When an object starts moving it deforms
space-time in such a way that the object looks heavier to the outside world
and the other way around, i.e. the object "notices" the outside world to be
heavier.
This means that locally no mass increase is measured, for the same reason
that locally no length contraction or time dilation is measured.

>You also seem to be falling into the same trap that Kelly did
>earlier, in not treating energy and momentum as separate
>components.  Most of the counterintuitive results of relativistic
>kinematics problems come from failing to understand that the
>conserved quantity in a reaction is a _vector_ quantity, and that
>the magnitude of that vector is calculated using Lorentz rather
>than Euclidean geometry.

I still don't see the trap where I fell in. You say that I should treat
momentum and energy as seperate components. But I don't see how/where I
treated them as one quantity.

>Taylor and Wheeler's wisdom on the subject is that the definition
>of mass is sqrt(E^2 - p^2); then every observer sees the same
>mass for the same object, no matter what their relative motion.

How do you measure E and p? E seems to be relativistic mass and p
relativistic momentum. (E=gamma*m_rest  p=gamma*m_rest*v)
I would measure the perceived relativistic mass and the relative velocity.
As far as I can see, doing that all observers will also agree about the rest
mass.

>> Now I only wonder, does such a fast moving particle excert greater
>> gravitation on a non-moving observer?
>
>This I can't answer with certainty.  Offhand, I'd say "no."  If
>the particle's mass doesn't change, then how could its
>gravitation change?

I don't know the answer for certain either, but when making the link with
length contraction and time dilation I would say that indeed a bigger mass
is measured.

>> Steve if the answer is yes, how do you explain that not using "relativistic
>> mass increase"?
>
>If, on the other hand, a moving object did exert greater
>gravitation than a stationary object of the same mass, I'd
>probably be looking for a relation to a quantity that did change,
>like the object's total energy.

So that would mean that some of the change in energy is change of
gravitational energy, from which I would conclude that it comes from extra
mass (or bending of space time).

Is it this translation of energy to mass that gives the trouble?

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