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Re: starship-design: Re: FTL travel

STAR1SHIP@aol.com writes:
 > In a message dated 4/7/00 12:48:35 AM Pacific Daylight Time, stevev@efn.org 
 > writes:
 > > STAR1SHIP@aol.com writes:
 > >   > In a message dated 4/6/00 11:18:40 PM Pacific Daylight Time, stevev@efn.
 > > org 
 > >   > writes:
 > >   > 
 > >   > >  K = m * ((1 / sqrt(1 - v^2/c^2)) - 1)
 > >   > >  
 > >   > >  K = kinetic energy
 > >   > >  m = object mass
 > >   > >  v = object velocity
 > >   > >  c = speed of light
 > >   > >  
 > >   > >  K = 1/2 * m * v^2 is only a low-speed approximation. 
 > >   > 
 > >   > 1/10 C is low speed so the K calculated is near exact. The relativistic 
 > >   > effects are insignificant though not zero.
 > >  
 > >  You're claiming that a smaller mass with an equal amount of kinetic
 > >  energy will go faster than c.  That's not what will happen; putting that
 > >  amount of kinetic energy into the smaller mass makes it go closer to,
 > >  but not faster than, c.
 > Steve,
 > You are so close but still you get no cigar. I claim there are two different 
 > velocities (Vreal and Vrel. to be calculated for the payload with one 
 > velocity (Vrel.) no faster than C as you claim. Focus and concentrate only on 
 > the problem I gave.

One thing that should be obvious from any study of relativistic physics
is that there is no velocity any more real than any other.  Conservation
of momentum and energy apply in all reference frames, not just the one
in which things move at some particular "Vreal".

 > Einsteinian physics does not throw out Newtonian physics but relies on them 
 > to transform measurements to Einsteinian values and so they can be 
 > transformed back to Newtonian physics. Transforms are called that because 
 > they go both ways and both ways are valid depending on the frame of reference 
 > being observer or observed. 

Relativistic physics is not a system for converting between Newtonian
and relativistic formulae.  Relativistic physics is its own statement of
the laws of physics that predicts very different behavior than Newtonian
physics for high relative velocities.  For low relative velocities it
turns out that Newtonian physics is a close approximation to
relativistic physics.  That doesn't mean you can transform any
relativistic physics problem into a Newtonian one.

 > The rocket at twice light speed travels between two stars a distance of 4 
 > light years.
 > The time onboard the ship measures two years. Using Einstein's time dilation 
 > formula for the given masses, two years ship time calculates to be 4.44.. 
 > years earth time (recalled from memory).
 > Dividing 4 light years by 4.44.... years and the velocity with respect to 
 > earth is observed on earth to be as you calculated as .89c (or .9c as I 
 > recall calculating).

You continue to operate under a mistaken assumption that you can
meaningfully combine measurements made in different frames.

If we're in a frame in which the stars are four light-years apart, and
we watch a ship travel between them while two years elapses on the
shipboard clock, then we can fairly easily calculate the velocity of the
ship in that frame.

t'^2 = t^2 - x^2

where t' is shipboard time, t is frame time, and x is the frame
distance, so if t' = 2 years and x = 4 light-years, then t is sqrt(20)
or about 4.472, and the ship's velocity in that frame is (x / t) = about
0.894 c.

In the rocket's frame, however, the stars aren't four light-years apart.
An observer on the rocket considers the destination star to be traveling
towards him at 0.894 c, and he measures the star to be 1.789 light-years
away at the start of his trip.

You really need to study a consistent presentation of relativistic
physics like Taylor and Wheeler's _Spacetime Physics_; you're basically
making several of the mistakes that beginning students of relativity
theory make.