Online Praxis 1996 April/OP4_96.ISO/surfen/astro/earthv/spacedri.doc

Text File | 1996-08-16 | 6KB | 108 lines

             The Cosmic Background Radiation Space Drive
                           A Physics Puzzle

                by John Walker -- [e-mail]
                        February 23rd, 1994

Here's  a  puzzle  I  first  thought of in the mid-80's, which I don't
recall having seen discussed.  Included is my (non-rigorous) solution,
as well as another proposed solution that contains a nasty booby trap.

Cosmic Background Radiation Space Drive
---------------------------------------

Define  the  laboratory  frame to be at rest with regard to the cosmic
background radiation (CBR) (e.g.  no  dipole  temperature  component).
Now  imagine  a  spaceship in motion relative to the laboratory frame,
its nosecone pointed in the direction of motion.  An observer  on  the
spaceship measuring the cosmic background will see a dipole variation,
with maximum blueshift in the direction  of  travel  relative  to  the
laboratory frame and maximum redshift in the opposite direction.

Thus,  at  the  ship's  nose  we  measure a higher temperature (due to
blueshift) than we do at the ship's tail, where the CBR is redshifted.
Given  the temperature difference, can we not extract work with a heat
engine, using a collector at the ship's nose as the  high  temperature
heat  source  and a radiator at the ship's tail as the low temperature
heat sink?

The work extracted by  the  heat  engine  can  then  be  converted  to
electricity  which,  connected  to  a flashlight mounted in the ship's
tail, accelerates the  ship,  as  its  momentum  must  increase  in  a
direction opposite that carried away by the photons ejected.

As  the  ship  is  accelerated  by the photon drive, the blueshift and
redshift increase as velocity  does,  and  so  consequently  does  the
temperature  difference  between  the  source and sink, increasing the
amount of work extracted by the heat  engine  and  the  power  of  the
photon drive.

Why is this not a "free energy star drive"?

Why It Doesn't Work
-------------------

It  can't work.  It might seem fine from the standpoint of an engineer
on the ship, who simply observes different temperatures fore  and  aft
and hooks up an engine between them, but from the laboratory frame the
ship appears to  be  committing  a  serious  moving  violation.   It's
gaining  energy  (whether  kinetic  energy  resulting  from the photon
drive, or just by charging a capacitor with the electricity  generated
from  the  heat engine), doing so by pumping energy from a source to a
sink at the same (laboratory frame)  temperature.   Bzzzt--second  law
violation!  So what have we overlooked?

Hypothesis 1: Radiation pressure drag.
    (This  is what I think is happening.) The fallacy lies in assuming
    the ship is moving inertially through empty space.  The ship is in
    fact  traversing  a  diffuse photon gas (the CBR), which creates a
    drag force counter to the direction of motion.  An object at  rest
    with  respect to the CBR feels no net force, since photons impinge
    upon it with the same  energy  from  all  directions.   An  object
    moving  with  respect  to  the  CBR  feels  an increased radiation
    pressure from the blueshifted photons coming from the direction of
    motion,   and   decreased   radiation  pressure  in  the  opposite
    direction, resulting in a  net  force  opposite  to  the  velocity
    vector.   This  CBR  drag decelerates the ship.  Using the Doppler
    shift temperature difference to extract work and propel  the  ship
    cannot  accelerate  the  ship  or even fully counter the CBR drag,
    since no heat engine can be 100% efficient.  The problem  is  thus
    equivalent  to a perpetual motion airplane which uses the relative
    wind to drive a windmill which drives a pusher propeller.

Hypothesis 2: Not a cycle.
    This can be argued entirely from the  ship  frame.   There  is  no
    violation of the second law since no closed cycle exists, any more
    than exploiting geothermal  energy  resulting  from  gravitational
    contraction,  or driving a turbine from a pressurised reservoir of
    gas.  The ship's heat engine is pumping heat from a hot source  to
    a cold sink and, in doing so equalising the temperature difference
    between them.  When the the source and  sink  temperatures  become
    equal,  the  engine  will  stop.  Fortunately a half-universe is a
    pretty big heat source and sink, so there's no near-term  risk  of
    running out.

    Seems  reasonable, doesn't it?  But if this argument were correct,
    consider what we'd observe from the laboratory frame.  As  before,
    the ship would be accelerating while creating an anisotropy in the
    CBR from which an observer in the laboratory frame  could  extract
    work.   Two  ships  accelerating in opposite directions could then
    cancel the effect on the CBR while both continuing to accelerate.

Consequences
------------

I thought of this puzzle in 1985 while musing about the fact that  the
universe  could  be  said to possess a preferred rest frame defined by
the CBR, and thinking through what consequences that might have on the
general assumption that all inertial frames are equivalent.  I thought
it was really cool to encounter a  puzzling  interaction  between  the
Doppler effect and the second law of thermodynamics.

It's  also amusing to note that the phenomenon of CBR drag would argue
for highly-streamlined ultrarelativistic  spaceships  which  minimised
frontal  area  subject  to blueshifted radiation pressure.  Thus pokey
interstellar  transports  may  look   like   flying   junkyards,   but
intergalactic fighters will be sleek enough even for Hollywood.