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From: freeman@spar.UUCP (Jay Freeman)
Newsgroups: net.space
Subject: Re: Speed of Light and beyond
Message-ID: <255@spar.UUCP>
Date: Mon, 20-May-85 15:07:35 EDT
Article-I.D.: spar.255
Posted: Mon May 20 15:07:35 1985
Date-Received: Thu, 23-May-85 02:23:58 EDT
References: <1776@mordor.UUCP> <5602@utzoo.UUCP>
Reply-To: freeman@max.UUCP (Jay Freeman)
Organization: Schlumberger Palo Alto Research, CA
Lines: 57
Summary: 

/* libation to line-eater */

In article <5602@utzoo.UUCP> henry@utzoo.UUCP (Henry Spencer) writes:
>> I know this is impossible, but what would happen if...
>> 
>> A ship could exceed the speed of light?
>
>More seriously, as I recall it, the basic answer to this from relativity
>(if we ignore tachyons, which are a messy case) is "does not compute".
>Faster-than-light speeds involve logical contradictions (notably, loss of
>the normal cause-and-effect relationship) according to special relativity.
>This being the case, the theory basically cannot give coherent predictions
>about such a situation.
>
>I'd be very interested to hear this contradicted by somebody who knows
>more about the subject...

I won't claim to know more about it, but that never kept me from
contradicting anybody :-)

The mathematics of special relativity does not strictly prohibit FTL speeds.
That mathematics says, in essence, that objects in the universe can be
divided into five classes:  (1) Things moving forward in time, slower than
light; (2) things moving forward in time, exactly at the speed of light;
(3) things moving faster than light (including infinitely fast, and also
including both forward and backward in time); (4) things moving backward
in time, at the speed of light; and (5) things moving backward in time,
slower than light.

The mathematics also says that the action of performing a "Lorentz boost"
-- the kind of transformation that has all those square roots of (one minus
vee square over c square) in it -- can NEVER move an object from one class
into another.  A Lorentz boost corresponds roughly to applying a classical
force to an object for a while -- perhaps more accurately to giving it a
classical kick in the pants, so that the physical interpretation of this
mathematics is roughly "if it's slower than light now, you can't make it
go FTL with classical forces."  But there is no objection to objects which
are already FTL (though there seems to be no experimental evidence of them,
either).  And there is no statement, (I think) that such non-classical events
such as particle decays cannot produce tachyons.

Many particle physicists, incidentally, will claim the "backwards in time"
objects are quite real, namely, as antiparticles.

It is indeed true that FTL implies breakdown of causality, but it is also
true that the mathematics of the Lorentz transformation contains no
assumption that causality holds in the first place.  This is an ADDITIONAL
assumption, which philosphers and physicists may put in or not, as they see
fit.  It is erroneous to state that "the Lorentz transformations prohibit
FTL because causality is then violated"; because the Lorentz transformations
do not feature causality as a postulate.

Incidentally, an object is moving "infinitely fast" when its world line is
(at least temporarily) perpendicular to the observer's time axis.

-- 
-- Jay Reynolds Freeman (Schlumberger Palo Alto Research)