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From: hadeishi@husc4.harvard.edu (mitsuharu hadeishi)
Newsgroups: sci.physics
Subject: Re: A Question
Message-ID: <590@husc6.HARVARD.EDU>
Date: Wed, 5-Nov-86 13:47:21 EST
Article-I.D.: husc6.590
Posted: Wed Nov  5 13:47:21 1986
Date-Received: Wed, 5-Nov-86 22:34:25 EST
References: <230@sri-arpa.ARPA> <572@epimass.UUCP> <2182@ecsvax.UUCP> <8597@sun.uucp> <1388@trwrb.UUCP>
Sender: news@husc6.HARVARD.EDU
Reply-To: hadeishi@husc4.UUCP (mitsuharu hadeishi)
Organization: Harvard Science Center
Lines: 44
Summary: You can accelrate as long as you like

In <1388@trwrb.UUCP> galins@trwrb.UUCP (Joseph E. Galins) writes:
>If the elevator is accelerating, then after a long, long time its speed will
>reach the speed of light then pass it.  I know that the problem here
>has to do with the fact that F=mA is false when the speed approches 'c'.
>In fact F approches infinity near 'c'.  So with a constant (or even increasing
>but finite) force, wouldn't the acceleration necessarly slow down as the rider
>approched 'c' and hence notice that he was in an elevator? 
>
>In other words, with a constant acceleration eventually you would be going
>at a speed of 'c' with no more acceleration therefore losing the 'gravity'
>feeling.  Then is it impossible to simulate gravity via acceleration for
>a 'long' period of time?

	No.  The point is, the acceleration is always "felt" in the
frame of reference of the person in the elevator.  However, this frame
of reference is continually accelerating (it is perhaps pedantically
more desirable to say the person in the elevator is instantaneously
at rest in frames of reference which are moving at continally greater
velocities relative to some fixed reference 'lab' frame.)

	To put it more simply, the acceleration as observed in a fixed
lab frame is continually decreasing; it decreases until it asymptotically
approaches zero.  However, the principle of special relativity states
that all reference frames are equivalent (where by "reference frame" I
mean non-accelerating coordinate frames).  That is, in a frame which
is moving relative to the lab frame "in the same direction" as the
elevator would register a "faster" acceleration.  So the observed accelration
depends on the reference frame in which you are measuring the
velocities and times.

	However, from the point of view of someone in the elevator,
the only accelration which is relevant is the one measure in the
frame in which s/he is instantaneously at rest.  That is, in the frame
which is "moving along" with the elevator so that at the instant of
measurement the elevator seems to be at rest.  Defined in this way
(this would be the acceleration "felt" by the observer in the elevator)
the acceleration could certainly remain constant for indefinite
periods of time (of course limitations of hydrogen gas drag and micro-
meteorite penetration would cause you to think twice and then again
before trying such a stunt.)  A quick calculation shows that,
for example, after accelerating for 1 year at 1 gravity you can approach
the speed of light to well within 1% (as measured from Earth.)

				-Mitsu