From: tagg@hg.uleth.ca (Nathaniel Tagg)
Subject: Re: time travel ?
Reply-To: tagg@hg.uleth.ca
Organization: University of Lethbridge
Date: Tue, 21 Jul 1992 22:19:28 GMT

In article <1992Jul21.173800.1509@wam.umd.edu>, mrmuon@next03pg2.wam.umd.edu (Eli John Hawkins) writes:
>In article <BrJn2K.5oz@undergrad.math.waterloo.edu>  
>pealbers@lambert.waterloo.edu (Paul E. Albers) writes:
>> 
>> In thinking about time travel (actually FTL travel) I came up with this
>> idea that I don't have the background to shoot down so I thought I would
>> give someone else chance to.
>> 
>> Assumptions.
>> 
>> Both time and space are quantized so there is a basic unit of time that
>> can't be divided and also a basic, indivisible unit for space.
>> 
>> This being the case, then every possible velocity, when expressed in  
>>these
>> units would be a rational number.  Now if the speed of light was
>> a irrational number, then as we sped up, we would go from being just  
>>below
>> the speed of light to just over it avoiding that nasty (1-v/c)^(-1/2).
>> 
>> So who can shoot this down first?  (no flames please, I'm a mathie, not
>> a physicist).
>> 
>> Paul
>   Quantization of space-time does not mean something so simple as being  
>made up of discrete units (nobody does know what it means but it's clearly  
>something real wierd). There are natural units based on universal  
>constants. The natural unit of velocity is definitely the speed of light,  
>so c=1 which is clearly not an irrational number.
>   Going faster than light wouldn't be made any easier by skipping the  
>velocity of light. Note that for v>c, (1-(v/c)^2)^(-1/2) is really nasty;  
>it's imaginary. In order to go faster than light you need to make your  
>mass imaginary.

    I've got no problem with imaginary mass; perhaps 'experienced' mass could
be defined as the absolute value of 'complex' mass (ie. times complex
conjugate, then square-rooted).  This is a neat idea to throw into a story
somewhere.  This sort of funky math happens all the time in quantum mechanics.
    However, the problem with this conjecture is that space quantization does
not work the way you suggest; a cartesian co-ordinate plane with tiny little
grid sizes, and every particle of matter 'snapping' to a grid intesection at
every discrete time interval.
    Actually, come to think of it, it may look like that. (You're right, it's
wierd.  I think some of the intellectual bigwigs like Hawking understand it,
but they're not telling.)  I think the problem is this: it looks just the same
in every frame of reference.  That is to say, as you speed up, the grid size
remains constant with respect to the speed of light.
    Let me see if I can explain so I understand it.  No, I can't.  (I just
re-wrote this paragraph three times and it isn't clear.)  Let's just say that
the grid lines (quantized space) bunch up as you get faster, making it just as
hard to get one more increment closer to the speed of light.  Time does this
too.  Or something. 
    In any case, the point is that since there is no absolute frame of
reference, there can be no absolute size of space quantization. So, no FTL
travel.  (I know this is true; I wish I knew exactly how it worked.)

Muddled,
--------------------------------------------------------------------------------
          Nathaniel Tagg               The U of Hell,  Lethbridge, AB
    "It's just a matter of putting one point seven one five three seven two
and two point two oh four six two eight together."     --The Doctor 
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