Re: About Tachyons --why do we face a situation where we need to worry abt them?
- From: "Bill Hobba" <bhobba@xxxxxxxxxxxxxx>
- Date: Thu, 14 Apr 2005 19:52:33 GMT
<baswin@xxxxxxxxx> wrote in message
news:1113496142.732052.217890@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
> The conventional texts derive the lorentz transforms from einstein two
> postulates (1. frame equivalence, 2. speed of light is constant). Upon
> deriving the transfromation equations, they make the observation that
> they do form a *group* and that v>c => m^2<0 and so on..
> But don't we expect that the transformations form a group?? ie why not
> make this a constraint to start with. A paper that does this is
>
http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=AJPIAS000044000003000271000001&idtype=cvips&gifs=yes
The group approach is well known to regular posters here - in fact it is
probably the best method. A good example of this approach is
http://groups-beta.google.com/group/sci.physics.relativity/msg/07fbb2e45180a599
> This is an old paper..but not many texts follows such methods.
True - but they probably should. The reason being the basis of SR is the
symmetry of the POR and groups are the natural language of symmetries. See
the following posts by Tom Roberts for a further discussion of this and why
SR is preferred to aether theories:
http://www.google.com/groups?selm=3838AC00.87B78404%40lucent.com
http://www.google.com/groups?selm=3838A838.81CE8090%40lucent.com
http://www.google.com/groups?selm=3838AA2A.829F46AD%40lucent.com
> It turns out that the transformation equations can be deteremined upto
> a scalar parameter (say a, which will be the speed of all massless
> particles)and if you make an additional assumption about causality,
> lorentz & galilean groups follow.
Yep.
> The point to be noted is that the
> constancy of the velo of light is not used. It follows from that
> derivation that if the parameter a is finite, then the existence of the
> invariant speed follows. We humans found this invariant speed
> (michelson-morley type expts etc.) and thus the value of that
> parameter.
> It also follows that v>a would lead to m^2<0 (conventional notion of
> masses)
> Now why am I talking about all of this in a post on tachyons??
>
> My point is that, if the derivation in the above paper (anb some other
> books too) is correct,
It is.
> it means that certain FUNDAMENTAL notions that
> we have about the world around us (isotropy, homogeneity, the *group*
> condition , or for that matter 'the equivalence of various ref frames)
> AUTOMATICALLY lead us to situation where the range of velocities that a
> particle can attain is 'divided' into two zones, with no criss
> crossing. I find it surprising that such a serious constraint should
> come out of the simple, 'obvious' assumptions that we made. Can anybody
> give a convincing reason as to why I should convince myself that such a
> constraint is indeed 'natural' ?
IMHO it is very natural and the essence of what SR is really about.
> Please note that issues of whether tachyons are imaginary are not of
> importance here.The point is that there is something different between
> v>c and v<c.
> Even if this post if rejected, I would appreciate a clarification to
> the question raised.
If tachyons did exist then there almost certainly would be no way of using
them to send information faster then light. Consider the following from
Rindler -
Introduction to Special Relativity page 17. Consider any signal or process
whereby an event P causes an event L (or whereby information is sent from P
to L) at 'superluiminal' speed U > c relative to some frame S. Choose
coordinates in S so that these events both occur on the x axis and let their
time and distance separations be delta t > 0 and delta x > 0. Then in the
usual second frame S' traveling at velocity v we have from the Lorentz
transformations: delta t' = gamma (delta t - v delta x/c2) = gamma delta t
(1 - vU/c2)] For c2/U < v < c we would then have delta t' < 0 - hence there
would exist frame in which L precedes P ie in which cause precedes effect ie
casualty is violated. This would put severe limits on any interaction with
tachyons.
Thanks
Bill
> Aswin
>
.
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