dietz@cs.rochester.edu (Paul Dietz) (01/25/89)
In article <8901241509.AA20873@NMSU.Edu> space-request+@ANDREW.CMU.EDU writes: >Those who find this FTL talk interesting will want to see this month's >Discover magazine, which has the cover story "Beyond Einstein". It >contains some fascinating reference to tachyon theory, etc. Nothing >for the hard-core physicist, but easy reading, at least. The article didn't mention one of the most peculiar attributes of tachyons. Consider a tachyon with imaginary rest mass iM and velocity u. Define beta = |u|/c and gamma = (beta^2 - 1)^(-1/2). The tachyon has momentum p = M u gamma and total energy E = M c^2 gamma. The ratio of momentum to energy is |p|/E = beta / c. Since beta can be arbitrarily large, a tachyon beam of fixed power can carry an arbitrarily large amount of momentum, and therefore provide any amount of thrust you desire. It would be amusing indeed if someone discovered tachyons and used them in a reaction drive. :-) Paul F. Dietz dietz@cs.rochester.edu
kluksdah@enuxha.eas.asu.edu (Norman C. Kluksdahl) (01/25/89)
In article <1989Jan24.121432.3544@cs.rochester.edu>, dietz@cs.rochester.edu (Paul Dietz) writes: > In article <8901241509.AA20873@NMSU.Edu> space-request+@ANDREW.CMU.EDU writes: > >Those who find this FTL talk interesting will want to see this month's > >Discover magazine, which has the cover story "Beyond Einstein". It > >contains some fascinating reference to tachyon theory, etc. Nothing > >for the hard-core physicist, but easy reading, at least. > > It would be amusing indeed if someone discovered tachyons and used > them in a reaction drive. > (Prior apologies for any notable discrepancies in what I am about to say--it has been 9 years since I took relativity, and I am trying to quote from memory) Now that the disclaimer is out of the way, let me briefly describe the work of Minkowski on relativity. If we consider a 2-dimensional space-time, with coordinates x and t, then the region of the coordinate system we can get to is a cone, described by t<0 and |x| < t, assuming that the equations for relativity are valid (and there is certainly no reason TO DATE to doubt those equations). However, if we multiply the mass of an object by i, and carefully manipulate the equations, we find that the slowest that an object can go is c, and that the permitted region of the space-time plane is now bounded by t > 0 and |x| > t. Moreover, the new, 'imaginary' plane can be viewed as a permutation of the original 'real' plane. Using this permutation, it can be shown that the 'imaginary' permitted region corresponds exactly to the 'real' region with x > 0 and |t| < x. I.e. changing the mass to an imaginary quantity can permit FTL travel in the 'real' space-time. Nothing earth-shaking about this. We just created a tachyon. Now for the fun part. If we assume that space-time, mass, velocity, etc. are complex quantities, then normal space that we perceive is merely the real part of space-time. Further, if we assume this 8-D structure is folded on itself such that Re(x) corresponds to the Im(y) axis, etc, then it is mathematically possible to show that Minkowski's transformation holds, and all the equations of special relativity are satisfied with the set of complex masses, velocities, momenta, and coordinates. What, you may be asking yourself, does this have to do with sci.space? Well, not a lot really. It just happens to be one of my favorite things to throw out whenever FTL discussions come up. Besides, someone might someday discover what 'i' really is, and find out that this postulation is correct. (Of course, by then I'll probably be dead, so it won't do me any good.) Norman Kluksdahl Arizona State University ..ncar!noao!asuvax!enuxha!kluksdah standard disclaimer implied
beres@cadnetix.COM (Tim Beres) (01/26/89)
In article kluksdah@enuxha.eas.asu.edu (Norman C. Kluksdahl) writes: > >Now for the fun part. If we assume that space-time, mass, velocity, etc. >are complex quantities, then normal space that we perceive is merely the >real part of space-time. Further, if we assume this 8-D structure is folded >on itself such that Re(x) corresponds to the Im(y) axis, etc, then it is >mathematically possible to show that Minkowski's transformation holds, and >all the equations of special relativity are satisfied with the set of >complex masses, velocities, momenta, and coordinates. > More of this reasoning can be found in _Future Magic_, by Dr. Forward. He attributes this theory to Penrose, not Minkowski - but it may be that Penrose has pursued it further. This book is fairly recent, copyright 1988, so this "imaginary" theory is still being pursued. Does anyone have any (readable to the non-physicist) references on this Minkowski/ Penrose theory? BTW: _Future Magic_ discusses a range of technologies that may come to pass in the future. Communication methods, space propulsion, space tethers, anti-gravity machines and time travel are some of the topics he tackles. He doesn't say that all these technologies *will* mature, just that there is some theoretical (and practiced, in some cases) basis for them to occur. The Universe has 8-D theory is used by Forward to speculate on FTL travel... Tim ------>MY SOAPBOX (I speak for myself) My nephew Mark, in a letter: Hi Uncle Tim my aquarium is great. 4 fish died but my crab is still living. [Some of us have good attitudes] Tim Beres beres@cadnetix.com {uunet,boulder,nbires}!cadnetix!beres