On Mon, 5 Nov 2018 at 00:40, David C Brown wrote: > It is actually *sqrt*(1-v^2/c^2) in the denominator > Whoops, yes - sqrt missed. . The only difference in the situation I described (velocities <=3D C ) is th= at the relativistic effects increase more slowly as C is approached. At 0.99999 C the contraction / expansion effect is only 0.0014 / 26.6. The Alpha Centauri trip now takes about 2 months. *V/C* *M* *D, T* 0.1 0.99 1.00 0.2 0.98 1.01 0.3 0.95 1.02 0.4 0.92 1.04 0.5 0.87 1.07 0.6 0.80 1.12 0.7 0.71 1.18 0.8 0.60 1.29 0.9 0.44 1.51 0.91 0.41 1.55 0.92 0.39 1.60 0.93 0.37 1.65 0.94 0.34 1.71 0.95 0.31 1.79 0.96 0.28 1.89 0.97 0.24 2.03 0.98 0.20 2.24 0.99 0.14 2.66 0.991 0.1339 2.73 0.992 0.1262 2.81 0.993 0.1181 2.91 0.994 0.1094 3.02 0.995 0.0999 3.16 0.996 0.0894 3.35 0.997 0.0774 3.59 0.998 0.0632 3.98 0.999 0.0447 4.73 0.999999 0.0014 26.59 1 0.00 #DIV/0! > That doesn't matter much when you confine your analysis tardyons - > particles confined to speeds below c. But you consider tachyons - > particles with velocities greater than c - it is very significant. If v= > > c then the denominator is a complex sum and since energy is a real scalar > the rest mass must also be complex > > Another peculiarity of tachyons is that their speed increases with > decreasing energy. Almost true. If energy is 0.5 x Mr x V^2 (Mr =3D relativistic mass) then as V passes through C (infinite energy) and then continues to increase energy will INITIALLY decrease from infinity to lower values as V increases and then at some fixed velocity will again start to increase With a little "playing" an interesting 'possible' phenomena may be suggested. Above LS the tachyon energy decreases to a non zero minimum as V increases. The same energy levels are achieved by the object below C above some minimum velocity. At about 0.9 C an object will have the same energy as it's a tachyonic partner at about 1.4C. For higher velocities < C there will be TWO velocities >C with the same energy - one C < Vt <1.4C and the other > 1.4C. Now for the real hand waving. *IF* one can "tuinnel" [tm] the lightspeed energy curve at constant energy you could transit for any 0.9 C < V < C to two Vt's > C. One always <=3D 1.4C and the other greater or much greater or much muchmuch ... greater. The closer the object get's to C before it "tunnels" The lower the first above Vt is and the higher the 2nd Vt is. The low Vt has the 'comforting' characteristic that you can "put the brakes on" normally. The second has the characteristic that, as you described, the harder you "brake" the faster you go. In a long ago partly written will-never-be-published story I named the FTL drive based on this effect an "Esaki Drive". For reasons which are or will be obvious enough :-). NB - E&OE. Back of brain says that the above description may have inverted some effect but the general idea should be "clear enough" for anyone who can be bothered reading it. The main hand wavings are equivalence of imaginary and real variables (at < C and FTL velocities) and quite how the tunneling is achieved in practice - left as an exercise for the student. Russell McMahon > Since the tachyon will continually lose energy by > Cherenkov (sp?) radiation it will be subject to constant acceleration so > ultimately all tachyons will be travelling at infinite speed > > And a particle carrying information faster than c will violate causality. > __________________________________________ > David C Brown > 43 Bings Road > Whaley Bridge > High Peak Phone: 01663 733236 > Derbyshire eMail: dcb.home@gmail.com > SK23 7ND web: www.bings-knowle.co.uk/dcb > > > > > *Sent from my etch-a-sketch* > > > On Sun, 4 Nov 2018 at 10:21, RussellMc wrote: > > > On Sun, 4 Nov 2018 at 20:18, Manu Abraham > wrote: > > > > > > > > > > ...Timeless ? Really ? > > > > > > > > One of the better non-rigorous treatment of the subject: > > > > > > > > > > > > > > https://www.amazon.com/World-Without-Time-Forgotten-Einstein/dp/046509294= 2/ref=3Dsr_1_2?ie=3DUTF8&qid=3D1541313457&sr=3D8-2&keywords=3DEinstein+and+= Godel > > > > > > > > > > Well, it's really beyond me, of course. As far as I understand, time > > > is the fundamental concept to any religion that I am aware of (could > > > be mistaken about the "any"). Ok. So, from where does this concept > > > arise? Some people think that we are living in a simulation, maybe it > > > is yet another dimension as some other think (that the human brain is > > > simply aping that concept). > > > > > > Too much to think on a Sunday morning .. ;-) > > > > > > > Again: Critiques and corrections welcome. Why is this rubbish rubbish ? > > :-). > > > > Simplistic: > > > > This doesn't deal with the great Godel's treatment, but shows the basic > > 'contract to zero or expand to infinity at light-speed" expression. > > The basic term which appears in mass time or space variation with chang= e > in > > velocity is > > > > k =3D (1-V^2/C^2) > > > > V=3D velocity. C =3D speed of light. > > > > This appears in the denominator for mass variation (asymptotes to > infinity > > at V=3DC) > > and in the numerator for distance and time (asymptotes to zero at V=3DC= ) > > > > At V=3D 0.1C k is only (1-0.1^2/1) =3D 0.99 and 1/k =3D 1.0101... > > ir At 0.1 x light speed mass increases by ~=3D 1% and time and distance > > contract to about 99% of original. > > It starts "to get out of hand" as V rises. > > > > As can be seen in the table below - you have to get VERY near light spe= ed > > before the photons start to huddle at anything like a point source :-). > > eg travelling from Alpha Centauri at 0.999999 of light speed the distan= ce > > contracts from about 4 light years to about 4/500,000 ly ~~=3D 4 light > > minutes (and/or the object would see a trip time of 4 minutes). > > > > Making the extra ":small" increase of 0.000001 of light speed so as to > > travel AT light speed increases the energy required to "infinite" for a= ll > > except particle with zero rest mass, AND for zero rest mass particles > > (which MUST ALWAYS travel AT light speed) brings distance and time to > zero > > - until the end of all things. (At least). (Probably). > > > > R > > > > M - mass, D - distance, T - time > > > > V/C D,T > > M > > 0.10 0.99 1.01 > > 0.20 0.96 1.04 > > 0.30 0.91 1.10 > > 0.40 0.84 1.19 > > 0.50 0.75 1.33 > > 0.60 0.64 1.56 > > 0.70 0.51 1.96 > > 0.80 0.36 2.78 > > 0.90 0.19 5.26 > > 0.91 0.17 5.82 > > 0.92 0.15 6.51 > > 0.93 0.14 7.40 > > 0.94 0.12 8.59 > > 0.95 0.10 10.26 > > 0.96 0.08 12.76 > > 0.97 0.06 17 > > 0.98 0.04 25 > > 0.99 0.02 50 > > 0.991 0.018 56 > > 0.992 0.016 63 > > 0.993 0.014 72 > > 0.994 0.012 84 > > 0.995 0.010 100 > > 0.996 0.008 125 > > 0.997 0.006 167 > > 0.998 0.004 250 > > 0.999 0.002 500 > > 0.999999 0.000002 500000 > > 1.00 0.00 #DIV/0! > > > > > > M D, T > > 0.10 0.99 1.01 > > 0.20 0.96 1.04 > > 0.30 0.91 1.10 > > 0.40 0.84 1.19 > > 0.50 0.75 1.33 > > 0.60 0.64 1.56 > > 0.70 0.51 1.96 > > 0.80 0.36 2.78 > > 0.90 0.19 5.26 > > 0.91 0.17 5.82 > > 0.92 0.15 6.51 > > 0.93 0.14 7.40 > > 0.94 0.12 8.59 > > 0.95 0.10 10.26 > > 0.96 0.08 12.76 > > 0.97 0.06 16.92 > > 0.98 0.04 25.25 > > 0.99 0.02 50.25 > > 1.00 0.00 #DIV/0! > > -- > > http://www.piclist.com/techref/piclist PIC/SX FAQ & list archive > > View/change your membership options at > > http://mailman.mit.edu/mailman/listinfo/piclist > > > -- > http://www.piclist.com/techref/piclist PIC/SX FAQ & list archive > View/change your membership options at > http://mailman.mit.edu/mailman/listinfo/piclist > -- http://www.piclist.com/techref/piclist PIC/SX FAQ & list archive View/change your membership options at http://mailman.mit.edu/mailman/listinfo/piclist .