Above light speed the particle will be deflected to a direction perpendicular to the speed of light, due to the imaginary factor, and will cease to exist (in this universe, at least). Cheers, Isaac Em dom, 4 de nov de 2018 19:37, RussellMc 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 = that > 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 scal= ar > > 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 increa= se > energy will INITIALLY decrease from infinity to lower values as V increas= es > 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 energ= y > 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 brak= es > 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 FT= L > drive based on this effect an "Esaki Drive". For reasons which are or wil= l > be obvious enough :-). > > NB - E&OE. Back of brain says that the above description may have inverte= d > 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 s= o > > ultimately all tachyons will be travelling at infinite speed > > > > And a particle carrying information faster than c will violate causalit= y. > > __________________________________________ > > 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, tim= e > > > > is the fundamental concept to any religion that I am aware of (coul= d > > > > 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 bas= ic > > > 'contract to zero or expand to infinity at light-speed" expression. > > > The basic term which appears in mass time or space variation with > change > > 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 distan= ce > > > 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 > speed > > > before the photons start to huddle at anything like a point source :-= ). > > > eg travelling from Alpha Centauri at 0.999999 of light speed the > distance > > > contracts from about 4 light years to about 4/500,000 ly ~~=3D 4 ligh= t > > > 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 t= o > > > travel AT light speed increases the energy required to "infinite" for > all > > > 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 > -- http://www.piclist.com/techref/piclist PIC/SX FAQ & list archive View/change your membership options at http://mailman.mit.edu/mailman/listinfo/piclist .