It is actually *sqrt*(1-v^2/c^2) in the denominator 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. 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 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 infinit= y > 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 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 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 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 zer= o > - 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 > --=20 http://www.piclist.com/techref/piclist PIC/SX FAQ & list archive View/change your membership options at http://mailman.mit.edu/mailman/listinfo/piclist .