Yes, the math works out. Whether it actually has physical meaning is kind of a philosophical question, but it's a useful tool. https://en.wikipedia.org/wiki/Proper_time#Examples_in_special_relativity is an example worth looking at.
On Sun, Jul 10, 2016 at 12:01 PM, Chris Albertson <albertson.ch...@gmail.com> wrote: > Is this a valid TN subject? It's about time but a little off of the usual > subject of 10Mhz oscillators. > > I heard of an alternate way to describe time dilation caused by velocity. > I think this makes it easier to understand but I've not been able to > verify the math. This alternate explanation also makes it easy to see why > we can never go faster than light. But I've not seen a mathematical > derivation so it could be wrong or just an approximation. > > Here goes: > > 1) We assume a 4 dimensional universe with four orthogonal axis, x, y, z, > and time (t) > 2) assume that at all times EVERY object always has a velocity vector who's > magnitude is "c", the speed of light. The magnitude of this vector (speed) > never changes and is the same for every particle in the universe. > > This at first seems a radical statement but how is moving at c much > different from assuming every partial is at rest in t's own reference > frame? I've just said it is moving at c in it's own reference frame. Both > c and zero are arbitrary speeds selected for connivance. > > How can this be? I know I'm sitting in front of my computer and have not > moved an inch in the last four hours. c is faster than that. Yes you are > stationary in (x,y,z) but along the t axis you are moving one second per > second and I define one second per second as c. Now you get smart and try > to move faster than c by pushing your chair backward in the Y direction at > 4 inches per second. So you THINK your velocity magnitude is the vector > sum of c and 4 inch/sec which is greater than c. BUT NO. Your speed > along Y axis causes time dilation such that your speed along T is now > slower than 1 second/second. In fact if you push your chair backward > along Y real fast at exactly c your speed along t axis is zero, time > stops. Try pushing your chair at 0.7071 * c and you find yourself moving > through t at 0.7071 sec/sec and the vector sum is c. You can NOT change > you speed from c all you can do to change the direction of the velocity > vector and your speed through time is determined by the angle between that > vector and the t axis. > > It works ok to just use one of the three spacial axis because we can always > define them such that (say) the Y axis points in the direction of motion. > So a plot of your speed in the dy,t plane covers the general case and looks > like an arc of radius c. > > If this works out then I have some work to do, like defining momentum as a > function of the area between the velocity vector and the t axis > > > -- > > Chris Albertson > Redondo Beach, California > _______________________________________________ > time-nuts mailing list -- time-nuts@febo.com > To unsubscribe, go to https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts > and follow the instructions there. _______________________________________________ time-nuts mailing list -- time-nuts@febo.com To unsubscribe, go to https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts and follow the instructions there.
