PROVE , if 2 events happen simoultaniously on a moving train with velocity v (from an observer on the train's point of view), then these 2 events will not appear to happen simoultaniously from an observing looking into the train from a rest frame.
I know I have to make use of the lorrentz' gamma factor here (1/(1-c^2/v^2)) here. but like, if 1 event happens on the front of the train, and another event happens on the back of the train simoultaniously (from the observer inside the train, so he thinks theyre happening at the same time), then the time dilation and length contraction should be = for each event, becasue each even is moving with velocity v?, thus the observer in the station on the rest frame should see no difference in events no?
HELLPP!!
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If both observers are coincident when light from the two events arrives, they both agree on "simultaneous". Up-path or down-path from that unique "sheet" of agreement, they will disagree.
So calculate how far apart they are when the light from event #1 arrives... and then #2.
Also, you have the formula for gamma wrong...
gamma= 1 / sqrt( 1 - (v/c)^2)... you show the v/c term inverted, and no square root.
Relativity is the theory that the rules of physics do no longer change from one inertial reference body and yet another. Any attempt that you may do on your laboratory at homestead could artwork both nicely in a convention coach or the stateroom of a deliver (presented the practice/deliver is basically cruising alongside and by no skill accelerating, bumping, rolling, or turning). This replaced into ordinary on account that before the time of Galileo. Newtonian mechanics contains relativity. incredibly, Newtonian mechanics artwork lower than excellent the following transformation (called the Galilean transformation) from one reference body (x,t) to a distinct (x',t') transferring at a speed v. x -> x' - vt' t -> t' it really is incredibly uncomplicated. all and assorted measures a similar time and their positions are off by utilising a sensible, intuitive quantity depending on the relative action. everybody consents on the time and distance between 2 activities. Now the problem is that the rules of electricity and magnetism (got here upon by utilising countless individuals and compiled by utilising Maxwell) aren't any more invariant lower than this modification. some individuals theory that the former idea of relativity does no longer note to electricity and magnetism--that the rules of E&M in uncomplicated words artwork with appreciate to an ether. Einstein, inspite of the indisputable fact that, assumed that relativity could note to E&M and that Newtonian mechanics could be flawed. He thereby stepped ahead particular relativity and derived new transformation rules (which had already been discovered by utilising Lorentz, so that they have his call). x -> gamma (x' - vt') t -> gamma (t' - vx' / c^2) lower than those new rules, no longer all and assorted measures a similar cases and distances between activities. That aspect of gamma is going from one at slow hurries up in the direction of infinity as you frame of mind the speed of light. transferring clocks run slow and transferring rulers are short!