Got wrong from right equations

[Prasanna Suman]

I got this problem while I was combining relativistic equations:



For particle which is in motion,
v = l /t
or, l = v * t
or, l= v * t0/(1-v^2/c^2)^(1/2) ' Relativistic equation for time "t"

If the particle was light,

l =(c * t0)/(1-v^2/c^2)^(1/2) ' Because velocity of light is always c; c*t0 is equal to l0

or l = l0 / (1-v^2/c^2)^(1/2)

But, the actual relation is l = l0 * (1-v^2/c^2)^(1/2)

I must have been wrong somewhere. Where?

 

[dextercioby]

You should have been consistent when plugging v--->c in your equations.

Daniel.

 

[bernhard.rothenstein]

use lorentz-einstein transformation

I got this problem while I was combining relativistic equations:



For particle which is in motion,
v = l /t
or, l = v * t
or, l= v * t0/(1-v^2/c^2)^(1/2) ' Relativistic equation for time "t"

If the particle was light,

l =(c * t0)/(1-v^2/c^2)^(1/2) ' Because velocity of light is always c; c*t0 is equal to l0

or l = l0 / (1-v^2/c^2)^(1/2)

But, the actual relation is l = l0 * (1-v^2/c^2)^(1/2)

I must have been wrong somewhere. Where?

Your light signal that starts at t=0 from x=0 generates the event after a time t of propagation (x=ct;t=x/c) in I. The same event detected from I' is (x'=ct';t'=x'/c) and so
l=(x-Vt)/(1-bb)^1/2=l'((1+b)/(1-b))
with b=V/c.
the best things a physicist can offer to another one are information and constructive criticism