Special relativity question driving me crazy....

[Newton-reborn]

TL;DR Summary

Lorentz transformation answers don't make sense

Hey guys. Noob here.
Question;
S frame = x,y,z,t
S' frame = x',y',z',t'
S' is moving with a speed v relative to S and t=t'=0 when origins coincide
v= 0.6c
find the coordinates of x = 4 & t = 0 in S'
When I use lorentz transformation, I get a negative t' and x' = 5. This doesn't make sense to me because t'=t=0 and reasoning tells me that x' should also be equal to 4. Please help. I appreciate any help

 

[RPinPA]

You just discovered "relativity of simultaneity". The clocks coincide at t = t' = 0 at the origin. But nowhere else.

And I'm not sure what reasoning tells you that x' = x, i.e. that there's no length contraction. But in fact the Lorentz transformation should give you length contraction, time dilation, and relativity of simultaneity.

 

[Newton-reborn]

Hey thanks for your response. If t=t'=0, why is it that when I use the lorentz transformation to find t' I do not get t'=0. This is what is confusing me. Thanks

 

[PeroK]

Hey thanks for your response. If t=t'=0, why is it that when I use the lorentz transformation to find t' I do not get t'=0. This is what is confusing me. Thanks

$t = t' = 0$ occurs only at the origin. At all other points, when $t = 0$ we have $t' \ne 0$.

 

[Sagittarius A-Star]

to find t' I do not get t'=0

The "absolute time", that Newton had assumed, does not exist. What you found with the LT is the "relativity of simultaneity". That is a consequence of the 2nd postulate of SR, the invariance of the speed of light under transformation from one inertial frame to another.

You can do a simple plausibility check: Please set in the LT x = c * t, in order to describe the movement of a light pulse, and then calculate x’/t’. That is the transformed speed of light, and you will get the
result: x’/t’ = c.

With the (old) Galilean transformation x’ = x - v*t and t’ = t, you would get x’/t’ = c-v.

 

[Newton-reborn]

Thanks guy. I had assumed that when the clocks were synchronized at the origin, they were also synchronized at all other points.