John232
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ghwellsjr said:Just to make sure we're on the same page here, you are referring to the wikipedia article on Time Dilation in the section called "Simple inference of time dilation due to relative velocity", correct?.
Correct.
ghwellsjr said:OK, well in the picture of the stationary light clock, they say that the period of the clock is Δt and they calculate it based on the speed of light and the distance between the mirrors. So I agree that t is the amount of time it takes for light, traveling at c, to travel a certain distance. But I don't see why you bring up solving for c--isn't c a known constant and you're solving for Δt, the time between two ticks? So I don't know why you think this leads to a wrong value for c. I have no idea what your concern is.
Okay, it says the observer in motion observers the photon to travel a distance cΔt'. I am saying that it doesn't. The observer at rest measures the hypotenus to be cΔt. The length of they hypotenus divided by the change in time would give the speed of light for the observer at rest and not the observer in motion. The observer in motion would measure the vertical distance divided by time prime to be the speed of light, not the other way around. I think the error comes in when you say that the observer at rest see's the photon to travel a vertical distance, the observer in motion also see's this as well, but is being compared to what an observer at rest see's(the hypotenus).
ghwellsjr said:In any case, the only way you would get a larger value for Δt (why are you dropping the delta?) is if the distance between the mirrors is greater. And if that is the case, the light clock is taking longer between ticks and therefore ticking at a slower rate.
I am saying that the light clock doesn't measure ticks, but in fact that time is actually warped by the same amount as the relation between the sides of two light triangles. Where each side represents how the speed of light is measured from each frame of reference. So by putting cΔt' as the vertical distance it explains how time has to be adjusted to allow for the observer in motion to measure c even though he see's the photon travel a shorter distance. So then he has to experience less time to fill in this shorter side of the triangle. The observer at rest has to measure more time in order to account for the greater distance the photon is seen to travel. That is how it is possible to get the proper time out of the light clock example simply by assigning the time variables differently.
Also, Δt√(1-v^2/c^2) ≠ √(1-v^2/c^2)/Δt
v ≠ ΔL√(1-v^2/c^2)/(Δt/√(1-v^2/c^2)
v ≠ ΔL√(1-v^2/c^2)/(√(1-v^2/c^2)/Δt)
v = ΔL/τ the gamma cancels,
(v ≠ ΔL/Δt) So since this does not equal the velocity put into the equation, if you found a velocity with dialated spacetime using ΔL and Δt, the theory breaks down. You could then take that new velocity and then find new values for ΔL and Δt, and then find another new velocity and so on etc. This is why I think the time dilation and the length contraction equation should both be directly porportional to gamma.
Δt'=Δt√(1-v^2/c^2) solving for the time variables reversed
ΔL'=cΔt' I assume the distance traveled by the photon is a different value
since the speed of light is constant
ΔL'=cΔt√(1-v^2/c^2) substitute Δt' from the first equation
ΔL'=ΔL√(1-v^2/c^2) ΔL=cΔt, this also works for the direction of motion
ΔL'=vΔt' if you assume v=v'
Solving for length in the vertical dimension doesn't assume space contraction in that direction since both observers would agree that the photon reached the same position after being measured. Neither one says the photon traveled a greater vertical distance and is a requirement of this calculation to form the right triangle.
I then found an equation that describes time dilation for an object under constant acceleration. It assumes that because of the Michelson-Morely experiment that an object under acceleration still measures the photon to travel in a straight line since the Earth was accelerating and the effects of gravity where balanced out.
Δt'=Δt√(1-(vi+vo)^2/4c^2) I still need to look into how this differs from
constant motion