Diablo® III

Time Dialation

Posts: 126
Someone in another thread asked about time dialation, but it no longer exist so I am starting a thread here.

An ship travels a distance vt (distance equals velocity times time). An observer at rest measures this distance with his own clock in units t. Someone on the ship measures a beam of light traveling perpendicular to its direction of motion to measure a beam of light to travel a distance ct', where t' is the number of units of time that someone on the ship would use. The observer at rest measures this same beam to travel a distance ct, that is traveling at an angle towards its direction of motion. You can then translate the vector vt down to the point where the photon has traveled the same distance perpendicular to the ship. This forms a right triangle. Then you can use the Pythagorean Therom to find the relation between the ship and the observer.

a^2+b^2=c^2
a=ct'
b=vt
c=ct

(ct')^2+(vt)^2=(ct)^2 Pythagorean Theorem

c^2t'^2=c^2t^2-v^2t^2 Distribute the square, and move v^2t^2 to other side

c^2t'^2=c^2t^2(1-v^2/c^2) Factor c^2t^2 from the right side

t'^2=t^2(1-v^2/c^2) Take the square root

t'=t sqrt(1-v^2/c^2) Learn to do algebra!

Notice this is not the same equation from the light clock example. People now refer to this t' as tau or the proper time. The only difference in the other time dialation formula is the time variebles are assigned differently (the other way doesn't make sense to me), and it assumes that you can find the dialated time by taking the inverse of the change in time(wrong relation to frequency). This clock doesn't tick, it is only a direct relation between the distance of the sides of a triangle, and the amount of time something would measure it to travel that distance. So in another words time does not slow down because the clock is seen to tick slower, time slows down because the clocks in the ship tick fewer times when an observer at rest sees light to travel a longer distance(all observers measure light to travel at the same speed in vacuum). Also note that these two equations can't be used together, and it has been said that Einstein even wrote this equation in his Special Theory of Relativity. I think it is the right one and the other should be thrown out. If you derive length contraction from "tau" you end up getting the same equation...
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Posts: 26
I'm a little confused about your last claim. The t' = t*(1-(v/c)^2) equation is a well-known result from special relativity. Are you trying to derive it using some other method, and then show it is incompatible with the more human-scale Galilean transformation L=vt?

I see what you mean about length contraction, though and that is in fact exactly what is happening: everyone sees light in motion at c, but the people observing the ship see that the light (in the ship's clock) has moved further than the people in the ship see, per bounce.
Edited by Turiski on 5/15/2012 4:00 AM PDT
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interestingly enough a post on "Time dialation" receives 1 response (make that two).

But a post on a .45 caliber hand gun is 7 pages strong (atm)

interestingly enough both have ties to vector physics.
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Posts: 425
interestingly enough a post on "Time dialation" receives 1 response (make that two).

But a post on a .45 caliber hand gun is 7 pages strong (atm)

interestingly enough both have ties to vector physics.


Well, this topic is quite interesting but also very complex. I'm having a hard time reading the equations on this format too.
I studied physics at the beginning of my computer engineer education, but I don't remember much now, lol.
I would say that a better example of time dilatation is any common application of einstein relativity's laws (where speeds are close to light speed).
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Posts: 126
I'm a little confused about your last claim. The t' = t*(1-(v/c)^2) equation is a well-known result from special relativity. Are you trying to derive it using some other method, and then show it is incompatible with the more human-scale Galilean transformation L=vt?
I am saying that should be the proper way to derive the equation to begin with. If you say L'=ct', then you get the same equation for length contraction as it is given in conjunction with the time dialation equation t'=t/sqrt(1-(v/c)^2).

L'=c(t sqrt(1-(v/c)^2) substitute from the time dialation equation for t'

L=ct the distance light has traveled

L'=L sqrt(1-(v/c)^2) substitute L in for ct

Now if you consider doing the same operation with the original light clock example it is easy to see that it shouldn't coincide with the length contraction equation. If they are manipulated in some way together they will give incorrect answers, since the difference between it and tau is only that the time variables have been exchanged.

Also, I would like to add that the exact speed and position of a particle can not be determined exactly. This proof assumes that it can. So if we can always know the exact speed of the photon then we can never know the exact position. Therefore, I don't think this will even be the final word on this theory, if it proves to be more correct.

Since the other time dialation equations result is the inverse of the change in dialated time, it comes out to be close to the same answer in some ranges. But, the accuracy to determine what one is true does not exist in experiments. For instance the plane that flew around the world with atomic clocks was barely accurate enough to find a difference that was on the last digit that it could measure too. So then both theories would be equally valid from this experiment.
Edited by Windscar#1524 on 5/31/2012 7:11 AM PDT
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