# Confusion between simultanety and time dialation

1. Jul 24, 2009

### firavia

Let events 1 and 2 occur at and in frame S. In frame S' they occur at

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if this is true than time dialation rule IS no more applicable cause as we know to calculate the location of an event or anything at a certain location in a frame of reference " S' " using the coordinates of the location of this same event in frame "S " we must use the contraction of length law which will give us the exact location of the event in the frame of S' and samely to determien the time using time dialation rule , if an event 1 occur at t = 3 sec according to the clock of frame S this same event will occur at time X s which is calculated using the time dialation method , t= t0 / (radical (1- (v sqaure / c square ) .

and if the 2 events occured at the same time in the frame of reference S , throught the time dialation rule they must occure SIMULTANELY in frame S' but at diferent time of occurence in frame S .

I'e understood time dialation correclty but now I am confusing , why if we want to calculate the time that a spacecraft reaches a star we do apply the law of time dialation using the time of the arrival of this spacecraft in the frame of another observer , isnt the arrival is considered an event , so why other events are not being calculated using the same law .

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2. Jul 25, 2009

### Staff: Mentor

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OK.

I don't understand what you're saying here. Your equations above--the Lorentz transformations--already include "time dilation" (and other factors).

The "time dilation" rule tells you that a moving clock is observed to run slow. That's distinct from simultaneity.

Again, it's not clear what you mean. You can certainly think in terms of events and translate their space-time coordinates from one frame to another. To do that one uses the full Lorentz transformations. In special cases you can apply simpler rules such as the time dilation formula. In the case of a spacecraft, which is essentially a moving clock, we can use the time dilation formula.

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3. Jul 25, 2009

### vin300

Those were started by voigt, but I want to know how to derive the time eqn
I think all that firavia wants to know is the difference between the eqns

Last edited: Jul 25, 2009
4. Jul 25, 2009

### Staff: Mentor

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On second reading, it looks like you mistyped one of the equations. I assume you meant:
$$x'_1 = \gamma(x_1 - vt_1)$$
$$t'_1 = \gamma(t_1 - vx_1/c^2)$$
$$x'_2 = \gamma(x_2 - vt_2)$$
$$t'_2 = \gamma(t_2 - vx_2/c^2)$$

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5. Jul 25, 2009

### Staff: Mentor

?
What do you mean? How to derive the time dilation formula from the Lorentz transformations?

6. Jul 25, 2009

### firavia

Can we say that the time needed according to a man inside a spacecraft in order reach the location of an event that might be for example " the flashing light sourse location" is the time calculated through time dialation rule ???

if yes than the time of occurence of an event is different than the time needed to reach the location of where the event will happen .

so I can conclude that it is due to length contraction 2 events that are occuring simultanesly in one frame cannot occure simultanesly in another frame . is that right .

lets take the example of a train , in the frame of a man standing on a platform the 2 flashings are happenng simultanesly and marking both ends of the train but in the frame of reference of a passenger inside the train the front flash light must happen before the back flashlight cause the location of the flashing sources according to this frame of refference are now closer to each other due to length contraction and the length of the train according to the passenger is now at its proper length , so in order to prevent a paradox and the 2 flash lights mark both ends of the train and due to geometrical changes one flash light msut occur before the other , but the location of each flashlights sources are calculated by the legnth contraction formula using the constants of velocity of the train , celerity and the location L0 of the 2 fflash lights sources seen by the man on the platform ..
what I am trying to say if one event is happening in one frame of reference can its occurence be calculated in another frame of reference using time dialation formula ?
or laurentz transformation must be used ??

can I say that simultaneity do exist because of length contraction and vice versa ???
what about the causality ???? isnt it broken how can 1 action that is causing the flash light to be initiated is being applied in one frame and in another frame that same action is causeing only one of the flash lights to happen ??? what is the cause of the other flashlight to occur ????

Last edited: Jul 25, 2009
7. Jul 25, 2009

### vin300

Somewhere in a previous thread, I had suggested using t=t0*/(gamma) but Jesse said that was wrong and the equation mentioned in firavia's post is to be used.What exactly makes the former different from the latter?

8. Jul 25, 2009

### Staff: Mentor

You need to give a specific example so I can understand what you mean.

Again, not sure what you mean.

Three distinct relativistic effects work together: length contraction, time dilation, and clock desynchronization.

To make sure we understand each other, we need a specific example with lengths and times defined.

I don't understand how causality comes into this. There are two flashes; one does not cause the other. Whether they happen simultaneously or not depends on the frame of reference.

9. Jul 25, 2009

### Staff: Mentor

Not sure what you mean by that equation.
The equations listed in this post are the complete Lorentz transformations. The time dilation formula is a special case that applies to a moving clock (or equivalent). Of course the time dilation formula can be derived from the more general Lorentz transformations.

10. Jul 25, 2009

### vin300

Looks like gravity of the situation is bending firavia's typetime
I had learnt a derivation of time dilation formula(the one with only gamma)What I want to know is how to derive this one

11. Jul 25, 2009

### Staff: Mentor

You are asking how to derive the Lorentz transformations? Here's a perfectly good discussion of the LT including a derivation: http://galileo.phys.virginia.edu/classes/252/lorentztrans.html" [Broken]

(Or just check out any relativity text.)

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