Lorentz transformations: time dilation Watch

hai2410
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#1
Report Thread starter 8 years ago
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If I want to find the measured proper time interval between two events in some moving frame S' (at speed v) where the two events have no spacial seperation, what do I need to sub into a Lorentz transformation of the form
 \Delta t'_{AB} = \gamma (\Delta t_{AB} + \dfrac{v \Delta x_{AB}}{c^2} )
(where a ' means the interval in S' and no dash is in another frame S)

I can show time dilation using the transformation from the frame S:

 \Delta t_{AB} = \gamma ( \Delta t'_{AB} +0)
since  \Delta x'_{AB} =0 which gives the familiar time dilation formula.

but using the other transformation I get confused.
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TableChair
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(Original post by hai2410)
If I want to find the measured proper time interval between two events in some moving frame S' (at speed v) where the two events have no spacial seperation, what do I need to sub into a Lorentz transformation of the form
 \Delta t'_{AB} = \gamma (\Delta t_{AB} + \dfrac{v \Delta x_{AB}}{c^2} )
(where a ' means the interval in S' and no dash is in another frame S)

I can show time dilation using the transformation from the frame S:

 \Delta t_{AB} = \gamma ( \Delta t'_{AB} +0)
since  \Delta x'_{AB} =0 which gives the familiar time dilation formula.

but using the other transformation I get confused.
Whatever \Delta x_{AB} is. Anyways, why do you want to do that, it's much easier using the other formula...
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hai2410
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(Original post by TableChair)
Whatever \Delta x_{AB} is. Anyways, why do you want to do that, it's much easier using the other formula...
My bad, two events 'A' and 'B' then the AB subscript means between those two.

and I merely want to see that they both give the same answer... and why, well, because i'm weird like that.
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TableChair
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(Original post by hai2410)
My bad, two events 'A' and 'B' then the AB subscript means between those two.

and I merely want to see that they both give the same answer... and why, well, because i'm weird like that.

I understand that, but you should be able to think of an equation for it. Hint, you know v and you want to get rid of delta x and replace it with a delta t...

Haha, that's a good trait.
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hai2410
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(Original post by TableChair)
I understand that, but you should be able to think of an equation for it. Hint, you know v and you want to get rid of delta x and replace it with a delta t...

Haha, that's a good trait.
Excellent. Works a treat. Cheers
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