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Length contraction v. time dilation 
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#1
Mar2408, 08:21 PM

P: 10

Bear with me. I am a lawyer, not a physicist.... I understand how the light clock demonstrates time dilation with special relativity. I think I understand length contraction.
Here is my question: at relativistic speeds, why does length contraction not affect the distance traveled by the light flash? In other words, why isn't the "V" shape of the light (as seen by the external observer) "squashed" and made more narrow by length contraction, thereby affecting the calculation of the distance traveled by the light etc.? Is it because the external observer would measure the distance using a meter stick on the frame of reference traveling at relativistic speed (which would likewise be contracted) or does the external observer use his own external meter stick that is not contracted? Thanks!! 


#2
Mar2408, 09:15 PM

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P: 2,361

The external observer uses his own external meter stick. He is measuring how long the light path is in his frame.



#3
Mar2408, 09:18 PM

P: 2,251

actually, it would make less sense (or be a less simple model) for length contraction to be observed in for meter sticks that are perpendicular to travel. suppose it did, if moving a meter stick that is parallel to the y axis in solely the x direction contracted length in all the x and y and z directions. then what wound happen if the object were moving in the x and y directions (at a 45^{o} degree direction)? if you slug out the math, would the contraction be the same? not if time dilates by a factor of [itex](1v^2/c^2)^{1/2}[/itex]. you would get some contraction for moving in the x direction for [itex]v/\sqrt{2}[/itex] velocity, and another contraction for moving the same speed in the y direction. but if the contraction in the y direction due to movement in the x direction is none, and the contraction in the y direction due to movement in the y direction is what we get in SR, then the math works out. 


#4
Mar2508, 06:30 AM

P: 997

Length contraction v. time dilation



#5
Mar2508, 08:47 AM

P: 666

If the previous responses still leave you uncertain, then maybe you could clarify a bit what it is you're asking.
Also, what "V" shape do you mean? Are you talking about the angular spread of a beam of light, e.g. from a flashlight? If so, and if the beam is parallel to the direction of motion, then rbj's respose is apt. On the other hand, are you talking about the "V" shape of the light cone as drawn on a spacetime diagram? These things weren't clear to me, but they affect the answer. (I know you don't mind my asking for clarification, since clear and unambiguous language is your stock and trade! ) 


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