Length contraction (no calculations)

  • #1

Main Question or Discussion Point

i am wondering when i read about planets or solar systems that are like 1million lightyears away, those that take into account length contraction, because if the light is traveling at the speed of light then the distance it has to go will contract.

also another (possibly) stupid question: formula for length contract is like

L=Lo/sqrt of 1-v^2/c^2

light travels at the speed of light so it will be L=Lo/0 which is impossible(zero in denominator)... does that mean length can't contract when it comes to light?
 

Answers and Replies

  • #2
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I recommend avoiding the use of the length contraction and time dilation formulas and focusing on the Lorentz transforms instead.

The length contraction formula is only valid for simultaneous pairs of events on two separate worldlines where the pairs are colocated in one of the frame. Here you do not have two separate worldlines and even if you did there is no frame where they would be colocated.

The length contraction formula simply does not apply, but the Lorentz transform does. There is no discernable advantage to the shorter formulas.
 
  • #3
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i am wondering when i read about planets or solar systems that are like 1million lightyears away, those that take into account length contraction, because if the light is traveling at the speed of light then the distance it has to go will contract.

also another (possibly) stupid question: formula for length contract is like

L=Lo/sqrt of 1-v^2/c^2

light travels at the speed of light so it will be L=Lo/0 which is impossible(zero in denominator)... does that mean length can't contract when it comes to light?
It is best to use the Lorentz transformations always until you have had practice in using them, otherwise you end up using the contraction and dialtion formulas inappropriately.

As it happens, the Lorentz contraction formula works in this case for a a frame that approaches the speed of light, since the speed of light in every frame must be c! A frame for light is therefore meaningless.

So yes, as the frame approaches the speed of light, the distance the earth has to travel to get to the origin in that frame approaches 0.
 
  • #4
Pengwuino
Gold Member
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light travels at the speed of light so it will be L=Lo/0 which is impossible(zero in denominator)... does that mean length can't contract when it comes to light?
It simply doesn't make sense to ask what distance the photon sees as the distance between 2 points. Length contraction only applies to massive particles that exclusively travel below the speed of light. It's a simple tenet of special relativity.
 
  • #5
I recommend avoiding the use of the length contraction and time dilation formulas and focusing on the Lorentz transforms instead.

The length contraction formula is only valid for simultaneous pairs of events on two separate worldlines where the pairs are colocated in one of the frame. Here you do not have two separate worldlines and even if you did there is no frame where they would be colocated.

The length contraction formula simply does not apply, but the Lorentz transform does. There is no discernable advantage to the shorter formulas.

LOL i dont know what the lorentz transformation formula is. (i hate physics now too confusing)
 
  • #6
Pengwuino
Gold Member
4,989
15
LOL i dont know what the lorentz transformation formula is. (i hate physics now too confusing)
Don't worry about it. I believe DS's explanation was too complex of an explanation for a simple question. All that really matters is the fact that it's meaningless to talk about what length a photon measures in relativity.
 
  • #7
HallsofIvy
Science Advisor
Homework Helper
41,833
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i am wondering when i read about planets or solar systems that are like 1million lightyears away, those that take into account length contraction, because if the light is traveling at the speed of light then the distance it has to go will contract.

also another (possibly) stupid question: formula for length contract is like

L=Lo/sqrt of 1-v^2/c^2

light travels at the speed of light so it will be L=Lo/0 which is impossible(zero in denominator)... does that mean length can't contract when it comes to light?
You seem to be misunderstanding "length contraction". That has nothing to do with the speed of light moving bewtween two places. The distance, as observed from one of the places would have to do with the speed of each place relative to the other or, as observed from a third place, the speed of the two places relative to the third.
 

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