Length contraction (no calculations)

In summary, the length contraction and time dilation formulas are not applicable in this scenario. It is best to use the Lorentz transformations instead. Length contraction only applies to massive particles that exclusively travel below the speed of light, and it is meaningless to talk about what length a photon measures in relativity.
  • #1
mousemouse123
10
0
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?
 
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  • #2
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
mousemouse123 said:
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
mousemouse123 said:
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
DaleSpam said:
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 don't know what the lorentz transformation formula is. (i hate physics now too confusing)
 
  • #6
mousemouse123 said:
LOL i don't 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
mousemouse123 said:
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.
 

1. What is length contraction?

Length contraction is a phenomenon in which an object's length appears shorter when it is in motion relative to an observer than when it is at rest. It is a consequence of Einstein's theory of special relativity.

2. How does length contraction occur?

Length contraction occurs due to the fact that the speed of light is constant for all observers, regardless of their relative motion. As an object's velocity increases, the distance between its front and back ends appears to decrease, resulting in a contracted length.

3. Is length contraction a real physical effect?

Yes, length contraction is a real physical effect that has been observed and verified through experiments. It is a fundamental aspect of Einstein's theory of special relativity and is an important concept in modern physics.

4. Does length contraction only occur in objects moving at near-light speeds?

Yes, length contraction is only noticeable in objects moving at speeds close to the speed of light. At everyday speeds, the effect of length contraction is negligible and cannot be observed.

5. Can length contraction be seen in everyday life?

No, length contraction is not noticeable in everyday life as it only becomes significant at speeds close to the speed of light. However, it has important implications for space travel and other high-speed technologies.

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