How Does Length Contraction Relate to Photons in Special Relativity?

[Chewy0087]

It's my understanding that gamma (the boost factor) for light is infinite which allows it to have energy (mc^2), however, this is the same factor for legnth contraction & time dilation, I'm not really concerned about time dilation as i thought photons don't experience time?

However, there is a definite "speed limit" to time, bieng 3 x 10^8 ms, however legnth is "infiniteley" contracted, right? So sureley it would have arrived already? I have a sneaky feeling this is also something to do with photons not experiencing time, but if someone could clear it up that'd be great.

Also, please correct my errors in wording, but answer the question mainly :P

Thankssss

 

[granpa]

gamma doesn't apply to light. only matter

 

[Chewy0087]

Right 0.o...I guess that's a serious flaw in my understanding of it all :P, but i just assumed that if it applied to the "m" in mc^2, it would apply to time dilation (which I assume it does, as photon's don't experience time) and as such, length contraction?

Can someone clear this up for me? , I'm confused.com

 

[JesseM]

It's my understanding that gamma (the boost factor) for light is infinite which allows it to have energy (mc^2)

It's not really meaningful to talk about gamma for light, since light doesn't have its own inertial rest frame. The first postulate of relativity says that the laws of physics should be the same in all inertial frames, and obviously light cannot be at rest in any sublight inertial frame, so giving light its own rest frame would violate this.

Also, the reason light can have energy is because the full equation for energy in relativity is $$E = \sqrt{m^2 c^4 + p^2 c^2}$$. Light's rest mass m is zero, but it has a nonzero momentum p (in quantum physics its momentum is given by p = hf/c, where h is Planck's constant and f is the frequency).

however, this is the same factor for legnth contraction & time dilation, I'm not really concerned about time dilation as i thought photons don't experience time?

For objects moving at a speed v slower than light, the factor is $$\gamma = \frac{1}{\sqrt{1 - v^2/c^2}}$$--the ticks of a clock are expanded by $$\gamma$$, and rulers are shrunk by $$1/\gamma$$.

However, there is a definite "speed limit" to time, bieng 3 x 10^8 ms, however legnth is "infiniteley" contracted, right?

No, 3 x 10^8 m/s is the limit for speed, i.e. distance/time. There is no upper limit on the factor that a moving clock's ticks can be dilated.

So sureley it would have arrived already? I have a sneaky feeling this is also something to do with photons not experiencing time, but if someone could clear it up that'd be great.

We can't talk about time dilation and length contraction for light itself, but we can talk about what happens in the limit as an object gets arbitrarily close to c (relative to whatever rest frame you're using--all speeds are relative!) For example, suppose a clock moves from one end of the galaxy to another at very close to the speed of light, such that in the galaxy's rest frame its time is so dilated that it only ticks forward by one second in the ~500,000 years it takes to make the trip in the galaxy's frame. In the clock's own rest frame its own time is running normally, but in its frame the galaxy is traveling at very close to the speed of light, so that its length is contracted down from ~500,000 light-years to just about 1 light-second, which explains why in this frame the clock only ticks 1 second between the times it passes each end.

 

[Chewy0087]

Thanks a lot Jessem, you made it really clear and concise, much clearer now! Thank yoo

 

[thenewmans]

How about we show what contraction might be like for light by getting really close and going 99.9999999999% of the speed of light. (twelve 9s) Andromeda is 2.5 million light years away according to Earth’s inertial frame of reference. But it’s only 2.5 light years away in ours. That’s closer than Alpha Centauri. If we went faster, we could cross the visible universe just as quickly as leaving the room. We wouldn’t experience much time at all. So it would be almost like being a photon.

 

[Chewy0087]

Yeah! :P

That was the point that really hit home, incidentally, i'd actually never thought of looking at at it relative to the point of view of a photon Jessem, i know that's what you've advised me activeley against doing, but that was what allowed me to understand it (along with your analogy)

special relativity is awwshum! :P