# Lorentz contraction and Time dilation (Special relativity)

A quick question.
It's been a long time since I had anything to do with special relativity, so I really can't remember much. But last night I was thinking about the "proof" of special relativity with the case of muons.
So basically:

Muons are created when particles hit the atmosphere. They can be detected on earth, even though they decay so fast, that even if they were to travel at the speed of light, they would not reach the surface of the earth. But, as stated, we do detect them.
The reason for this is, that if I, as an observer on the earth, look at the muon, I see it's internal clock go slower, and therefore it has "more" time to reach the earths surface, before it decays. In the reference frame of the muon, it's clock is not changed, but instead the length of which it needs to travel is contracted, and therefore it doesn't need to travel as far, and can actually reach the surface before it decays.
If I'm not mistaken, that's how it works, right ?

Now, what happens when particles doesn't have an internal clock ? I mean, a photon will not decay, and I'm guessing some other particles doesn't either ? So how do I, as an observer, see it, and how does the particle itself see it ?

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ghwellsjr
Gold Member
A quick question.
It's been a long time since I had anything to do with special relativity, so I really can't remember much. But last night I was thinking about the "proof" of special relativity with the case of muons.
So basically:

Muons are created when particles hit the atmosphere. They can be detected on earth, even though they decay so fast, that even if they were to travel at the speed of light, they would not reach the surface of the earth. But, as stated, we do detect them.
The reason for this is, that if I, as an observer on the earth, look at the muon, I see it's internal clock go slower, and therefore it has "more" time to reach the earths surface, before it decays. In the reference frame of the muon, it's clock is not changed, but instead the length of which it needs to travel is contracted, and therefore it doesn't need to travel as far, and can actually reach the surface before it decays.
If I'm not mistaken, that's how it works, right ?
Sort of right.

Don't make the mistake of saying that a particle with mass, no matter how small, can travel at the speed of light.

Also, when you look at the muon traveling rapidly toward you, you're not going to see it's internal clock going slower, you're going to see it going much faster. What you're describing is Time Dilation which means that in your rest frame, the clock is going slower, but it won't look like that to you. I'll explain later.

Now, what happens when particles doesn't have an internal clock ? I mean, a photon will not decay, and I'm guessing some other particles doesn't either ? So how do I, as an observer, see it, and how does the particle itself see it ?

You can watch a muon coming towards you, that is, you can see it being created in the upper atmosphere and you can see it travel down but think about this. The image of its creation is going to also travel down towards you at the speed of light and right behind it is the muon so there will be a very short period of time between when you see it start and when it actually gets to you. And during that brief period of time, you have to watch its clock advance however much its going to advance so even though it is advancing slower than your clock, you will see it advancing much quicker. This also means that although it may have taken several microseconds for it to make the trip, the duration of the image that you see will be very much shorter than that.

Now think about the image that you see of the creation of the muon. It may have taken several microseconds for it to get to you but you cannot observe its progress. If you were to measure how long it took from when you see it until you see it...it's the same thing. So you cannot watch light's progress as it is traveling toward you. Does that make sense to you?

Now as to your question about how a particle traveling at light speed sees "it", whatever "it" is, we have to call those kinds of question meaningless, mainly because time does not apply to particles moving at the speed of light. Don't make the mistake of thinking that time slows down until it reaches zero because they can never reach the speed of light and so the concept of time doesn't apply for particles that travel at the speed of light and they can never go slower than the speed of light.

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That seems to make sense :)

Thank you.