Time dilation and length contraction

[AdamBenHamo]

I've recently been thinking more about special relativity, and while I understand the Lorentz factor and how to apply it to find correct solutions, I'm still stuck on the link between the effects of length contraction and time dilation, are they permutation of the same thing from different reference frames? How do they link together mathematically? Any light shed on this at all would be really helpful! Thanks in advance!

AdamBenHamo

 

[ghwellsjr]

I've recently been thinking more about special relativity, and while I understand the Lorentz factor and how to apply it to find correct solutions, I'm still stuck on the link between the effects of length contraction and time dilation, are they permutation of the same thing from different reference frames? How do they link together mathematically? Any light shed on this at all would be really helpful! Thanks in advance!

AdamBenHamo

It's not just the Lorentz factor that you need to use to find correct solutions, it's the Lorentz Transformation that will link them together mathematically.

 

[AdamBenHamo]

Thankyou ghwellsjr, but that doesn't quite answer my question, it's no so much the solutions that I have a problem finding, but the symmetry between the two phenomena that I can't quite get my head around!

 

[ghwellsjr]

Drawing a spacetime diagram helps a lot. Have you done that or have you studied the threads where I have done it?

 

[Nugatory]

Thankyou ghwellsjr, but that doesn't quite answer my question, it's no so much the solutions that I have a problem finding, but the symmetry between the two phenomena that I can't quite get my head around!

The muon lifetime measurements are a good way of seeing the relationship. You could try #27 in this fairly recent thread: https://www.physicsforums.com/showthread.php?t=679937

 

[nitsuj]

...on the link between the effects of length contraction and time dilation, are they permutation of the same thing from different reference frames? How do they link together mathematically?

I'd agree they are permutations of an interval.


length / time = speed

speed is limited, the limited speed is invariant. Lower speeds are not invariant.