Time dilation and length contraction

AdamBenHamo
Messages
13
Reaction score
0
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
 
Physics news on Phys.org
AdamBenHamo said:
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.
 
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!
 
Drawing a spacetime diagram helps a lot. Have you done that or have you studied the threads where I have done it?
 
AdamBenHamo said:
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
 
AdamBenHamo said:
...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.
 
Thread 'Can this experiment break Lorentz symmetry?'

Thread 'Can this experiment break Lorentz symmetry?'

1. The Big Idea: According to Einstein’s relativity, all motion is relative. You can’t tell if you’re moving at a constant velocity without looking outside. But what if there is a universal “rest frame” (like the old idea of the “ether”)? This experiment tries to find out by looking for tiny, directional differences in how objects move inside a sealed box. 2. How It Works: The Two-Stage Process Imagine a perfectly isolated spacecraft (our lab) moving through space at some unknown speed V...
View full post »

Thread 'Relativator (Circular Slide-Rule): Simulated with Desmos - Insight'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. The Relativator was sold by (as printed) Atomic Laboratories, Inc. 3086 Claremont Ave, Berkeley 5, California , which seems to be a division of Cenco Instruments (Central Scientific Company)... Source: https://www.physicsforums.com/insights/relativator-circular-slide-rule-simulated-with-desmos/ by @robphy
View full post »

Thread 'A sufficient condition for integrability of equation ##\nabla g=0##'

In Philippe G. Ciarlet's book 'An introduction to differential geometry', He gives the integrability conditions of the differential equations like this: $$ \partial_{i} F_{lj}=L^p_{ij} F_{lp},\,\,\,F_{ij}(x_0)=F^0_{ij}. $$ The integrability conditions for the existence of a global solution ##F_{lj}## is: $$ R^i_{jkl}\equiv\partial_k L^i_{jl}-\partial_l L^i_{jk}+L^h_{jl} L^i_{hk}-L^h_{jk} L^i_{hl}=0 $$ Then from the equation: $$\nabla_b e_a= \Gamma^c_{ab} e_c$$ Using cartesian basis ## e_I...
View full post »

Similar threads

I Question about length contraction
Replies
45
Views
5K
I What causes time dilation and length contraction
Replies
10
Views
2K
B Why does length contraction occur and how does it relate to time dilation?
2
Replies
63
Views
5K
I Please explain how length contraction and time dilation result in a constant c
Replies
4
Views
122
B Check my understanding of Time Dilation and Length Contraction
Replies
11
Views
2K
I Length contraction and time dilation
Replies
36
Views
4K
B Reciprocal time dilation
Replies
14
Views
1K
I How time dilation is a permanent change and length contraction not?
Replies
13
Views
2K
B What does symmetry of time dilation really mean?
Replies
16
Views
2K
I Does SR Length Contraction Halve Space Travel Time?
Replies
17
Views
2K

Hot Threads

Recent Insights

Back
Top