Time Dilation Vs. Length Contraction

In summary: You can't get a strip by rotating a line.In summary, the conversation discusses the concepts of time dilation and length contraction in special relativity, and whether they occur together or separately. The concept of the relativity of simultaneity is also mentioned. It is noted that c must remain constant under a Lorentz transformation, and that length contraction and time dilation are not analogous.
  • #1
Kirsten-maths
1
0
I'm having a major mental block to special relativity - i understand it the principle of it but seem to be struggling with time dilation and lenth contraction. I've spent a while thinking that time dilation and length contraction happen both togethor like you can't get one without the other... but my maths isn't working out, (and I'm a maths student...) is it either time dilation or length contraction? Or was i right the first time its both?

I'm using an example of a muon created in the Earth's atmosphere 3km up, with a speed of 0.99c

Cheers in advance for any help :)
 
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  • #2
Right, it is both. From the frame of Earth, the muon, if it had a radius, would be contracted. The muon's "clock" also time dilates at .99 c, so ticks slower, and the muon takes longer to decay as the Earth frame views it, so it passes further through our atmosphere. From the point of view of the frame of the muon, it is Earth that is contracted, so the atmosphere is less than 3 km as it enters it. The muon decays in its normal time within its own frame, so again, it travels further through the contracted atmosphere before it decays.
 
  • #3
Kirsten-maths said:
I'm having a major mental block to special relativity - i understand it the principle of it but seem to be struggling with time dilation and lenth contraction. I've spent a while thinking that time dilation and length contraction happen both togethor like you can't get one without the other... but my maths isn't working out, (and I'm a maths student...) is it either time dilation or length contraction? Or was i right the first time its both?

I'm using an example of a muon created in the Earth's atmosphere 3km up, with a speed of 0.99c

Cheers in advance for any help :)

Usually there are 3 things you have to take into account. They are "length contraction", "time dilation" and "the relativity of simultaneity". The last item is usually overlooked or misunderstood and is usually at the root of most well known paradox examples. The equation for the relativity of simultaneity is given as [tex]\Delta T = L_0*v/c^2 [/tex] where [tex]L_0[/tex] is the proper separation of two clocks at rest wrt each other in the rest frame of the clocks. [tex]\Delta T[/tex] is the apparent difference in the elapsed times of two clocks that are moving relative to an observer if the two clocks are synchronised in their rest frame. Even better, to avoid confusion when carrying out calculations, it is better to use the full Lorentz transformations as they automatically take the relativity of simultaneity into account, rather than the length contraction and time dilation equations .
 
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  • #4
The really simple, not at all rigorous argument is that c has to stay the same under a Lorentz transformation, and c is a distance divided by a time, so you can't just have length contraction without time dilation or vice versa.
 
  • #5
bcrowell said:
The really simple, not at all rigorous argument is that c has to stay the same under a Lorentz transformation, and c is a distance divided by a time, so you can't just have length contraction without time dilation or vice versa.
Yes, and, like yuiop said, you also need the relativity of simultaneity. Without that, you'll never get c to remain c simply by dividing a contracted (smaller) length by a dilated (larger)time.
 
  • #6
Ugh, two years later I've realized that my #4 was totally wrong. Length contraction and time dilation are not analogous. Here's a long thread about that: https://www.physicsforums.com/showthread.php?t=299857 One easy way to see that they're not analogous is that the world-line of a clock is a line, whereas the world-line of a ruler is a strip.
 

1. What is the difference between time dilation and length contraction?

Time dilation and length contraction are both concepts that arise from Einstein's theory of relativity, but they refer to different phenomena. Time dilation refers to the slowing down of time for a moving object, while length contraction refers to the shortening of an object's length in the direction of its motion. In other words, time dilation affects the perception of time, while length contraction affects the physical dimensions of an object.

2. How does time dilation affect our perception of time?

Time dilation occurs when an object is moving at a high speed, close to the speed of light. In this scenario, time appears to slow down for the moving object compared to an observer at rest. This means that for the moving object, time is passing slower than it would for an observer at rest, leading to a difference in perception of time.

3. Why does length contraction occur?

Length contraction occurs because of the fact that the speed of light is constant for all observers, regardless of their relative motion. This means that as an object approaches the speed of light, its length in the direction of its motion will appear to shorten from the perspective of an outside observer. This is because the object's speed is causing the distance between its front and back ends to appear shorter.

4. Can we observe time dilation and length contraction in everyday life?

While we cannot observe time dilation and length contraction directly in our everyday lives, we can observe their effects in certain situations. For example, GPS satellites need to account for time dilation in order to provide accurate location information on Earth. Additionally, particle accelerators, such as the Large Hadron Collider, rely on the principles of time dilation and length contraction to function properly.

5. Are time dilation and length contraction accepted theories in the scientific community?

Yes, time dilation and length contraction are both well-established theories in the scientific community and have been extensively tested and confirmed through various experiments and observations. They are fundamental principles of Einstein's theory of relativity and have been integral in shaping our understanding of space and time.

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