Length contraction clarification

Click For Summary

Discussion Overview

The discussion revolves around the concept of length contraction in the context of special relativity, specifically focusing on two iron rods and the separation between them as observed from a moving frame. Participants explore various scenarios regarding the effects of relative motion on measurements of length and separation, addressing both theoretical implications and practical observations.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • Some participants assert that the separation between the rods does undergo length contraction when observed from a moving frame.
  • Others clarify that length contraction is a phenomenon observed due to relative motion, emphasizing that it is not an intrinsic change in the objects themselves.
  • A participant questions the observer's frame of reference, suggesting that the interpretation of the scenario could vary based on whether the observer or the rods are in motion.
  • There is a discussion about the implications of the Lorentz transformations and how they relate to the concept of length contraction.
  • Some participants express confusion over the phrasing of questions regarding length contraction, suggesting that it may lead to misunderstandings about the nature of the phenomenon.
  • One participant humorously illustrates the relativity of motion by comparing it to observing objects from different frames, using an analogy involving turkeys.
  • There is a request for clarification on the term "tiny there's," which is speculated to refer to tiny threads connecting the rods.

Areas of Agreement / Disagreement

Participants generally agree that length contraction occurs due to relative motion, but there is no consensus on the implications of specific scenarios or the interpretation of the observer's frame. The discussion remains unresolved regarding the nuances of how length contraction applies to the separation between the rods and the conditions under which it is observed.

Contextual Notes

Participants highlight the importance of clearly defining the frame of reference when discussing length contraction, as misunderstandings can arise from ambiguous phrasing. The discussion also touches on the relationship between length contraction and the Lorentz transformations, indicating that further exploration of these concepts may be necessary for clarity.

  • #31
The common usage of the word 'interval' implies a separation in time. Such as the 'interval between cooking and eating'. So 'space-interval' can be confusing.

But if 'space-interval' has been defined, eg as simultaneous measurement

##x'_2-x'_1 = (\gamma t_1 + \gamma\beta x_2) - (\gamma t_1 + \gamma\beta x_1) = \gamma\beta(x_2-x_1)##

no confusion can arise whatever word is used.

It is not clear what the motives are for the OP's questions. It seems learning is not the priority.
 
Physics news on Phys.org
  • #32
Last edited:
  • #33
I think the other answerers were following the answer posted by tiny tim

What tiny tim said is wrong
The distance between the rods won't contact, because if you consider this thought experiment, you'll understand it

"Imagine you are the observer waiting to see a space racing. The track is exactly 1 Light second long. I am sitting in a rod A & There is another rod B infront of me which is kept 100km away from me.
YOUR STOPWATCH IS AIMING AT MY SPEED.

This setup is moving at 99.999999999% of c with respect to YOU. According to your prediction If the distance between my rod and the rod ahead of me contract, then I'll reach the end line before it ticks 1 second in YOUR STOPWATCH!

You can think in another way too
What if there is NO rod in front of the First Rod?
 
  • #34
tiny-tim said:
well, that refers to taylor and wheeler's "spacetime physics",

which calls s2 the interval squared, not the interval

in other words, taylor and wheeler agree with me, that that wikipedia page is wrong, and "interval" is one-dimensional

I must agree. WIKI's page is misleading, if not mistaken IMO. A spacetime interval has a length s, and its square is not the spacetime interval itself. The "spacetime interval" is that which possesses the length of s, and "that" is the line element (or path) between the 2 reference events in 4d spacetime. s2 is just the distance squared, ie a squared spacetime interval. The metric being the function describing the spacetime interval's length s. So when WIKI says ...

WIKI said:
The reason s2 is called the interval and not s is that the sign of s2 is indefinite.

While I understand the point they are making regarding the possible polarities of s2, I do not see how that justifies labeling a "squared distance" the spacetime-interval itself.

Thank You,
GrayGhost
 
  • #35
Trojan666ru said:
This setup is moving at 99.999999999% of c with respect to YOU. According to your prediction If the distance between my rod and the rod ahead of me contract, then I'll reach the end line before it ticks 1 second in YOUR STOPWATCH!

You can think in another way too
What if there is NO rod in front of the First Rod?

Try this:

1) Write down the coordinates of the two events "I am at the start line" and "I am at the finish line". Use the Lorentz transforms to find the coordinates of these two events for the observer at rest relative to the track. That covers the case in which there is no second rod in front of the first rod.

2) Now suppose that there is a second rod in front of the first. Do the same calculation for that one. Use this and the result from the previous step to calculate the distance between the rods according to the observer at rest relative to the track. You will see that distance is contracted.
 
  • #36
this is the wrong interpretation of LT. It is measuring one
end of the rod at one place while the other end of rod at
another place.
This is wrong.
Because when you measure the end point, the front point
moves forward to different point.
 
  • #37
The formula for spacetime interval is given by,
ds2 =- (cdt)2 + dl2
After a little bit of algebra we get
dt =|ds2|^1/2/c = dt[1
- (v/c)^2]^1/2.
The following
dt = |ds2|^1/2/c
is the expression for the proper time difference not
only for observers at rest in the coordinate system but
for all observers, however they move,
 
  • #38
Trojan666ru said:
What tiny tim said is wrong
The distance between the rods won't contact
No, that part of what tiny tim said is correct (most of what he said is correct, only that one very small post wasn't).

You can write the worldline of the endpoint of any rod as ##(t,x)=(t,p_i)## where p_i is the position of the i'th endpoint in the rest frame. If you do a Lorentz transform on that then you can get the worldline in the primed frame, set t'=0 and see the distances. You will see that they all contract.
 
  • #39
Trojan666ru said:
this is the wrong interpretation of LT. It is measuring one
end of the rod at one place while the other end of rod at
another place.
This is wrong.
Because when you measure the end point, the front point
moves forward to different point.

The at-rest observer can calculate the length of a rod by taking the time at which the front of the rod passed over the starting line of the track and subtracting that from the time at which the rear of the rod passed over the starting line. That gives us the time it took for the rod to pass that point, and we multiply that by the speed to get the length of the rod.

The same technique works to get the distance between the rods; we just use the times when the back of the leading rod and the front of the trailing rod pass the at-rest observer (or anything else that is at rest relative to him).

I really really strongly suggest that you try these calculations for yourself.
 
  • #40
Trojan666ru said:
After a little bit of algebra we get
dt =|ds2|^1/2/c
You made a mistake with your algebra. This is not true in general, although it is true for dl=0.
 

Similar threads

  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 166 ·
6
Replies
166
Views
15K
  • · Replies 63 ·
3
Replies
63
Views
6K
  • · Replies 24 ·
Replies
24
Views
3K
  • · Replies 33 ·
2
Replies
33
Views
3K
  • · Replies 38 ·
2
Replies
38
Views
5K
  • · Replies 12 ·
Replies
12
Views
2K
  • · Replies 11 ·
Replies
11
Views
2K
  • · Replies 52 ·
2
Replies
52
Views
6K
  • · Replies 11 ·
Replies
11
Views
3K