Is there a solution for the behavioural contradiction in RT?

  • Context: Undergrad 
  • Thread starter Thread starter Foppe Hoekstra
  • Start date Start date
  • Tags Tags
    Contradiction
Click For Summary
SUMMARY

The discussion centers on the behavioral contradiction in the context of rotating systems and special relativity, specifically involving a circular train of wagons equipped with synchronized printers. When these printers simultaneously mark the rail, observers in different frames perceive distances differently due to Lorentz transformations. The key conclusion is that while the distance between dots in a stationary frame (SF) is L, the contracted distance perceived by the moving frame (MF) is γL, leading to a paradox that is resolved by understanding the loss of simultaneity in rotating systems. This paradox has been previously analyzed in various forms within the forum.

PREREQUISITES
  • Understanding of Lorentz transformations in special relativity
  • Familiarity with the concept of simultaneity in different reference frames
  • Knowledge of the Ehrenfest paradox and its implications
  • Basic principles of rotational motion and its effects on length measurement
NEXT STEPS
  • Study the Ehrenfest paradox in detail to grasp its relevance to rotating systems
  • Explore the relativity of simultaneity and its mathematical foundations
  • Investigate the implications of length contraction in non-inertial frames
  • Learn about Einstein's synchronization method for clocks in moving systems
USEFUL FOR

Physicists, students of relativity, and anyone interested in the complexities of motion in special relativity, particularly in understanding the nuances of rotating systems and simultaneity.

  • #31
Foppe Hoekstra said:
Nevertheless it is the shorter wagon that puts its dots at the larger distance!
I don't believe this is correct, assuming you mean "further apart as measured by the track rest frame". It would be correct if you were Einstein synchronising your clocks, but you aren't.

With Einstein-synchronised clocks, the "simultaneous print" of the wagons is non-simultaneous in the track rest frame. Thus the length contracted wagon produces a longer spacing because its back printer prints before its front printer (as described in the track frame).

But you aren't using Einstein synchronisation - all your clocks are synchronised in the track rest frame, even when they are in motion (I assume the clocks in the inertial wagon are not Einstein synchronised either). Thus the length-contracted wagon will print a short spacing.
 
Physics news on Phys.org
  • #32
Foppe Hoekstra said:
RS: From the full story: "Every printer has a clock that is synchronized when the train is at rest and thereafter the train is accelerated to a constant velocity v. Thus all clocks are accelerated in the same way and so all clocks will develop the same deviation in relation to SF. So all clocks will still be synchronized in RS when the train is at speed."
As soon as the clocks are accelerated they will no longer be synchronized along that direction (your choice of direction spoils any symmetry). I believe they will, however, return to synchronization if the train is brought to rest.
 
  • #33
hutchphd said:
I believe they will, however, return to synchronization if the train is brought to rest.
Yup. A simple argument from symmetry guarantees this. No clock is treated any differently than any other, so they must all share the same reading when re-united.
 
  • #34
Foppe Hoekstra said:
Which brings us to another point: namely that a consistent theory does not necessarily need to be true.

You're referring to Newtonian mechanics, of course?
 
  • #36
The OP question has been answered in a number of different ways. The thread will remain closed.
 
  • Like
Likes   Reactions: weirdoguy

Similar threads

  • · Replies 32 ·
2
Replies
32
Views
4K
  • · Replies 25 ·
Replies
25
Views
2K
  • · Replies 75 ·
3
Replies
75
Views
7K
  • · Replies 125 ·
5
Replies
125
Views
20K
  • · Replies 46 ·
2
Replies
46
Views
14K
  • · Replies 4 ·
Replies
4
Views
1K
  • · Replies 5 ·
Replies
5
Views
4K
  • · Replies 70 ·
3
Replies
70
Views
9K
  • · Replies 0 ·
Replies
0
Views
5K
  • · Replies 35 ·
2
Replies
35
Views
29K