2

I am currently delving into the intricacies of Einstein's theory of relativity and striving to grasp its fundamental essence and implications.

Your assistance would be greatly appreciated. Here's my thought experiment concerning special relativity:

Suppose my friend and I are moving toward each other at a relatively high speed, V, each in our own spaceship. We have agreed to measure the time intervals between the same two events and then erect a vertical rod in our spaceship, with the length corresponding to our time interval measurement. We assume the rods are perpendicular to the direction of our motion and are equipped with markers at their top ends. As we pass each other at a constant speed, V, the shorter rod will naturally scratch a mark on the longer rod. After this encounter, we check our rods. The question is, who will have the mark?

Note 1: Clearly, I have designed this theoretical experiment to maintain symmetry between my friend and me throughout the two events.

Note 2: We assume the rods are perfectly perpendicular to our motion (and sufficiently lengthy) so that no length contraction will be observed.

Qmechanic
  • 201,751
Kyriakos
  • 23
  • Why do you think the lengths will be different? – ProfRob Jan 27 '24 at 09:53
  • The business with the sticks is a complete irrelevance. The participants in the experiment can compare their timings in any number of ways without it making a difference to the underlying principle. If the set-up is truly symmetrical, you and your friend will each record the same time between the events. – Marco Ocram Jan 27 '24 at 11:27

4 Answers4

2

You need to specify whether or not the protagonists in your thought experiment are using knowledge of special relativity to arrive that the value of 'the time interval between two events'.

Here is why that matters:
Let's say that the two events consist of traveller A passing two waypoints. For traveller A no procssing is needed, traveller A only has to record what his clock reads at the instant of passing each waypoint.

However, for traveller B assigning a time interval to A passing the two waypoints in succession requires processing data. Transmission delay and relativistic effects must be taken into account.


One way to maintain symmetry is to set the two waypoints such that each traveller first passes one waypoint, then the two travellers pass each other, and then the two travellers pass the second waypoint, with the waypoints equidistant from the point where the two travellers pass each other. (There will be relativistic effects, but with the setup symmetric then between traveller A and B the effects will drop away against each other.)

Your description doesn't give enough information. On one hand you specify that your intent is to 'maintain symmetry between me and my friend', but on the other hand you appear to allow the two events to be not symmetric with respect to the travellers.


If the two events are not symmetric for the two travellers then relativistic effects must be taken into account.

Cleonis
  • 20,795
  • Hello Cleonis, thank you for your contribution. I am pretty sure in special relativity the time we record events in our frame of reference , is NOT the time that we 'see' them happening but its the spontaneous recorded time at the events location in our frame of reference. I believe when we talk about the time that an event occur in our frame reference we always mean as it would be recorder by an observer at that spot at that time – Kyriakos Jan 27 '24 at 10:00
1

The answer depends on the locations of the two events that define the interval that you are measuring.

If the events occur are at the same location as each other in your reference frame then they occur at different locations in your friends reference frame, and the symmetry between you and your friend is broken. On the other hand, if the events occur at the same location in your friend's reference frame they they occur at different locations in your reference frame, and once again the symmetry is broken.

If you chose the events to occur at a location that is, say, always half way between you and your friend (so that the location of the events moves towards you and also moves towards your friend) then symmetry is retained - and in this case you will both measure the same interval between the events.

Note that I am assuming that each observer measures the time interval between the events using an accurate clock at rest in their own reference frame, and does not attempt to convert this time interval into another reference frame.

gandalf61
  • 52,505
  • That's my thought as well: but here is where i get stuck. If we both measuring events that are happening in my friend's spaceship (rest at his frame of reference), then I will measure them as more lengthy than my friend will (and we will both agree on that). In this logic i will measure all the life process that are happening in his spaceship as more lengthy than he will. The same he will measure though about myself and my life process, as more lengthy. The question in my mind is what then we are going to observe when we pass each other. Who will be younger? – Kyriakos Jan 27 '24 at 10:52
  • If the events are at rest in your friend's reference frame then the time interval that you measure will be longer than the time interval that your friend measures. But that is fine because by making the two events at rest in your friend's reference frame (and so at different locations in your reference frame) the scenario is no longer symmetric. – gandalf61 Jan 27 '24 at 14:47
0

After they have measured the time intervals (in their own frames of reference) each observer is able to use their knowledge of Einstein's equations and their relative motions to work out the other observer's measured time interval. The time intervals each observer calculates will agree with the time interval measured by the other observer and communicated by the length marked on the other observer's stick.

Peter
  • 1,859
0

We have agreed to measure the time intervals between the same two events and then erect a vertical rod in our spaceship, with the length corresponding to our time interval measurement.

As we pass each other at a constant speed, V, the shorter rod will naturally scratch a mark on the longer rod.

In case of symmetry, there won't be a shorter and a longer rod, as they measure the same time that they need to determine the length of the rod.

A problem might be that you need to synchronise the two observers and define some event that is symmetric for both. This could be obtained by placing two people in a rocket and have them fly away from some central object and get back in a similar way. This will be different from having only one of them fly away, as is the asymmetrical situation in the typical twin paradox.

The culprit is mostly in

the same two events

There are no same events for different observers. Simultaneity is relative.

We can create a symmetric situation (like the two observers starting from a single point and follow a procedure in opposite directions). In that case observations are similar but even then the idea of simultaneity is not active and it is just symmetry that makes measurements of time between two events similar (a broken clock is right twice a day).

Sextus Empiricus
  • 1,076