I Light clock confusion

1. Oct 22, 2015

DAC

Hello PF.
Sometime ago I posted a question about the light clock train thought experiment. I didn't understand the answer, so if I may I'll ask it again.

In the light clock on the train thought experiment, the clock is calibrated to each time the light strikes the mirrors, which are 1 metre apart. The motion of the train means the mirror to mirror path increases, say to 1.2metres apart, so the clock takes longer to tick over.

What happens if the clock is now calibrated to tick over each time the light travels one metre? The light's path with motion is still diagonal, but if it is measured in one metre lengths, the clock ticks at the same rate in both frames.
The counter argument is it can't be done because, different frames will disagree on how many metres the light has gone between any two ticks. i.e. it's a "red herring ".

But 1metre is the same length in both frames. otherwise the thought experiment doesn't work.
Regards.

Last edited by a moderator: Oct 30, 2015
2. Oct 22, 2015

Simon Bridge

However, it sounds like the description of the problem is confused.

3. Oct 22, 2015

Staff: Mentor

A light clock ticks once each time the flash of light hits the mirrors, so you calibrate it by moving the mirrors closer together or farther apart so that it ticks at the desired rate.

There's no calibration that makes it tick at the same rate according to someone who is moving relative to the clock and someone is at rest relative to the clock because positioning the mirrors to make it right for one of them (the light travels one meter between the mirrors according to that observer) makes it wrong for the other one.

4. Oct 22, 2015

Staff: Mentor

A light clock ticks each time that the light makes a round trip. You can make two adjustments, one is to change the length of the clock. This changes the physical tick rate. The other is to change the counter increment. This changes the unit of time displayed.

It is unclear which you mean, but neither approach will make the rate frame invariant.

5. Oct 22, 2015

Staff Emeritus
Can we a) have a better title and b) a link back to the other thread we are supposed to be discussing? It is hard to discern what this thread is really about.

6. Oct 22, 2015

Staff: Mentor

Last edited: Oct 30, 2015
7. Oct 31, 2015

DAC

Another way to present this is to imagine starting with the two mirrors and the light pulse, and temporarily no sensors.
We obviously will still get the perpendicular, and the diagonal light path generated from the train's motion.
Now install sensors at one metre centres along both light paths. The light activates the sensors for every one metre travelled at c.
And one metre is the same one metre in both frames,otherwise subsequent Pythagorean calculations wouldn't work.
So the distance between mirrors doesn't change. The light path with motion still alters by the same amount. The sensors location however, does change.

8. Oct 31, 2015

Staff: Mentor

This doesn't make any sense. There is only one light path. It is the same light path described in two different frames.

You certainly could design a light clock with sensors along the length of the clock. However, it would not remove time dilation. All it would do is make the analysis more complicated by introducing relativity of simultaneity also. The reason the traditional simple light clock is used is not because we could not think of something more complicated, but rather that it is so simple that the conclusion is unavoidable. Any time you find yourself confused about something you need to simplify the scenario as much as possible to retain the confusing effect but nothing else.

Here, you are confused about time dilation. So stick with the standard light clock that shows only time dilation and does not involve length contraction or relativity of simultaneity. With the standard light clock there are only two adjustments possible, the length and the counter increment. Time dilation remains regardless of which you adjust. Do you understand that?

9. Oct 31, 2015

Simon Bridge

One could install two sets of sensors, one in the track frame and one in the train frame... but, like DaleSpam says, it's an unneeded complication thatbonly confuses things further.

10. Oct 31, 2015

Staff: Mentor

A reference frame isn't a container that you can put objects into or take them out of. A given object, like a sensor, is always in every frame. In some frames it may be moving, and in some frames it may be stationary. But it is always in every frame.

I am sure you know this, but the OP may not, so I am just clarifying. I believe that what you meant to say "one at rest in the track frame and one at rest in the train frame".

11. Oct 31, 2015

Simon Bridge

By "in a reference frame", I mean _stationary_ wrt that frame. Correct.
Hope that clears things up.

A central confusion arises from not being clear on this point so good catch.

12. Nov 1, 2015

sweet springs

13. Nov 1, 2015

Mister T

At that speed $\gamma=1.2$.

It already is calibrated that way! It makes no difference if the train is moving or not. Perhaps you mean to calibrate it so that it now reads one metre of light travel time per tick in the frame of reference in which the train tracks are at rest? Doing so would mean that the beam travels a distance of one metre in the frame in which the tracks are at rest. To the people on board the train this means calibrating the clock so that it ticks once every $\frac{1}{1.2}$ metre of light travel time, or once every $\frac{10}{12}$ of a metre of light travel time. To get it to do this they will have to shorten the height of the clock to $\frac{10}{12}$ metres.

Nope, the path length will be $\frac{10}{12}$ metres on board the train as measured by observers on the train, one metre as measured by observers at rest on the tracks..

No, it's the vertical distance of $\frac{10}{12}$ metres that is the same in both frames, but it's the same only because it's a distance measured perpendicular to the direction the train is moving.

Last edited: Nov 1, 2015
14. Nov 1, 2015

bahamagreen

There is still confusion about the terms "tick", "clock", and now "path length" because no one seems to be understanding the OP's question.

The OP is defining a "tick" as the mark between the periods of one meter light propagation; NOT the bouncing of the light off the mirrors.
The OP is defining a "clock" as the "ticks" defined above; NOT the light and mirrors configuration.

Both these definitions are based strictly on the invariance of c for all inertial frames.

As long as people are thinking that a "tick" must be mirror contacts and a "clock" must be based on mirror contact ticks (and complete path length between the mirrors), then the OP's question won't be grasped, much less answered.

I think DAC is wanting to know the reasoning behind choosing the usual light clocks ticks (path length between mirror contacts) when the "c clock" ticks (period of one meter propagation invariant for all frames) seems more appropriate for SR scenarios.

15. Nov 1, 2015

Staff: Mentor

DAC can comment and clarify his question, but such a device as you describe does not seem possible to build. We talk about the usual "ticks" and mirror contacts because such a device is (in principle) possible to build. If you built such a device (as the standard light clock) then it would indeed be a clock that would keep accurate time in its rest frame, and it would indeed have time dilation in frames where it moves.

Even if DAC would like to talk about a different scenario, time dilation itself is clearly demonstrated by the standard scenario. Proposing different scenarios, particularly more complicated ones, is just a common way to try to avoid facing the conceptual challenge presented by the standard light clock. By making a more complicated scenario, the student avoids directly confronting the challenge of the simple scenario. The complications themselves add distractions from the core issues that the student then focuses on instead.

Last edited: Nov 1, 2015
16. Nov 1, 2015

DAC

17. Nov 1, 2015

Staff: Mentor

How? I cannot think of a possible mechanism.

The standard light clock mechanism is simple to understand and analyze. Even if you propose a different clock mechanism, it won't change any of the conclusions for the standard light clock.

18. Nov 1, 2015

DAC

[Q
Which is your one light path?
I am not querying the standard light clock. I understand it. I am however offering a what if the clock were different

19. Nov 1, 2015

DAC

OK. If a clock were to tick over once for every one metre travelled why wouldn't it be the same in both frames, given one metre ( perpendicular distance between mirrors ), is the same in both frames.

20. Nov 1, 2015

Staff: Mentor

Please describe the actual mechanism of your different clock. Let's call it the DAC clock.