Understanding Light Clock Confusion on Moving Trains - A Discussion

[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.

EDIT: link to previous thread https://www.physicsforums.com/threads/light-clock-calibration.779163/

 

[Simon Bridge]

Please provide a link to the previous answers and explain what it was about those answers that you do not understand... otherwise you'll just get the same answers.

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

 

[Nugatory]

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.

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.

 

[Dale]

What happens if the clock is now calibrated to tick over each time the light travels one metre?

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.

 

[Vanadium 50]

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.

 

[Dale]

@DAC I have edited the thread title. Please PM me with a link to the previous thread so I can post it and reopen this thread.

EDIT: the link has been added to the OP and the thread is reopened.

 

[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 traveled 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.

 

[Dale]

Now install sensors at one metre centres along both light paths.

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?

 

[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.

 

[Dale]

One could install two sets of sensors, one in the track frame and one in the train frame

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".

 

[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.

 

[sweet springs]

Hi.
Let me understand exactly the situation you stated. Is is as drawn below?
http://i.stack.imgur.com/vcFOS.png
in
http://physics.stackexchange.com/qu...-perpendicular-to-the-direction-of-light-beam

 

[Mister T]

Hello PF.
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 1.2 metres apart, so the clock takes longer to tick over.

At that speed $\gamma=1.2$.

What happens if the clock is now calibrated to tick over each time the light travels one metre?

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.

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.

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..

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

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.

 

[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.

 

[Dale]

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.

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.

 

[DAC]

Hi.
Let me understand exactly the situation you stated. Is is as drawn below?
http://i.stack.imgur.com/vcFOS.png
in
http://physics.stackexchange.com/qu...-perpendicular-to-the-direction-of-light-beam

No, your diagram shows the standard light clock, but if you think of the clock ticking over, rather on mirror to mirror hits, but every one metre traveled by the light, then that is what I'm thinking.
Regards.

 

[Dale]

No, your diagram shows the standard light clock, but if you think of the clock ticking over, rather on mirror to mirror hits, but every one metre traveled by the light, then that is what I'm thinking.

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.

 

[DAC]

[Q

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?

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

 

[DAC]

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.

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

 

[Dale]

I am however offering a what if the clock were different

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

 

[Dale]

OK. If a clock were to tick over once for every one metre travelled

HOW?!? Simply repeating what you wish would happen does not help explain how. You are repeating your desire. I am asking for a design, not a desire.

 

[Mister T]

I am however offering a what if the clock were different

Not in any way that you've described. You want the light to keep traveling upward, ticking off one unit of time for every meter of distance it travels? And since the distance between ticks is one meter in both reference frames the time between ticks must also be the same in both frames because the speed of light is the same in both frames?

Is that what you're saying?

But the light won't travel the same distance in both frames. From the point of view of someone standing on the tracks, the light will have to travel along a diagonal line to hit each tick. The distance along the diagonal line is 1.2 meters, according to your original post. Everything I said in Post #13 will still apply.

If you do not agree, and you want us to understand what you're saying, you're going to need to post a diagram along with an explanation of what you're talking about.

 

[Dale]

For reference, a standard light clock would be described like this:

Mount a mirror on one end of a one meter bar. On the opposite end mount an emitter, detector, and counter. A pulse of light is emitted from the emitter, and when the reflection is detected another pulse is immediately emitted and the counter is incremented by 2/299792458.

That is what I am looking for in terms of level of description.

 

[DAC]

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

OK.
If the mirrors are one metre apart, the stationary frame will tick over every mirror to mirror which is the same as every one metre, so we are half way there

With motion the light's path changes, say it is now 1.1 metres. Why can't that 1.1 metres still be measured in one metre lengths as in the stationary frame?

As I have said before, it is where you place the sensors, every one metre, that matters.

 

[DAC]

Not in any way that you've described. You want the light to keep traveling upward, ticking off one unit of time for every meter of distance it travels? And since the distance between ticks is one meter in both reference frames the time between ticks must also be the same in both frames because the speed of light is the same in both frames?

Is that what you're saying?

But the light won't travel the same distance in both frames. From the point of view of someone standing on the tracks, the light will have to travel along a diagonal line to hit each tick. The distance along the diagonal line is 1.2 meters, according to your original post. Everything I said in Post #13 will still apply.

If you do not agree, and you want us to understand what you're saying, you're going to need to post a diagram along with an explanation of what you're talking about.

Thanks for your ( and everyones replies ).

Yes the light travels a longer distance but that doesn't affect a clock ticking over every one metre. It has further to go but at the same tick rate.

 

[DAC]

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.

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.

 

[DAC]

Your post is the closest yet

 

[DAC]

Thanks for your ( and everyones replies ).

Yes the light travels a longer distance but that doesn't affect a clock ticking over every one metre. It has further to go but at the same tick rate.

Not in any way that you've described. You want the light to keep traveling upward, ticking off one unit of time for every meter of distance it travels? And since the distance between ticks is one meter in both reference frames the time between ticks must also be the same in both frames because the speed of light is the same in both frames?

Is that what you're saying?

But the light won't travel the same distance in both frames. From the point of view of someone standing on the tracks, the light will have to travel along a diagonal line to hit each tick. The distance along the diagonal line is 1.2 meters, according to your original post. Everything I said in Post #13 will still apply.

If you do not agree, and you want us to understand what you're saying, you're going to need to post a diagram along with an explanation of what you're talking about.

See diagram below.

 

[jbriggs444]

As I read the drawing...

You have two long parallel mirrors some distance strictly less than one meter apart. You aim a laser into the gap between the mirrors and shoot a pulse of light in a direction chosen so that the distance between points of reflection is exactly one meter. You count a "tick" (of approximately 3 nanoseconds) each time the beam of light reflects from a mirror.

Is that what you are depicting?

When analyzing a train-track conundrum, this design has the problem that the aim angle used by the train clock will not match the aim angle used by the track clock when measured using the frame of reference of either track or train.

Edit: The angle of the laser gun can be calculated and will be the same for a train light clock as for a track light clock. The difference is that the trajectory of a train light pulse will not be measured in the track frame to follow a trajectory at the calculated angle. And vice versa.

 

[Dale]

As I have said before, it is where you place the sensors, every one metre, that matters.

How do you place the sensors to achieve this? In the standard light clock the sensor placement is clear, you use a rod of fixed length and place the mirror on one end and the emitter and sensor on the other end.

How are the sensors placed in the DAC clock? As you say, the sensor placement matters, so you must be able to specify a way to place them correctly. I cannot see a way to do it.

 

[Mister T]

See diagram below.

You posted this diagram in response to my request that you post a diagram and an explanation.

So, where is the explanation? People are still guessing at what your diagrams mean. To me it looks like the conventional light clock. The diagonal path still has a length of $1.2$ meters, and if you calibrate that clock in the way you described in your original post by inserting a sensor so that it ticks when the light beam moves a distance of $1.0$ m, as measured by an observer at rest on the tracks, the vertical component of the distance traveled by the light beam will be $\frac{10}{12}$ meters. So the analysis in Post #13 is still relevant. The only difference is that the people on the train, instead of reducing the mirror separation distance to $\frac{10}{12}$ meters, will insert a sensor a distance of $\frac{10}{12}$ meters above the lower mirror. If the people on the train want the clock to tick more than once they have a problem. They can insert another sensor below the first one so that by the time the beam moves another $\frac{10}{12}$ meters (having bounced off the upper mirror in the process) it will hit it, but before that it will hit the first sensor a second time, messing things up. I suppose they could remove that first sensor before that happens, and move it to the location where it needs to be for the third tick. And so on. None of that will change the analysis of Post #13.

Your diagram shows multiple sensors with some horizontal space between them. That diagram shows things from the perspective of an observer at rest on the tracks. But the sensors have no horizontal spacing in a frame of reference in which they are at rest. Each asterisk in your diagram is placed at the location where the beam will be after $1$ meter of light travel time, but observers on the train will measure that time to be $\frac{10}{12}$ meter of light travel time..

 

[DAC]

How do you place the sensors to achieve this? In the standard light clock the sensor placement is clear, you use a rod of fixed length and place the mirror on one end and the emitter and sensor on the other end.

How are the sensors placed in the DAC clock? As you say, the sensor placement matters, so you must be able to specify a way to place them correctly. I cannot see a way to do it.

 

[DAC]

In the stationary frame the sensors are placed each time light travels one metre. Which is the same as each time the light travels mirror to mirror. Do you agree?

In the moving frame we know the lights path is diagonal. The platform observer watching that path, and knowing one metre is one metre, ( perpendicular distance between mirrors ), marks out one metre lengths along the lights path.

 

[Janus]

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

That's the whole point. Assume you have two light clocks moving relative to each other. in each frame, for someone at rest with a particular clock that particular clock it takes a set time to tick once. If the mirrors are 1 meter apart then each tick of his clock is 1/299,792,458 of a second apart. But for that same person the light bouncing back and forth between the mirrors of the clock that is moving with respect to him travels a longer path at the same speed as the light travels between his clock's mirrors. Thus compared to his own light clock, the moving light clock ticks slower.

Here's an animation that illustrates what I mean (it also shows pulses bouncing back and forth between mirror separated along the line of motion, but we can ignore those for now as they were meant to show the need for length contraction.)
Each dot is a light pulse bouncing between mirror and in this situation the pulse start when the clocks are next to each other. This is to show how the dot bouncing back and forth between the "moving: clock moves at the same speed as the one bouncing back and forth between the stationary one, as shown by the expanding circle.

Note that as the pulses initially leaves at the start they both keep a constant distance from their point of origin. And by the time the pulse traveling straight down reaches the mirror the one on the diagonal has only gotten 1/2 the way to its mirror.

Thus in the frame from which this animation is shown the stationary clock goes from 0 to 1 in one round trip of the vertical pulse, and makes two round trips in the time it takes for the pulse bouncing between the moving mirrors once thus his clock goes from 0 to 2 in that time. Also keep in mind that for someone at rest with the clock shown as moving in this animation, it is his clock that is at rest with an identical clock with him will go from 0 to 1 in during 1 round trip. Thus a time period measured as 1 by the moving clock, is measured as 2 by the stationary clock.

It should also be pointed out that from the perspective of the clock shown as moving in this animation, it is the clock shown as stationary that is moving (from right to left) and that compared to his light clock it is the "stationary" clock in this animation that is running slow by a factor of 1/2.

In other words which clock is Moving and running slow depends on which clock you are at rest with respect to.

 

[Mister T]

In the stationary frame the sensors are placed each time light travels one metre. Which is the same as each time the light travels mirror to mirror. Do you agree?

No. Your diagram shows that the sensors are placed in between the mirrors, so that the beam of light hits the sensor before it hits the mirror. If those sensors are in between the mirrors in one frame, they'll be in between the mirrors in the stationary frame.