Undergrad Understanding Light Clock Confusion on Moving Trains - A Discussion

[Herman Trivilino]

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.

 

[Herman Trivilino]

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.

 

[Dale]

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.

If I want to build a light clock I can give a list of components to my purchasing department and a list of assembly instructions to my machine shop. Your DAC clock is impossible, or it doesn't work the way you think it does.

Please provide a list of parts and assembly/operation instructions like this:

1 meter rod
1 light source
1 light sensor
1 mirror
1 counter

Mount the mirror on one end of the 1 meter rod. Mount the source, sensor, and counter on the opposite end. Flash a light pulse from the source. Wait to detect the reflection from the mirror back to the sensor. On sensing the pulse immediately flash another and increment the counter by 2/299792458 s.

 

[Herman Trivilino]

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 the light beam hitting the sensor before it hits the mirror.

I'm trying to figure out what it is you want out of this conversation. Do you plan to simply make assertions that contradict fact until you happen to hit upon one that we agree with, thus giving you the confirmation that you seek?

We respond to every one, explaining that it's wrong. You ignore salient portions of those explanations.

We respond to every one, asking for clarification. You ignore salient portions of those requests.

Do you see that your strategy is not headed along a path to success? You'll not get us to agree with erroneous propositions, so if you don't want to listen to our responses, and you don't want to comply with our requests, it seems this conversation serves no purpose for anyone other than to sharpen the skills of those refuting your propositions.

So, do you have a meaningful response to DaleSpam's request for a design, or to my explanation of why your clock won't do what you want it to do?

The fact of the matter is that the standard analysis of the light clock leads to a prediction that matches the way real clocks behave. Your analysis of the DAC clock leads to a prediction that doesn't match the way real clocks behave. So even if you somehow find a flaw in the analysis of the light clock, any correction to the analysis will have to give the same correct result that we have now, a result that matches the way real clocks behave. And any correction to the analysis of the DAC clock will have to meet the same criterion. Otherwise, why would anyone be interested in the analysis of a hypothetical clock that behaves in way that's significantly different from the way real clocks behave?

 

[DAC]

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..

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.

Yes the moving frame is longer. No it doesn't take longer to tick over, when it ticks over every one metre.

 

[Herman Trivilino]

Yes the moving frame is longer. No it doesn't take longer to tick over, when it ticks over every one metre.

If the distance is longer, the time taken to travel that distance is longer. Because the speed of light is the same in both cases.

 

[DAC]

If I want to build a light clock I can give a list of components to my purchasing department and a list of assembly instructions to my machine shop. Your DAC clock is impossible, or it doesn't work the way you think it does.

Please provide a list of parts and assembly/operation instructions like this:

1 meter rod
1 light source
1 light sensor
1 mirror
1 counter

Mount the mirror on one end of the 1 meter rod. Mount the source, sensor, and counter on the opposite end. Flash a light pulse from the source. Wait to detect the reflection from the mirror back to the sensor. On sensing the pulse immediately flash another and increment the counter by 2/299792458 s.

If the one metre light clock is " impossible " , then my enquiry has run its course and we can leave it at that.
Regards.

 

[bahamagreen]

Maybe not a mechanism, but a procedure?

From the 1905 paper, Einstein:
We imagine further that at the two ends A and B of the rod, clocks are placed which synchronize with the clocks of the stationary system, that is to say that their indications correspond at any instant to the “time of the stationary system” at the places where they happen to be. These clocks are therefore “synchronous in the stationary system.”

EA is imagining these indicator clocks in the moving system to instantaneously and continuously synchronize with their location mates in the stationary system.

Instead of the locations of the moving rod ends A and B we let the presence of the light ray trigger an indication from the stationary clocks, does this procedure enable what we are calling sensors? Seems the stationary clocks would be sufficient to provide a stationary observer with time and location information to determine when the light emitted in any moving system has propagated one meter in the stationary system.

The basis of the DAC Clock is to be able to do just that... determine the length of light travel using the “time of the stationary system”.

 

[Herman Trivilino]

The basis of the DAC Clock is to be able to do just that... determine the length of light travel using the “time of the stationary system”.

Yup, and as I showed it gives the same result as the conventional light clock. The only problem is that DAC refuses to face the conceptual difficulties associated with understanding that.

 

[bahamagreen]

So can we summarize that the moving observer will not agree with the stationary observer that the indicator clocks of the stationary system are synchronized and that this applies to DAC clocks, conventional light clocks, any clocks?

Also, relativity of simultaneity seems to be derived from time and distance measures... is it a separate thing from time dilation and length contraction, or is it the result of them, or is it the cause of them?

 

[Nugatory]

Also, relativity of simultaneity seems to be derived from time and distance measures... is it a separate thing from time dilation and length contraction, or is it the result of them, or is it the cause of them?

It is the cause of them.
-The length of an object is the distance between where one end of the object is and where the other end is at the same time.
-Your time is dilated relative to mine when at the same time that my clock reads something, your previously synchronized clock reads something less.

Both concepts depend on simultaneity (we used the words "at the same time" above) so relativity of simultaneity means that different observers disagreeing about simultaneity will also disagree about length and elapsed time.

 

[Dale]

If the one metre light clock is " impossible " , then my enquiry has run its course and we can leave it at that.

OK. If you figure out how you would build a DAC clock, then please open a new thread with the proposed design. We can help you analyze it and understand why it would be subject to time dilation.

Thread closed.