# Stopped Clock Paradox - Analysis
**URL:** https://www.ilovephilosophy.com/t/stopped-clock-paradox-analysis/37079
**Category:** Science, Technology, and Math
**Created:** [October 13, 2013, 7:57pm UTC](https://www.ilovephilosophy.com/t/stopped-clock-paradox-analysis/37079 "2013-10-13T19:57:04Z")
**Posts on this page:** 20
**Page:** 3
### Author:  [@James\_S\_Saint](https://www.ilovephilosophy.com/u/James_S_Saint)
#### Post date: [October 16, 2013, 9:10pm UTC](https://www.ilovephilosophy.com/t/stopped-clock-paradox-analysis/37079/41 "2013-10-16T21:10:45Z")
PhysBang, you seem to be misunderstanding a couple of things.
There is this process of synchronization that uses a light sphere in order to ensure SR synchronization. So to syncronize all clocks while still stationary;
1. set the train clock to zero (or actually any clock)
2. calculate the amount of time required for light to get to each other clock
3. advance each other clock to pre-read your calculation, but do not start any clock yet.
4. start the train clock and have it send light out toward all other clocks
5. Start each clock as that light reaches each one.
In that way, you are certain that all clocks will be synchronized to properly reflect the speed of light for the frame that you are in, in this case, the station’s and train’s.
What you don’t seem to be catching is that
A) each engine begins at exactly the same time based upon their own synchronized clocks.
B) They each apply the exact same thrust to the rails below them.
C) And thus they each accelerate at exactly the same rate up to the exact same speed.
So from the point of view of the station, the distance between those engines has no choice but to remain the same. Relativity doesn’t say anywhere that just because one engine is a mile away and the other is 2 miles away, the more distant one requires any different force on it so as to accelerate up to the same speed as the one at 1 mile away. That would be pretty silly.
In our case, we have a “rubber car” attached to each engine with our “train clock” centered. So from the station’s perspective, the length from the rear engine to the train clock to the front engine must remain exactly as it was before the engine began moving. No length contraction.
---
### Author:  [@phyllo](https://www.ilovephilosophy.com/u/phyllo)
#### Post date: [October 16, 2013, 9:30pm UTC](https://www.ilovephilosophy.com/t/stopped-clock-paradox-analysis/37079/42 "2013-10-16T21:30:12Z")
From the frame of reference of the train, the train is getting longer because of stretching rubber.
The force on front and rear are not equal.
Is there any point at all to this bizarre setup?
---
### Author:  [@James\_S\_Saint](https://www.ilovephilosophy.com/u/James_S_Saint)
#### Post date: [October 16, 2013, 9:46pm UTC](https://www.ilovephilosophy.com/t/stopped-clock-paradox-analysis/37079/43 "2013-10-16T21:46:13Z")
> [@phyllo](#):
>
> From the frame of reference of the train, the train is getting longer because of stretching rubber.
>
> The force on front and rear are not equal.
>
> Is there any point at all to this bizarre setup?
What do you mean that it is not equal???
The rubber car isn’t to be so strong as to pull the train together, merely strong enough to support a stop-clock in the center, maybe a couple of bungie cords.
And I already gave the reason I set it up that way .
---
### Author:  [@phyllo](https://www.ilovephilosophy.com/u/phyllo)
#### Post date: [October 16, 2013, 10:03pm UTC](https://www.ilovephilosophy.com/t/stopped-clock-paradox-analysis/37079/44 "2013-10-16T22:03:45Z")
Pretty simple. Rubber won’t stretch unless it has a unbalanced force applied to it.
While you think that the train has not compressed…
In the train frame, the train is longer and the station is still compressed as before.
The point of all this??
---
### Author:  [@James\_S\_Saint](https://www.ilovephilosophy.com/u/James_S_Saint)
#### Post date: [October 16, 2013, 10:26pm UTC](https://www.ilovephilosophy.com/t/stopped-clock-paradox-analysis/37079/45 "2013-10-16T22:26:11Z")
> [@phyllo](#):
>
> Pretty simple. Rubber won’t stretch unless it has a unbalanced force applied to it.
>
> While you think that the train has not compressed…
> In the train frame, the train is longer and the station is still compressed as before.
>
> The point of all this??
Pretty simple.
The rubber never stretches any more than it started, because the distance never changes.
The train’s reference frame, both engines together with the rubber and the train clock, does not perceive any change in their own distance. As far as they are concerned, the rail track is moving under them, not them.
The station perceives that both train engines, rubber, and train clock accelerate identically up to the exact same speed. Thus the station doesn’t perceive any change in distance either.
No length contraction of the “train” from either perspective.
That is the point.
---
### Author:  [@phyllo](https://www.ilovephilosophy.com/u/phyllo)
#### Post date: [October 16, 2013, 10:58pm UTC](https://www.ilovephilosophy.com/t/stopped-clock-paradox-analysis/37079/46 "2013-10-16T22:58:23Z")
There is no free lunch.
If the rubber didn’t stretch then there would be no point in placing it there. The rubber would not stretch unless there was unequal motion on either side of it. There is no unequal motion without unequal acceleration. There is no unequal acceleration without unequal force.
---
### Author:  [@James\_S\_Saint](https://www.ilovephilosophy.com/u/James_S_Saint)
#### Post date: [October 17, 2013, 12:39am UTC](https://www.ilovephilosophy.com/t/stopped-clock-paradox-analysis/37079/47 "2013-10-17T00:39:12Z")
So you agree that the rubber is not going to stretch any more than it was already and to the station, the distance between the two engines will remain constant?
---
### Author:  [@James\_S\_Saint](https://www.ilovephilosophy.com/u/James_S_Saint)
#### Post date: [October 17, 2013, 1:05am UTC](https://www.ilovephilosophy.com/t/stopped-clock-paradox-analysis/37079/48 "2013-10-17T01:05:36Z")
So then if the rubber never stretches or compresses, why make it rubber?
Why not use steel?
And if you use steel, why not just use the original train car?
And while we’re at it, why not just make the whole thing just a long car with “4-wheel drive”, front and rear.
… and still no length contraction.
But then if the train length isn’t contracting, why should the station length contract?
---
### Author:  [@phyllo](https://www.ilovephilosophy.com/u/phyllo)
#### Post date: [October 17, 2013, 1:27am UTC](https://www.ilovephilosophy.com/t/stopped-clock-paradox-analysis/37079/49 "2013-10-17T01:27:35Z")
I’m just going to leave now while I still have my sanity.
Rubber train. 
---
### Author:  [@James\_S\_Saint](https://www.ilovephilosophy.com/u/James_S_Saint)
#### Post date: [October 17, 2013, 1:28am UTC](https://www.ilovephilosophy.com/t/stopped-clock-paradox-analysis/37079/50 "2013-10-17T01:28:21Z")
> [@phyllo](#):
>
> I’m just going to leave now while I still have my sanity.
>
> Rubber train. 
Come on now. We’re making progress.
---
### Author:  [@James\_S\_Saint](https://www.ilovephilosophy.com/u/James_S_Saint)
#### Post date: [October 17, 2013, 5:45am UTC](https://www.ilovephilosophy.com/t/stopped-clock-paradox-analysis/37079/51 "2013-10-17T05:45:22Z")
While you’re mulling that one over, here is something else.
Back when the train was standing still and the clocks were synchronized, the engines had timers on them, counted as clocks, that were also synchronized so that the engines would know when to start. And what if those timers kept running?
Again, we have a situation wherein there is equality of state, equality of treatment, and equality of result. Each clock/timer on the train is accelerated identically. There is no means for them to get out of sync. The fact that one is further from some station up the track certainly can’t cause that timer to become different than the other. So the station knows that even though those three clocks/timers might read differently than its own, they cannot be reading differently than each other. It doesn’t matter what they might look like as they pass by at half the speed of light, because the station knows that regardless of perception, they absolutely must be reading the same (assuming nothing else has interfered).
So when the train stop-clock becomes aligned with the station clock, whatever time it reads is what both timers must be reading as well. And whatever that time happens to be (precalculated), is what triggers the flashers. So the station can know that the flashers really have gone off simultaneously simply because there is no logical option. That was the original Stopped Clock Paradox scenario.
So now we have two independent means to ensure that the flashers cannot be out of sync with each other and really are “simultaneous”; timers and side track arms set at the length of the train, by either perspective. And we didn’t even have to see/perceive anything in order to know it. There is no alternative.
So now we are back to the original anime.
Both the train AND the station know without doubt that the flashers really have to be going off together, simultaneously, and have two means to verify it. So what are they REALLY going to perceive?
A) Station clock stops
B) Train clock stops
C) Both clocks stop
D) Neither clock stops
E) The universe ends and we wake up
---
### Author:  [@PhysBang](https://www.ilovephilosophy.com/u/PhysBang)
#### Post date: [October 17, 2013, 4:09pm UTC](https://www.ilovephilosophy.com/t/stopped-clock-paradox-analysis/37079/52 "2013-10-17T16:09:41Z")
> [@James S Saint](#):
>
> In that way, you are certain that all clocks will be synchronized to properly reflect the speed of light for the frame that you are in, in this case, the station’s and train’s.
Reference frames do not belong to objects. We can speak of the (though there are really infinitely many) reference frame in which the station is at rest (in a given direction) and the reference frame in which the train is at rest. However, in this case, we also consider a number of different reference frames in which the train is momentarily at rest, since the train is accelerating.
> [@](#):
>
> What you don’t seem to be catching is that
> A) each engine begins at exactly the same time based upon their own synchronized clocks.
> B) They each apply the exact same thrust to the rails below them.
> C) And thus they each accelerate at exactly the same rate up to the exact same speed.
I assume that you mean to apply this description in the reference frame in which the station is at rest.
> [@](#):
>
> So from the point of view of the station, the distance between those engines has no choice but to remain the same.
Except that in SR, we know that, regardless of the amount of engines on the train, the train contracts. In the reference frame in which the station is at rest, some of the energy applied by the engine goes into the electromagnetic forces between the molecules of the train. After all, a leading engine does pull the train and a trailing engine does push the train; this force must be transmitted in some manner.
> [@](#):
>
> Relativity doesn’t say anywhere that just because one engine is a mile away and the other is 2 miles away, the more distant one requires any different force on it so as to accelerate up to the same speed as the one at 1 mile away. That would be pretty silly.
But a change in reference frame may change when we claim that an object is a given distance away from another object. So what force is applied when differs in different reference frames. Look at the Lorentz transformations and notice the presence of the spatial coordinate in the transformations.
> [@](#):
>
> In our case, we have a “rubber car” attached to each engine with our “train clock” centered. So from the station’s perspective, the length from the rear engine to the train clock to the front engine must remain exactly as it was before the engine began moving. No length contraction.
So you are stipulating that the properties of the rubber are exactly that to give way enough to exactly counter the length contraction experienced by the train at the speeds of the example. Fine. This means that, in a reference frame co-moving with the train, the “moving” train gets longer as it goes down the track.
---
### Author:  [@PhysBang](https://www.ilovephilosophy.com/u/PhysBang)
#### Post date: [October 17, 2013, 4:20pm UTC](https://www.ilovephilosophy.com/t/stopped-clock-paradox-analysis/37079/53 "2013-10-17T16:20:30Z")
> [@James S Saint](#):
>
> Again, we have a situation wherein there is equality of state, equality of treatment, and equality of result. Each clock/timer on the train is accelerated identically. There is no means for them to get out of sync.
Except what we expect from SR. Run the numbers and see if you can verify that the clocks remain in sync given the definition of remaining in sync. (Hint: see section 2 of “On the Electrodynamics of Moving Bodies”.) Bear in mind when you claim that they read as they do. This is something dependent upon choice of reference frame.
So if the clocks do remain synchronized in the frame of reference in which the station is at rest, what relationship do they bear to events in the frame in which the train, after all accelerations, is at rest?
> [@](#):
>
> So when the train stop-clock becomes aligned with the station clock, whatever time it reads is what both timers must be reading as well. And whatever that time happens to be (precalculated), is what triggers the flashers. So the station can know that the flashers really have gone off simultaneously simply because there is no logical option. That was the original Stopped Clock Paradox scenario.
Except that you have not yet described what happens in the reference frame in which the train is at rest.
> [@](#):
>
> So now we have two independent means to ensure that the flashers cannot be out of sync with each other and really are “simultaneous”; timers and side track arms set at the length of the train, by either perspective. And we didn’t even have to see/perceive anything in order to know it. There is no alternative.
Yes, you have a test that we know, because of muon decay, must fail.
Just assign numbers to the example and show us the transformations. Better yet, go to some other forum where you have posted this and show us the numbers someone else gave you.
---
### Author:  [@James\_S\_Saint](https://www.ilovephilosophy.com/u/James_S_Saint)
#### Post date: [October 17, 2013, 5:43pm UTC](https://www.ilovephilosophy.com/t/stopped-clock-paradox-analysis/37079/54 "2013-10-17T17:43:56Z")
Are you seriously suggesting that I can apply an SR formula to engine1 to calculate a distance traveled and then apply the exact same formula to an identical engine2 to calculate a distance traveled, and I will get a different distance traveled for them?
Show us that operation, if you will. “Do the math”.
---
### Author:  [@PhysBang](https://www.ilovephilosophy.com/u/PhysBang)
#### Post date: [October 17, 2013, 8:43pm UTC](https://www.ilovephilosophy.com/t/stopped-clock-paradox-analysis/37079/55 "2013-10-17T20:43:13Z")
> [@James S Saint](#):
>
> Are you seriously suggesting that I can apply an SR formula to engine1 to calculate a distance traveled and then apply the exact same formula to an identical engine2 to calculate a distance traveled, and I will get a different distance traveled for them?
The relative order of some events, and the duration between these events, differs between reference frames in SR. You talk as if something that is simultaneous in one frame is simultaneous in all frames.
> [@](#):
>
> Show us that operation, if you will. “Do the math”.
As soon as you assign a velocity to the train and fill in some of the other details of your scenario, then we can go carefully through the example.
Or we could use the numbers from here: [physicsforums.com/showthread.php?t=580632](http://www.physicsforums.com/showthread.php?t=580632)
---
### Author:  [@James\_S\_Saint](https://www.ilovephilosophy.com/u/James_S_Saint)
#### Post date: [October 17, 2013, 9:03pm UTC](https://www.ilovephilosophy.com/t/stopped-clock-paradox-analysis/37079/56 "2013-10-17T21:03:25Z")
> [@PhysBang](#):
>
> > [@James S Saint](#):
> >
> > Are you seriously suggesting that I can apply an SR formula to engine1 to calculate a distance traveled and then apply the exact same formula to an identical engine2 to calculate a distance traveled, and I will get a different distance traveled for them?
>
> The relative order of some events, and the duration between these events, differs between reference frames in SR. You talk as if something that is simultaneous in one frame is simultaneous in all frames.
Did I say anything about multiple frames?
If I apply a formula for acceleration (dictating future location) to a mass, I end up with a distance, an “amount of change in location”.
You are suggesting that if I apply that same formula to a different mass of the same size, I will get a different distance.
Please show us your formula for that.
> [@PhysBang](#):
>
> > [@](#):
> >
> > Show us that operation, if you will. “Do the math”.
>
> As soon as you assign a velocity to the train and fill in some of the other details of your scenario, then we can go carefully through the example.
I gave you exact details of the initial state and even how it got to be at that state (the light-sphere synchronization). Velocity = 0 for all participants = one frame of reference.
You can choose any force you like so as to accomplish whatever acceleration you like, as long as you use the same force value for both cases.
Show us how the distance traveled by engine1 is different than the distance traveled by engine2.
---
### Author:  [@PhysBang](https://www.ilovephilosophy.com/u/PhysBang)
#### Post date: [October 17, 2013, 9:53pm UTC](https://www.ilovephilosophy.com/t/stopped-clock-paradox-analysis/37079/57 "2013-10-17T21:53:50Z")
> [@James S Saint](#):
>
> > [@PhysBang](#):
> >
> > > [@James S Saint](#):
> > >
> > > Are you seriously suggesting that I can apply an SR formula to engine1 to calculate a distance traveled and then apply the exact same formula to an identical engine2 to calculate a distance traveled, and I will get a different distance traveled for them?
> >
> > The relative order of some events, and the duration between these events, differs between reference frames in SR. You talk as if something that is simultaneous in one frame is simultaneous in all frames.
>
> Did I say anything about multiple frames?
Yes, yes you did. Anyone who can read can see your writing above, “… an SR formula…” To what do you think SR formulas apply, if not to changes between frames?
> [@](#):
>
> I gave you exact details of the initial state and even how it got to be at that state (the light-sphere synchronization). Velocity = 0 for all participants = one frame of reference.
Yet again you dodge the question. What is so bad about trying to give a decent physical scenario?
I suppose if I have the time, then I will use the numbers from here: [physicsforums.com/showthread.php?t=580632](http://www.physicsforums.com/showthread.php?t=580632)
---
### Author:  [@James\_S\_Saint](https://www.ilovephilosophy.com/u/James_S_Saint)
#### Post date: [October 17, 2013, 9:58pm UTC](https://www.ilovephilosophy.com/t/stopped-clock-paradox-analysis/37079/58 "2013-10-17T21:58:50Z")
> [@James S Saint](#):
>
> PhysBang, you seem to be misunderstanding a couple of things.
>
> There is this process of synchronization that uses a light sphere in order to ensure SR synchronization. So to synchronize all clocks while still stationary;
>
> 1. set the train clock to zero (or actually any clock)
> 2. calculate the amount of time required for light to get to each other clock
> 3. advance each other clock to pre-read your calculation, but do not start any clock yet.
> 4. start the train clock and have it send light out toward all other clocks
> 5. Start each clock as that light reaches each one.
>
> In that way, you are certain that all clocks will be synchronized to properly reflect the speed of light for the frame that you are in, in this case, the station’s and train’s.
>
> What you don’t seem to be catching is that
> A) each engine begins at exactly the same time based upon their own synchronized clocks.
> B) They each apply the exact same thrust to the rails below them.
> C) And thus they each accelerate at exactly the same rate up to the exact same speed.
>
> So from the point of view of the station, the distance between those engines has no choice but to remain the same. Relativity doesn’t say anywhere that just because one engine is a mile away and the other is 2 miles away, the more distant one requires any different force on it so as to accelerate up to the same speed as the one at 1 mile away. That would be pretty silly.
>
> In our case, we have a “rubber car” attached to each engine with our “train clock” centered. So from the station’s perspective, the length from the rear engine to the train clock to the front engine must remain exactly as it was before the engine began moving. No length contraction.
Do you need it in braille?
---
### Author:  [@PhysBang](https://www.ilovephilosophy.com/u/PhysBang)
#### Post date: [October 18, 2013, 1:12am UTC](https://www.ilovephilosophy.com/t/stopped-clock-paradox-analysis/37079/59 "2013-10-18T01:12:19Z")
> [@James S Saint](#):
>
> Do you need it in braille?
It would be nice if you would look at the actual responses to your wild claims before simply repeating them and dodging important questions.
Let’s look, yet again, at the specific passages that you colored in blue:
> [@James S Saint](#):
>
> So to synchronize all clocks while still stationary;
That clocks are synchronized while stationary is not a guarantee that they remain synchronized. In your fantasy physics, this may be the case, but experiment reveals that your fantasy physics doesn’t match reality.
> [@](#):
>
> In that way, you are certain that all clocks will be synchronized to properly reflect the speed of light for the frame that you are in, in this case, the station’s and train’s.
Again, that clocks are synchronized while stationary is not a guarantee that they remain synchronized. In your fantasy physics, this may be the case, but experiment reveals that your fantasy physics doesn’t match reality.
> [@](#):
>
> A) each engine begins at exactly the same time based upon their own synchronized clocks.
> B) They each apply the exact same thrust to the rails below them.
> C) And thus they each accelerate at exactly the same rate up to the exact same speed.
In the reference frame of the station. This is not the case in other reference frames, e.g., the reference frame in which the train, after all force is applied, is at rest.
> [@](#):
>
> So from the point of view of the station, the distance between those engines has no choice but to remain the same.
Unless there is something you are missing: e.g. length contraction.
> [@](#):
>
> In our case, we have a “rubber car” attached to each engine with our “train clock” centered. So from the station’s perspective, the length from the rear engine to the train clock to the front engine must remain exactly as it was before the engine began moving. No length contraction.
Except that there is length contraction, because the train is actually stretching as it moves.
If you want to do this all in standard Newtonian mechanics, then fine. If you want to know what SR says will happen, then use SR. If you want to introduce some fantasy physics, then give us the details in advance on how to do a problem in physics with your fantasy physics.
---
### Author:  [@James\_S\_Saint](https://www.ilovephilosophy.com/u/James_S_Saint)
#### Post date: [October 18, 2013, 2:03am UTC](https://www.ilovephilosophy.com/t/stopped-clock-paradox-analysis/37079/60 "2013-10-18T02:03:20Z")
PhysBang, I’m not seeing any of your equations, which has convinced me that you don’t have any.
Deferring me over to your church doesn’t help. I am well aware of what your church preaches, “Believe, have faith, and burn the heretics”. I’ve seen it all before.
And this is an example;
> [@PhysBang](#):
>
> Except that there is length contraction, because the train is actually stretching as it moves.
The miracle of contraction through stretching. Except I don’t see any “stretching” in their rituals. Maybe they should study a little yoga.
PhysBang, I don’t care if you want to have faith in that church. Such things are up to you. But how about stop calling it “Science”.
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