Time dilation and 2 identical clocks

[Ross Arden]

Hi

Couldnt figure this out

U have 2 identical clocks where a pulse of light goes from a light source (a), reflects off a mirror (b) and goes to the end (c)

A person is stationary wrt one clock and another clock is in a spaceship moving, relative to the observer, in the direction v at velocity v

The clock in the spaceship is shown at time t1, t2 and t3

Theory says the observer should see the clock in the spaceship ticking slower than the clock at rest wrt the observer.

If the height of the clock is H and its length is L the observer will deduce the clock in the spaceship ticks at 2H/c. The observer will deduce the stationary clock will tick at some time greater than 2H/c ...is that right?

 

[Ibix]

You can't make a clock with a pendulum that swings one way and then stops. So that isn't a clock, unless you put a mirror at point c so that the light comes back to point a, in which case more analysis of the return tick is needed.

If you aren't aware of the relativity of simultaneity, you should google that term.

 

[Ross Arden]

its not a pendulum clock!

 

[Ross Arden]

there is no pendulum in an hour glass

 

[Ibix]

its not a pendulum clock!

It's not a clock full stop, unless it has a mirror at c. It doesn't complete a cycle so there's no way to compare any other clock to it without invoking a simultaneity convention.

there is no pendulum in an hour glass

True. But it measures one unit of time at a point (the neck of the glass). If you want to measure any more than that you need to turn it over, then turn it over, then turn it over. And there you have your cyclic motion.

Your design does not measure time at a point because a and c are not co-located. So it doesn't work as a sand timer since it mixes up space and time, and interpreting its results depends on your simultaneity convention (did you google the relativity of simultaneity?). And it doesn't work as a regular clock because it doesn't cycle.

 

[Sorcerer]

Ibix, what you're saying is that it only works as a clock if the start of the cycle ends at the same location in space with respect to the person using it to measure time, correct?

 

[PeroK]

Hi

Couldnt figure this out

U have 2 identical clocks where a pulse of light goes from a light source (a), reflects off a mirror (b) and goes to the end (c)

A person is stationary wrt one clock and another clock is in a spaceship moving, relative to the observer, in the direction v at velocity v

The clock in the spaceship is shown at time t1, t2 and t3

Theory says the observer should see the clock in the spaceship ticking slower than the clock at rest wrt the observer.

If the height of the clock is H and its length is L the observer will deduce the clock in the spaceship ticks at 2H/c. The observer will deduce the stationary clock will tick at some time greater than 2H/c ...is that right?

Ah, I see what you have done. The light clock is supposed to fire light vertically upwards and be reflected vertically back down. This is what happens when the clock is at rest with respect to an observer. The distance traveled by the light is $2H$; hence the time for an up and down light trip is $2H/c$.

But, if the light clock is moving with respect to an observer, then the light will travel in a triangle, hence further. And, since the speed of light is invariant, this will take longer and the observer will conclude that the moving light clock is running slow.

But, to an observer moving with the light clock, the light will be going up and down vertically and the clock will be running normally.

 

[Ibix]

Ibix, what you're saying is that it only works as a clock if the start of the cycle ends at the same location in space with respect to the person using it to measure time, correct?

Yes - that's a clearer way to phrase it. So you can just about get away with calling a sand timer a clock because you can talk about the proper time between the events of the sand starting to slide through the neck of the glass and finishing sliding through. You can also talk about the proper time between the events "light leaves a" and "light arrives at c", but this doesn't correspond to the proper time of anyone at rest with respect to the device.

So I suppose one could argue that it's a clock (in the narrow sense of a one-shot sand timer) for a very specific observer, one who happens to be passing a at the time the light is emitted and happens to be passing c at the time the light is received. And time dilation will work out as usual if this frame is used as the rest frame. But that's a bit odd - that isn't the rest frame of the device.

On balance, I stand by "that is not a clock". A lot of highly specific caveats must apply to regard it as a clock.

 

[Sorcerer]

As suspected. Then, correct me if I'm wrong, it makes no sense to talk about measuring time unless you are either next to both the clock and the event or have some means of synchronization with the clock that is next to the event. In other words the interval of space through which the event transpires should be zero as you measure the time (unless there is some method of synchronization).

Nor does it make any sense to talk about a length unless the interval of time through which the object moves is zero as you measure the length (unless you again have some method of synchronization).

Yes? No? In the ball park?

 

[Herman Trivilino]

As suspected. Then, correct me if I'm wrong, it makes no sense to talk about measuring time unless you are either next to both the clock and the event or have some means of synchronization with the clock that is next to the event. In other words the interval of space through which the event transpires should be zero as you measure the time (unless there is some method of synchronization).

If two events occur at the same location then the time that elapses between them is called a proper time. To an observer moving relative to these two events they will of course not occur in the same place. He can measure the time that elapses between them, but he will need two clocks, one at the location of the first event and one at the location of the second event. If he synchronizes them (this is where the convention that @Ibix mentioned comes in) then he will indeed be able to measure the time that elapses between them, and he will find that elapsed time to be larger than the proper time. This is what's called time dilation.

The twist is that to an observer present at both events those two clocks that the moving observer uses will not be properly synchronized.

 

[Ross Arden]

It's not a clock full stop, unless it has a mirror at c. It doesn't complete a cycle so there's no way to compare any other clock to it without invoking a simultaneity convention.
True. But it measures one unit of time at a point (the neck of the glass). If you want to measure any more than that you need to turn it over, then turn it over, then turn it over. And there you have your cyclic motion.

Your design does not measure time at a point because a and c are not co-located. So it doesn't work as a sand timer since it mixes up space and time, and interpreting its results depends on your simultaneity convention (did you google the relativity of simultaneity?). And it doesn't work as a regular clock because it doesn't cycle.

the purpose of a clock is to measure time whether that be eternity or cooking an egg ... in the scenario I depicted the egg timer in the spaceship would time the cookig of the egg faster than the egg time external to the space ship...is that right?

 

[Ross Arden]

there are many natural, and probably unnatural, phenomena that can be used to measure time, ie the rotation of a neutron star, atomic phenomena, but do not have a feed back loop such as a pendulum. Where it is cast in stone that a device used to measure time must have a "feed back" mechanism such as a pendulum?

another one would be the half life of radioactive materials, time measurement with no feed back mechanism

In the scenario I depicted even if there was only one tick of the clock, say the guy doing the experiment was testing the clock to see if it worked. Even after only a single "tick" of the clock they would have to conclude the clock in the spaceship was going to run fast

 

[Ibix]

the purpose of a clock is to measure time whether that be eternity or cooking an egg ... in the scenario I depicted the egg timer in the spaceship would time the cookig of the egg faster than the egg time external to the space ship...is that right?

You can't use the setup described in your OP to time an egg. Let’s assume the pan is at the "start" end of your tube. You send out the light pulse and start cooking your egg. But when do you stop? It can't be when the light reaches the far end of the tube because you can't know when that happens. You must either have a real clock to tell you when you predict that the light pulse has reached the other end, or you must use a telescope to watch the far end and turn off the pan when you see the light arrive. In the first case your v-tube is not acting as a clock. In the second case you need to factor in the light travel time between "light arrives at end of tube" and "you see it arrive". In either case you will find normal time dilation applies.

there are many natural, and probably unnatural, phenomena that can be used to measure time

But all of these work at a single point and can be used as a clock at that point. Yours doesn’t, unless you add a telescope or some other kind of return leg, so you can't use it as a clock (at least, not in its rest frame) because you can't tell when the end of a tick happens.

 

[Ross Arden]

put the pan at the detector end of the tube. An egg timer is placed at the light source. Each time a grain of sand falls thru the egg time a light pulse is triggered. The egg timer has 500 grains of sand. A counter is placed at the pan. when the counter gets to 500 the heat is tuned off. the egg timer is oriented with the direction of movement of the space ship

If the experiment is conducted million of times the counter in the spaceship will turn off consistently quicker than the one external to the space ship

 

[Ibix]

put the pan at the detector end of the tube. An egg timer is placed at the light source. Each time a grain of sand falls thru the egg time a light pulse is triggered. The egg timer has 500 grains of sand. A counter is placed at the pan. when the counter gets to 500 the heat is tuned off. the egg timer is oriented with the direction of movement of the space ship

So you turn on the heat when you get the flash corresponding to "first grain falls" and turn it off when you get the flash corresponding to "last grain falls"? This is basically watching a standard egg-timer through a telescope. The egg-timer is the only clock in this setup.

 

[Ross Arden]

the counter located in the spaceship turns off/on the heat. As the timer in the spaceship turns off the heat early the egg in the spaceship is not fully cooked , where as the egg external to the spaceship is

l

 

[Ross Arden]

the set up external to the spaceship is identical to the setup internal to the spaceship

 

[Ibix]

I think you need to explain clearly where you have egg timers and where you have pans, and which ones are moving with the rocket and which ones are moving with the stick man.

 

[Ross Arden]

see pic

 

[Ross Arden]

the setup next to the stick man is identical, minus the rocket of course

 

[Ibix]

According to your illustration you have an egg timer, which sends light pulses down a tube to a cooker which remains on as long as pulses continue to arrive.

There is no clock here except for the egg timer.

Ditto the setup outside. Both eggs will cook; both observers will claim the other one cooked slower.

 

[Ibix]

I invite you to do the full Lorentz transforms if you think otherwise.

 

[Ross Arden]

the egg timer send pulses, the pulses are counted, the cooker starts at the first pulse and turns off at the 500th pulse on the counter. So the cooker in the spaceship starts before the cooker stationary wrt to the stick man. And, the cooker in the spaceship turns off before the cooker stationary wrt to the stick man.

 

[Ross Arden]

first you would need to prove that a LT was the appropriate analysis of this system, as there is no feed back

 

[Ibix]

first you would need to prove that a LT was the appropriate analysis of this system, as there is no feed back

Are you seriously suggesting that this experiment isn't consistent with special relativity? If so, please read the rules on personal theories. If not, you don't seem to be following my verbal explanations of where you are going wrong, so the only thing I can do is suggest that you do the maths. Happy to help if you are having problems with it.

the egg timer send pulses, the pulses are counted, the cooker starts at the first pulse and turns off at the 500th pulse on the counter. So the cooker in the spaceship starts before the cooker stationary wrt to the stick man. And, the cooker in the spaceship turns off before the cooker stationary wrt to the stick man.

You need to use the Lorentz transforms to analyse this correctly.

 

[Nugatory]

first you would need to prove that a LT was the appropriate analysis of this system, as there is no feed back

I'm not understanding this comment. The Lorentz transformation is, by definition, the way get from the statement "Event E happened at position $x$ and time $t$ in one frame" to "Event E happened at position $x'$ and time $t'$ in this other frame". There's no feedback assumed or implied.

 

[Ibix]

Actually, you don't need the full Lorentz transforms. You simply observe that, in the rocket frame, the timer starts at t'=0 and finishes at t'=500, so the egg starts cooking at t'=T and finishes at t'=500+T, where $T=2\sqrt{L^2/4+H^2}/c$ in terms of the sizes given in #1. It's immediately obvious that if the normal time dilation formula applies to the timer's duration, the same scale factor applies to the cooking. You could, after all, add another egg timer beside the pan and start it when the cooker turns on. It'll run out just as the cooker turns off.

So either the standard time dilation formula does not work for any clock or it shows that the egg cooks exactly as I have been saying - both see the other's egg cooking slower.

 

[Ross Arden]

Are you seriously suggesting that this experiment isn't consistent with special relativity? If so, please read the rules on personal theories. If not, you don't seem to be following my verbal explanations of where you are going wrong, so the only thing I can do is suggest that you do the maths. Happy to help if you are having problems with it.
You need to use the Lorentz transforms to analyse this correctly.

I don't know how to do an LT

 

[Ross Arden]

the other interesting aspect of this is if the direction of the rocket is reversed the egg cooks slower!

 

[Ross Arden]

time dilation wrt the egg timer - as mentioned the egg timer is aligned with the direction of the rocket

also I have no allowed for length contraction of the egg timer