Time dilation explaination with mechanical clock instead of light clock

[R Power]

This page http://en.wikipedia.org/wiki/Time_dilation clearly explains time dilation by exampling with the light clock. But how can it be explained if suppose there was a simple mechanical clock instead of light clock. So, now for moving observer there is no light (in light clock) to follow longer path and hence elongate one second but only a second hand that rotates.

 

[Doc Al]

This page http://en.wikipedia.org/wiki/Time_dilation clearly explains time dilation by exampling with the light clock. But how can it be explained if suppose there was a simple mechanical clock instead of light clock. So, now for moving observer there is no light (in light clock) to follow longer path and hence elongate one second but only a second hand that rotates.

The principle of relativity tells us that all clocks must behave similarly and demonstrate identical time dilation. The advantage of the light clock is that it's easy to analyze.

 

[R Power]

The principle of relativity tells us that all clocks must behave similarly and demonstrate identical time dilation. The advantage of the light clock is that it's easy to analyze.

You are right! but can you explain ? It will help me further understand time dilation.

 

[Doc Al]

I don't think there's any simple way of deducing time dilation using mechanical clocks, if that's what you're looking for. (At least I've never seen such a demonstration.)

 

[R Power]

I don't think there's any simple way of deducing time dilation using mechanical clocks, if that's what you're looking for. (At least I've never seen such a demonstration.)

I've tried it! In this case, second hand traces an arc at 6 deg/sec to show one second increment, so when an observer travels with speed of light c beside the clock, the second hand for him will trace the arc + the elongated distance (the locus will be a big arc) appearing due to motion of traveling observer(as in case of light clock light had to travel greater distance) but since velocity of second hand can't be "6deg/sec + c" with respect to traveler i.e it can't exceed speed of light..so it will take more time to trace 6 deg.

 

[Saw]

You are right! but can you explain ? It will help me further understand time dilation.

The standard interpretation of SR stops at this level. Nature conforms to the Principle of Relativity (PoR) and that is it. My personal view is that this is not enough. I think we should put forward hypotheses about the root causes for that, but this is not usually regarded as necessary.

If you want my view, the answer is clear: the mechanical clock also suffers time dilation (as per the same pattern as the light clock) because a clock is a moving thing inside an enclosed space; the clock ticks when the moving thing bounces against the walls or otherwise changes direction. The cause for this "acceleration" is an electromagnetic interaction (light) or any another force that does its job in a manner that is analogous, at least for this purpose, to light.

 

[R Power]

What about my explanation in post #5?

 

[Saw]

What about my explanation in post #5?

I myself did not catch it.

 

[mangaroosh]

I've been wondering about this as well.

If the light clock were to be replaced with say, an infinitely precise pendulum clock, how would the thought experiment be explained then?

Would it be different if the thought experiment were "re-located" to deep space, using the infinitely precise pendulum clock?

 

[questionpost]

I don't get what the problem is. Any clock measures time, so when the fabric of space is distorted, time will flow slower, and thus any clock measurement will be slower since the flow of events is slower proportionally to the gravity. Although I will admit I don't quite understand completely why the shape of a well actually makes time run slower, but we know that it does. That's why if you are in an airplane, your clock will run ever-so-slightly faster than clocks on the ground.

 

[bahamagreen]

The request for an explanation is a good one.

If you take for granted that all possible clocks will be identically time dilated, then using the light clock as your generic clock in all subsequent though experiments is fine.

But all must admit that light is a very special entity with extraordinary properties, and if you are attempting to verify the universality of clock dilation in your own thinking before moving to just take it for granted, it makes sense to wonder what would be the effect on the actions of a mechanical clock - something with size and mass. It makes sense to wonder that different orientations of the oscillating and rotating parts of the clock might change their lengths and radii in one dimension, and therefore effect centers of mass, centers of rotation, and thereby effect linear and angular accelerations, etc.

This is not just "physical processes slowing down"... there are gross mechanical effects to account for, as well as smaller things in chemistry like molecular bonds, orbitals, and even smaller things, etc.

Surely someone has done this analysis and demonstrated that all these effects must balance out so that the mechanical clock may be replaced with the simple light clock without reservation?

 

[harrylin]

I don't get what the problem is. Any clock measures time, so when the fabric of space is distorted, time will flow slower, and thus any clock measurement will be slower since the flow of events is slower proportionally to the gravity. Although I will admit I don't quite understand completely why the shape of a well actually makes time run slower, but we know that it does. That's why if you are in an airplane, your clock will run ever-so-slightly faster than clocks on the ground.

I'm afraid that you confound gravitational time dilation with special relativistic time dilation; for a lucid discussion those are better not mixed up.

 

[harrylin]

The request for an explanation is a good one.

If you take for granted that all possible clocks will be identically time dilated, then using the light clock as your generic clock in all subsequent though experiments is fine.

But all must admit that light is a very special entity with extraordinary properties, and if you are attempting to verify the universality of clock dilation in your own thinking before moving to just take it for granted, it makes sense to wonder what would be the effect on the actions of a mechanical clock - something with size and mass. It makes sense to wonder that different orientations of the oscillating and rotating parts of the clock might change their lengths and radii in one dimension, and therefore effect centers of mass, centers of rotation, and thereby effect linear and angular accelerations, etc.

This is not just "physical processes slowing down"... there are gross mechanical effects to account for, as well as smaller things in chemistry like molecular bonds, orbitals, and even smaller things, etc.

Surely someone has done this analysis and demonstrated that all these effects must balance out so that the mechanical clock may be replaced with the simple light clock without reservation?

The course of progress was originally like that, but failure to either do that or to demonstrate the contrary led to relativity theory. Thus from then on one adjusts physical laws such that they adhere to the relativity principle, and insofar as this is done well, analyses based on those laws should find the same. It's similar to the principle of conservation of energy: it's easy to construct an apparatus that is so complex that it is a big job to demonstrate by means of the laws of Newton etc., that the principle of conservation of energy is not broken.

 

[R Power]

In case of light clock even, when observer travels at some speed, path of photon appears elongated to the moving observer now the velocity of observer should have been added to velocity of light which we know is not possible so the overall velocity of photon for the observer is constant i.e c (which causes dilation) but does this mean that photon has to slow its speed down in order to maintain total speed(photon speed + speed of observer) equal to speed of light?

 

[harrylin]

In case of light clock even, when observer travels at some speed, path of photon appears elongated to the moving observer now the velocity of observer should have been added to velocity of light which we know is not possible so the overall velocity of photon for the observer is constant i.e c (which causes dilation) but does this mean that photon has to slow its speed down in order to maintain total speed(photon speed + speed of observer) equal to speed of light?

The speed of light can not be affected by observation. Consequently it is the observation of the observer that is altered by the observer's speed (together with his choice of clock synchronization), and not the photon which propagates unaffected by the observer.

 

[R Power]

Consequently it is the observation of the observer that is altered by the observer's speed (together with his choice of clock synchronization), and not the photon which propagates unaffected by the observer.

The clock was relatively moving for the observer(for he himself was moving) and the photon in the clock which was traveling at speed c must now be moving with [ c+observer or clock speed] but that is not possible, so it travels with c. That means the photon in moving clock (to the observer) still travels with c for the observer which is only possible when the photon slows its speed down by an amount equal to the speed of clock (or observer) so that to observer it still moves with speed c.

When clock at rest...

speed of photon = c
speed of photon to observer = c

When clock moves...

speed of clock = v
speed of photon = c
speed of photon to observer= c+v
but that is not possible...
so let speed of clock = v
speed of photon = c-v
speed of photon to observer = c-v+v = c.

 

[harrylin]

The clock was relatively moving for the observer(for he himself was moving) and the photon in the clock which was traveling at speed c must now be moving with [ c+observer or clock speed] but that is not possible, so it travels with c.[..]

To elaborate, it depends on the reference system that the observer chooses. Apparently you have him choose a system in which he is moving, which is less common in this kind of discussions; commonly one refers to a system in which the observer is in rest. In a system in which the observer is measured to have velocity v and the light velocity c, their relative velocity (in jargon "closing velocity") is the vector subtraction (c-v) - this is so by mathematical definition. As a matter of fact, that is also how GPS receivers calculate.

 

[lalbatros]

Man-made mechanical clocks might not be well suited for this analysis.
After all, it is almost impossible practically to test time dilation with such clocks.

I see two "mechanical" alternatives:

1) atomic clocks that are based on a (quantum) mechanical system, indeed
2) astronomical bodies

Given that several astronomical observations support special relativity, it is very likely that time dilation could be explained by taking an astronomical system as an example. This would amount to comparing astronomical observations made in differents frame of references.

I was impressed by a paper from Julian Barbour on the nature of time:

http://platonia.com/nature_of_time_essay.pdf

Starting from this point of view would not only offer you some insight about how to answer your question, but it would also invite you to reflect about your question itself.

 

[R Power]

To elaborate, it depends on the reference system that the observer chooses. Apparently you have him choose a system in which he is moving, which is less common in this kind of discussions; commonly one refers to a system in which the observer is in rest. In a system in which the observer is measured to have velocity v and the light velocity c, their relative velocity (in jargon "closing velocity") is the vector subtraction (c-v) - this is so by mathematical definition.

Whether the clock is moving or the observer, its one hand same thing for the observer. I prefer taking observer to be mobile because if clock is moving (say at very high speed) then photon will not move along with clock and at some instance it will miss one of the reflectors. Moreover, the speed will be c+v (although that's not possible) which is why dilation occurs.

 

[harrylin]

Whether the clock is moving or the observer, its one hand same thing for the observer. I prefer taking observer to be mobile because if clock is moving (say at very high speed) then photon will not move along with clock and at some instance it will miss one of the reflectors. Moreover, the speed will be c+v (although that's not possible) which is why dilation occurs.

Sorry, that's simply wrong. Effectively you call "1+1=2" "not possible". Did you learn SR? A detailed presentation can be found in section 3 of:
http://www.fourmilab.ch/etexts/einstein/specrel/www/
Most textbooks have a clearer derivation but lack the clarifications concerning c+/-v.

 

[questionpost]

It seems like the problem is how clocks measure time depending on their speed. If they are going fast, then relative to the speed of time, which is c, time flows slower, so to the clock other things would have time flowing at a faster rate and we wouldn't see the ticking go as fast, and with traveling very close to the speed of light, there's some property of space that only allows speed to increase in a sort of "asymtotic" way as to only come infinitely clsoe to c, so the way you add speeds in v=(u+a) in terms of vectors is only an approximation at low speeds, not high near-light speeds.

 

[harrylin]

It seems like the problem is how clocks measure time depending on their speed. If they are going fast, then relative to the speed of time, which is c, time flows slower, so to the clock other things would have time flowing at a faster rate and we wouldn't see the ticking go as fast, and with traveling very close to the speed of light, there's some property of space that only allows speed to increase in a sort of "asymtotic" way as to only come infinitely clsoe to c, so the way you add speeds in v=(u+a) in terms of vectors is only an approximation at low speeds, not high near-light speeds.

A vector addition isn't a system transformation - but these are often confused. In a single reference system, as Einstein phrased it in the section that I pointed at, "the ray moves relatively to the initial point of [the moving system] k, when measured in the stationary system, with the velocity c-v".
Obviously, the distance variation over time between two moving entities as expressed in a single reference system is the vector subtraction of their velocities. And of course, such basics of vector algebra has nothing to do with time dilation, the topic of this thread.

My main point here is to stress (to the OP) that "relativistic velocity addition" is in reality a transformation equation between two independent systems of measurement.

 

[R Power]

And of course, such basics of vector algebra has nothing to do with time dilation, the topic of this thread.

But in the light clock article, when the observer is moving the light should have traveled at c+speed of observer but according to STR its speed remains constant and hence dilation occurs. Thus basic velocity addition fails at speed of light.

 

[harrylin]

But in the light clock article, when the observer is moving the light should have traveled at c+speed of observer but according to STR its speed remains constant and hence dilation occurs. Thus basic velocity addition fails at speed of light.

That "velocity addition" is a system transformation, as I already mentioned... moreover the "hence" confounds cause and effect (the observer's instruments cannot affect the light ray's speed!). And as you started with "but", it may be helpful if you can tell me why you think that the sentence that I cited from the SR derivation is not basic vector algebra.

 

[salvestrom]

But in the light clock article, when the observer is moving the light should have traveled at c+speed of observer but according to STR its speed remains constant and hence dilation occurs. Thus basic velocity addition fails at speed of light.

I think of it in this order: physical processes are 'hampered' by high velocity, described as time dilation, and so the speed of light is observed to be constant regardless of reference frame. In other words, the speed of light is constant because of time dilation.

As for what time dilation is... I'm on board with your description of the mechanical clock. A pendulum swinging in the direction of motion of its parent clock will, as it is accelerated closer to the speed of light, eventually need to move faster than c in order to keep swinging, before the rest of the clock does.

This is calculated to require infinite energy and is therefore considered impossible. I see no reason not to describe any mechanism in such a fashion - even our ultra-precise atomic clocks. At increasing speed these clocks can no longer decay at the same rate, owing to increasing amounts of energy required to do anything. So too the aging of a human, the rotting of fruit and the material decay of a spaceship transporting either.

 

[questionpost]

Isn't "velocity addition" not even the actual way your suppose to measurement and is nothing more than an approximation at low speeds? Why are people basing understandings off of it?

 

[harrylin]

Isn't "velocity addition" not even the actual way your suppose to measurement and is nothing more than an approximation at low speeds? Why are people basing understandings off of it?

Sorry I can't parse your sentence ... can you parse the sentence of Einstein's 1905 paper that I cited in post #22?
I hope that you understand the fundamental difference between a velocity difference in a single reference system, and the "velocity addition" equation for a transformation of one reference system to another one.

 

[A.T.]

If the mechanical clock would not be dilatated by the same amount as the co-moving light clock, you would run into paradoxes. Imagine the clocks trigger a bomb when they go out-of-synch. All observers must agree on whether the bomb exploded or not. But some observers would observe the clocks in-synch (those at rest to the clocks), some out-of-synch (those moving relative to the clocks).

Another way to think about it: On the atomic level, a mechanical clock also depends on EM-force fields, in which changes propagate at c.

 

[Saw]

Another way to think about it: On the atomic level, a mechanical clock also depends on EM-force fields, in which changes propagate at c.

I agree with that. I said something similar in post #6 above:

the mechanical clock also suffers time dilation (as per the same pattern as the light clock) because a clock is a moving thing inside an enclosed space; the clock ticks when the moving thing bounces against the walls or otherwise changes direction. The cause for this "acceleration" is an electromagnetic interaction (light) or any another force that does its job in a manner that is analogous, at least for this purpose, to light.

Why don't books ever mention this physical explanation? It is true that, if mechanical clocks did not suffer TD as per the same pattern as light clocks, the principle of relativity would suffer. But the principle of relativity is a description of how nature works, it is not the reason why it works that way. In this sense, it can be noted: if we had found out TD first in mechanical clocks, we would then say that light clocks must conform to the same pattern or otherwise the principle of relativity would be broken. Isn't that circular reasoning?

 

[Dale]

the principle of relativity is a description of how nature works, it is not the reason why it works that way.

This is a useless complaint because it applies to all of science. All science, including the principle of relativity, is a description of how nature works, not a reason why. If you are unwilling to accept such explanations then you do not want a scientific explanation.

if we had found out TD first in mechanical clocks, we would then say that light clocks must conform to the same pattern or otherwise the principle of relativity would be broken. Isn't that circular reasoning?

No. Circular reasoning would be something like: mechanical clocks time dilate, so by the principle of relativity light clocks time dilate, so mechanical clocks time dilate.

In general, you can take any logically self-consistent set of statements, and divide them up into a set of axioms and a set of theorems such that the axioms logically imply all of the theorems. The set of axioms is not unique, in other words, you can swap the place of some of the theorems and the axioms such that what was previously a theorem is now an axiom and the previous theorems logically imply the previous axioms. There is nothing circular about either selection of axioms.