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

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

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

Ive 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 travelling 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

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

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 explaination 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'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 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

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

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

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.