What Causes Moving Clocks to Measure Slower? Explained

[Grimble]

TL;DR Summary

Einstein wrote: As a consequence of its motion the clock goes more slowly than when at rest.
[Albert Einstein (1879–1955). Relativity: The Special and General Theory. 1920.

XII. The Behaviour of Measuring-Rods and Clocks in Motion]

After much deliberation I can finally see and understand what you have all spent so much time and patience explaining to me!
I can see that to observe the 2nd postulate; 'the speed of light in a vacuum is the same for all observers, regardless of the motion of the light source or observer' a moving clock has to measure more time than a stationary clock.

But what intrigues me is how does that work? The math demands that if speed is constant more time must pass in a moving frame of reference between the same two spacetime events. What are the mechanics of how this works?

 

[vanhees71]

It's the Maxwell equations, which are a relativistic classical field theory which provide the "mechanics", i.e., the dynamical laws of electric charge-current distributions and the electromagnetic field.

 

[PeroK]

But what intrigues me is how does that work? The math demands that if speed is constant more time must pass in a moving frame of reference between the same two spacetime events. What are the mechanics of how this works?

There is no mechanics because there is no such thing as a "moving" reference frame; only a frame moving relative to another. There is a symmetry in that the "stationary" frame is moving relative to the "moving" frame, so your conclusion could equally be that more time must pass in a stationary frame of reference between the same two spacetime events.

In any case, this cannot be true. The time between two events is different in different frames, but it is not the case (and cannot be the case by symmetry) that the time in frame A is always more than in frame B - in terms of the difference in time coordinates between any pair of events.

 

[Mister T]

But what intrigues me is how does that work?

You need more than two clocks to see how it works. Why? Because there is motion involved. Therefore two clocks in motion relative to each other can share the same location once, but not more than once. You cannot tell from this alone if one is running slower than the other.

What you have to do is wait for some time to pass, and when you do that the clocks no longer share the same location. Let's say you have a clock and I have a clock, and we carry them with us wherever we go. We are in motion relative to each other but when we share the same location we synchronize our clocks. Then I wait an hour (as measured by my clock, of course) and I wish to know what your clock now reads. To do that I need a clock, at rest relative to me, that shares your new location. That clock needs to be synchronized with my clock, and if I do the synchronizing then I'll conclude that it's your clock that's running slow.

On the other hand, if you are the one with the two clocks and you do as I did, you'll conclude that it's my clock that's running slow.

The only way this symmetrical situation can occur is if we each have different notions of simultaneity. When I synchronize my clocks, you won't agree that that I did it correctly and will therefore observe that the clocks are not synchronized. When you synchronize your clocks I will likewise observe that you did it incorrectly.

This is not a mechanical effect.

 

[Dale]

What are the mechanics of how this works?

I would say it is less mechanics and more geometry.

 

[Vanadium 50]

This is not a good question.

There is no such thing as a moving clock.
All (good) clocks measure one second per second.

 

[Grimble]

Clock A and clock B are synchronised at event S.
They have a relative velocity v.
After time t each will calculate that the other's clock to take longer to tick than their own clock.

As judged from K, the clock is moving with the velocity v; as judged from this reference-body, the time which elapses between two strokes of the clock is not one second, but seconds, i.e. a somewhat larger time. As a consequence of its motion the clock goes more slowly than when at rest. Here also the velocity c plays the part of an unattainable limiting velocity.

6​

That is each clock will run slow as observed from the other clock.
As I understand it these are physical scientific facts.
I just wondered if there is a simple mechanical explanation of how this occurs. We are not talking about rocket science here, but two clocks in relative motion. Physical objects in motion = mechanics (or it did when I was at school)
Is it unreasonable to think there should be some reason why this is true?

​

 

[Dale]

I just wondered if there is a simple mechanical explanation of how this occurs

Why not a simple geometrical explanation instead?

Is it unreasonable to think there should be some reason why this is true?

Well, personally I do think it is a little unreasonable to expect a mechanical explanation for everything. Is there no room in the theater of valid explanations for geometrical ones?

 

[hutchphd]

Here is one answer:
Because all clocks must be equivalent to a "light clock", and that analysis can be
found everywhere.

If you want to ask "why" again you are referred to Feynman about "why"questions:

 

[PeroK]

I just wondered if there is a simple mechanical explanation of how this occurs. Is it unreasonable to think there should be some reason why this is true?

​

Imagine you set two rockets in relative motion, both traveling back to Earth at the same speed relative to Earth, but coming from opposite directions. Then, on each rocket they construct a clock.

a) In the Earth frame, both clocks run slow by the same amount. So, the mechanical clock construction process must have been deficient to the same extent.

b) But in the frame of each ship, the clock in the other ship is running even slower than it is when measured in the Earth frame. And this doesn't tie up with any mechanical defect of a "moving" clock.

The point is that time dilation means just that. It's time itself that dilates; it's not the mechanical malfunction of the clocks.

 

[Ibix]

I just wondered if there is a simple mechanical explanation of how this occurs.

Not really, except for simple clocks like the light clock. As Dale has pointed out, the simple explanation is geometrical. The clocks measure "distance" through spacetime. But they are not moving along parallel lines. Just as the marks on two non-parallel lines do not line up, the ticks of the clocks are not simultaneous.

 

[Mister T]

Clock A and clock B are synchronised at event S.
They have a relative velocity v.
After time t each will calculate that the other's clock to take longer to tick than their own clock.

Can you explain the procedure you would use to reach that conclusion? (Hint: I tried to do that for you in Post #4.)

I just wondered if there is a simple mechanical explanation of how this occurs. We are not talking about rocket science here, but two clocks in relative motion. Physical objects in motion = mechanics (or it did when I was at school)

Imagine that your mechanical devices are two light detectors, each attached to the end of a long straight rod (another mechanical device). You use the apparatus to calculate the speed of a light beam moving parallel to the rod. Do you have a mechanical explanation for why you always get the same value for the speed of the light beam?

 

[New Simplicio]

Poincare asked Einstein what his mechanics were for Special Relativity. Einstein said there was no mechanics.

 

[Nugatory]

Is it unreasonable to think there should be some reason why this is true?

There are two ways of thinking about what’s going on here (and if you dig into the math you’ll find that they’re actually pretty much the same). Neither involves any mechanical effect on either clock.
1) You and I are start out together on a flat plain and then walk at the exact same speed but in slightly different directions - say I walk 15 degrees south of due east and you walk 15 degrees north of due east. Both of us will find that we are pulling ahead of the other - we have to look back over our shoulders to see the other, and as @Dale says, this is geometry, not any mechanical effect. Time dilation is the same thing except happening on the $t$ axis instead of the $x$ axis.
2) Relativity of simultaneity explains time dilation, again with no mechanical effect. This has been explained in many other posts here - if you can’t find one of them let me know and I’ll point you to one of them.

[Edit - here are some of those posts:
https://www.physicsforums.com/threads/special-relativity-time-issues.846242/post-5307390
https://www.physicsforums.com/threads/weird-time-dilation-question.883303/post-5552719]

 

[Grimble]

Thank you gentle folk, one and all...
What you are saying is what I was thinking - confirming that you have no simple mechanical explanation.
What I understand from you is that it is due to time dilation and the nature of time - which no one has a good non circular definition for...
I am happy with that.

 

[robphy]

I can see that to observe the 2nd postulate; 'the speed of light in a vacuum is the same for all observers, regardless of the motion of the light source or observer' a moving clock has to measure more time than a stationary clock.

But what intrigues me is how does that work? The math demands that if speed is constant more time must pass in a moving frame of reference between the same two spacetime events. What are the mechanics of how this works?

While ultimately it is the spacetime geometry that is responsible for the effect,
it may be helpful to analyze a system [the light clock] that operationally motivates the effect.
However, it's not enough to analyze spatial-diagrams of transverse light clocks--
--one should really draw spacetime-diagrams of ticking [longitudinal] light clocks.

• the "ticking of the longitudinal light clock" shows the "mechanism"
  of how elapsed time corresponds to arc length of a worldline on a spacetime diagram
• the speed of light principle and the relativity principle
  can be used to construct the light clock of another inertial observer,
  in accordance with special relativity
• the relativity principle will also imply that these clock effects
  extend to other clock mechanisms that are also carried by an inertial observer
• the resulting spacetime diagram carries geometrical information
  that can be used to do calculations graphically (encoding the usual textbook formulas)

For more info,
https://www.physicsforums.com/insights/spacetime-diagrams-light-clocks/
and some interactive material:
https://www.geogebra.org/m/HYD7hB9v#material/UBXdQaz4 (spacetime diagrams of a pair of longitudinal light clocks)
https://www.geogebra.org/m/XFXzXGTq (spacetime diagrams of a pair of light clocks, Michelson Morley apparatus)


(
These older posts of mine might also be helpful
https://www.physicsforums.com/threads/question-about-time-dilation.936160/post-5915546
and
https://www.physicsforums.com/threads/question-about-time-dilation.936160/post-5915580
and
https://www.physicsforums.com/threads/measuring-michelson-morley-light-beams.955108/post-6113174
)

 

[martinbn]

Thank you gentle folk, one and all...
What you are saying is what I was thinking - confirming that you have no simple mechanical explanation.
What I understand from you is that it is due to time dilation and the nature of time - which no one has a good non circular definition for...
I am happy with that.

I think you are missing the point. It is not that they don't have a simple mechanical explanation. There isn't one. It is not a question of no one has come up with one yet. No one can ever do that.

 

[jbriggs444]

I think you are missing the point. It is not that they don't have a simple mechanical explanation. There isn't one. It is not a question of no one has come up with one yet. No one can ever do that.

One can come up with a mechanical explanation (e.g. Lorentz Ether theory). But, since that theory is both more complicated than and experimentally indistinguishable from Special Relativity, it is pointless discussing it.

 

[vanhees71]

Clock A and clock B are synchronised at event S.
They have a relative velocity v.
After time t each will calculate that the other's clock to take longer to tick than their own clock.
That is each clock will run slow as observed from the other clock.
As I understand it these are physical scientific facts.
I just wondered if there is a simple mechanical explanation of how this occurs. We are not talking about rocket science here, but two clocks in relative motion. Physical objects in motion = mechanics (or it did when I was at school)
Is it unreasonable to think there should be some reason why this is true?

​

​

As I said, the reason is that the dynamics of electromagnetic fields (and all other today known fields) obey equations of motion, describing their dynamics, which are compatible with the relativistic spacetime description but not compatible with the Newtonian spacetime description. That's indeed, how Einstein found the special theory of relativity in 1905: The Maxwell equations, which accurately describe all phenomena related to the electromagnetic field, including the motion of charged matter interacting through the em. field and the creation of the electromagnetic field from the moving matter, are not compatible with the Galilean spacetime model, particularly they are changing their form when changing from one inertial reference frame (where a body stays in uniform linear motion when no forces act on it) to another inertial frame moving against the first with a constant velocity.

The idea at the time was that maybe there's a preferred reference frame, defined by a mysterious medium called the "aether" which should carrying the electromagnetic field (waves) as air carries sound waves. Then Maxwell's equations would be valid only in a special inertial reference frame, determined as the rest frame of this ficitious aether. There were some attempts to experimentally prove the existence of this aether. The most famous one was the Michelson-Morley experiment, using the motion of the Earth around the Sun to maybe find the "aether wind" with a clever interference measurement with light, but the puzzling result was that no aether wind whatsoever could be observed.

Einstein figured out that the there's indeed no observable fact of this ominous aether, and that the solution was not to change the Maxwell equations such as to get it compatible with Newtonian spacetime, because this leads to theories of the electromagnetic phenomena, which are not correctly desribing them. Particularly all the properties of light, which indeed had been identified as behaving precisely like the electromagnetic waves as predicted by Maxwell (Hertz 1888). So Einstein concluded that the description of space and time had to be altered such that the transformation from one inertial frame to another leaves the Maxwell equations invariant. Then it's clear that there's no preferred inertial reference frame but that you cannot distinguish different inertial frames from each other through any electromagnetic means, but that must also be the case for the mechanics, i.e., the dynamical description of moving bodies, i.e., the mechanics had to be modified rather than the Maxwell equations, and indeed Einstein could find the correct equations of motion for mechanics within the new spacetime description, which was shortly thereafter identified as a pretty simple mathematical structure, called a Minkowski space, i.e., an elegant four-dimensional geometrical space, pretty similar to the Eucliden three-dimensional space we are used to.

 

[PeterDonis]

What I understand from you is that it is due to time dilation and the nature of time - which no one has a good non circular definition for...

Spacetime geometry is a non-circular definition.

 

[Ibix]

What I understand from you is that it is due to time dilation and the nature of time - which no one has a good non circular definition for...
I am happy with that.

As others have noted, this isn't a good characterisation of what we are saying. Historically, we deduced some mathematical relationships from experimental results and eventually realized that they could be interpreted as implying the existence of spacetime as a Minkowski manifold. With the benefit of hindsight, we now start by assuming the existence of spacetime and show that we can derive everything from there.

If you take the historical view, time dilation and the symmetry thereof follow from a lot of experiments and imply the existence of spacetime. If you take the modern view, time dilation follows from our definition of spacetime and there are a lot of experiments that confirm the resulting predictions. Neither approach is circular. The first approach is how we developed the theory. The second approach is how we wish we'd developed the theory.

 

[Dale]

What I understand from you is that it is due to time dilation and the nature of time

Nobody said anything remotely like this. Frankly, this sort of thing is very irritating

time - which no one has a good non circular definition for...

(proper) Time is what a clock measures.

Good non circular definition of time