Acceleration does not effect clocks?

[edpell]

Imagine in empty space a pendulum consisting of a small weight suspended above a large weight and displace so that it swings back and forth with period T. Now imagine accelerating (in the right direction) so that the effective gravity felt by the small weight increases. The period will then decrease.

So what do we mean when we say acceleration does not effect clocks?

Is this pendulum not a clock?

 

[bcrowell]

When we talk about clocks and rulers in relativity, we mean idealized ones. A clock could be affected by sitting in direct sunlight, but that doesn't mean that the rate at which time flows depends on sunlight.

As an example, Einstein's 1905 paper says, "If one of two synchronous clocks at A is moved in a closed curve with constant velocity until it returns to A, the journey lasting t seconds, then by the clock which has remained at rest the traveled clock on its arrival at A will be (1/2)tv^2/c^2 second slow. Thence we conclude that a balance-clock* at the equator must go more slowly, by a very small amount, than a precisely similar clock situated at one of the poles under otherwise identical conditions."

The 1923 Methuen translation has a the following footnote by Sommerfeld:

*Not a pendulum-clock, which is physically a system to which the Earth belongs. This case had to be
excluded.

(Einstein was actually wrong about the equator/pole thing.)

Here's a good explanation of the clock "postulate:" http://math.ucr.edu/home/baez/physics/Relativity/SR/clock.html

It's not actually logically independent of the other postulates of SR. See p. 9 of http://www.phys.uu.nl/igg/dieks/rotation.pdf

 

[edpell]

*Not a pendulum-clock, which is physically a system to which the Earth belongs. This case had to be excluded.

The pendulum clock I propose has one small weight say 1Kg and one large weight say 1000Kg. The Earth is not required or in fact desired.

 

[bcrowell]

The pendulum clock I propose has one small weight say 1Kg and one large weight say 1000Kg. The Earth is not required or in fact desired.

You don't get to use any clock you want. The only kind of clock that's relevant is an idealized clock that isn't subject to effects like this. For example, if we see that quartz wristwatches, atomic clocks, and spring-wound alarm clocks all agree regardless of variations in gravity, but pendulum clocks disagree with them, then we say that a pendulum clock is a lousy approximation to an idealized clock, and we know not to use it.

 

[edpell]

Would it be fair to say only clocks that use the electromagnetic force or the weak force or the strong force are covered by the "acceleration does not affect clocks" idea?

 

[A.T.]

Imagine in empty space a pendulum consisting of a small weight suspended above a large weight and displace so that it swings back and forth with period T. Now imagine accelerating (in the right direction) so that the effective gravity felt by the small weight increases. The period will then decrease.

Of course you can build a clock that is affected by acceleration. But that is just a flaw of your clock design and not time dilation. You can also build a clock that is affected by temperature, but this doesn't mean that temperature is causing time dilation.

So what do we mean when we say acceleration does not effect clocks?

It means it has no universal effect on all clocks.

Would it be fair to say only clocks that use the electromagnetic force or the weak force or the strong force are covered by the "acceleration does not affect clocks" idea?

You can use pendelum clocks. You just have to account for the error due to acceleration, to get the correct time that an ideal clock would measure.

 

[edpell]

Would it be fair to say it is impossible to build a clock that uses gravity as its force and meets the clock postulate?

 

[bcrowell]

Would it be fair to say only clocks that use the electromagnetic force or the weak force or the strong force are covered by the "acceleration does not affect clocks" idea?

I don't think so. For instance, if I use intense magnetic fields to accelerate a quartz clock, it might have the side-effect of messing up its measurement of time.

BTW, it turns out that the word the Methuen translation renders as "balance-clock" was "unruhuhr," which the Methuen translation renders as "balance-clock." They aren't talking about a balance in the sense of a gravitational balance, they're talking about a balance wheel http://en.wikipedia.org/wiki/Balance_wheel coupled to a coil spring. In other words, it's a spring clock.

 

[bcrowell]

Would it be fair to say it is impossible to build a clock that uses gravity as its force and meets the clock postulate?

You can't build any clock that satisfies the clock postulate. It's a statement about idealized clocks, not a statement about real clocks. As A.T. has pointed out, you can take any physical clock, including a pendulum clock, and make it a better approximation to an ideal clock by applying corrections.

 

[matheinste]

Would it be fair to say only clocks that use the electromagnetic force or the weak force or the strong force are covered by the "acceleration does not affect clocks" idea?

Rindler- Essential Relativity. Page 43.

-----If an ideal clock moves through an inertial frame, we shall assume that acceleration as such has no effect on the rate of the clock i.e., that its instantaneous rate depends only on its instantaneous speed--.

----This we call the clock hypothesis. It can also be regarded as the definition of an “ideal” clock. By no means all clocks meet this criterion----. On the other hand, the absoluteness of acceleration ensures that ideal clocks can be built, in principle. We need only take an arbitrary clock, observe whatever effect acceleration has on it, then attach it to an accelerometer and a servomechanism that exactly cancels the acceleration effect. By contrast, the velocity cannot be eliminated.-----

Matheinste

 

[bcrowell]

This we call the clock hypothesis. It can also be regarded as the definition of an “ideal” clock. By no means all clocks meet this criterion----. On the other hand, the absoluteness of acceleration ensures that ideal clocks can be built, in principle. We need only take an arbitrary clock, observe whatever effect acceleration has on it, then attach it to an accelerometer and a servomechanism that exactly cancels the acceleration effect. By contrast, the velocity cannot be eliminated.

Sweet argument :-)

The Baez link above also discusses the possibility that an ideal clock could be sensitive to higher derivatives of its velocity, and Rindler's argument clearly extends to that possibility as well.

The paper by Dieks that I linked to above gives a different prescription, which is simply to build a light-clock, and make its size small. I suppose you can also use extrapolation to remove the effect of finite size completely, since you know the form of the size-dependence. E.g., you can build light clocks with sizes L and 2L, and just extrapolate to L=0 in the appropriate way.

[EDIT] After thinking about this some more, I think both Dieks' argument and Rindler's are incomplete. Dieks proves that a certain type of clock is ideal if you make it small enough, but it doesn't give us any reason to think that the time measured by this type of clock is universal, in the sense that ideal clocks of this type can be made to agree with ideal clocks of other types. Rindler shows that any type of clock can be made ideal, but (unless there's more to his argument than what you quoted above) he seems to be assuming that the size of the clock doesn't matter, whereas the size is actually crucial. If the clock is too big, then we can't define simultaneity at different points within the clock, and therefore we can't tell whether the acceleration measured by the accelerometer is one that should be applied during a particular time interval on the clock next to it.

 

[Al68]

Would it be fair to say only clocks that use the electromagnetic force or the weak force or the strong force are covered by the "acceleration does not affect clocks" idea?

I'd say that the clocks covered by the "acceleration does not affect clocks" idea are clocks that are unaffected by acceleration. The point of the clock hypothesis isn't to make a claim about clocks, its to define an ideal clock.

 

[bcrowell]

I'd say that the clocks covered by the "acceleration does not affect clocks" idea are clocks that are unaffected by acceleration. The point of the clock hypothesis isn't to make a claim about clocks, its to define an ideal clock.

Well, I think there's a reason that Rindler calls it the "clock hypothesis" and not the "clock postulate" (as some authors do) or the "clock definition." It's not an independent postulate because it follows from the ordinary postulates of SR. It's not just a definition, because it asserts that we can make real clocks that closely approximate the behavior it describes.

 

[matheinste]

Rindler shows that any type of clock can be made ideal, but (unless there's more to his argument than what you quoted above) he seems to be assuming that the size of the clock doesn't matter, whereas the size is actually crucial. If the clock is too big, then we can't define simultaneity at different points within the clock, and therefore we can't tell whether the acceleration measured by the accelerometer is one that should be applied during a particular time interval on the clock next to it.

There was no more to his argument in the text. What you say does make things more than a little complicated.

I think most of us agree that, if, in theory, we propose an ideal clock, even if not absolutely obtainable in practice, this removes any effects of acceleration in any thought experiment we care to develop logically from the postulates of SR, such as the perennial twin scenario.

But then we have the problem of practical experimental verification of such thought experiments with real clocks. I am happy that some real clocks very closely mimic ideal clocks and so any experimental results depending on them are trustworthy.

Matheinste.

 

[ThomasT]

So what do we mean when we say acceleration does not effect clocks?

That γ is unaffected by acceleration.

Quoting Baez from the link provided in post #2 by bcrowell:

The clock postulate can be stated in the following way. First, we take the rate that our frame's clocks count out their time, and compare that to the rate that a moving clock counts out its time. Before the clock postulate was ever thought of, all that was known was that when the moving clock has a constant velocity v (measured relative to the speed of light c), this ratio of rates is the "gamma factor"

γ = (1 - v2) ^-1/2

The clock postulate generalises this to say that even when the moving clock accelerates, the ratio of the rate of our clocks compared to its rate is still the above quantity.

Again, from Baez:

But note: the clock postulate does not say that the rate of timing of a moving clock is unaffected by its acceleration. The timing rate will certainly be affected if the acceleration changes the clock's speed of movement, because its speed determines how fast it counts out its time (i.e. by the factor γ).

 

[edpell]

OK this makes sense. The integral of the acceleration gives a velocity. The clock hypothesis is that regardless of the path (i.e. acc fast then slowly or acc slowly and then fast, etc) it is only the final velocity that effects the final clock rate.

 

[Naty1]

I think I'm getting a "relativity" headache but the above posts make sense...

The timing rate will certainly be affected if the acceleration changes the clock's speed of movement,

Thinking about the implications of relativity never seems to end..no wonder it took two decades for it to be generally understood and accepted...

so rotating a clock at constant acceleration should not affect its timing. I think "speed" is a better description than velocity used immediately above...

 

[matheinste]

----But note: the clock postulate does not say that the rate of timing of a moving clock is unaffected by its acceleration. The timing rate will certainly be affected if the acceleration changes the clock's speed of movement, because its speed determines how fast it counts out its time (i.e. by the factor γ).----

Note the proviso "if the acceleration changes the clock's speed of movement". It is possible to accelerate a clock without changing its speed. In such cases certain real clocks are unaffected by acceleration to a very high experimental accuracy.

Matheinste.

 

[bcrowell]

----But note: the clock postulate does not say that the rate of timing of a moving clock is unaffected by its acceleration. The timing rate will certainly be affected if the acceleration changes the clock's speed of movement, because its speed determines how fast it counts out its time (i.e. by the factor γ).----

Note the proviso "if the acceleration changes the clock's speed of movement". It is possible to accelerate a clock without changing its speed. In such cases certain real clocks are unaffected by acceleration to a very high experimental accuracy.

I think you're misinterpreting what the clock hypothesis is about. There is no issue of accelerating with a change in speed or without a change in speed. The question is simply whether it is possible to construct a clock such that, to a good approximation, the time read on the clock is $\int ds$ (or something similar to that, if you want a -+++ metric instead of +---).

 

[matheinste]

I think you're misinterpreting what the clock hypothesis is about. There is no issue of accelerating with a change in speed or without a change in speed. The question is simply whether it is possible to construct a clock such that, to a good approximation, the time read on the clock is $\int ds$ (or something similar to that, if you want a -+++ metric instead of +---).

Doesn't the clock hypothesis say that an ideal clock is unaffected by acceleration?

I was pointing out that on the face of it the quote from Baez could be (mis)interpreted as saying that ideal clocks were affected by acceleration without a change in speed and the poster was using that quote as supporting a contrary view.

Matheinste.

 

[bcrowell]

Doesn't the clock hypothesis say that an ideal clock is unaffected by acceleration?

That's a loose way of phrasing it, but it lends itself to misinterpretation. A more mathematically precise way of saying it, which isn't subject to the same misinterpretation, is that clocks exist that approximately measure $\int ds$.

I was pointing out that on the face of it the quote from Baez could be (mis)interpreted as saying that ideal clocks were affected by acceleration without a change in speed and the poster was using that quote as supporting a contrary view.

If the statement is that ideal clocks are affected by acceleration without a change in speed, then that statement can be either true or false, depending on what the words are taken to mean.