How do relativistic effects change oscillation of the balance wheel in mechanical watch causing it to tick slower?

[Ibix]

They're measuring different quantities that, because they are using frame-dependent language, they happen to each call by the same name.

Well, they're using the same procedure to measure a quantity, so it isn't entirely unreasonable of them to use the same name for it. @Jurgen M - that is the problem underlying everything in this thread - two experimenters in relative motion apply the same procedure (wait for the balance wheel to tick once and compare to clocks at rest) but get different quantities. It shouldn't be overly surprising that this happens - an obvious example is measuring a passing car's speed using a Doppler radar gun from a roadside or from a different moving car. Relativity just increases the range of cases where things can be different. IIRC, Bondi calls it making "public" quantities (that everyone agrees on) into "private" ones (that people get different values for).

 

[PeterDonis]

they're using the same procedure to measure a quantity, so it isn't entirely unreasonable of them to use the same name for it.

I only said it was sloppy, not that it was unreasonable. An issue that often has to be dealt with in physics is that our natural, reasonable way of talking about things is sloppy in this way, which works fine in ordinary conversation, but it can lead to confusion when greater precision is needed, as it is in physics.

 

[Dale]

Well, they're using the same procedure to measure a quantity, so it isn't entirely unreasonable of them to use the same name for it.

Yes, although with frame dependent quantities, say X, there is no such thing as just “X” but only “X with respect to frame Y”. That is one of the major issues communicating about these things. Particularly with the OP who seems to have no inclination to speak clearly despite my repeated suggestions

 

[PeroK]

They're not measuring the same quantity. They're measuring different quantities that, because they are using frame-dependent language, they happen to each call by the same name. It would be better to avoid the sloppy terminology altogether and make it clear that they are measuring two different invariants, for example by describing each one mathematically as a contraction of the same object's 4-momentum with different 4-vectors describing different measurement devices in different states of motion.

If that's sloppy terminology (to talk about the kinetic energy or velocity of an object), then I doubt that many undergraduate physics books would satisfy your criteria. How on Earth is anyone to begin to study physics if we can't communicate in terms of kinetic energy?

 

[PeterDonis]

If that's sloppy terminology (to talk about the kinetic energy or velocity of an object)

I didn't say that was sloppy. I said it was sloppy to talk about "kinetic energy relative to A" and "velocity relative to A" as if they were the same quantities as "kinetic energy relative to B" and "velocity relative to B". If you just say "kinetic energy" or "velocity" without specifying what specific frame or observer they are relative to, that's basically what you're doing; you're implying that, oh, they're all just the same quantity anyway, so there's no need to specify what they're relative to. But there is a need to specify what they're relative to.

 

[Nugatory]

Observer with watch see normal clock tick rate, observer moving in relation to clock see slower tick rate.
So we have two different results.

We need to be clear about what they are seeing. Bob is moving past Alice at .8c and they both zero their clocks - and because we’re trying to compare the clock rates they have to be able to observe each other’s clocks, so let’s also give them powerful telescopes to watch one another.

An observation is a statement of the form “Alice looked into her telescope when her clock read X; she saw Bob’s clock reading Y” (and likewise for Bob looking back at Alice). Clearly everyone is going to agree about the contents of these observations - they are simple statements of fact about the image in a telescope.

 

[PeterDonis]

We need to be clear about what they are seeing. Bob is moving past Alice at .8c and they both zero their clocks - and because we’re trying to compare the clock rates they have to be able to observe each other’s clocks, so let’s also give them powerful telescopes to watch one another.

An observation is a statement of the form “Alice looked into her telescope when her clock read X; she saw Bob’s clock reading Y” (and likewise for Bob looking back at Alice). Clearly everyone is going to agree about the contents of these observations - they are simple statements of fact about the image in a telescope.

Note, though, that the times each one sees in their telescopes on the other's clocks are not the same as the "time dilated" times calculated according to their inertial frames. The times they actually see are the relativistic Doppler shifted times, which can be thought of as the inertial frame "time dilated" times with relativistic Doppler shift and light travel time delay applied. But I actually prefer starting from the Doppler shifted times, since those are the direct observables, and treating the "time dilated" times as calculated times, obtained from the directly observed Doppler shifted times by applying corrections for light travel time delay. The fact that those corrections require adopting the simultaneity convention of a particular frame makes it clearer where in the logic the frame-dependent element enters.

 

[Sagittarius A-Star]

...but has to subtract out the light travel time to interpret what he sees. And how he does that turns out to be equivalent to making a choice of reference frame.

Isnt frame of reference same as observer, abstract coordinate system from which we are observes object?

No, frame of reference is not the same as observer. Several observers can be at rest at different spatial coordinates of the same frame of reference. To agree on a common time, their wrist-watches should have been synchronized by a mechanism, which Einstein described. If an observer is stationed at A with a clock, he can estimate the time of events occurring in the immediate neighborhood of A:

§ 1. Definition of Simultaneity.
Let us have a co-ordinate system, in which the Newtonian equations hold. For verbally distinguishing this system from another which will be introduced hereafter, and for clarification of the idea, we shall call it the "stationary system."
...
If an observer be stationed at A with a clock, he can estimate the time of events occurring in the immediate neighbourhood of A by looking for the position of the hands of the clock, which are simultaneous with the event. If a clock be stationed also at point B in space, — we should add that "the clock is exactly of the same nature as the one at A", — then the chronological evaluations of the events occurring in the immediate vicinity of B, is possible for an observer located in B. But without further premises, it is not possible to chronologically compare the events at B with the events at A. We have hitherto only an "A-time", and a "B-time", but no "time" common to A and B. This last time (i.e., common time) can now be defined, however, if we establish by definition that the "time" which light requires in traveling from A to B is equivalent to the "time" which light requires in traveling from B to A. For example, a ray of light proceeds from A at "A-time" $t_{A}$ towards B, arrives and is reflected from B at B-time $t_{B}$, and returns to A at "A-time" $t'_{A}$. According to the definition, both clocks are synchronous, if

$$t_{B}-t_{A}=t'_{A}-t_{B}$$
We assume that this definition of synchronism is possible without involving any inconsistency, for any number of points, therefore the following relations hold:

1. If the clock at B be synchronous with the clock at A, then the clock at A is synchronous with the clock at B.
2. If the clock at A be synchronous with the clock at B as well as with the clock at C, then also the clocks at B and C are synchronous.

Thus with the help of certain (imagined) physical experiences, we have established what we understand when we speak of clocks at rest at different places, and synchronous with one another; and thereby we have arrived at a definition of "synchronism" and "time". The "time" of an event is the simultaneous indication of a stationary clock located at the place of the event, which is synchronous with a certain stationary clock for all time determinations.

In accordance with experience we shall assume that the magnitude
$$\frac {2{\overline {AB}}}{t'_{A}-t_{A}}=V,$$
is a universal constant (the speed of light in empty space).

We have defined time essentially with a clock at rest in a stationary system. On account of its affiliation to the stationary system, we call the time defined in this way "the time of the stationary system."

Source:
https://en.wikisource.org/wiki/Translation:On_the_Electrodynamics_of_Moving_Bodies

 

[Jurgen M]

at 4:56 he get t'= 20s x 0.8 = 16s

what is 0.8 ?

 

[Sagittarius A-Star]

what is 0.8 ?

$0.8 = 1/\gamma$, see in the video at 2:00

 

[Jurgen M]

$0.8 = 1/\gamma$, see in the video at 2:00

Without any calucualtion I would say that loking from frame S' at t=20s(in S'), clock inside frame S must show 16s as well.

I must do it by mayself on paper and pen to completely understand what happening here.
It is hard to follow him without paper and pen with my knowledge..if only I had drunk less in high school/university when learn physics, even we never learned einstein physics..

 

[Sagittarius A-Star]

I like this video. He has 1 clock at rest with reference to frame S' and 2 clocks at rest with reference to frame S. He argues with the relativity of simultaneity: The 2 clocks at rest in frame S tick synchronous to each other according to frame S and tick with an offset to each other according to frame S'. You can calculate this with the Lorentz-transformation.

Without any calucualtion I would say that loking from frame S' at t=20s(in S'), clock inside frame S must show 16s as well.

For symmetry reasons this would be correct, if you had 2 clocks at rest with reference to frame S' (which you would now define as the "stationary system") and compare it to only 1 clock, that is at rest with reference to frame S (which you would now define as the "moving system").

 

[Jurgen M]

Is speed of light constant in non inertial frame (accelerated car) too?

 

[PeroK]

Is speed of light constant in non inertial frame (accelerated car) too?

In general, for an accelerating reference frame speeds are simpler to measure locally. The concept of measuring the speed of something that is distant becomes problematic. The same is true in the curved spacetime of GR, where gravity is involved.

The postulate about the speed of light becomes that the local speed of light (i.e. as measured by a local observer is always $c$).

 

[Dale]

Is speed of light constant in non inertial frame (accelerated car) too?

No, the coordinate speed of light in a non-inertial frame may be different from c. However, in all frames, including non-inertial frames, light is a null geodesic. That is the coordinate-independent statement that reduces to "the speed of light is c" in inertial frames.