I Angular momentum of an atom within a rigid body in motion

[Nugatory]

If so then the results of the Hafele Keating experiment disprove the principle.

The discrepancy between the clock on the ground and the clock on the aircraft is not explained by the motion of the aircraft. Consider that the ground clock was moving with the Earth's rotation, with the orbit of the Earth around the sun, with the sun's orbit around the galactic core, and the galaxy's drift through intergalactic space... What makes the trajectory of the Earth clock so special?

 

[PeterDonis]

something must be physically affecting the tick rate of clocks in motion as otherwise their indicated times would not vary.

This argument is wrong. You have already been told why it is wrong in this thread. Consider the odometer analogy in post #40. Do the different odometer readings for drivers who take different routes between two points mean that "something must be physically affecting the tick rate" of the odometers?

If so then the results of the Hafele Keating experiment disprove the principle.

No, they don't. You have already been told why in this thread. See above.

There is nothing stated or implied in the first postulate that motion is not something physical.

"Not physical" in this connection means "not invariant" (because "motion" is frame-dependent) or "not directly observable" (because there is no experiment you can do that will tell you that you are "moving" in any absolute sense). So your statement is wrong; the first postulate does say that motion is "not physical" in this sense.

My original question is "Considering an atom within a rigid body, does the angular momentum of an electron within the atom vary when the body is put in motion?"

And the question as you originally phrased it is not well-defined, which is why it does not have a single well-defined answer.

Some of the responses provided on this forum suggest that the answer is yes

Because if "angular momentum" includes "orbital angular momentum around some chosen external point", then an electron in an atom at rest relative to that point does have different "angular momentum" than an electron in an atom that is moving relative to that point. But this definition of "angular momentum" is frame-dependent; it's not something you directly measure, it's something you calculate after you've chosen a particular point, which implies choosing a particular frame in which that point is at rest.

However, when physicists talk about the "angular momentum" of an electron in an atom, they normally don't mean the frame-dependent thing above. They mean the angular momentum (orbital plus spin) of the electron relative to the nucleus of the atom, which is not frame-dependent and which can be directly observed, and which is the same regardless of the atom's state of motion relative to some external point. As has already been explained in this thread.

which implies that motion will have a physical effect.

No, it implies that some definitions of "angular momentum" are frame-dependent. See above.

If there is no physical effect on a body when put into motion

"Put into motion" is ambiguous. If it just means choosing a different frame of reference without doing anything to the body itself, obviously this has no physical effect. But if it means exerting an actual force on the body, which will change its motion relative to other bodies, obviously this does have a physical effect. But if you use the same term to refer to both of these things, obviously you're just going to confuse yourself.

there should be no need to take into account relativistic effects.

This is fallacious reasoning, both because of the issue just stated above and because "relativistic effects" include things that are directly observable.

A clock ticking at its highest possible tick rate could be considered to be at rest relative to any other clock ticking at a slower rate.

Wrong, for two reasons.

First, as has already been explained (see my reference to the odometer analogy above), "tick rate" is the wrong way to think about this issue. The correct way to think about it is "distance through spacetime, i.e., elapsed time, along different paths".

Second, there is no such thing as "highest distance through spacetime" in any general sense. To give that any meaning, you first have to pick two particular events in spacetime--for example, "clocks all start out together in a run of the H-K experiment", and "clocks all come back together after completing a run of the H-K experiment". Once you have picked two particular events, then yes, there will be some particular path through spacetime (worldline) that has the longest possible length (elapsed time) between those events. Or, more generally, you can always compare elapsed times along different paths through spacetime between those two chosen events, and those comparisons will be invariant--all observers will agree on them and they are independent of any choice of reference frame. (Note, btw, that in the actual H-K experiment, none of the paths taken in the experiment were the absolute longest possible paths between the two relevant events, but, as just noted, the comparisons between the elapsed times on the different clocks are still invariant.)

 

[PeterDonis]

@james fairclear you have gotten multiple responses saying the same things in different ways in this thread. There is no point in continuing to go around in circles. If all you can do is to continue to restate your (wrong) claims based on your (wrong) understanding of what relativity says, this thread can simply be closed as it will go nowhere.

 

[james fairclear]

The "stationary" clock is in motion relative to the "moving" clock. It, likewise, ought to be physically altered by the relative motion. Neither clock can claim to be "really" at rest or "really" moving. That is what Einstein was saying above.

All clocks tick at their highest tick rate in a reference frame where they are at rest; and all other clocks are ticking relatively slowly as measured by that clock. Every clock can claim to be ticking normally. As indeed it is.

"All clocks tick at their highest tick rate in a reference frame where they are at rest".

By your definition a clock is always in a reference frame where it is at rest! From this definition it follows that the tick rate of a clock will never vary which is contradicted by the evidence of the Hafele Keating experiment.

'Neither clock can claim to be "really" at rest or "really" moving'.

A clock can claim to be at rest if its tick rate is the highest possible tick rate. If 2 previously synchronised clocks are set in relative motion and then brought back together, the clock indicating an earlier time can be considered to be the one that was moving faster than the other clock (ignoring gravitational effects).

 

[PeroK]

A clock can claim to be at rest if its tick rate is the highest possible tick rate.

Can you give an example of an object that you believe is at rest? That definitely is not moving?

 

[james fairclear]

Consider an analogy: you and I both drive from New York to Washington, DC. You take the direct route, straight down the East Coast; I take a roundabout route by way of Pittsburgh, PA. The odometer on my car registers more distance traveled when we meet up again than yours does. Does that mean the "distance rate" of my odometer was different from yours? No; both of our odometers registered one mile per mile. The route I took just had more miles in it than yours: our paths had different lengths.

Similarly, in a "twin paradox" scenario (or a "triplet" scenario such as the H-K experiment), everyone's clock ticks at the same rate: one second per second. But the different paths through spacetime that each observer takes have different numbers of seconds in them: they have different spacetime lengths. That's why the different observers have aged differently when they meet up again: "elapsed age" is a measure of (timelike) distance traveled through spacetime, just as elapsed odometer mileage on a car is a measure of distance traveled through space.

Your driving analogy is only applicable to time dilation if the odometers measure the same distance despite the fact that we have traveled different distances.

The implication then is that 1 odometer was measuring distance at a different rate to the other. We could then conclude for example that the the average speed on the roundabout route was much faster and that therefore speed affects the measuring rate of an odometer.

 

[james fairclear]

The discrepancy between the clock on the ground and the clock on the aircraft is not explained by the motion of the aircraft. Consider that the ground clock was moving with the Earth's rotation, with the orbit of the Earth around the sun, with the sun's orbit around the galactic core, and the galaxy's drift through intergalactic space... What makes the trajectory of the Earth clock so special?

The discrepancy between the clock on the ground and the clock on the aircraft can only be explained by the relative motion between the clocks as that was the only material difference between the 2 clocks in the experiment.

 

[Nugatory]

From this definition it follows that the tick rate of a clock will never vary which is contradicted by the evidence of the Hafele Keating experiment.

No, from that definition it follows that what you are calling the tick rate is a frame-dependent quantity.

And - although I'm not sure that saying this again is going to do you any good - the different elapsed time measurements in the HK experiment and the twin paradox are not explained by different tick rates. If the airborne experimenters in the HK experiment were to be in continuous communication with the ground station, they would find that the effect of their relative speed is that the ground clock was ticking more slowly than their own at all times. So if what you're calling the "tick rate" were what mattered, the ground-based clock would be the one that ticked less often.

(This is using the simultaneity convention of the momentarily comoving inertial frame, the only sensible way of comparing tick rates. The alternative, ticks per second of proper time, leads to the tautological conclusion that both clocks are ticking at a rate of one second per second).

 

[PeterDonis]

Your driving analogy is only applicable to time dilation if the odometers measure the same distance despite the fact that we have traveled different distances.

Wrong. Odometers measure distance traveled through space. Clocks measure distance traveled through spacetime. The analogy is valid.

What is invalid is your belief that any path through spacetime between two given events must have the same "length", which is just as nonsensical as the belief that any two paths in space between two locations must have the same length. The fact that there is a path of shortest length in space between two locations does not mean all paths through space between those two locations have that length. Similarly, the fact that there is a path of longest timelike length between two given events in spacetime does not mean all paths through spacetime between those two events have that timelike length.

 

[Nugatory]

@james fairclear There is no point in you continuing to post into a thread when you are refusing to listen.

You will no longer be able to post into this thread.

 

[PeterDonis]

The discrepancy between the clock on the ground and the clock on the aircraft can only be explained by the relative motion between the clocks as that was the only material difference between the 2 clocks in the experiment.

No, the relative motion was not the only material difference. The different clocks took different paths through spacetime; that is the material difference. The relative motion is one side effect of that, but not the only one.

 

[PeterDonis]

You will no longer be able to post into this thread.

Which, since he was the OP of the thread, means the thread is now closed.