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metastable

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In summary: Of course, there may be complications if the clocks are not brought back in the same exact state they were in when they were loaded onto the space station.

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metastable

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Ibix

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Generally, elapsed time is a measure of the "length" of an object's worldline. If you sync clocks then move them in the same way then they have identical worldlines, so identical elapsed times and are obviously in sync at the end. If they don't move in the same way then they have different worldlines that may or may not have the same elapsed time so they may or may not end up in sync.

The answer for your scenario therefore depends (in principle) on details of how you load and unload the clocks, since that's where you could be treating them differently. Such differences are almost certainly negligible.

The answer for your scenario therefore depends (in principle) on details of how you load and unload the clocks, since that's where you could be treating them differently. Such differences are almost certainly negligible.

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A.T.

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Is there no simpler scenario possible to get to the point?metastable said:

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jbriggs444

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I would expect the result to "average out", but have no clue how to begin assessing second order effects.

One can arrange to slowly move the clocks from a common box at the start of the ride to their respective cars and slowly move the clocks back to the box after the ride. The only interesting part of the scenario is what happens during the ride.

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metastable

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Ibix said:If they don't move in the same way then they have different worldlines that may or may not have the same elapsed time so they may or may not end up in sync.

The answer for your scenario therefore depends (in principle) on details of how you load and unload the clocks, since that's where you could be treating them differently. Such differences are almost certainly negligible.

So if the clocks are brought back to the space station will they remain in sync with a 7th clock that remained on board the whole time?

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jbriggs444

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For a space station in low Earth orbit, I believe that time dilation from orbital speed dominates over the earthbound time dilation from gravitational potential. The space station clock will be slow relative to the clocks that took a holiday at the theme park.metastable said:So if the clocks are brought back to the space station will they remain in sync with a 7th clock that remained on board the whole time?

Barring some

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Ibix

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No.metastable said:So if the clocks are brought back to the space station will they remain in sync with a 7th clock that remained on board the whole time?

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A.T.

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Why do you need 7 clocks for this?metastable said:...7th clock...

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metastable

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If I understand the scenario correctly, the 6 clocks are out of sync during the loop the loops, but return to synchrony at the end of the ride. But I suppose you are correct 5 or fewer clocks might do to confirm whether I have a correct understanding.A.T. said:Why do you need 7 clocks for this?

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A.T.

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Maybe also ask yourself if you really need all the other stuff.metastable said:But I suppose you are correct 5 or fewer clocks might do to confirm whether I have a correct understanding.

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metastable

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Ibix

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jbriggs444

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As I understand it, it is only in the weak field limit that gravitational time dilation and velocity time dilation can be successfully modeled as independent effects that combine linearly.metastable said:

GPS is a good worked example where the tick rate of clocks that are moving and are at altitude has been calculated and measured.

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metastable

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Ibix said:

I think it is a very simplified case compared to the study of gravitational and velocity time dilation effects in the previously discussed more complicated scenario involving canceling galactic orbital velocity with a 215km/s burn, performing Oberth maneuvers at periapsis with each passing star, followed by a final Oberth maneuver in proximity to Sagittarius A*.

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Ibix

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That doesn't answer the question. What are you hoping to learn here? Why are you inventing difficult-to-generalise scenarios involving roller coasters and surface-to-space transfers?metastable said:I think it is a very simplified case compared to...

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metastable

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PeterDonis

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metastable said:I think it is a very simplified case

Your definition of "simplified" does not appear to be the same as anyone else's.

metastable said:

Extreme velocity means more time dilation. Extreme gravitational fields mean more time dilation. That's about the best that can be done at a "B" level given the generality of what you're asking. Thinking up various complicated scenarios that are difficult and time consuming for other people to analyze won't change that.

If you want more detail than that, you need to learn the actual math, so that you can do the calculations yourself instead of trying to outsource them to other PF posters.

Thread closed.

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Nugatory

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For that, you will have to follow a more disciplined path. Start by learning special relativity (in the simplest case of no gravity and no acceleration) and understanding how velocity-based time dilation is related to the relativity of simultaneity. Get comfortable with applying the Lorentz transformations. Use them to resolve the twin paradox and Bell's spaceship paradox.metastable said:

Because you eventually want to understand gravitational effects, next you'll need to learn the geometrical approach to SR; this is usually an early chapter in GR textbooks, and the treatment in Taylor and Wheeler's "Spacetime Physics" is also good.

After this you'll be able to start considering problems in which gravity is relevant. Not ethat "extreme" gravitational fields implies that the weak field approximation doesn't apply, so be cautious about anything you read that doesn't show the math.

During a roller coaster ride, the clocks experience various forces such as acceleration, deceleration, and changes in direction. These forces can affect the internal mechanisms of the clocks, causing them to run at slightly different speeds and leading to desynchronization.

Yes, it is possible to keep multiple clocks in sync after a roller coaster ride. However, it may require adjustments or recalibration of the clocks to ensure they are running at the same speed.

Aside from the forces experienced during the ride, other factors such as the quality and precision of the clocks, the duration and intensity of the ride, and the temperature and humidity can also affect the synchronization of clocks after a roller coaster ride.

There are some methods that can help prevent clocks from desynchronizing after a roller coaster ride. These include using high-quality and precise clocks, minimizing the duration and intensity of the ride, and keeping the clocks at a stable temperature and humidity.

No, the synchronization of clocks after a roller coaster ride cannot be used as a measure of the ride's intensity. The desynchronization of clocks is influenced by various factors, and it is not a reliable measure of the ride's intensity.

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