Synchronization of Earth clocks

In summary, when comparing two clocks in a non-inertial frame, the clock with the least acceleration will age more. This can be seen by considering an inertial observer at the center of the Earth and calculating the elapsed times of two accelerating observers making a loop from event A to B. The clock that goes against the rotation will age more due to reduced total acceleration. This is known as the Sagnac effect.
  • #1
psmitty
16
0
If we have two clocks, one stationary at surface of Earth, and the other one very slowly moved at the surface of Earth, in the direction of Earth rotation, the clock that made the trip should be running ahead of the same stationary clock once it makes a complete circle and stops where it started from (if I got it right).

In an inertial frame, they should remain synchronized at low relative speeds, but on Earth, being a non-inertial frame, no matter how slowly you move a clock, it goes out of sync when you move it.

Also, if you move it half way in one direction, and return it back, it will get back to sync with the stationary one.

Should this be considered as time dilation, some sort of a or change in simultaneity? I mean, for a slowly moving clock, this difference in time seems to be a function of Earth's rotation speed and clock's traveled distance along the surface.

So how do I get this function for time difference?
 
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  • #2
I'm new to relativity, but this is my understanding.

It is the "time" traveled in an accelerated frame that causes times to differ, not the actual movement direction.

It is only the relative delta of time spent at larger speeds during movement of two clocks with respect to each other that counts

If you accelerate it in order take it around the earth, then decelerate it to stop it, The clock will be slower. If you never decelerated and just did a checkpoint at that time when the clock passed the time difference would be slightly greater because the clock was moving longer at high speed.

If you take off on a round trip to the nearest star and get yourself to relativistic speeds by spending a lot of time accelerating or a lot of energy to accelerate fast, then come back to the same place where you left that clock, the time difference would be much larger. If you wanted to stop over and visit that star (decelerate). The time difference would still be large, but not as large as in the previous case because the subject would spend less time near the speed of light.

In all four cases of the five clocks may have returned at the same time, but all clocks would show different times.
 
  • #3
psmitty said:
Should this be considered as time dilation, some sort of a or change in simultaneity? I mean, for a slowly moving clock, this difference in time seems to be a function of Earth's rotation speed and clock's traveled distance along the surface.

So how do I get this function for time difference?
Are you looking for a full GR analysis or do you just want to treat the Earth as a rotating massless sphere in flat spacetime? If the latter you might look at analyses of the Sagnac effect which often use rotating frames...pages 102-106 of this book might also be helpful (gives the line element ds^2 in a rotating frame, which can be used to calculate elapsed time along any parametrized curve)...likewise p. 84 of this book gives a "time dilation" formula for [tex]d\tau /dt[/tex] in a rotating frame (rate at which clock time [tex]\tau[/tex] is increasing relative to coordinate time t)
 
  • #4
JesseM said:
Are you looking for a full GR analysis or do you just want to treat the Earth as a rotating massless sphere in flat spacetime?
I don't think the GR analysis gives a different result than the SR analysis, because the clock is moving along an equipotential. It's just the Sagnac effect.
 
  • #5
psmitty said:
Should this be considered as time dilation, some sort of a or change in simultaneity? I mean, for a slowly moving clock, this difference in time seems to be a function of Earth's rotation speed and clock's traveled distance along the surface.

So how do I get this function for time difference?
Assuming you are only interested in the special relativity approach we can ignore gravity completely.

Basically you want to compare the elapsed times of two accelerating observers making a loop from event A to B.

The simplest way to do this is to consider a third observer who is inertial, for instance an observer at the center of the Earth. He sees two clocks with two different accelerations going from event A to event B. Then it is simply a matter of calculation to verify that the clock with the least acceleration will age most. Which is the clock that goes against the rotation, because this will reduce the total acceleration.
 

Related to Synchronization of Earth clocks

1. How do we synchronize Earth clocks?

Earth clocks are typically synchronized using a standard called Coordinated Universal Time (UTC). UTC is based on highly accurate atomic clocks and is adjusted periodically to account for the Earth's rotation. This ensures that all clocks around the world are synchronized to the same time.

2. Why is it important to synchronize Earth clocks?

Synchronizing Earth clocks is important for maintaining accurate timekeeping for various systems and activities. This includes international communication, financial transactions, and GPS navigation. It also helps to avoid confusion and discrepancies in scheduling and time-sensitive events.

3. How often are Earth clocks synchronized?

Earth clocks are synchronized multiple times a year through a process called leap seconds. Leap seconds are added to UTC to account for the gradual slowing of the Earth's rotation. This keeps UTC in sync with the Earth's position and ensures that clocks are accurate.

4. Are all Earth clocks synchronized to the same time?

Yes, all Earth clocks are synchronized to UTC, which is the global standard for timekeeping. This means that regardless of the time zone or location, all clocks around the world are synchronized to the same time at any given moment.

5. How does daylight saving time affect the synchronization of Earth clocks?

Daylight saving time (DST) does not affect the synchronization of Earth clocks. While DST may change the local time in certain regions, it does not affect the overall synchronization of Earth clocks to UTC. This is because DST is accounted for in the time zone offset, not in the synchronization of clocks to UTC.

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