Atomic Clock Time Dilation Experiment

In summary, two atomic clocks placed on a satellite and on the ground are synchronized. After one year, due to the effects of both special and general relativity, the clock on the satellite will be slightly ahead of the clock on the ground. This is due to the time dilation caused by the high speed and the gravitational field experienced by the satellite. While the average speed of the satellite is 103m/s, the time dilation is not detectable by any current atomic clocks. However, in the real world, GPS satellites run slightly faster than clocks on Earth due to the combined effects of special and general relativity.
  • #1
HarleyM
56
0

Homework Statement



Two atomic clocks are synchronized. One is placed on a satellite which orbits around the Earth at high speeds for a whole year. The other is placed in a lab and remains at rest with respect to the earth. You may assume both clocks can measure time accurately to many significant digits.

a)Will the two clocks stil be synchronized after one year?
b) imagine the speed of light is much lower than its actual value. How would the results of this experiment change if the speed of light was only twice the average speed of the satellite? Explain your reasoning using a calculation.

Homework Equations



Δtm = Δts/√(1-v2/c2)

The Attempt at a Solution



a) I calculated the Δtm using a theoretical velocity (3x103m/s) and a theoretical Δts 3.1x107 (about how many seconds per year)

When calculated using Δtm = Δts/√(1-v2/c2) I find no time dilation.. 3.1x107/0.9999999999= 3.1x107

but the fact that the clocks can go to many significant digits worries me, I think they may not be synchronized after the experiment because of the obvious time dilation that will inevitably take place.. any input here would be awesome!

b) using the same theoretical #'s, and changing the speed of light of course, I determined much more time dilation would occur as expected, as objects approach the speed of light time dilation becomes very significant.

Δtm=3.1x107/√(1-1x10-6)
=31,000,015.5 s

significant time dilation as speed becomes closer to speed of light, or in this case speed of light becomes closer to speed of satellite.

Does everything seem logical and ok?

Thanks !
 
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  • #3
HarleyM said:
Two atomic clocks are synchronized. One is placed on a satellite which orbits around the Earth at high speeds for a whole year. The other is placed in a lab and remains at rest with respect to the earth. You may assume both clocks can measure time accurately to many significant digits.

HarleyM said:
When calculated using Δtm = Δts/√(1-v2/c2) I find no time dilation.. 3.1x107/0.9999999999= 3.1x107

Average speed of a satellite is about 103m/s in orbit
Going by this value, we find that γ ≈ 1
so i don't think there is much difference and that there is any atomic clock that will be able to calculate that ...
 
  • #4
SO yes, there is time dilation, but it is not detectable even by the most sensitive of atomic clocks?
 
  • #5
HarleyM said:
SO yes, there is time dilation, but it is not detectable even by the most sensitive of atomic clocks?

Lets say it is not detectable by nearly all of the atomic clocks we have till now ! :biggrin:
 
  • #6
ok, thank you very much for your help ! :)
 
  • #7
What you haven't taken into account is time dilation due to GR. While the clock in orbit will experience time dilation relative to the grounded clock due to the differential velocity, the clock on the ground will experience time dilation relative to the orbiting clock due to the gravitational field.
 
  • #8
alexg said:
What you haven't taken into account is time dilation due to GR. While the clock in orbit will experience time dilation relative to the grounded clock due to the differential velocity, the clock on the ground will experience time dilation relative to the orbiting clock due to the gravitational field.

Yes, 103m/s is the velocity of satellite wrt earth
 
  • #9
Looking at the real world GPS, they actually run faster than clocks on earth. Gravitational time dilation is greater than SR time dilation.

543px-Orbit_times.svg.png


From wiki:

For example, the relativistic time slowing due to the speed of the satellite of about 1 part in 10^10, the gravitational time dilation that makes a satellite run about 5 parts in 10^10 faster than an Earth based clock
 
  • #10
HarleyM said:
You may assume both clocks can measure time accurately to many significant digits.

Did they not include this in the question so that you would be able to mention the fact that there is Time dilation that is noticeable between the clocks? Similar to the early experiments with atomic clocks and airplanes?

I know next to nothing about Physics, just trying to learn myself and that was how I read the question.
 
  • #11
thats how I interpreted it as well, but I believe I got the question right. I guess its all about how you explain the answer.
 

1. What is an atomic clock time dilation experiment?

An atomic clock time dilation experiment is a scientific experiment that tests the effects of time dilation on atomic clocks, which are extremely precise timekeeping devices that use the oscillations of atoms to measure time. This experiment aims to demonstrate the effects of Einstein's theory of relativity, specifically the concept of time dilation, which states that time moves slower for objects in motion.

2. How does an atomic clock time dilation experiment work?

In an atomic clock time dilation experiment, two atomic clocks are synchronized and then one is placed in motion while the other remains stationary. After a period of time, the two clocks are compared and the one that was in motion will have recorded less time than the stationary clock, demonstrating the effects of time dilation.

3. Why is an atomic clock used in this experiment?

Atomic clocks are used in this experiment because they are extremely precise and accurate timekeeping devices. By using these clocks, scientists are able to measure very small differences in time and demonstrate the effects of time dilation on a microscopic level.

4. What is the importance of the atomic clock time dilation experiment?

The atomic clock time dilation experiment is important because it provides evidence for the concept of time dilation and supports Einstein's theory of relativity. It also has practical applications in fields such as space travel and satellite navigation, which require precise timekeeping.

5. What are some potential challenges in conducting an atomic clock time dilation experiment?

One potential challenge in conducting an atomic clock time dilation experiment is ensuring that the clocks are synchronized accurately. Any small discrepancies in synchronization can affect the results of the experiment. Additionally, the experiment must be conducted in a controlled environment to minimize any external factors that could affect the results. Another challenge is the high cost and specialized equipment required for this experiment.

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