4 ms·

This is because Shortt clocks are pendulum clocks whose oscillation period directly depends on the gravitational acceleration. Quarz oscillators and atomic cloc

by fsh 6y ago

This is because Shortt clocks are pendulum clocks whose oscillation period directly depends on the gravitational acceleration. Quarz oscillators and atomic clocks are not affected by this.

mikewarot 6y ago
It took a while to sink in that gravity isn't anywhere near as simple as I usually think it is. I understand Gravitational Acceleration at the surface of the earth is on the order of 9.81m/sec^2 I also understand that if you take clocks to the mountains, they run slightly faster. What would happen if you put a clock at the bottom of a mine shaft a few miles down? (In an air-conditioned room, of course) How does the math work?
- fsh 6y ago
  A pendulum is a mechanical oscillator in which gravity provides the restoring force. For small oscillation amplitudes, the oscillation frequency of a pendulum of length l is 1/(2pi)sqrt(g/l), where g is the gravitational acceleration. Pendulum clocks are therefore directly affected by the local strength of gravity. This is usually not a problem because g is fairly stable and only the most advanced pendulum clocks were able to resolve some slight variations due to the tides. Other clock oscillators, such as balance wheels or quartz crystals do not show this effect. The reason why atomic clocks run differently at different heights is due to General Relativity. In GR, there is no such thing as a gravitational force. Instead, the presence of mass changes the shape of space and time itself. In the limit of small masses and low velocities, the resulting equations of motion exactly reproduce the ones from Newtonian mechanics. On top of that, it turns out that a difference in gravitational potential between two locations also results in a slightly different progression of time. In the classical limit, the gravitational time dilation is given by the the gravitational potential divided by the speed of light squared. Not too far from the surface of the earth this comes out to approximately 1E-16/m (9.8 m/s^2/(3E8 m/s)^2). The best optical clocks are stable on the level of 1E-18, so they can resolve a high difference on the cm level due to the gravitational time dilation.
  - mikewarot 6y ago
    What would be the dilation at the center of the earth? Classical gravity there would be zero.
    - fsh 6y ago
      The gravitational force would indeed be zero and a pendulum clock would not work. But the gravitational redshift between to locations is given by the potential difference, not by the local force. The potential difference between the surface and center of the earth can be calculated using Gauss' law and comes out to be 1/2gR, where g is the gravitational acceleration at the surface and R is the earth radius. As a result, a clock at the center of the earth would run slower than one at the surface by 3.5E-10.

by fsh 6y ago

This is because Shortt clocks are pendulum clocks whose oscillation period directly depends on the gravitational acceleration. Quarz oscillators and atomic clocks are not affected by this.

mikewarot 6y ago

It took a while to sink in that gravity isn't anywhere near as simple as I usually think it is. I understand Gravitational Acceleration at the surface of the earth is on the order of 9.81m/sec^2 I also understand that if you take clocks to the mountains, they run slightly faster. What would happen if you put a clock at the bottom of a mine shaft a few miles down? (In an air-conditioned room, of course) How does the math work?

fsh 6y ago
A pendulum is a mechanical oscillator in which gravity provides the restoring force. For small oscillation amplitudes, the oscillation frequency of a pendulum of length l is 1/(2pi)sqrt(g/l), where g is the gravitational acceleration. Pendulum clocks are therefore directly affected by the local strength of gravity. This is usually not a problem because g is fairly stable and only the most advanced pendulum clocks were able to resolve some slight variations due to the tides. Other clock oscillators, such as balance wheels or quartz crystals do not show this effect. The reason why atomic clocks run differently at different heights is due to General Relativity. In GR, there is no such thing as a gravitational force. Instead, the presence of mass changes the shape of space and time itself. In the limit of small masses and low velocities, the resulting equations of motion exactly reproduce the ones from Newtonian mechanics. On top of that, it turns out that a difference in gravitational potential between two locations also results in a slightly different progression of time. In the classical limit, the gravitational time dilation is given by the the gravitational potential divided by the speed of light squared. Not too far from the surface of the earth this comes out to approximately 1E-16/m (9.8 m/s^2/(3E8 m/s)^2). The best optical clocks are stable on the level of 1E-18, so they can resolve a high difference on the cm level due to the gravitational time dilation.
- mikewarot 6y ago
  What would be the dilation at the center of the earth? Classical gravity there would be zero.
  - fsh 6y ago
    The gravitational force would indeed be zero and a pendulum clock would not work. But the gravitational redshift between to locations is given by the potential difference, not by the local force. The potential difference between the surface and center of the earth can be calculated using Gauss' law and comes out to be 1/2gR, where g is the gravitational acceleration at the surface and R is the earth radius. As a result, a clock at the center of the earth would run slower than one at the surface by 3.5E-10.