# Twin Paradox and General Relativity

*Most recent answer: 10/22/2007*

Q:

is the twins paradox the only example of gravity affecting time? isnt the time varyation due to thay the clock in the tower traveling faster and further due to the rotation of the earth,

- chris (age 18)

horsham westsussex England

- chris (age 18)

horsham westsussex England

A:

Great question, Chris!

The twin "paradox" we discuss in several other answers to questions on this web site deals with an effect which is easy to explain with special relativity -- moving clocks run slow. A clock that is taken away at high speed, accelerated to turn around, and brought back, will read less time than an identical clock which doesn’t go on the trip.

As you correctly mention, there are additional effects Gravity has on time. Clocks that are deep within gravitational fields run slower than ones that are farther out. If the earth did not rotate, you could put a clock at the bottom of a tower and a clock at the top of a tower and the clock at the top of the tower would run faster than the one at the bottom. The difference is quite small, however, and you have to be very careful that other effects (the special relativistic time dilation effect in particular) are not bigger than the gravitational effect. For example, you could compare the clocks halfway up the tower and arrange it so that each clock undergoes the same speed versus time journey from the middle of the tower to the top and bottom, and do the same thing at the end of the experiment when the clocks are brought together for comparison.

As you even more correctly state, the fact that the Earth rotates complicates the experiment -- the clock at the top of a tower is moving faster (in the reference fram of the Earth) than the one at the bottom and therefore the special-relativistic time dilation will make it run slow relative to the one at the bottom of the tower. (Viewed from the point of view of the clock’s ’accelerating’ frame, the same effect seems like a General Relativistic effect. mbw) So if you did a real experiment with a real earth and a real tower (the clocks would probably be some maser or other atomic frequency standard, which produces electromagnetic waves, which conveniently could be used to interfere with a similar system at the bottom of the tower and the change in constructive/destructive interference over time would be a very sensitive measure), you would have to correct for the special relativistic time dilation just due to the motion. (This correction, however, is quite small compared to the gravitational effect. mbw)

Actually, the experiment done at Harvard used the Mossbauer effect, a really amazing feature of solids whereby a material can absorb a photon within a narrow absorption resonance which is not broadened by the Doppler shift due to the recoil of an atom after the absorption. In effect, the entire block of absorbing material picks up the recoil momentum. So if the absorption resonance is very narrow and matched to a narrow emission line, then the absorption rate is very very very sensitive to slow motions of the absorber and the emitter via the ordinary Doppler effect. By putting the emitter at the top of a tower and the absorber at the bottom, and making one move slowly towards (or away from) the other, the absorption rate can be scanned out versus the doppler shift, and the time dilation effects can be measured with extreme precision. You can exchange the emitter and the absorber for cancellation of some systematic uncertainties.

Sources:

Pound and Rebka, "Apparent wieght of Photons"

Phys. Rev. Lett. 4 337 (1960)

Pound and Snider "Effect of gravity on nuclear resonance"

Phys. Rev. Lett. 13 539 (1964)

Pound and Snider "Effect of gravity on gamma radiation"

Phys. Rev. B 140, 788 (1965)

Well done!

Tom Junk

The twin "paradox" we discuss in several other answers to questions on this web site deals with an effect which is easy to explain with special relativity -- moving clocks run slow. A clock that is taken away at high speed, accelerated to turn around, and brought back, will read less time than an identical clock which doesn’t go on the trip.

As you correctly mention, there are additional effects Gravity has on time. Clocks that are deep within gravitational fields run slower than ones that are farther out. If the earth did not rotate, you could put a clock at the bottom of a tower and a clock at the top of a tower and the clock at the top of the tower would run faster than the one at the bottom. The difference is quite small, however, and you have to be very careful that other effects (the special relativistic time dilation effect in particular) are not bigger than the gravitational effect. For example, you could compare the clocks halfway up the tower and arrange it so that each clock undergoes the same speed versus time journey from the middle of the tower to the top and bottom, and do the same thing at the end of the experiment when the clocks are brought together for comparison.

As you even more correctly state, the fact that the Earth rotates complicates the experiment -- the clock at the top of a tower is moving faster (in the reference fram of the Earth) than the one at the bottom and therefore the special-relativistic time dilation will make it run slow relative to the one at the bottom of the tower. (Viewed from the point of view of the clock’s ’accelerating’ frame, the same effect seems like a General Relativistic effect. mbw) So if you did a real experiment with a real earth and a real tower (the clocks would probably be some maser or other atomic frequency standard, which produces electromagnetic waves, which conveniently could be used to interfere with a similar system at the bottom of the tower and the change in constructive/destructive interference over time would be a very sensitive measure), you would have to correct for the special relativistic time dilation just due to the motion. (This correction, however, is quite small compared to the gravitational effect. mbw)

Actually, the experiment done at Harvard used the Mossbauer effect, a really amazing feature of solids whereby a material can absorb a photon within a narrow absorption resonance which is not broadened by the Doppler shift due to the recoil of an atom after the absorption. In effect, the entire block of absorbing material picks up the recoil momentum. So if the absorption resonance is very narrow and matched to a narrow emission line, then the absorption rate is very very very sensitive to slow motions of the absorber and the emitter via the ordinary Doppler effect. By putting the emitter at the top of a tower and the absorber at the bottom, and making one move slowly towards (or away from) the other, the absorption rate can be scanned out versus the doppler shift, and the time dilation effects can be measured with extreme precision. You can exchange the emitter and the absorber for cancellation of some systematic uncertainties.

Sources:

Pound and Rebka, "Apparent wieght of Photons"

Phys. Rev. Lett. 4 337 (1960)

Pound and Snider "Effect of gravity on nuclear resonance"

Phys. Rev. Lett. 13 539 (1964)

Pound and Snider "Effect of gravity on gamma radiation"

Phys. Rev. B 140, 788 (1965)

Well done!

Tom Junk

*(published on 10/22/2007)*