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According to Einstein's general relativity, massive bodies should cause gravitational redshift.

How accurately has this been measured?

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    $\begingroup$ What research have you done? Without research, why are you Asking that here, instead of doing some research then coming here with detailed Questions about which parts of your results were unsatisfactory? $\endgroup$ – Robbie Goodwin Aug 7 '20 at 23:26
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A recent test (2018) using atomic clocks aboard two satellites found general relativity's gravitational redshift prediction to be accurate to $(+0.19 \pm 2.48)\times10^{-5}$.

This was not a planned experiment and the satellites had accidentally been delivered on elliptic rather than circular orbits in 2014. They were useless for their original purpose of navigation. Instead of taking a complete loss, the satellites were repurposed for experimentation.

Previously the most accurate measurement was taken in 1976 by Gravity Probe A which had an accuracy of 70 parts per million. The new test improves the accuracy by a factor of 5.6.

See the paper, "A gravitational redshift test using eccentric Galileo satellites".

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    $\begingroup$ Could you explain what the units of measurement are for that value? $\endgroup$ – StayOnTarget Aug 7 '20 at 13:33
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    $\begingroup$ @UuDdLrLrSs: that is undoubtably a fractional error, so the measured and predicted values agree within $2$ parts in a million. $\endgroup$ – Ross Millikan Aug 7 '20 at 13:54
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    $\begingroup$ @RossMillikan thanks but I didn't mean the scale, but the actual units. eg, meters... $\endgroup$ – StayOnTarget Aug 7 '20 at 13:55
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    $\begingroup$ @UuDdLrLrSs: Fractional errors have no units. The article is saying that the observed gravitational redshift is as predicted to within this error. $\endgroup$ – Ross Millikan Aug 7 '20 at 14:00
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    $\begingroup$ @UuDdLrLrSs It’s like a percentage. Like “I’m 99 per cent sure” means “I’m 1 % uncertain,” meaning your uncertainty is $1\:\%=10^{-2}$ . . . except this is on the order of $10^{-5}$. $\endgroup$ – gen-ℤ ready to perish Aug 7 '20 at 15:40
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Fifty years, ago, the Pound-Rebka experiment demonstrated gravitational blue shift on Earth in a tower at Harvard, to an accuracy of 10%.

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