My question is about comparing the time dilation of a clock on a spinning disk versus a clock in the vicinity of a massive object. It seems there should be a connection between the two, because of the equivalence principle, but I'm missing something because I don't quite get the answer I would expect.(adsbygoogle = window.adsbygoogle || []).push({});

These are my reasoning steps:

1. The relation between the proper time of a clock rotating uniformly with [itex]\omega [/itex] at a distance ##r ## from the center, and a clock at rest at the center is:

[tex]\Delta t_r = \sqrt{1-r^2\omega^2/c^2}\Delta t_\text{center}[/tex]

2. The relation between the proper time of a clock inside a spherical gravitational field and the proper time of a clock far away is:

[tex]\Delta t_r = \sqrt{1-\dfrac{2GM}{rc^2}}\Delta t_0[/tex]

3. Now lets say we want to rotate our clock such that the centrifugal acceleration reproduces the effect of the gravitational acceleration, so we impose

$$ r\omega^2 = \dfrac{GM}{r^2} $$

but then we get two different relations for the time. Why?

[tex]\Delta t_r = \sqrt{1-r^2\omega^2/c^2}\Delta t_\text{center}[/tex]

[tex]\Delta t_r = \sqrt{1-2r^2\omega^2/c^2}\Delta t_0[/tex]

4. Now of course, there is no reason why the radius should be the same, so let me rephrase the question. We can always pick ##r## and ##\omega## such that the centrifugal acceleration reproduces the effect of gravity:

$$ r\omega^2 = \dfrac{GM}{R^2} $$

From the equivalence principle we would expect that these two cases should be equivalent, so the proper times of the two clocks should be the same. We can fix ## \Delta t_0=\Delta t_\text{center} ## if they are not moving with respect to each other. However, the relations we get are not quite the same, but still depend on the radius:

[tex]\Delta t_r = \sqrt{1-r^2\omega^2/c^2}\Delta t_\text{center}[/tex]

[tex]\Delta t_r = \sqrt{1-2rR\omega^2/c^2}\Delta t_0[/tex]

Why is that? Isn't this result contradicting the principle of equivalence? Or is there a mistake in my reasoning?

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Rotating Disk and Time Dilation

Loading...

Similar Threads - Rotating Disk Dilation | Date |
---|---|

I Clocks ON a rotating disk: What happens?? | May 7, 2017 |

B Do particles of a rotating disk just change position or also spin? | Mar 25, 2017 |

I Time dilation of a rotating disk | Mar 11, 2017 |

Disk rotating in a gravitational field, like a clock | Nov 20, 2014 |

Rotating disks and time dilation | Oct 23, 2009 |

**Physics Forums - The Fusion of Science and Community**