Question

Apparently there is a gravity anomaly in the Hudson Bay Area in Canada: gravity is "missing" or it is slightly less than it is in the rest of the world.

Does that mean that things in the Hudson Bay Area would theoretically be at a higher gravitational potential, and consequently clocks would run faster there? Would people living there have "more time" than people in other parts of the world - even if over their lives it only amounted to a few nanoseconds?

Answer 1

Yup. Just a special instance of gravitational redshift, which has been tested with atomic clocks at different elevations or flown on airplanes, precision clocks in orbit, etc.

Relativistic effects of anomalies due to lower rock density or underground voids aren't any different from the effects of just being at a higher elevation.

Just one thing to clarify, though, since it is commonly misunderstood, even if it's clear to you. Time still passes at one second per second over there just as it does here or anywhere. If someone is going to live for exactly 100.00000 years, they'll live for 100.00000 years on Mt. Everest if they're born there and stay there all the time, and they'll live for 100.00000 years at the bottom of the ocean if they spend their whole life there. It's only in the comparison of clocks that start together, travel apart, then come together again, that we find 100.00000 years on Mt. Everest doesn't match 100.00000 in the deep. This is the famous twin "paradox". Alternatively, an observer by one clock could watch the other clock with binoculars, and see it ticking faster or slower. This is redshift, and can be due to motion or due to differences in gravitational potential.

So yes, someone near Hudson Bay area can tell the boss "I'll get it done in an hour", rush over to where the anomaly is strongest, and have a leisurely 1.0000000003 hours to finish up that report. By the precision stopwatch the boss uses, 1.0000000000 hours have gone by when the report lands on his desk. This is assuming miraculous travel times. (Made up numbers. Exact calculation = exercise for the student!)

There's plenty of reading on the web about gravimetry and the geoid - an accurate detailed shape of the Earth based on gravitational potential, for background to understanding the funny business at Hudson Bay.