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Physics, Astronomy & Cosmology / Re: Are clocks ticking faster where gravity is stronger?
« on: 08/05/2018 18:10:11 »Ok - I get where you are coming from @chiralSPONo, it doesn't. GRACE is measuring the local field strength at a fixed altitude. From this, you could calculate the field strength at any other fixed altitude (say, Mean Sea Level). This means that the map does not represent the value of g at the actual physical surface, But the difference in measured g at the same altitude for different parts of the globe.
But:Being higher up on the mountain places one further out of the gravitational well than being in the valley.
Being placed further outside of a gravity well is a gravity potential consideration, rather than a strength of gravity consideration. If GRACE feels more acceleration (stonger gravity) over a mountain, compared to a valley, then a clock on that mountain, or in that valley will be feeling the same difference.
So let's say that our reference altitude is Mean Sea level. This means that an object sitting in valley floor at MSL in the Andes would feel more gravity and weigh more than an object sitting at MSL in Western Australia. But it does not mean that an object sitting on a peak of the Andes would feel a stronger gravity and weigh more than it would in Western Australia, which is at a lower altitude. If you look at the image from GRACE, you will note that the scale at the bottom is marked in milligals. A "gal" ( which named after Galileo) is 1cm/sec^2. a milligal is 1/1000 of that. Between The region of the Andes and Western Australia, we get a difference of ~50 milligals or ~5e-7g (with 1g being standard Earth surface gravity)
That's a really small variation in g. Compare this to the actual difference in surface gravity when you take the altitude of the surface into account. Kumarina, in Western Australia is 610m above MSL, and the tops of the Andes are over 6000 m above MSL. Going from MSL to 610 m above causes a decrease in local gravity of ~0.00019g. Going from MSL to 6000 m, causes a decrease of ~0.00188g or about 10 times more a decrease. And both of these completely swamp out the 5e-7 g difference caused by local variations in the Earth gravitational field. So a clock on a mountain peak of the Andes still weighs less than it would in Kumarina, Australia, despite the local variations in the Earth's gravitational field.
But again, even if this were not the case, As I already pointed out, GR would still predict that a clock would run faster on the mountain top ( It would just change the exact amount of the differential. For example, if we assume a 1g standard at MSL, and compare a clock at MSL to one on top of a mountain, If gravity strength lower at the top of the mountain than it is at MSL, a clock there will run faster than the one at MSL by a smaller factor, than if the gravity was stronger at the top than at MSL. It would take more work to climb from MSL to the peak against gravity that gets stronger as you climb, than it would to do so against gravity that gets weaker as you climb.)
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