Monday, July 31, 2017

Newton said that gravity is a force that pulls objects. Einstein said that gravity is a curvature in spacetime that pushes objects. Can you clarify?

https://www.quora.com/

In the end, a force arises when a particle tries to follow a spacetime geodesic that deviates from a straight line, mostly due to the presence of “time curvature”, that is, due to the fact that clocks tick at different rates at different points in a gravitational field.

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Viktor T. Toth
Viktor T. Toth, IT pro, part-time physicist
First of all, before you read any further: Go and grab something heavy. Say, a brick. Feel it in your hands. Feel as it is trying to pull your hands down.
If you do not feel a force, you need not read any further. Please leave the room. I’ll wait a few seconds while you grab your things.
[…]
OK, now that we have established that gravity is a force, let’s take a look at how it works.
Newton’s law of gravitation is an example of action-at-a-distance: two bodies influencing each other over a distance without anything mediating that influence. This troubled Newton so deeply, he delayed publishing his work on gravity for many years; and even after it was published, he had deep misgivings, as evidenced, e.g., by these words from a letter to Bentley in 1692 or so: "It is inconceivable that inanimate Matter should, without the Mediation of something else, which is not material, operate upon, and affect other matter without mutual Contact [...] Gravity must be caused by an Agent acting constantly according to certain laws".
In the late 1800s, thanks to the work of Maxwell, the concept of a field was born in physics. Electricity and magnetism (and incidentally, light) were explained by the concept of the electromagnetic field and its fluctuations. Soon it became evident that gravitation must also be mediated by a field. But what form shall that field take?
Gravity has an important property: Unlike other interactions, gravity is universal. All material particles respond to gravitation the same way, regardless of their material composition or other properties. This is what made Einstein realize that gravity is necessarily a geometric theory: that is to say, the effects of gravity are indistinguishable from the effects of acceleration, so if the latter can be described using geometry, so can the former.
But let me now jump ahead a bit and ask… could we not describe other forces, e.g., electromagnetism, using geometry? And the answer is that we can… but with an unpleasant twist. The geometry “experienced” by particles with different charge-to-mass ratios will differ. There will also be a “reference” geometry, the one sensed by neutral particles that do not respond in any way to the electromagnetic field.
In contrast, because gravity is universal, all particles experience the same geometry. Not only that, but there are no gravitationally neutral particles, so there is no reference geometry that we can explore or measure. Really, the only geometry in town is that determined by gravity.
So whereas for electromagnetism, the geometric interpretation is either a curiosity or a useful mathematical tool depending on your preference, for gravity, it has unique significance. This is what allows us to proclaim that gravity and spacetime curvature are really the same thing, because no matter what you use to measure spacetime: rulers, beams of light, etc., you will experience the same distorted geometry when gravity is present.
In the end, a force arises when a particle tries to follow a spacetime geodesic that deviates from a straight line, mostly due to the presence of “time curvature”, that is, due to the fact that clocks tick at different rates at different points in a gravitational field. This force may be a fictitious force like the infamous centrifugal force, or it may be a real force, like the centripetal force, when there is something (say, a floor) in a body’s way preventing the body from following a geodesic. Either way, it is a very real force that you can feel, measure with a force gauge, or even experience as pain if you are clumsy enough to drop the aforementioned brick on your feet.

TL;DR: Gravity is a force. It is mediated by a field that has a geometric interpretation. This geometry applies uniformly to all particles as the only geometry that can be measured or experienced, because gravity is universal.
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