I Gravity as Curvature of Spacetime: Understanding Einstein's Theory

[EPR]

Just wanted to point out that i have never seen a better depiction of Einsteinian gravity, if a little hard to swallow and somewhat baffling to human intuition.

In the following experiment prof. Brian Cox(he used to be on this forum?) says:

"Isaac Newton would say that the ball and the feather fall because there’s a force pulling them down: gravity,’.
But Einstein imagined the scene very differently.

"The “happiest thought of his life” [as Einstein called it] was this; the reason the bowling ball and the feather fall together is because they’re not falling.

"They’re standing still. There is no force acting on them at all."He reasoned that if you couldn’t see the background, there’d be no way of knowing that the ball and the feathers were being accelerated towards the Earth.

"So he concluded they weren’t."

So, the ball and the feather are not falling. They are standing still. What moves is the observer through 4D spacetime experiencing the curvature of spacetime as gravity.

 

[PeterDonis]

Moderator's note: Moved thread to relativity forum.

 

[PeterDonis]

the ball and the feather are not falling. They are standing still

Yes. More precisely, one can always adopt a local inertial frame in which the ball and the feather are at rest.

What moves is the observer through 4D spacetime experiencing the curvature of spacetime as gravity.

Note that this is a different meaning of the word "move". "Moving" through spacetime is not the same as moving through space.

 

[PeroK]

So, the ball and the feather are not falling. They are standing still.

Here's the thing. Imagine another ball much further from the Earth. It, too, is "standing still". But, gravity is weaker further from the Earth, hence, relative to the Earth, the second ball is not accelerating as fast as the first.

The two balls, therefore, are both standing still yet moving relative to each other.

Interesting!

 

[PeterDonis]

an observer standing on Earth would detect this relative motion of the balls and deduce they are falling in a gravitational field?

however for an observer freely falling with the balls they are both at rest

No. The relative motion of the balls in the case @PeroK described is frame invariant. It is a manifestation of tidal gravity, aka spacetime curvature.

 

[kent davidge]

No. The relative motion of the balls in the case @PeroK described is frame invariant. It is a manifestation of tidal gravity, aka spacetime curvature.

ah, ok. the accelerating frame (according to earth) of the freely falling observer can have only one of the balls at rest at a time. correct?

 

[PeterDonis]

the accelerating frame (according to earth) of the freely falling observer can have only one of the balls at rest at a time. correct?

Yes.

 

[strangerep]

The two balls, therefore, are both standing still yet moving relative to each other. Interesting!

Gotta love geodesic deviation.