Most people reading this thread will be familiar with images such as this one which depicts how a massive object distorts/bends the space in which it is embedded (and, as shown here, how, if massive enough, the object can become pinched off from that space, i.e. form a black hole). And, last but not least, similar depictions demonstrating how two masses will move towards each other due to the combined effect of each one’s warping of space.
I should say that I assume these images apply on all scales of mass and distance in the same way that Newton’s apple reminded him that the laws of gravity apply as much for an apple’s mass from tree-top height as they do for the lunar mass from a quarter million miles away.
How should we interpret these type of images when thinking about gravity on our familiar, human scale? Does the last one above, in particular, fairly represent what goes on when, say, I let a ball drop from my hand onto the ground? In other words, do either of the following “descriptions” apply:
a) the space between the ball and the floor gradually diminishes until it’s zero (i.e. when the ball meets the floor)?
Or,
b) as the ensemble (hand, ball, floor) moves through space-time, there is a favoured trajectory formed for the ball by the curvature induced by the mass of the floor (i.e. the Earth) and even a little bit due to the curvature caused by the mass of the ball?
Thanks!
Most people reading this thread will be familiar with images such as this one which depicts how a massive object distorts/bends the space in which it is embedded (and, as shown here, how, if massive enough, the object can become pinched off from that space, i.e. form a black hole). And, last but not least, similar depictions demonstrating how two masses will move towards each other due to the combined effect of each one’s warping of space.
I should say that I assume these images apply on all scales of mass and distance in the same way that Newton’s apple reminded him that the laws of gravity apply as much for an apple’s mass from tree-top height as they do for the lunar mass from a quarter million miles away.
How should we interpret these type of images when thinking about gravity on our familiar, human scale? Does the last one above, in particular, fairly represent what goes on when, say, I let a ball drop from my hand onto the ground? In other words, do either of the following “descriptions” apply:
a) the space between the ball and the floor gradually diminishes until it’s zero (i.e. when the ball meets the floor)?
Or,
b) as the ensemble (hand, ball, floor) moves through space-time, there is a favoured trajectory formed for the ball by the curvature induced by the mass of the floor (i.e. the Earth) (and even a little bit due to the curvature caused by the mass of the ball) which directs the ball to the floor?
Thanks!
It’s properly thought of as the curvature of spacetime. The problem with thinking of it as the curvature of space is can be illustarted by two particles with the intially the same trajectory (i.e. their velcoities are intially pointing in the same direction), the paths the two particles take can quickly diverge. For example imagine a ball thrown parallel to the Earth surface a 1 m/s compared to a beam of light shone parallel to the Earth’s surface. The ball’s velocity will quickly change until it’s almost at right angles to it’s orginal velocity, whereas it’d be extremely difficult to detect any change in the photon’s trajectory due to the presence of the Earth. If gravity were the curvature of space we would expect it’s effect to be independent of velocity.
In spacetime objects travelling at different velcoities necessarily have different worldines. This can be seen from that if the worldines of two objects meet at an event and they have different velocities (at that event), then the larger the relative velocity, the larger the hyperbolic angle between the two worldlines will be.
