APOD: NGC 922: Collisional Ring Galaxy (2012 Dec 17)

[neufer]

Interesting. Where did you get that?

I think he's just using the time it takes to fall 1 AU under the gravitational acceleration of the Sun.

Yes, half an orbit for an elliptical major axis of 1 AU (vs. a full orbit for an elliptical semi-major axis of 1 AU).

As you say, that is how bodies with mass behave under gravitation, which is modeled as a distortion of spacetime. It doesn't describe the motion of spacetime itself. Indeed, as I understand GR, the motion of spacetime isn't even a defined concept. I don't know- physically or mathematically- what it means for "space to disappear" into a black hole or any other mass. Under GR, space is a coordinate system, not a physical thing.

Throw a ball up in the air and the ball follows a slightly curved space-time trajectory at the speed of light that falls back to Earth. What we perceive is a slow parabolic trajectory of the ball in space over time... but space itself can be thought of as actually falling back into the earth (carrying the ball with it).

Click to play embedded YouTube video.

Curves in space-time do distort space (i.e., the standard image of space with a "pucker") at any given time but this is actually relatively minor. The Earth definitely does NOT go around the Sun due to the minor "space pucker"

Rather, the Earth goes around the Sun due to the collapse of space (i.e., the dynamic image of space "a waterfall cascade") into the Sun as time proceeds.

Pucker, n.

• 1. A fold; a wrinkle; a collection of folds.
  2. A state of perplexity or anxiety; confusion; bother; agitation.

[Chris Peterson]

Throw a ball up in the air and the ball follows a slightly curved space-time trajectory at the speed of light that falls back to Earth. What we perceive is a slow parabolic trajectory of the ball in space over time... but space itself can be thought of as actually falling back into the earth (carrying the ball with it).

If thinking of space that way provides an analogy that gives you a useful visualization tool, great. It doesn't seem to work for me, and from a more rigorous GR standpoint, I don't think the idea is physically meaningful. The distortion of spacetime is treated as a transformed coordinate system- the coordinates of one point in spacetime are not moving with respect to the coordinates of another point due to the presence of a massive body- which is what I'd consider to define the actual motion of spacetime.

[neufer]

Throw a ball up in the air and the ball follows a slightly curved space-time trajectory at the speed of light that falls back to Earth. What we perceive is a slow parabolic trajectory of the ball in space over time... but space itself can be thought of as actually falling back into the earth (carrying the ball with it).

If thinking of space that way provides an analogy that gives you a useful visualization tool, great. It doesn't seem to work for me, and from a more rigorous GR standpoint, I don't think the idea is physically meaningful. The distortion of spacetime is treated as a transformed coordinate system- the coordinates of one point in spacetime are not moving with respect to the coordinates of another point due to the presence of a massive body- which is what I'd consider to define the actual motion of spacetime.

Definitions of space-time are highly arbitrary and
are mostly for calculations, bookkeeping & conceptualization.

What is NOT arbitrary (i.e., what is actually physically real) are the Ricci and Riemann curvature components of space-time.

Space-time curves convergently into local gravitation bodies and all free falling space coordinates (whether arbitrarily fixed to baseballs, the Earth or Voyager 1) are FORCED to be attracted to local gravitation bodies (i.e., they are constantly being sucked into such bodies).

The most important point IMO is that no one should be left with the impression that the Earth curves around the Sun because space itself is curved. The Earth curves around the Sun because space is dynamic.

[Chris Peterson]

The most important point IMO is that no one should be left with the impression that the Earth curves around the Sun because space itself is curved. The Earth curves around the Sun because space is dynamic.

I would disagree completely with that assessment. The Earth moves in the path it does because of geodesics and the static curvature of space in this region. I have no idea what it even means to suggest that space (or spacetime) is "dynamic".

[neufer]

The most important point IMO is that no one should be left with the impression that the Earth curves around the Sun because space itself is curved. The Earth curves around the Sun because space is dynamic.

I would disagree completely with that assessment. The Earth moves in the path it does because of geodesics and the static curvature of space in this region. I have no idea what it even means to suggest that space (or spacetime) is "dynamic".

"Space is dynamic" means that space is curved in time.

Over a period of 64 days all of the space through which the Earth orbits at 30km/s
will have collapsed into the Sun because space-time is curved in that focused way.

It is not unlike my epidermis shedding onto my keyboard:

<<The stratum corneum is the outermost layer of the epidermis, and is made up of 10 to 30 thin layers of continually shedding, dead keratinocytes. As the outermost cells age and wear down, they are replaced by new layers of strong, long-wearing cells. The stratum corneum is sloughed off continually as new cells take its place, but this shedding process slows down with age. Complete cell turnover occurs every 28 to 30 days in young adults, while the same process takes 45 to 50 days in elderly adults.>>

[Markus Schwarz]

Definitions of space-time are highly arbitrary and
are mostly for calculations, bookkeeping & conceptualization.
What is NOT arbitrary (i.e., what is actually physically real) are the Ricci and Riemann curvature components of space-time.

What is arbitrary and relative are the coordinates used. As are the components of any tensor. What is independent of coordinates, and, hence, is physically meaningful, are the tensors themselves. Of course, you need to adopt a coordinate system to calculate a physical quantity, but you have to check whether the result is independent of the coordinates.

Space-time curves convergently into local gravitation bodies and all free falling space coordinates (whether arbitrarily fixed to baseballs, the Earth or Voyager 1) are FORCED to be attracted to local gravitation bodies (i.e., they are constantly being sucked into such bodies).

What exactly do you mean by "space-time curves"? Do you mean the paths taken by particles or the coordinate lines? Since you emphasized the coordinates, keep in mind that these are precisely the quantities that have no physical meaning. What is physically meaningful are the paths taken by particles, all of which are affected by gravitation. Free falling coordinates are adopted for calculations of free falling particles. In these coordinates the metric components depend on time, since the infalling observer notices an increase in the gravitational pull.

I go back to my question: how do you propose to build a "space-flow-o-meter", which would measure the "flow of space"? All you can measure is the flow of particles.

[neufer]

Space-time curves convergently into local gravitation bodies and all free falling space coordinates (whether arbitrarily fixed to baseballs, the Earth or Voyager 1) are FORCED to be attracted to local gravitation bodies (i.e., they are constantly being sucked into such bodies).

What exactly do you mean by "space-time curves"? Do you mean the paths taken by particles or the coordinate lines?

What I mean by "space-time curves" are the coordinate line curves that are due to Ricci and Riemann curvature.

Since you emphasized the coordinates, keep in mind that these are precisely the quantities that have no physical meaning. What is physically meaningful are the paths taken by particles, all of which are affected by gravitation.

Time & space have a physical meaning that we can keep track of
with arbitrary: clocks, measuring sticks and coordinate systems.

Free falling coordinates are adopted for calculations of free falling particles. In these coordinates the metric components depend on time, since the infalling observer notices an increase in the gravitational pull.

A infalling observer could only notice an increase in gravitational tidal forces (i.e., Ricci curvature).

I go back to my question: how do you propose to build a "space-flow-o-meter",
which would measure the "flow of space"? All you can measure is the flow of particles.

Precisely!

A "space-flow-o-meter" would make use of the flow of particles
the same way that one might measure the "flow of a stream" by dropping
(biodegradable) floating bodies into the flow and keeping track of their motion.

Or one could observe the motion of natural floating bodies such as
Sir Arthur Eddington did with the starlight photons "floating" past the sun
(although the use of photons is often a somewhat trickier proposition as Michelson & Morley found out).