Entanglement doesn't have any connection to time. It just means that the outcome of a measurement of one particle is correlated with the outcome of a measurement of the other. Those measurements could be performed at any times.

Perhaps I should say there's no unique choice for a universal "now". "Now" would be a 3D surface in 4D spacetime that intersects the point "earth in the year 2023". But there are lots of possible choices you could make in defining this surface, and none of these choices are more correct than the others.

The CMB frame is different in different places. It's also the frame of a comoving observer -- that is, one who is moving only due to the expansion of the universe and does not have further ("peculiar") motion. So if we consider distant galaxies in some direction, they are receding in that direction, and so is their CMB frame.

It's the center-of-momentum frame for all of the CMB photons (within some volume of space), not the frame of individual photons. It's also the frame in which the CMB temperature is the same in all directions. If you're moving with respect to that frame, you'll find that the CMB is hotter (blueshifted) in the direction of your motion and colder (redshifted) in the opposite direction. That's what we find, and the magnitude of this effect tells us that we are moving at 370 km/s with respect to the CMB.

yes, fixed, thanks!

When we say that the universe is 13.7 billion years old, this is actually in the rest frame of the cosmic microwave background, not that of the Earth. However, the difference due to gravitational time dilation (mostly due to the galactic potential) and kinematic time dilation (since we're moving at ~370 km/s with respect to the cosmic microwave background) is of order one part in a million, so any ambiguity in the age of the universe due to time dilation is much smaller than the measurement uncertainty in the "13.7 billion years" value.

More generally, the question of whether the age of the universe depends on where you are depends entirely on what convention you adopt. There is no such thing as a universal "now". If you wanted, you could define that "now" means the elapsed time, in the cosmic microwave background frame, is 13.7 billion years. This convention is called "synchronous gauge" and is commonly used in cosmology calculations. Under this convention, the age of the universe does not depend on position.

For other conventions, like the "Newtonian gauge" that is also commonly used in calculations, the age of the universe does depend on position.

> But is it a separation of molecules? That is, would an object just rip apart into pieces?

It's this one.

Tidal forces stretch objects along the radial direction (toward and away from the gravitating body) and compress them along the other directions. Spaghettification is the result of tidal forces taken to the extreme.

Right, the infalling object can't escape into our universe after it crosses the event horizon. In the idealized black hole construction, the infalling object will, however, escape into another universe (via a white hole) if it avoids hitting the singularity.

> An argument can be made that gravity exerts no net force, just using Newton's law and symmetry.

That's what Newton believed, but a more careful look reveals that the integral over all space that determines the gravitational force does not converge to a well defined value. See for example the dynamics of Newtonian cosmology.

Consider Newtonian gravity. If an object falls directly into the gravitating body with no sideways motion, it will simply collide. It's orbital angular momentum that causes the object to be ejected back outward.

How does this work? If you write down the equation of motion for the orbital distance r, two forces emerge. One is the gravitational attraction, which scales as 1/r^(2). The other is a centrifugal repulsion term, which scales as L^(2)/r^(3), where L is the angular momentum. As the distance r becomes small, the centrifugal repulsion eventually dominates, ejecting the object back out to apocenter, as you say.

This works because the attractive force scales as 1/r^(2) at distance r. If the attractive force scaled as 1/r^(3) or steeper, then the centrifugal repulsion would be no longer guaranteed to overpower the gravitational attraction at sufficiently small radii, so there would be nothing to prevent the orbiting object from eventually colliding with the central gravitating body.

While gravity in general relativity can't be exactly described by a radial force law, the same basic idea applies. See for example how a number of 1/r^(3), 1/r^(4), etc. terms arise in the post-Newtonian expansion (scroll to equation 203).

That's true for nonrotating black holes, anyway. In the idealized rotating black hole solution, it is actually possible for the centrifugal repulsion to overpower the gravitational attraction! This is what leads to the crazy conformal diagram for a rotating black hole that suggests you can fall in and emerge back out in a different universe. However, there are many good reasons to expect that this idea does not work for realistic black holes and is just an artifact of the idealized construction.

Indeed, that's one reason to be highly skeptical of that study. The "cosmological coupling" doesn't make sense in the context of general relativity. The global scale factor is not locally even a thing. In certain cosmological spacetimes, the scale factor isn't even uniquely defined globally.

The authors motivate the cosmological coupling by citing the behavior of black holes placed in otherwise homogeneous universes. Such black holes grow over time, but they grow by accreting the surrounding fluids (which are present due to the assumption of homogeneity), not by magically eating the scale factor, as the authors seem to suggest.

The only interpretation of the black-holes-as-dark energy idea that might make sense relativistically is that black holes have a negative-pressure coupling to other black holes. Then as the black holes separate from each other due to cosmic expansion, the negative pressure feeds them mass. This achieves the same outcome without positing a magical coupling to the global expansion factor.

Repeating a response I made to a similar question elsewhere in the thread:

Relative velocities of distant objects aren't well defined in curved spacetimes. It's often said that distant objects are receding faster than light, and there are standard ways of writing down their distance such that the distance grows faster than the speed of light. However, there is no relativistically meaningful sense in which these objects are moving faster than light in relation to us. Also, the distance isn't uniquely defined either.

In intuitive terms, the relative velocity is the angle between two vectors in spacetime. Imagine drawing two arrows on a sheet. If those arrows are in the same place, you can measure the angle between them. If they are in different places, but the sheet is flat, you can also define the angle between them uniquely. However, if they are in different places and the sheet is not flat, the angle between the arrows is not uniquely defined.

The CMB rest frame is the frame of a comoving observer, that is, one who is at rest with respect to their (cosmologically) immediate surroundings. At different locations, the CMB rest frames are different. There's no global "center of momentum frame" if the universe is homogeneous, only local ones.

(I should also note that in curved spacetimes, reference frames only make sense locally. However, this is more minor consideration, in a certain technical sense. While the impact of the difference in the velocities of different comoving observers scales linearly with their separation, the impact of curvature scales as the square of the separation. So the latter only becomes important at very large separations.)

That's a bit different because that idea refers to the curvature of space, not spacetime. Space is a 3D surface in 4D spacetime. There are lots of possible choices of spatial surface, but there is a unique choice that makes the universe homogeneous (statistically the same everywhere on the surface). The curvature of this particular choice of spatial surface can indeed inform us as to whether the universe will eventually collapse.

> The typical answer (summarized) is that "local mass interaction totally overcomes spatial expansion, so only the gravitional effect exists in local systems", but it still seems that there would still have to be some accounting that some of the gravitional "pull" is having to be "used up" to counteract the expansion.

This is indeed the typical answer but it's not correct. Expansion of space doesn't affect particle dynamics at all. It's just a mathematical convention.

See for example this entry of the askscience FAQ

Not quite because as I noted, dark energy supplies gravitational repulsion. In the big rip, the energy density of dark energy increases over time, and so does the repulsive force. That is what rips everything apart.

(Observations currently do not support that the energy density of dark energy is increasing.)

Relative velocities of distant objects aren't well defined in curved spacetimes. It's often said that distant objects are receding faster than light, and there are standard ways of writing down their distance such that the distance grows faster than the speed of light. However, there is no relativistically meaningful sense in which these objects are moving faster than light in relation to us. Also, the distance isn't uniquely defined either.

In intuitive terms, the relative velocity is the angle between two vectors in spacetime. Imagine drawing two arrows on a sheet. If those arrows are in the same place, you can measure the angle between them. If they are in different places, but the sheet is flat, you can also define the angle between them uniquely. However, if they are in different places and the sheet is not flat, the angle between the arrows is not uniquely defined.

Cosmic expansion really does just mean that things are moving apart in a uniform way. There is nothing fundamentally physical about the idea that space itself is expanding; that's just a mathematical convention that is convenient in some contexts. (It's a coordinate choice.)

Thus, the gravitational attraction of the matter in the universe slows the expansion precisely as it would slow the expansion of a distribution of matter inside the universe. Indeed, Newtonian gravity predicts exactly the correct expansion dynamics for a matter-dominated universe. Similarly, the gravitational repulsion of the dark energy accelerates the expansion (although there is some subtlety to this).

Further reading on expanding space not being a physically real phenomenon:

• A diatribe on expanding space

• The kinematic origin of the cosmological redshift

• On The Relativity of Redshifts: Does Space Really "Expand"?

Further reading on cosmological dynamics with Newtonian gravity:

• The dynamics of Newtonian cosmology

• or more generally, just search for "Newtonian cosmology"

In the metric of spacetime, spatial distances and temporal distances enter with the opposite sign. In ordinary Euclidean geometry, the distance between two points separated by x, y, and x along each cardinal direction is sqrt(x^(2)+y^(2)+z^(2)). In the Minkowski geometry of flat spacetime, on the other hand, the (proper time) separation between two points separated by x, y, and z along the cardinal directions and t in time is sqrt(t^(2)-x^(2)-y^(2)-z^(2)). As a result, a straight line turns out to be the longest path between two points. (Technically, it's the path with the longest proper time between two timelike-separated points.)

But there's no paradox because there is an objective preferred frame in a universe that loops around, which is imposed by the choice of at what times you "connect the opposite edges" of the universe.

Imagine the Earth is already moving with respect to the preferred frame imposed by the universe's geometry. Then depending on the direction of travel, the traveler could potentially be moving slower than the Earth, with respect to that preferred frame.

I think the point you are missing is that the universe is (statistically) the same everywhere. This means that there will always be light reaching you from some distance -- and hence some time -- and the objects that you see at that distance/time have similar statistics to what happened in our own past.

I was referring to a toroidal universe, since its spacetime can be flat. Bringing in spacetime curvature complicates things unnecessarily!

However, the spherical universe does have a (local) preferred frame: the frame of a comoving observer.

It might help to realize that the elapsed time for each object is just the length of its path in spacetime. This should make it clear that there is never any ambiguity about whose elapsed time is longer. Just compare path lengths.

In the traditional twin paradox, the question is whether a straight line (twin who stays behind) or a bent line (twin who travels) is longer. The straight line is longer, due to the particular form of the spacetime metric.

In your last paragraph you are asking, what happens if we bend spacetime into a cylinder-like shape, so that time goes along the cylinder and space goes around the cylinder? There is still no ambiguity: you are now simply comparing the length of a path drawn along the cylinder with a path that circles around the cylinder like a helix.

In particular, the two twins' situations are not symmetrical because when you bend the spacetime into a cylinder, you have to choose a special reference frame. That's the frame in which spatial surfaces exactly loop back on themselves and time points exactly along the cylinder. Try physically bending a sheet of paper into a cylinder so that the edges just meet. You will probably choose to make the corners meet as well, but that is just one option. You could also offset the corners as much as you want. These different possibilities correspond to different preferred frames.

So the two twins' elapsed times will depend on how fast they are moving with respect to this preferred frame.

An asteroid and an asteroid-mass black hole have the same mass.