3D Map of the 4D Universe

Factual Questions
1

I asked this question in an IMHO thread that immediately died. Assuming that the lack of responses isn’t due to it being a stupid question, I’m posting it here in GQ, which I think is more appropriate anyway:
Let’s say we’re several decades into the future and now have a perfect telescope that can identify and measure the relative velocity of every single star in the observable universe. Not only can this telescope do those things, it can also determine the age, size and type of each of these trillions and trillions of stars. At this moment, this superscope, known as the SS, takes a snapshot of literally every thing out there.

Since we’re so high tech now, we’ve also developed a super duper computer known as the SDC. The SDC is linked to the SS, so that all of the data collected is immediately stored. Connected to the SDC is the greatest 3D printer ever developed. Let’s call it the G3DP. This G3DP can immediately create a mini-replica of the universe as seen by the SS. In just a few moments we have nice little desk globe-sized replica of the universe as seen by SS just a few moments ago.

At this point, one might ask, isn’t this mini-universe created by the G3DP an accurate map of the universe? The answer would be “no”. In reality, the light coming from stars that are furthest from us is a lot older than light from nearer places in the cosmos. So you can’t say it’s accurate because each of the trillions of stars recorded is as of a different point in time in it’s life cycle. We can’t say that replica is a true map of the universe as it is today.

But hold on, remember that the SS was also able to capture all of that other data about every star. So the SDC knows that the red giant 5 billion light years away is now a black hole and the other star at the edge of our replica has now become a neutron star and about to merge with another one. The SDC can basically “forecast” the current position of every star observed by the SS when it took its snapshot.

So now we ask the SDC to have the G3DP print out a new replica, this time adjusted for time and distance; i.e. the current position of everything out there.

Can we now say that this replica is truly an accurate map of the universe today?

Next,

It turns out that another advanced civilization billions of light years away happens to do the exact same thing, at the exact same point in time, using the same (or equally powerful) technology as us. Certainly its replica would look different then ours. After all, that civilization’s observable universe is different than ours. There are places that it can see that we can’t, and vice versa. So the 2 replicas won’t be the same. However, since both civilizations can observe each other, there are portions of the replicas that are common, particularly everything in the space between us, plus extended to portions beyond.

If we just viewed the common space that exists within both replicas, will it look the same?

For argument’s sake, assume that the SDC can adjust for gravitational lensing, gravity from dark matter, etc. when producing its forecast.

2

Some people like to compare the universe to clockwork, but there are some events that are unpredictable and measurements that are uncertain. So you would not be able to forecast the position of every single star in the universe or know exactly when it might explode. For that matter, we try to do a good job constructing ephemerides of the local solar system, but even there there are chaotic motions, and nobody can tell you exactly when Phobos will be torn apart, when the Great Red Spot will die down, etc.

3

If we had a magic absolutely perfect system and some aliens had a magic absolutely system then they would both by definition have to match absolutely perfectly or the systems would not be absolutely perfect.

4

I think the OP’s assumption is “as perfect as the laws of physics allow”. For example, our model may differ from the aliens’ if their galaxy is moving relative to ours. In that case we won’t agree on which events are simultaneous even given “as perfect as possible” equipment, so we will have different models.

5

At the very least, length contraction due to the movement of the two civilizations respective to each other would make the models different. There’s no reason to assume any frame of reference is the one almighty and true rest frame.

6

Well, we can all agree on a frame at rest with respect to the background radiation… (NB the Earth is moving at hundreds of km/s with respect to this frame!)

7

Would that method of determining a rest frame have the same result here as it would half way across the visible universe?
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8

The notion of rest frame (and SR) only really applies to local space. But the expansion of the universe causes distant observers to recede from one another. All observers (in any location) at rest relative to the CMBR are said to be comoving, meaning that they are stationary in local space, but still mutually receding along with the Hubble Flow, the expansion of the universe. Two such observers would be at constant comoving distance (that concept of distance factors out the expansion of the universe), and in the same rest frame in the only meaningful sense in an expanding universe; but the proper distance between them would be increasing.

9

Even worse, a large fraction of the visible universe is expanding away from us at a speed faster-than-light, so we share no common frame of reference at all. You would have to calculate to positions of every star in the universe to ensure that this hypothetical clockwork model was accurate - an impossible task in an expanding universe.

In practice it wouldn’t even be possible to create an accurate model of the Milky Way galaxy - too many objects moving in near-chaotic orbits - the calculation would be too complex, even if we could ignore the effects of the rest of the universe. I’ve hear proposals to use pulsars as a kind of interstellar Galactic Positioning System, since they emit very regular pulses and are highly predictable; the problem is we can never really be sure exactly where a pulsar is at the moment, only where it was in the past, so this Galactic Positioning System would get increasingly inaccurate the further away from Earth we get in 4D space. On top of this, pulsars do occasionally suffer starquakes and change their emissions in a fraction of a second, making this hypothetical GPS system inaccurate in the very long term.

10

The OP assumes that each of two observers has the technology to access all the information that’s theoretically available at some point in time from the overlapping portion of two observable universes. I think the OP’s question is similar to consideration of observers in the same (comoving) position, but at two different times. Ignoring practical considerations (such as whether a galaxy is hidden behind a gas cloud) it probably amounts to asking whether the evolution of the universe is completely deterministic?

11

I expect the evolution of the universe is probably a/ deterministic and b/ impossible to determine in practice, because of practical considerations.

12

Theoretically, “yes”. But, then . . .

“In theory, theory and practice are the same. But, in practice, they are different.” --Unknown (Probably Ben Brewster)

13

Perhaps the two most critical limitations are:

We cannot know the state of the universe on the other side of the boundary of our visible universe, but that universe exists and is visible to objects on that boundary. In as much as that unseeable part of the universe can affect objects that fall within our visible universe, we cannot predict what effect they will cause.

There probably intrinsically isn’t enough information available. The information content available to our simulation computation is limited by the time for observation, bandwidth and signal to noise we have from those distant sources. All well and good to have a few photons creating a galaxy like smudge in our sensors, but getting enough information for the trillions of galaxies out there to predict over the course of billions of years their evolution is going to run up against some fundamental limits. That they have been red shifted into the province of thermal noise and beyond isn’t helping matters. There comes a point where a sufficiently distant galaxy provides us with little more information that than would allow us to say, “right now it is probably about like what we see here” as anything more concrete.

Which in a sense is the ultimate answer to the question. Given our current understanding, we posit that stuff at any distance from us, accounting for the flow of time, is pretty much like it is here now.

14

The process of getting 3D spaces from a 4D spacetime is called ‘spatial slicing’ or foliation. Not all spacetimes can be (globally) spatially sliced, but those that can are called ‘globally hyperbolic’ and any standard model of the Universe is globally hyperbolic. Lots of different spatial slicings would be possible, but standard cosmological models have a special spatial slicing in which the spatial curvature is constant on each slice. So our replica is special, but it could be argued that there are other replicas that are just as accurate or that the relativity of the situation makes the question impossible to answer.

Yes it would be, due to the globally special nature of the replica(s).