Stationary Centre of Universe Defined?

[Ryan O'Dine]

You know on reflection, Sol, I don't think my objection was wrong. Here's the OP again:

If the Universe uniformly expanded from a very small singularity doesn't that mean that the original position of the singularity defines a centre point of the Universe that is absolutely/Universally stationary?

To me, that's describing an absolute, Newtonian space. ynot's subsequent difficulties with curved space further suggest someone rejecting relativity.

Unless I'm simply reading him wrong.

 

[dasmiller]

That's not really correct. The universe does not have a center, but it does have a preferred rest frame. There is a background of cosmic microwave radiation visible everywhere in the universe, and it defines a rest frame: only observers moving with the "right" velocity will observe it as isotropic, everyone else sees a dipole in it due to Doppler shift.

But am I correct in thinking that the 'right' velocity depends very much on where you are? Here in the Milky Way, the 'right' velocity is . . well, ~0 with respect to the Milky Way. For someone in a galaxy a billion parsecs from here, the 'right' velocity is 77,000 km/s outward (in Milky Way coordinates) (ignoring the messy question of simultaneity for two points separated by 3B LY). So the rest frame itself is expanding?

 

[shadron]

What should the Bermuda Triangle properly be called then?

a figment

 

[ben m]

That's not really correct. The universe does not have a center, but it does have a preferred rest frame. There is a background of cosmic microwave radiation visible everywhere in the universe, and it defines a rest frame: only observers moving with the "right" velocity will observe it as isotropic, everyone else sees a dipole in it due to Doppler shift.

Actually, due to CMB fluctuations, the dipole you see is a combination of Doppler and an unknown primordial dipole. Observers in different locations will see different primordial dipoles and disagree on the "rest frame".

 

[Thabiguy]

But am I correct in thinking that the 'right' velocity depends very much on where you are? Here in the Milky Way, the 'right' velocity is . . well, ~0 with respect to the Milky Way. For someone in a galaxy a billion parsecs from here, the 'right' velocity is 77,000 km/s outward (in Milky Way coordinates) (ignoring the messy question of simultaneity for two points separated by 3B LY). So the rest frame itself is expanding?

No - the rest frame is local. Perhaps you're speaking from experience with special relativity, where inertial frames are global and can be used to talk about arbitrarily distant objects. But in general relativity, where space can be curved, this is no longer generally true and reference frames can only be applied to local regions of space. You can't generally use a local frame on distant objects and expect meaningful results; the paradox you mention is just a practical illustration of that.

So there is no global rest frame in our universe (in special-relativistic sense). But for each location, we can uniquely define a local rest frame, and furthermore, we can describe the relationship between these local frames as we move from place to place.

 

[sol invictus]

You know on reflection, Sol, I don't think my objection was wrong. Here's the OP again:

To me, that's describing an absolute, Newtonian space. ynot's subsequent difficulties with curved space further suggest someone rejecting relativity.

So you don't think general relativity is capable of describing a space that expands from a fixed central point? It is, of course, and that fact doesn't violate any deep principles. It's just not the universe we live in.

But am I correct in thinking that the 'right' velocity depends very much on where you are? Here in the Milky Way, the 'right' velocity is . . well, ~0 with respect to the Milky Way. For someone in a galaxy a billion parsecs from here, the 'right' velocity is 77,000 km/s outward (in Milky Way coordinates) (ignoring the messy question of simultaneity for two points separated by 3B LY). So the rest frame itself is expanding?

The rest frame is expanding, yes. But whether you regard those 'right' velocities as different is a matter of coordinate choice. That is, one can (and usually should) choose coordinates in which galaxies are at fixed (or almost fixed) coordinate position. Those are called "comoving coordinates" because they move with the expansion, and the spacetime looks particularly simple expressed in terms of them.

Actually, due to CMB fluctuations, the dipole you see is a combination of Doppler and an unknown primordial dipole. Observers in different locations will see different primordial dipoles and disagree on the "rest frame".

That's true, but only at the level of roughly 1 part in 10,000 (at least in the part of the universe we can see). And the two effects (Doppler and intrinsic dipole) are actually distinguishable at higher order.

 

[bokonon]

Haven't read the whole thread, but...

Even if it's not possible to plant a marker and have tourists visit a unique "Site of the Big Bang," would it be theoretically possible to compute a center of gravity for the universe at some point in time? How about now?

 

[Ziggurat]

I think my “problem” is that I don’t accept the language of theoretical or modern physics.

But you don't even understand that language. So denying it's true when it's clear you don't even know what it is just makes you look foolish.

Not accepting doesn’t mean not understanding

That is correct. It is possible for someone to understand but not accept. But you still don't understand.

As far as I’m concerned a triangle is Euclidean and can’t be drawn on the surface of a sphere.

A triangle on a curved manifold can be defined rigorously and consistently (three geodesics connecting three different points), and that definition is equal to your more familiar triangle in the special case of Euclidean. Nobody cares about your objections to the semantic choices of mathematicians.

Your refusal to consider curvature is quite reminiscent of the dynamics in Flatland.

 

[Ziggurat]

Haven't read the whole thread, but...

Even if it's not possible to plant a marker and have tourists visit a unique "Site of the Big Bang," would it be theoretically possible to compute a center of gravity for the universe at some point in time? How about now?

No. If the universe is infinite, then how would you ever go about doing that? And if it's not infinite, then it's closed, and wraps around on itself. Where is the center of mass of the surface of a sphere? You might say that it's the center of the sphere, but 1) that isn't part of the surface, and 2) it's an extrinsic geometry perspective, but all we have access to is intrinsic geometry, and the intrinsic geometry may be all that's real.

 

[ben m]

And the two effects (Doppler and intrinsic dipole) are actually distinguishable at higher order.

I'm surprised. Can you point me to a reference for that?

 

[sol invictus]

I'm surprised. Can you point me to a reference for that?

This paper discusses a related issue, although not quite the one we want. http://prola.aps.org/abstract/PRD/v67/i6/e063001

But actually I want to modify my response. You said "Actually, due to CMB fluctuations, the dipole you see is a combination of Doppler and an unknown primordial dipole. Observers in different locations will see different primordial dipoles and disagree on the "rest frame"." What I really should have responded is that a true primordial dipole is nothing other than a bad choice of coordinates. In other words a spacetime with a primoridal dipole can always be converted into one with zero primordial dipole (essentially by a Lorentz boost). Of course it could be that in that new frame there is a dipole in the matter distribution; that is, that matter is not at rest on average in the CMB rest frame, but that's another issue.

 

[bokonon]

No. If the universe is infinite, then how would you ever go about doing that? And if it's not infinite, then it's closed, and wraps around on itself. Where is the center of mass of the surface of a sphere? You might say that it's the center of the sphere, but 1) that isn't part of the surface, and 2) it's an extrinsic geometry perspective, but all we have access to is intrinsic geometry, and the intrinsic geometry may be all that's real.

You've lost me, and it's probably pointless to come back with a GPS and try again.

The earth clearly has a center of gravity. The solar system does. The galaxy does. The local group does. At what point does the collection of objects in the (I'm presuming finite) universe cease to have a center of gravity?

I guess I'm just one more guy who can't wrap his head around "closed and wraps around on itself" as anything but imaginary mumbo jumbo that may mean something to a mathematician but doesn't map to anything in the real world. Doesn't matter, I guess; it's not like I was hoping to be the first to plant a flag and open a concession stand.

 

[Hokulele]

I guess I'm just one more guy who can't wrap his head around "closed and wraps around on itself" as anything but imaginary mumbo jumbo that may mean something to a mathematician but doesn't map to anything in the real world. Doesn't matter, I guess; it's not like I was hoping to be the first to plant a flag and open a concession stand.

Think of it like a Möbius strip. You can start at any point on the strip, walk around the entire thing, and end up back where you started. You can define a small square patch of it as "My Patch" (solar system), a larger area, including your patch, as "My Area" (galaxy), and so on up the size chain until you have defined, "My Möbius Strip" (universe), which encompasses the entire strip. Your patch may have a center, your area may have a center, but because it is one continuous surface with only two edges (not four), you cannot define a center of the entire strip.

 

[bokonon]

Think of it like a Möbius strip. You can start at any point on the strip, walk around the entire thing, and end up back where you started. You can define a small square patch of it as "My Patch" (solar system), a larger area, including your patch, as "My Area" (galaxy), and so on up the size chain until you have defined, "My Möbius Strip" (universe), which encompasses the entire strip. Your patch may have a center, your area may have a center, but because it is one continuous surface with only two edges (not four), you cannot define a center of the entire strip.

Sure, that makes perfect sense.

Now, let's say I draw a couple of lines one inch apart on the Mobius Strip (yeah, I could be fancy and cut&paste your two-dotty-o, but I'd rather be snarky and not, because I don't even know what to call it), and exclude that area.

Now, I can make a good case that the "center of what's left" is the line equidistant from the two lines I've drawn which doesn't fall within the area I've excluded. [ETA: I'm guessing that would be the center of the inch on the other side of the paper.]

Can I similarly exclude some arbitrary region of the universe -- say, the solar system -- and reasonably ask "What is the center of gravity of what's left"?

Frankly, I'd rather live in a universe that doesn't go all ouroboros on me.

 

[Ziggurat]

You've lost me, and it's probably pointless to come back with a GPS and try again.

The earth clearly has a center of gravity. The solar system does. The galaxy does. The local group does. At what point does the collection of objects in the (I'm presuming finite) universe cease to have a center of gravity?

If the universe is infinite, well, you can always define a center of mass for a finite section of it, but your question becomes somewhat like asking when does an increasing number reach infinity. It doesn't.

If the universe is finite, well, locally the universe is fairly flat. But at some point for a finite universe, the larger the scale you look at, the more curved it becomes. And as it becomes more and more curved (and starts curving back on itself), the less and less meaningful "center of mass" becomes, until it's totally meaningless when you include the whole universe.

I guess I'm just one more guy who can't wrap his head around "closed and wraps around on itself" as anything but imaginary mumbo jumbo that may mean something to a mathematician but doesn't map to anything in the real world.

It's a direct analogue to a 2D surface forming the surface of a sphere, but in higher dimensions: wrap a 3D space around a 4D sphere. The basic consequence is the same: the space is finite but without boundaries. Go straight in any direction and you'll eventually end up back where you started.

 

[Ziggurat]

Think of it like a Möbius strip.

Gah! No! Don't do that! Mobius strips swap parity. Big no-no physically.

 

[Hokulele]

Gah! No! Don't do that! Mobius strips swap parity. Big no-no physically.

Yeah, I was just trying to think of another analogy that wasn't the surface of a sphere, since ynot and bokonon seem to be still considering the the sphere as a 3D solid, rather than a 2D surface.

 

[Hokulele]

Frankly, I'd rather live in a universe that doesn't go all ouroboros on me.

Why?

 

[bokonon]

Why?

Makes it harder for my enemies to sneak up behind me.

 

[Ziggurat]

Makes it harder for my enemies to sneak up behind me.

Then start accelerating and never stop. That will create an event horizon behind you, and you'll be safe from that direction. Of course, there's a downside: frontal attacks will come at ever-increasing velocities.