How fast is Earth traveling due to the Hubble constant?

[Drakkith]

@Drakkith: If there was an infinite number of "little points of matter", I wonder if they wholly or partly coincided in a space-time location and thus occupied only a finite (perhaps small in total) space at a given time or if they occupied infinite space. The latter seems likelier given the premise but also problematic and probably impossible. If they all inflated as Big Bangs and we have infinite matter and energy, expansion would be impossible, because there'd be no place to go.

Ah, that's the issue here. You're thinking of expansion as the universe expanding into unoccupied space. As far as we can tell, this is not the case. Unbound objects simply get further apart over time as a result of the the large-scale geometry of the universe. I wish I had a good way of explaining it that would make immediate, intuitive sense. But I don't. You'd have to get into much more detail than anything so far provided in this thread. Try starting here: http://www.astro.ucla.edu/~wright/cosmology_faq.html

The shorter version of the problem is in saying the supply of matter and energy already exists infinitely far in all directions, not simply that there's no evidence that there is not an infinite supply of matter and energy infinitely far in all directions. A result of the infinite number of "little points of matter" with noncoincident nonoverlapping loci or of the infinite supply of matter and energy is that in that case the universe should not be expanding but getting denser.

While we aren't certain what caused the universe to begin expanding in the first place, this is in no way a contradiction to an infinite universe. I think the key here is to look at the density of matter and energy in the universe. If we assume for the moment that the universe is expanding and has been for the last 13 billion years or so (which is certainly supported by observations), and we also assume the universe is infinite in size, then there is a critical density of matter and energy below which the universe will continue to expand forever and above which the universe will eventually cease expanding and contract. This ignores the recent discovery of an accelerating expansion, but let's keep it simple for the moment.

So an infinite number of Big Bangs seems not to have happened (you didn't say they did) and, if there was an infinite number of "little points of matter", they must not all have produced Big Bangs, simultaneously or otherwise; and the supply of matter and energy must be finite and extend only finitely far.

Consider that you're building an understanding of the universe based on extremely incomplete knowledge of all of the methods to describe and model the universe used by professionals who have spent their entire careers doing so. That's a poor way of learning about a subject.

 

[Chronos]

The gold standard in cosmology is measured relative to the CMB rest frame. That happens to be about 370 km/sec for the solar system,

 

[Nick Levinson]

@Bandersnatch:

Correcting an error of mine: Yes, an infinitely-large plane (or line or solid) has no center.

That the evidence is of the universe of matter and energy being infinitely large when at the same time we are uable to perceive beyond a certain finite distance (~63 gly) does not rule out finity of the universe's size even where it does not end short of what we can perceive. This would not be impermissibly claiming something without evidence but claiming a limit on the meaning of given evidence and merely allowing for something that's therefore not disproven, as long as we acknowledge the inherent weakness of the last something.

@Chronos: That's about 850,000 mph, less than the motion of Earth even when not counting the effect of Hubble. Thank you for the start.

@Drakkith: Thank you for the FAQ and its links. I started getting into it.

@phinds: You're right on infinity within infinity and I should have caught that (I read the New York Times' blog article on the Hilbert), but, while mathematical possibilities are valid, few people would say that my hand is composed of an infinite amount of matter, thus having infinite mass and weight, and I'm still focused on the original question, for which I did both Googling and a forum search (there were about half a dozen topics in response and I checked them before posting), and the tentative conclusion I reached above, which seems to still be standing. I don't mean to be in people's way. Thank you.

 

[phinds]

... few people would say that my hand is composed of an infinite amount of matter, thus having infinite mass and weight

I have no idea what you are talking about, nor do I understand why you say "few" people would say that (perhaps you were being ironic?). NOBODY would say that so it seems like you have set up and knocked down some kind of straw man argument. I'm missing your point.

 

[Bandersnatch]

This conclusion?:

A result of the infinite number of "little points of matter" with noncoincident nonoverlapping loci or of the infinite supply of matter and energy is that in that case the universe should not be expanding but getting denser.

Why? Where's the density increase coming from?
Take a test volume in an infinite 3D space filled homogeneously with matter. The test volume V contains a finite number of particles n, which gives some initial density ρ.
Now increase all distances. The density in the test volume goes down.

I count a center as being part of a torus (<http://mathworld.wolfram.com/Torus.html>, as accessed 3-18-17) and by extension of any 2D or 3D geometric shape even if the center would therefore be outside of the universe so shaped

That centre only makes sense if you embed a 2D surface in 3D space, which we readily do in order to help us visualise the geometric relationships of the lower dimensional space. For a being living its 2D life on the 2D surface of a torus or a sphere, the concept of the third dimension is alien. The beings can't point towards the 3D centre of curvature of the 2D surface, any more than we can point towards 'up' in the 4th dimension (can you?).
If that's the centre of expansion you're asking about, and about the recession velocity of Earth w/r to it, then I have no idea what answer you're expecting.

and no entire universe, with any nonzero thickness of matter, can be only two-dimensional. If the exact boundary (finiteness of extent requiring some kind of boundary even if we have another term for that) of the universe can only be approximated because, say, molecules move around, then the location of the center can only be approximate, but it would still exist.

Again, you're misusing the analogies! All the 2D shapes mentioned so far are analogies of 3D shapes that our universe can be. In the analogy of a 2D sphere, the universe is confined to the 2D surface, with 0 thickness. Same with torus or a plane. We simply imagine a space with one less dimension, so that we can visualise the spatial relationships by embedding it in a 3D space.
A 2D sphere is an analogy of a 3D hypersphere (aka 2-sphere), where 3D space is finite and curves upon itself so that going in one direction gets you back to where you started. It does not have a thickness in the 4th dimension (what would that even mean for us, 3D beings?).
A 2D toroidal surface is an analogy of a 3D hypertorus with similar relationships, and an infinite 2D plane represents an infinite 3D volume.

That the evidence is of the universe of matter and energy being infinitely large when at the same time we are uable to perceive beyond a certain finite distance (~63 gly) does not rule out finity of the universe's size even where it does not end short of what we can perceive. This would not be impermissibly claiming something without evidence but claiming a limit on the meaning of given evidence and merely allowing for something that's therefore not disproven, as long as we acknowledge the inherent weakness of the last something.

You're absolutely correct that it is possible that somewhere outside of what we can see, physics is different and it may even permit some edge (or space unicorns, or whatever). But then everything goes, and you can't ever build a model that you could use to make sensible predictions.
So what we do in cosmology, is use one major assumption - that of homogeneity and isotropy ('cosmological principle'). We see that in the patch of the larger whole that we inhabit, everything looks remarkably the same everywhere we look, at least on large scales, so we assume that this doesn't change beyond the edge of what we can see. After all, it seems unlikely that we'd be living in a special place that happens to be so uniform. This let's us work with what we've got, and make some statements as to the whole. It goes without saying that it is a mere extrapolation from a small set of data, but it is not a weak statement either.
By the way, the current cosmological models accommodate both infinite and finite universes (e.g. a hypersphere or a hypertorus). They just not include any with boundaries.

 

[Drakkith]

@phinds: You're right on infinity within infinity and I should have caught that (I read the New York Times' blog article on the Hilbert), but, while mathematical possibilities are valid, few people would say that my hand is composed of an infinite amount of matter, thus having infinite mass and weight, and I'm still focused on the original question, for which I did both Googling and a forum search (there were about half a dozen topics in response and I checked them before posting), and the tentative conclusion I reached above, which seems to still be standing. I don't mean to be in people's way. Thank you.

I'm not sure what conclusion you're talking about. No one would would claim that your hand is composed of an infinite amount of matter because it clearly isn't. The "points of matter" I mentioned above are not mathematical points of zero size, they are non-zero sized sections of the universe that have a finite amount of matter in them.

 

[Nick Levinson]

@phinds: While it's true that a one-inch ruler contains an infinite number of points, I think we were going too far with claims on infinity as precluding finding the speed of Earth in terms of Hubble. Although I'm not an expert in the field, I don't think it is usually claimed that the universe that is infinitely large in extent contains matter and energy infinitely far in all spatial directions. There are usually hypothesized or theorized limits. But if limits are not recognized even as reasonable possibilities, then we can't find a center (or we can designate anywhere as an arbitrary center) and in that case we can't determine a meaningful speed for any arbitrary object toward or away from any other if they can't both be located at the same time because of a barrier (e.g., the ~63 gly limit) on distant observation. Mathematical constructs are useful; one person invented n-dimensional space where n > 3 about a century before anyone invented a practical use for it and long before string theory (in which, the last time I looked, n <= ~25 although it may have grown since). But while there is definitely an infinite number of points within an atomic particle, a computer manufacturer nowadays can offer a material that is only 3 molecules thick, and we don't describe that as having an infinite number of molecules or atomic particles along a straight line perpendicularly through the surfaces of the material. I've run into a claim in lay science that when an event could produce either of two outcomes then both could, or do, occur in different universes; but that would lead to an infinite number of universes, each with matter and energy, and while some scientists apparently claimed that the mathematics supported this view I was relieved to find that the mathematics also supported other narratives that contradicted that view. My hand has an infinite number of points in it; I don't preclude someone making a claim that leads to the conclusion that I knocked down. You have more confidence than I do that no one would put it forth; I'm happy to settle for not many people putting it forth, especially people whose views would normally form a scientific consensus.

@Bandersnatch:

No, the one I labeled as my tentative conclusion. It's in post #23.

The density increase would be coming from there being an infinite number of points of matter. The test volume you propose is in an infinite space that has matter, but not necessarily infinite matter; but if that space had infinite matter then I think we'd have a conceptual problem.

The observer limited to existing in two spatial dimensions may as well be on a flat surface for all they'd know. Nonetheless, the 3D doughnut has a center even if it's not touching what you'd eat, and the center is not the entire hole but a point, albeit only approximately locatable if the doughnut's surface is too irregular for precise calculation of the center. I think that a regular hypercube has a determinable center but someone who knows more about the geometry of four spatial dimensions would know better than I do; even if I'm right about regular hypercubes, I don't know how to calculate a center for an irregular hypercube and maybe there isn't one, although I doubt there isn't one.

For the sake of answering my original question, maybe we're going too far afield, and maybe unnecessarily, in dealing with 2D objects rather than 3D objects. The universe is 3D. The estimated number I wanted is one relative to our 3D universe of matter and energy.

I wasn't arguing that the laws of physics are different (although that claim makes sense in some contexts and it has been applied as potentially true to a fraction of a second after the Big Bang and to possible universe/s of matter and energy that preceded the Big Bang) but that the known local present-day physics prevents observing beyond ~63 gly and thus that there may or may not be matter and energy in our universe beyond that distance.

As I understand the cosmological principle, it relies on observing a large volume. But we're limited in how large a volume we can observe and we can hardly argue that we are observing a random sample of all that exists. We are observing what is local to us, albeit in a large locality. That nonrandomness creates a weakness in the principle. Occam's razor is a valid way of thinking and of producing answers, but always tentatively. The perception of the sun traveling around Earth satisfied the razor until it didn't and a new explanation of known data had to be developed. The fish in an aquarium filled with water would be well advised not to assume there's water on the other side of the glass wall it can't penetrate, even if both water and glass are invisible to the fish, as fish who have leaped out discover the breathtaking finiteness of the water supply.@Drakkith:

My tentative conmclusion is in post #23.

In response to: "The 'little point of matter' contained what would become our current observable universe. But right next to it was another 'little point of matter' that because another observable universe just beyond our own." (I assume "because" was supposed to be "became".) That means there is an infinite number of nonzero-size universes of matter and energy. The argument for that seems to be that there is matter and energy everywhere as far as we can observe so, lacking evidence to the contrary, presumably there is matter and energy everywhere beyond the limit of our observability. I don't think we can know that (we are not randomly sampling all of the existing universes of matter and energy without an observability limit in order to describe our locality) and I think that carries the contradiction already touched on. Being nonzero in size and at least one being quite large, the mass is high. Granted even an atom of any element (and I assume significantly above absolute zero in temperature) is mostly space, I assume the reason for an atom to be mostly space is not that another atom mostly hasn't gotten around to moving into occupy available space but because it's unavailable due to forces within the atom. So if space is infinite but matter and energy are infinitely large and these are not just mathematical constructs then in order to add more matter and energy we need more space for it to occupy or we need to allow for more density, and those not having happened is why my hand is not infinitely heavy. Thus, finity rules. While space (including time and n spatial dimensions) that can be occupied by matter and energy is infinite, matter and energy cannot be. We likely have not observed all of it and we may reasonably conclude there there is some we are unable to observe and that we are unable to determine just how much matter and energy is beyond our ability to observe, but that is not to say that it is infinite in quantity.

A tangential issue that probably should be a separate thread: Could there simply have been a finite number of little points of matter at the time of the Big Bang and, if they did not all bang at once, could have a banging one absorbed some or all nonbanging ones?

 

[phinds]

@phinds: While it's true that a one-inch ruler contains an infinite number of points, I think we were going too far with claims on infinity as precluding finding the speed of Earth in terms of Hubble.

Well, you can think that if you like, but you would be wrong. It's a meaningless concept and infinity has nothing to do with it. You have a talent for mixing concepts that have nothing to do with each other.

Although I'm not an expert in the field, I don't think it is usually claimed that the universe that is infinitely large in extent contains matter and energy infinitely far in all spatial directions.

wrong again.

There are usually hypothesized or theorized limits.

If there are limits, it's not infinite. Please provide a citation so we can see what you are talking about.

But if limits are not recognized even as reasonable possibilities, then we can't find a center (or we can designate anywhere as an arbitrary center) and in that case we can't determine a meaningful speed for any arbitrary object toward or away from any other if they can't both be located at the same time because of a barrier (e.g., the ~63 gly limit) on distant observation.

For objects that are inside a single bound system, no, it's not a problem and recession has NOTHING to do with it. For objects that are in different bound systems, you have to talk about recession velocity, not proper velocity but the fact that there is no center has nothing to do with it. Once again, you are mixing concepts that have nothing do with each other.

Mathematical constructs are useful; one person invented n-dimensional space where n > 3 about a century before anyone invented a practical use for it and long before string theory (in which, the last time I looked, n <= ~25 although it may have grown since). But while there is definitely an infinite number of points within an atomic particle, a computer manufacturer nowadays can offer a material that is only 3 molecules thick, and we don't describe that as having an infinite number of molecules or atomic particles along a straight line perpendicularly through the surfaces of the material.

You've set up a meaningless strawman argument and knocked it down. The infinite number of mathematical points in a given particle (or in ANY non-dimensionless volume) has zero to do with the fact that it's just one particle or some finite number of particles.

I've run into a claim in lay science that when an event could produce either of two outcomes then both could, or do, occur in different universes; but that would lead to an infinite number of universes, each with matter and energy, and while some scientists apparently claimed that the mathematics supported this view I was relieved to find that the mathematics also supported other narratives that contradicted that view.

The many worlds theories are contentious, and as a practical engineer, I don't find it useful or interesting to discuss them.

My hand has an infinite number of points in it; I don't preclude someone making a claim that leads to the conclusion that I knocked down. You have more confidence than I do that no one would put it forth; I'm happy to settle for not many people putting it forth, especially people whose views would normally form a scientific consensus.

Wrong again. No reasonable, sane person with scientific knowledge would possibly conclude that your hand has infinite mass. It is nonsensical. Are you talking about something else?

 

[Drakkith]

A tangential issue that probably should be a separate thread: Could there simply have been a finite number of little points of matter at the time of the Big Bang and, if they did not all bang at once, could have a banging one absorbed some or all nonbanging ones?

You may misunderstand what I was getting at with my explanation. These small sections of universe represent observable universes. But they are arbitrary sections. I could just as well talk about a region of equal size whose center lies halfway between the centers of our observable universe (viewed from here on Earth) and one of the sections bordering our own. This would be its own observable universe to an observer located there and would contain parts of our own observable universe and parts from the region lying just outside.

In response to: "The 'little point of matter' contained what would become our current observable universe. But right next to it was another 'little point of matter' that because another observable universe just beyond our own." (I assume "because" was supposed to be "became".) That means there is an infinite number of nonzero-size universes of matter and energy. The argument for that seems to be that there is matter and energy everywhere as far as we can observe so, lacking evidence to the contrary, presumably there is matter and energy everywhere beyond the limit of our observability. I don't think we can know that (we are not randomly sampling all of the existing universes of matter and energy without an observability limit in order to describe our locality) and I think that carries the contradiction already touched on.

You're right in that we can't know that. But that's not a contradiction to anything. Trying to impose boundary conditions upon the universe can problematic from the standpoint of General Relativity. It can lead to discontinuities in the metric of spacetime depending on what those boundary conditions are. Discontinuities are not really allowed. They result in singularities or other things which usually signal the breakdown of a theory. There are conditions where our universe is finite and wraps around on itself, avoiding those discontinuities, but we haven't seen evidence for that yet. So instead of selecting one of several different possible models for a finite universe, several of which can be problematic and none of which do we have evidence for, we prefer to model the universe as being infinite and acknowledge that future observations could change that.

Being nonzero in size and at least one being quite large, the mass is high. Granted even an atom of any element (and I assume significantly above absolute zero in temperature) is mostly space, I assume the reason for an atom to be mostly space is not that another atom mostly hasn't gotten around to moving into occupy available space but because it's unavailable due to forces within the atom.

The idea that an atom is mostly space is also problematic, as the concept of size for an elementary particle is different than what you'd imagine. But I think that's a topic for another thread.

So if space is infinite but matter and energy are infinitely large and these are not just mathematical constructs then in order to add more matter and energy we need more space for it to occupy or we need to allow for more density, and those not having happened is why my hand is not infinitely heavy.

You mean that your hand is not infinitely dense because atoms take up space? Well, yes.

Thus, finity rules. While space (including time and n spatial dimensions) that can be occupied by matter and energy is infinite, matter and energy cannot be. We likely have not observed all of it and we may reasonably conclude there there is some we are unable to observe and that we are unable to determine just how much matter and energy is beyond our ability to observe, but that is not to say that it is infinite in quantity.

The phrase "finity rules" may apply to the amount of matter in your hand, that is irrelevant and unrelated to the universe as a whole. There certainly can be an infinite amount of matter and energy in an infinitely large universe. Such a situation is fully supported by our math and theories. You don't have to believe or accept that, but it is the mainstream view and further claims that it isn't possible will result in a warning for misinformation since PF is here to teach people about mainstream physics, not to argue about it or convince people that it is correct.