[Halc]

The center of gravity of Earth exists (is real and present), and lacks a nonzero dimension.

You should attack this more. I can think of counters to both assertions.

For one, nothing in physics acts on this center of gravity. That alone makes it questionably real.
For instance, take two stars whose mutual center of gravity just happens to fall in Earth's path.  Nothing will happen when Earth gets there since there's nothing actually there.

I already asserted that it moves faster than light. Real things can't do that.

About it being a point: The position of any particle is probably (most interpretations deny it) not real.  There is only a probability that it will be measured in a given place. Hence lacking position, a particle has no center of gravity and any center of gravity of a collection of such indeterminate particles is similarly indeterminate.  OK, the errors average out, but the center of mass of Earth is thus possibly from here to there.  It has width, albeit one much less than a Planck length, and thus 'makes no physical sense'.

PS  I agree with Alan's post above.

[Bill S]

It's a poor phrase, because logically it means "Bigger than you can imagine small" "Infinitesimal" is the mathematical term you are looking for.

A poor phrase, indeed. Outside its mathematical definition: “an indefinitely small quantity; a value approaching zero”, I would suggest it has no real meaning.

Apparently! Surely everyone else can distinguish between the local absence of stuff that could be present at a point, and the universal non-presence of stuff that couldn't.

That is one of many examples of a response that is fine, in itself, but in which the essential issue definitely lacks a non-zero presence. 
As usual, I’m rushing responses in odd moments, but I will try to clarify the “issue”.  Need to look at some more posts first though.

[Bill S]

Lacking a nonzero dimension means having zero spatial (or spatiotemporal, or indeed any of the 256 dimensions that pay the rent for string theorists) extent in any direction. What it doesn't mean is "having zero dimensionality", because a point is defined by the confluence of vectors.

Thanks Alan. Just another example of my poor choice of terms; arising, no doubt, from my “hitch-hiker” status.

[Halc]

Let's go with a proof then.

P1 X is a fundamental particle
P2 X occupies volume (or space in at least one dimension)
C1 The material of X on one side is spatially separated from the material of X on the other side.
C2 X is comprised of the two chunks of material on one side and the other (X is made of parts)
C3 X is not fundamental.

P1 and C3 are contradictory, thus at least one of the premises is false.

Let's go with another 'proof'.

If a fundamental particle had some sort of nonzero width, it would have angular inertia and thus angular momentum.  While a proton (not fundamental) has this sort of 'orbital' angular momentum, nothing fundamental does. It has 'spin', but that is just a name give to a quantum property of how the particle behaves in a magnetic field.

[Bill S]

Wiki says: “elementary particles still possess a spin angular momentum”; so there is probably much to discuss, but, although interesting, I think it is a subject for another thread.

[Halc]

elementary particles still possess a spin angular momentum

This is the quote in context, in angular momentum page:

it turns out that the notion of a quantum particle literally "spinning" about an axis does not exist. Nevertheless, elementary particles still possess a spin angular momentum, but this angular momentum does not correspond to spinning motion in the ordinary sense.

Morton Tavel, a professor of physics at Vassar College, quoted in a sci-American article

When certain elementary particles move through a magnetic field, they are deflected in a manner that suggests they have the properties of little magnets. In the classical world, a charged, spinning object has magnetic properties that are very much like those exhibited by these elementary particles. Physicists love analogies, so they described the elementary particles too in terms of their 'spin.'

Unfortunately, the analogy breaks down, and we have come to realize that it is misleading to conjure up an image of the electron as a small spinning object. Instead we have learned simply to accept the observed fact that the electron is deflected by magnetic fields. If one insists on the image of a spinning object, then real paradoxes arise; unlike a tossed softball, for instance, the spin of an electron never changes, and it has only two possible orientations. In addition, the very notion that electrons and protons are solid 'objects' that can 'rotate in space' is itself difficult to sustain, given what we know about the rules of quantum mechanics. The term 'spin,' however, still remains."

My bold and other style edits.
The bit about the proton seems weird, given that they are actually objects with a nonzero radius that can rotate in space.

https://www.forbes.com/sites/startswithabang/2017/04/19/why-does-the-proton-spin-physics-holds-a-surprising-answer/#83185dc2c3a5

There are two things that contribute to angular momentum: spin, which is the intrinsic angular momentum inherent to any fundamental particle, and orbital angular momentum, which is what you get from two or more fundamental particles that make up a composite particle

What they call 'orbital angular momentum' (dotted italic references throughout this post) is actually the proton physically spinning, which it can because it, being made of spatially separated parts, is not a point particle.
The intrinsic angular momentum (underlines throughout) is the same thing the wiki article is speaking about, which electrons and everything else has. This is the quantum spin you always hear about.

The article goes on in considerable depth. A good read if you're interested. Nice illustrations.

[Bill S]

This is the quote in context

That's why I said there is probably much to discuss, but find time to post is getting difficult again, so I didn't want to divert from my, not very successful, attempt to move back towards the OP.

Thanks for the links.

[Bill S]

Was the BB the beginning of the Universe?  Of course, scientific veracity is not a matter of democratic “vote”, but informed opinion seems, widely, to hold that this is our best current theory.  Given that response; the next question must be: “Did anything exist before the BB?”.  A few decades ago, the answer usually found was, “nothing”.  However, two things have happened to that “nothing” over time. 

1. It has become more “somethingy”, while still being referred to as nothing.  This lets in different definitions of nothing, which then lead to confused thinking/communication.

2. It has been replaced by the idea that there would almost certainly have been something, but we don’t know what it was.  This must be the “safer” option, but still leaves the question as to the whether we can say something about this “something”, that is not simply conjecture or philosophy.

Speculations can, and do, go in various directions from here, but two questions predominate.

1.  If there was nothing before the BB, could there have been a BB?
2.  If there was something before the BB, must it be eternal/infinite?

Informed opinion is certainly not unanimous on the answer to Q1.  There are those who hold that something could “emerge” from nothing, but I have yet to find an explanation that didn’t involve treating “nothing” as “something”.  A “get-out clause” is that science works with models, and we cannot model “nothing”.  How satisfying is this?

Answers to Q2 often devolve into discussions that, at best, are peripheral to the essential issue.  A major problem seems to be that, however much the people providing the explanation insist that eternity is not a length of time, they inevitably lapse into treating it as though it were.  Infinite regression is often a major component of these lines of reasoning, and the presence of the word “infinite” leads to an apparent assumption that the “sequence” under discussion is actually infinite, i.e. it somehow extends to infinity.  This may be acceptable in principle, but has no practical counterpart. 

[Bill S]

In the following 10 points, I attempt to pull together some of my own thoughts about infinity/eternity.  In no way am I suggesting that this is anything more than the ruminations of a “hitch-hiker”.

1.  Infinity is not just a very big number.  In fact, it is not a number at all.

2.  Eternity is not just a very long time.  It is not time, and has no direct relationship to time, other than in our finite reasoning, and in our need to form a mental picture of “for ever”.

3.  Something that is finite can never become infinite.  Even the assertion that a finite object could “increase for ever” is misleading, because it assumes the possibility of an infinite progression.  This is often expressed as “progressing towards infinity”, or “approaching infinity”.  One example of this is the theoretical possibility is that our Universe could expand for ever.  This may be true, but it can never reach infinity, in fact, it must always be infinitely far away; and then only if the concept of distance from infinity has any real meaning, which I doubt.

4.  Mathematical infinities are theoretical concepts that are unbounded, but not necessarily infinite.  I wouldn’t try to argue with the value of infinity, as a concept, in mathematics, but it seems there are those who do.   Max Tegmark, regards infinity as “…the ultimate untested assumption.”  He says: “All of our problems with inflation and the measure problem come immediately from our assumption of the infinite.”  This must raise the question: How can we test for infinity?  Surely such a test would require an infinite amount of information, which, in a finite Universe would be unattainable. 

5.  Cantor’s “absolute infinity” may be infinite, but this cannot be proved nor disproved.  This, taken in conjunction with points four and six, suggests that infinity/eternity is not something that is amenable to mathematics, nor can it be adequately dealt with in our finite “reality”.  I am not advocating that we should not think about infinity/eternity; on the contrary, we should think about it, but stop trying to force it into a mathematical mould. 

[Bill S]

6. Unbounded entities may be subjected to mathematical processes, but attempting to do this to infinity leads to     nonsensical answers.

Consider the “infinite” sequence of rational numbers.  A sample segment, e.g. 10 – 20, can be “isolated” without having any effect on “the whole”.  You can do anything mathematically permissible with these ten numbers, without directly influencing any of the others.  You can multiply 10 by 3, which gives you 30, but to suggest that this has some effect on a conceptual 30 that “exists” elsewhere in the sequence, makes no sense. 

What are you left with if you consider that you have, somehow, removed your sample from the “infinite” succession?  It cannot be two finite halves, because finite quantities are measurable, and this would give you a measure of infinity.  A usual response is that both “halves” are infinite, and mathematically, that may be acceptable, but otherwise, there are problems.  The sequence before your sample ends at 9, so by definition, it isn’t infinite.  The other sample, if reversed, ends at 11 - same problem.  Also, you have subtracted something from infinity, which you could not do if infinity were not a number.  If you are to maintain that the sequence is infinite, any work you do on it must be done without influencing the whole; otherwise you divide infinity.  Mathematically, you can do this, because, in actuality, there is no “whole”.  The sequence of rational numbers can be considered as infinite, simply because it is, like Hilbert’s Hotel, a mental concept that can never be physically realised.  It is a tool used to count objects, and objects exist in finite quantities.  Undoubtedly, someone will argue that you can also count abstract ideas, but the chances are they will not find an example of an abstract idea that is not the product of a finite mind. 

7.  Multiplying or dividing infinity makes no practical sense because the result would have to be infinite.

We have seen how this works with the sequence of rational numbers, but how might this be applied to (absolute) infinity?

To a great extent, the same reasoning applies.  Dividing infinity must result in either two infinities, which, excluding mathematical quasi-infinities, cannot be possible.  Or, it must result in two finite halves, with the implications for measuring infinity which we saw above.

A corollary of this is that there can be no change in infinity/eternity, because this would lead to a situation in which there would be eternity before the change, and eternity after the change.  Barbour has, perhaps more than most, tried to give some “substance” to the idea of timelessness, but even he seems to let suggestions of time slip in.  Platonia is timeless, but he talks of “pathways”.  To me, pathways suggest traffic, traffic involves movement and change.  I struggled with parts of this book, so I may have missed an explanation for the role for pathways in a timeless domain. 

8.  In practice, nothing can be added to infinity, because it is already everything.

9.  There cannot be more than one (absolute?) infinity, because it must contain everything.

10.  Nothing can be taken away from infinity, because, either, the remaining quantity would still be infinite, or it would be finite; in which case it could be measured, and if added to the fraction subtracted, would give a measure of infinity.  Therefore, it makes no sense to talk of something being taken away.  Furthermore, if infinity is everything, there is nowhere for any “being” to be, “who” might do the taking.  Nor is there anywhere for the extracted quantity to go.

[Bill S]

My guess is that everyone who has exercised the patience to wade through these ramblings will have, long since, spotted the glaring problem with this line of thinking, in relation to the OP.

If the cosmos is infinite/eternal, and the cosmos is the “precursor” of our Universe; how could the BB, or anything else, have happened without dividing infinity/eternity?  Must we not be left with eternity before and after the existence of the Universe?

The act of asking these questions demonstrates that eternity is being visualised as a length of time.  Only if eternity is a length of time can there be a “before” and “after”.  It is tempting to think of timeless eternity as a static “now”, but, of course, someone will point out that “now” is a time related term.  Face it – we don’t have the language.

There is a way round the problem; David Bohm did much to introduce and develop it, so it has a pedigree.  What I have been referring to as the cosmos, roughly equates to Bohm’s “Implicate Order”.  His concept of “wholeness” is a very important factor. 

The timeless/changeless nature of the cosmos means that we have to look, critically, at the idea that there could be any “parts” of eternity that would be distinguishable from any other parts.  Like Barbour’s “pathways”, there would seem to be no role for “parts” in a realm in which there was no time to facilitate the making of distinctions between them.  Differentiation is redundant.  What we perceive as differences are features of the “Explicate Order”.

Our Universe equates to the “Explicate Order”.  It has time (with a defined arrow) and change.  It has distinctions between individuals and groups.  It is elucidated by the laws of physics and is well described by mathematics.  It is our reality, and we are constrained by its exigencies.

What remains now is to integrate the two concepts; to see how the Universe relates to the cosmos.  Understanding the cosmos is where an appreciation of the impact of “Wholeness” is essential.  Simply saying that every part of the cosmos is the cosmos, in its entirety, expresses the basic idea, but is still borrowing terminology from the Explicate Order.  There are no parts.  The whole just is. 

The corollary of this is that our Universe is the cosmos.  Our reality is a deceptive “shadow” of the whole.  Our perception of time, change and separation arises as a consequence of our partial perspective, and our need to make sense of our world; the world into which evolution fitted us to survive.

[alancalverd]

If the cosmos is infinite/eternal, and the cosmos is the “precursor” of our Universe; how could the BB, or anything else, have happened without dividing infinity/eternity?  Must we not be left with eternity before and after the existence of the Universe?

Infinite, yes. Eternal, yes, because in the absence of stuff there is no change and without change, time is meaningless. Precursor, yes: something happened within the infinite universe to produce the observable  universe, which is  clearly a division (it has a boundary) of the entire universe. So what?

I dislike your use of "cosmos" to denote something larger than the observable part of the universe. I think the general use of the term denotes exactly the observable bit, and universe clearly means "everything". All those events and objects we call cosmic are obviously observable.

[Halc]

Was the BB the beginning of the Universe?  Of course, scientific veracity is not a matter of democratic “vote”, but informed opinion seems, widely, to hold that this is our best current theory.  Given that response; the next question must be: “Did anything exist before the BB?”.  A few decades ago, the answer usually found was, “nothing”.  However, two things have happened to that “nothing” over time. 

Sorry, but I cannot think how any of this jives with science.  The BB theory is an explanation of the evolution of the universe since the BB, but not a model of how it came to be in the first place.  So it is the beginning of time as we know it (that which is measured by seconds or by vibrations of certain atoms, neither of which exists outside the BB), but the theory does not posit the absence of anything 'on the other side', which is arguably not 'before' and certainly doesn't posit 'nothing'. I'm no expert in the theories that do concern such things, and have little opinion on them, so I'll just say that theories exist, and I'm not aware of any of them suggesting a 'nothing', although 'no thing' is appropriate since the typical 'thing' we know like an atom likely doesn't exist there. All the theories seem to fall under 2) below, and not 1) here.

2. It has been replaced by the idea that there would almost certainly have been something, but we don’t know what it was.  This must be the “safer” option, but still leaves the question as to the whether we can say something about this “something”, that is not simply conjecture or philosophy.

Conjecture yes.  Philosophy no, since these are typically QM theories and lead to models that make predictions.
I'm more interested in the philosophical aspect, which doesn't concern the nature of what's outside our little chunk of spacetime and concerns more which how any of it comes to exist at all, and my conclusion was that the very wording (the bolded part) is biased and makes assumptions that should instead be questioned.

There are those who hold that something could “emerge” from nothing, but I have yet to find an explanation that didn’t involve treating “nothing” as “something”.

I agree with this.

A “get-out clause” is that science works with models, and we cannot model “nothing”.  How satisfying is this?

I've never seen a scientific model positing something from nothing. It seems contradictory. Science concerns the mechanism involved, and no viable mechanism does a 'something from nothing'. It is thus a philosophical stance, and a weak one since it defies logic for the reasons you give.
It also assumes the something is caused, which I find to be a mistake. Maybe it is, but making any assumptions at all seems dangerous. I've learned to discard as many assumptions as possible. Some are really difficult.

Answers to Q2 often devolve into discussions that, at best, are peripheral to the essential issue.  A major problem seems to be that, however much the people providing the explanation insist that eternity is not a length of time, they inevitably lapse into treating it as though it were.  Infinite regression is often a major component of these lines of reasoning, and the presence of the word “infinite” leads to an apparent assumption that the “sequence” under discussion is actually infinite, i.e. it somehow extends to infinity.  This may be acceptable in principle, but has no practical counterpart.

Language issues aside, our universe seems infinite in some ways: There is no apparent boundary to spacetime except the big bang itself, and possibly the big rip on the other side. Doesn't mean it isn't bounded, but the boundary isn't apparent. So it could work either way. I don't think it matters. The existence (as opposed to its nonexistence) of either a finite nor an infinite structure can be explained. It being finite or not seems to play no role in this essential issue.

3.  Something that is finite can never become infinite.

Trying to find exceptions to this. How about this?:
The acceleration required of my ship to escape yonder black hole is finite and increases as the ship approaches it. At the event horizon, that required acceleration (G force) becomes infinite. It's an admittedly abstract thing. The ship isn't capable of that, so it's going to fall in.
Two lines in a plane intersect in a finite distance, but as you rotate one of them, that intersection point becomes infinitely far away.  Not a point infinitely far away, but rather the lack of such a point regardless of distance.  Again, an abstract thing, not physical.

[alancalverd]

Only if eternity is a length of time can there be a “before” and “after”. 

I disagree. Things change. Rabbits breed, nuclei decay. This defines before and after. Nothing to do with eternity.

[Bill S]

I dislike your use of "cosmos" to denote something larger than the observable part of the universe.

I’ve explained before why I tend to follow Gribbin’s terminology, I certainly do not expect others to follow.  Should I assume that you would replace “cosmos” and “Universe” with “infinite universe” and “observable  universe”? 

Infinite, yes. Eternal, yes, because in the absence of stuff there is no change and without change, time is meaningless.

I think that is largely in agreement with what I am saying. 

Precursor, yes: something happened within the infinite universe

In the “infinite universe” in which there is no change and no time; “something happened” ??  You've left me way behind, there.

[Bill S]

Sorry, but I cannot think how any of this jives with science.  The BB theory is an explanation of the evolution of the universe since the BB, but not a model of how it came to be in the first place.

If that is your understanding of the quote from me; all I can say is that we speak different languages.  Your introduction of “dancing”, if intentional, is a colourful usage.

these are typically QM theories

You seem to be saying that QM theories are applicable to the “something” posited as a precursor to the Universe.  Could that be right?

I've never seen a scientific model positing something from nothing. It seems contradictory.

Sometimes I wonder if we are saying the same thing, in different languages.

   A major problem seems to be that, however much the people providing the explanation insist that eternity is not a length of time, they inevitably lapse into treating it as though it were.

Your response seem to reinforce this.  Was that intentional?

3.  Something that is finite can never become infinite.

So in neither of the “exceptions” you give is actually an exception, but then, I think you acknowledge that; so was there a point that I've missed?

[Bill S]

Only if eternity is a length of time can there be a “before” and “after”.

Perhaps I should have said “Only if eternity is a length of time can there be a “before” and “after” associated with eternity. 

However, if you put that quote back in context, I think you may find that your “Rabbits breed, nuclei decay…” is not really a helpful response.

[Halc]

Sorry, but I cannot think how any of this jives with science.  The BB theory is an explanation of the evolution of the universe since the BB, but not a model of how it came to be in the first place.

If that is your understanding of the quote from me; all I can say is that we speak different languages.  Your introduction of “dancing”, if intentional, is a colourful usage.

Jibes then.  Typo, sorry.

these are typically QM theories

You seem to be saying that QM theories are applicable to the “something” posited as a precursor to the Universe.  Could that be right?

As a precursor to and cause of the big bang, yes.  I don't pretend to understand it all. Look at some of Sean Carroll's publications. He's on top of that sort of stuff. I'm only mildly interested since I don't really care what caused the big bang. That event didn't do anything silly like 'cause existence', except it sort of did since it caused the only sort of existence that makes sense to me.

   A major problem seems to be that, however much the people providing the explanation insist that eternity is not a length of time, they inevitably lapse into treating it as though it were.

Your response seem to reinforce this.  Was that intentional?

I personally don't use the word 'eternity' to mean anything except a length of time. But I do use the word 'eternal' to mean 'not contained by time'.

So in neither of the “exceptions” you give is actually an exception, but then, I think you acknowledge that; so was there a point that I've missed?

Nope. Just a habit to look for exceptions whenever somebody makes a statement with 'always' or 'never' in it somewhere.

[alancalverd]

The relation of eternity to time mirrors that of infinity to number. It has nothing to do with before and after, any more than infinity has anything to do with larger and smaller. We are at a point in an eternal, infinite universe, and there are more rabbits today than yesterday. But even if the universe  is of finite duration and extent, the observation remans true, so we have a definition of "after" (and "more"). It just happens that there  are more subtle and convenient ways of measuring the passage of time than counting rabbits.

If quantum mechanics turns out not to describe what preceded the big bang, it's no big deal. We'll just have to find some other means of describing it, and preferably one that reduces to QM if t > 0. Physical laws are descriptive, not prescriptive.

[Bill S]

It has nothing to do with before and after.................. We are at a point in an eternal, infinite universe,

If we are at a point, does that not imply that there is a before and after relative to that point?

Physical laws are descriptive, not prescriptive.

If I have ever given the impression that I did not agree with this, it was certainly not intentional.
If you were referring: “….   It is elucidated by the laws of physics”, I am at a loss to see how that could be interpreted as saying that the laws of physics are prescriptive.