Science a GoGo's Home Page Forums General Discussion Physics Forum Does "infinitely small" differ from non-existent?

If something could become infinitely small, would it still exist?

On reflection, I should perhaps add to my OP that I accept that a distinction can be made mathematically.

For example; in modelling a black hole as a singularity I am saying that it is infinitely small. I then get an answer that appears to model black holes fairly well. Obviously, I could not achieve the same result if I were to model the BH as non-existent.

However, this does seem to be another case in which a mathematical "reality" might not be a physical reality.

Question: Does a singularity interact gravitationally with the cosmos? If the answer is yes, then it exists

...we are, of course, informed that the answer, in the form of the black hole, is yes.

On the other hand, my infinitely small Rolls Royce is another matter

Let's not forget that before we can take this as an assertion that something infinitely small exists, we have to answer one other question: Is the centre of a black hole a singularity?

If it is not, then a singularity may have a lot in common with your Rolls Royce - and mine.

Certainly true. Let's just say that according to prevalent theory, "infinitely small" doesn't necessarily mean "non-existent". Intuition makes it very easy to doubt that conclusion, especially among those of us who have no clue re the mathematical physics supporting the theory; but then, intuition is proving to be a poor back seat driver in modern physics.

Might this not be because intuition is based on very restricted field of vision? If this is so, should we not strive to expand that field of vision, perhaps by looking at things that don't fit comfortably within our familiar 4 dimensions?

My math is a long way away from a point where I could even think of being critical of mathematical physics, but I still think we have to take care not to assume that mathematical reality = actual reality, whatever that might be.

Re intuition, yes, it's being said by notables (Sir Martin Rees included, if I'm not mistaken) that the human mind may be quite incapable of grasping concepts beyond those which served our evolution. It follows that the process of discovery should gradually unveil realities that are alien to our comprehension, and further, that it may unearth signposts that are completely invisible to us.

Re mathematical reality, you are surely right; and I think the mathematicians are fully aware of the fact that maths can describe not only what exists, but also what doesn't exist. Observation and experiment are the verifiers.

While mathematicians may be fully aware of the correlation between maths and reality; discussions, particularly about infinity, on numerous threads strongly suggest that this awareness may be rare outside the maths community.

Yes, indeed. We forum users, by and large, find ourselves thrashing around in a sea of relative ignorance, while the experts - conspicuous by their absence - get on with their business.

Let's try a step by step, non-mathematical, look at B Hs.

1. A stellar BH is formed when a star of appropriate size collapses.

2. Before the star collapses, the BH does not exist.

3. If the centre of a BH is a singularity, the singularity does not exist until the BH has collapsed sufficiently.

4. BHs do not last for ever, therefore they are not eternal.

5. If the BH is not eternal, nor is the singularity.

6. This line of thought suggests that singularities must become infinite.

7. Nothing that is finite can become infinite.

Breaking it down in this way gives those with greater knowledge than I have a chance to locate any inconsistency.

The mathematical (!) symbol of infinity is = ( ∞ );.
Then the math symbol of "infinitely small" is 1/ ( ∞);.
According to Planck and Einstein the physical (!)
symbol of "infinitely small" is = h.
Then math symbol 1/infinity is equal to physical symbol h.
It means the "infinitely small" - 1/infinity = h is real
quant-particle and ' it still exists' .
================.
Socratus.

You seem to be saying that something that is of finite size can become smaller until it reaches a point where you can say this is now infinite. Would you also claim that this could happen in the case of something that is increasing in size?

socratus

In fact Planck and Einstein didn't say that. They said that the
smallest amount of energy that could exist was related to
Planck's constant. Using the law of conservation of energy
and Einsteins relativity sets a minimum size to anything.
So when something gets down to the Planck length that is small,
but not infinitely so.

This of course is one of the things that is confusing.
Relativity tells us that a black hole has an infinitely small
singularity at the center, but quantum physics tells us that
nothing can be small enough to be considered infinitely small.
This is one of the problems with physics today. Relativity
has been thoroughly tested and it is completely consistent with
experimental data. But quantum mechanics has also been
thoroughly tested, and it is also consistent with experimental
data. So the 2 major branches of modern physics don't agree
with one another. Theoretical physicists are struggling to
come up with a theory that fixes the problems by uniting
the 2 branches.

Of course the most prominent theory, if you can really call
it that, is string theory. I personally have my doubts,
but I certainly don't know enough about it to cast a
vote.

Bill Gill

Perhaps the important thing to remember is that not everything that is permitted by relativity is necessarily physically possible. For example, for example, past directed time travel is permitted, but is very unlikely. The infinitely small may be permitted, but there is, as far as I am aware, no evidence that anything can become infinitely small.

OK, but perhaps we have to then consider the difference between a vacuum and absolute nothing. A vacuum has physical dimensions. Absolute nothing won't have any dimensions at all.

This, perhaps, is different to being infinitely small?

Any takers?

Hi, Paul, welcome to the discussion. It's always good to have fresh input, hopefully it stops us "regulars" from getting stuck in ruts of our own making.

I think you have raised a couple of interesting points.

1. As you rightly point out: "A vacuum has physical dimensions. Absolute nothing won't have any dimensions at all." In other words, a vacuum is something (although that may not have been realised before the advent of quantum theory), while nothing is, quite simply, nothing.

2. Is there a difference between nothing and something that is infinitely small? which is a paraphrase of the OP.

I suspect that this is something that could be debated for hours without reaching a point where everyone necessarily agreed. This would tend to suggest that, either, it is a matter of opinion, or that more work needs to be done on the concept of infinity, as distinct from mathematical infinities.

My own opinion is that "infinitely small" and infinitely large" are concepts that arise out of our necessarily finite understanding of infinity. Neither has any real validity in terms physical infinity, but both may be valid in terms of our attempts to explain specific points.

Does that make sense? If not, that's probably because I have not expressed it very clearly.

Thanks for extending your welcome, Bill.

There are many different approaches to quantum mechanics. In some ways it's been used to justify a previously proposed theory.

By examination of experimental results we can agree that a neutron can indeed be in two places at the same moment in time.

We can fairly state that our understanding of time itself is not accurate. Therefore we can conclude that the results of such experiments have little value.

Further - we do not really know what constitutes a neutron. Perhaps that's the problem??

If we know what a neutron really is, then perhaps it would be blindingly obvious as to how it can be in two places simultaneously.

Rgds,

P - over and out.

Unfortunately, whenever there’s an attempt to discuss a high level abstract concept; words can become a cumbersome vehicle that comes up short.

IMHO, the moment that you used the word “something” meant that it would exist.

I liked Redewenur’s reasoning that if something infinitely small interacts with other things that exist then it must exist. This caused me to wonder if I could “up the ante” and declare that; if it was detectable then it exists. This would allow for something infinitely small that doesn’t interact with anything to still exist (through Socratic reasoning perhaps).

Later on in the thread, the inadequacies of semantics show up again in your discussion with Paul:

“…consider the difference between a vacuum and absolute nothing. A vacuum has physical dimensions. Absolute nothing won't have any dimensions at all.”

I have no problem envisioning “something” that is not matter or empty space. This void could be as large as you like (dimensional) and would exist.

It could be that the term “absolute nothing” as it pertains to physics is being misconstrued by me. Perhaps the way that it was defined (described) was unintentional. Perhaps the definition should have been “that which doesn’t exist”. Now, it doesn’t exist and it is also dimensionless.

At first this might seem picky but it actually shed’s light on the OP: I propose, that as it pertains to physics; if it is dimensionless it doesn’t exist. If it is dimensional (infinitely small/ large) it does exist.

On another thread; infinite progression/regression was discussed. Regardless of the “blow-by-blow” mechanics of it; the concept is palatable enough. In the grand scheme (of the cosmos); our local universe would be infinitely small but we exist none-the-less.

There's a lot to think about in these last two posts.

Paul, I'm going to come back to your observations about being in two places at once. My elderly grey cells no longer hold on to as much information as they used to, so I have to rely to some extent on notes, which then have to be found!

Kirby, while I think we should try to avoid slipping into semantic wrangling, I agree on the importance of ensuring that we are all using words in a way that avoids confusion.



Look again at the sentence you quoted. The "something" was something only at the point at which it obviously existed. The question could also be: "If something could become infinitely small, would it still be something?"

Personally, I think this is a redundant question, because I can see no way in which something of finite size can become infinitely small, or large.

Redewenur’s reasoning could also be re-worded to ask a slightly different question. E.g. If something reacts with other things, can it be infinitely small?



I agree completely. Would you agree that you can turn this round the other way and say: if it exists it is detectable, at least theoretically?

Wow! That needed a bit of thought.

If it is "something", it exists.
It is infinitely small, so it has no dimensions, so it can never be detected.
It doesn’t interact with anything, so we have no way of knowing it exists.
If we don't know it exists, how do we know it is something in the first place?

This has to be another example of the difficulty of discussing the infinite in finite language. It's that spider in Flatland, again.

What are the dimensions of the infinitely small?

“Kirby, while I think we should try to avoid slipping into semantic wrangling, I agree on the importance of ensuring that we are all using words in a way that avoids confusion.”

I remember one time when a philosophically oriented friend and I spent hours discussing and defining the word “fear”. We went through this exercise because when he finally used the word in a declarative statement (that only took a few seconds); I knew exactly what he was talking about. This was communication at its best and it resulted in a successful realization.

“Look again at the sentence you quoted. The "something" was something only at the point at which it obviously existed. The question could also be: "If something could become infinitely small, would it still be something?"

My humble opinion is that “something” infinitely small could exist. I offered up the infinite progression/regression analogy for a couple of reasons: it is the only “concrete” example that I could think of. It would be hypocritical for me to cite BHs since I think that the singularity is theoretical only. (In practice, I “believe” that the core is dimensional.)

“Personally, I think this is a redundant question, because I can see no way in which something of finite size can become infinitely small, or large.”

This is fine. I‘m not looking for converts. Your conviction in this area is intriguing and I want to understand. How do you reconcile our finite universe with spatial infinity?

I know that for me, the compatibility between the finite and the infinite is achieved through scope. At maximum scope the “totality” is not a discrete value but rather, akin to a mathematical function. Although there is no discrete dimension to grab hold of; it is still dimensional.

“Redewenur’s reasoning could also be re-worded to ask a slightly different question. E.g. If something reacts with other things, can it be infinitely small?”

Yes…but I can only think of one example…only one physical application.

“I agree completely. Would you agree that you can turn this round the other way and say: if it exists it is detectable, at least theoretically?”

Yes. I agree. For instance; the “undetectable” could be detected by the process of elimination.

For starters, like my paycheck... Naw, that’s not a good analogy (since it’s zero).

The geometric dimensions are infinitely small. It’s interesting to note that; even in this universe, Planck’s limits can’t “save me”. IMO, theoretically, an infinitely small object would be the sole occupant of a Planck volume and would not tolerate another infinitely small object in the immediate proximity.

Perhaps time is a good analogy. There's no problem envisioning time or the present to be infinitely small but it progresses none-the-less. This probably wouldn't hold true if it wasn't for the discrete operational nature of the cosmos.

Elsewhere I have mentioned my long and probably rambling notes on infinity and various subjects linked to time travel. I wrote these notes as though I were writing a book, destined to be read by people like myself who lack a scientific background. In fact I shall probably be the only reader.

This is a small extract.

I invite you to consider the possibility that the cosmos is infinite. (Whenever I use the word “infinite” I include “eternal” within the term, unless otherwise stated). I am, here, picking up the idea that the four dimensions of spacetime that we experience are only a shadow of a higher-dimensional reality that is beyond our reach. Furthermore, I am suggesting that the cosmos has an infinite number of dimensions, or perhaps that should be regarded as just one infinite dimension, which we cannot experience. Like zero, whatever you divide, or multiply infinity by, it remains unchanged. However, unlike zero, infinity should remain unchanged if you try to add something to it, or subtract something from it, because, if it is truly infinite, whatever you “add” will already be part of it, and whatever you try to subtract will still remain part of it, otherwise, it would no longer be infinite. Even when trying to explain this idea, we run into problems with terminology. Strictly, we should not talk about “parts” of infinity; surely, it has no parts; that is of the essence of infinity. Leaving aside the mathematical “infinities” that we looked at earlier; it feels as though no part of a true infinity should be thought of as being finite, because a true infinity cannot be sub-divided. In eternity, time should receive the same treatment, it to is eternal; of course this is also a contradiction in terms; what I should really say is that time, as we understand it does not exist. There is no passage of time, as such, nor do we pass through time. We live in an eternal, unchanging now. The reason that we cannot actually experience this eternal now, nor can we experience more than four of the eleven dimensions of ‘M’ theory, nor the twenty-six dimensions of an earlier version of string theory, nor the numberless dimensions of an infinite cosmos, nor whatever your personal choice of dimensions might be, is that we are, so to speak, trapped in the four dimensions of spacetime. All we can be sure of is that we are restricted to experiencing three dimensions of space and one, seemingly very linear, dimension of time. What we experience is a four dimensional “shadow” of an infinite dimension, the nature of which we cannot begin to visualise, any more than an inhabitant of flatland could visualise our three dimensions of space.

I find myself wondering if quantum weirdness, which must include bi-location, could arise from the possibility that in "looking at" quantum objects and their behaviour, we are getting some small insight into infinite reality, in which there is no separation in time or space.

If my idea that we live in an infinite cosmos, of which we can experience only part, is right, then it could be that the more we learn about the quantum world, the nearer we might come to understanding infinity. It's only a thought, but science is dotted with examples of thoughts that have later been picked up by more able people who have turned them into enduring theories.

Bill S.

Thank you for sharing.

Ya know, there’s this thing that I call the 95/5 rule. On internet forums, we spend 95% of the time discussing the 5% that we disagree on and 5% of the time discussing the 95% that we do agree on. Unfortunately, this can create illusion that it is we that are disagreeable.

We agree on the importance of infinities as it pertains to reality. We are polar opposites when it comes to how this is “delivered”. In addition, we are on the extreme ends of our camps. You are 100% parallel and I am 100% serial. You are multiverse and I am megaverse. This is cool. It’s too bad governments can’t disagree the way we do.

It’s obvious that you spent considerable time on this. Why? I don’t mean the usual standbys like curiosity… For me, it was a childhood spark when I asked “What happens after you die?” I guess ya gotta get equipped before you can answer that. What about you? Where’s the goal line?

“All we can be sure of is that we are restricted to experiencing three dimensions of space and one, seemingly very linear, dimension of time.”

Seems sane to me.

“We live in an eternal, unchanging now.”

Not so sane. What do you mean by unchanging?

What purposes do the other dimensions serve? How do you account for apparent change?

"...we are, so to speak, trapped"

I liked that.

Kirby, I like your 95/5 rule; Should it be called Gillis's law? If nothing else, that would create a division between those who insisted on spelling it with an apostrophe-s and those who wanted just an apostrophe.

What have I said that makes you think I am pro-multiverse? Have I been playing devil's advocate too well? Don't encourage me, or I might start posting my multiverse notes.



I have probably said this before, but it started a few years ago with thinking about past-directed time travel. I felt sure it was not on, and set out to look for some sort of evidence. To my surprise, it linked into thoughts I had wrestled with about infinity for many years.

What do you understand by "megaverse"? We might have more common ground there than you think.

“What have I said that makes you think I am pro-multiverse?”

A couple of things: You are a proponent of infinite dimensions. From other posts it seems that you are more comfortable with M theory style systems.

“To my surprise, it linked into thoughts I had wrestled with about infinity for many years.”

The relationship between past directed time and multiverses would certainly be interesting and probably unique. I’m definitely curious.

“What do you understand by "megaverse"?”

Nothing that we haven’t discussed before. When I spoke of infinite progression/regression after I serialized it; we agreed that the resulting infinite universes could be termed mega. Parallel schemes like M theory would be termed multi in order to differentiate. However, there always seems to be speculation about multiple universes occupying or sharing the same space.

One of the things that I like about IPR is that each sequential universe is as concrete and real as this one. BTW, if this were true; there is hope for detection while the other schemes don’t seem to offer any hope for verification other than Socratic means. (I hope to address this in more depth on another thread (that already exists.)

I remain open to all systems…especially new ones. I’m also interested in any unique relational setups.

For instance in your last post; the relationship between time and apparent change would be key and most likely unique. Likewise the relationship between past time travel and multiverse.

The link I mentioned was between past-directed TT and infinity, rather than the multiverse. However there seems to be a considerable body of opinion than hails the multiverse as the only vehicle for TT to the past. I have to say I found what looked to me like a few serious problems with that, though.

If time actually progresses, then the present is merely a convention by which we separate our expectation of the future from our belief that we can remember the past. As such, it has no existence of its own, and can be said neither to be finite or infinite.

Seems to me that 'present' can be defined only in relation to consciousness, so if someone can answer the question "What is consciousness?" then we might gain some a key insight into the meaning of 'time' and 'present'. I'm sure that, unfortunately, nobody can answer the question. Still no harm in philosophising, so long as we recognise it for what it is.

If something cannot be infinitely small does this include time itself? We have a reasonable definition in Plank's time.

Because it's defined it can't be infinitely small.

So, if Plank's time IS the smallest unit of time, what is ocurring between these very small (yet not infintessimal) time 'frames'?

Are there timeless gaps between each frame?

How do we define these?

How do we quanity their magnitude if they exist outside of time itself? Are they infinitely large, or infinietly small?

Would you say that time can be defined only in relation to consciousness, or only the present?

Whether one regards time as static or flowing it is difficult to see how it would be possible to cross a gap between quanta of time.
Although very happy with the idea of quantised time, I think there would have to be no timeless gaps.

I think it most likely that time is as inextricably linked to consciousness as it is to space; that not only can there be no consciousness without spacetime, but no spacetime without consciousness.

"The problems highlighted by the cat-in-a-box experiment raise some very deep questions. What for example are the requirements needed to qualify as a 'conscious observer'? Do the probability waves of particles spread out again when not observed and particles somehow become less 'real', as described by the Copenhagen Interpretation? Does the universe exist only because we are here to observe it?"

http://www.thekeyboard.org.uk/Quantum%20mechanics.htm

"Does the Universe Exist if We're Not Looking", at:

http://www.scribd.com/doc/208321/Does-the-Universe-Exist-if-Were-Not-Looking-Discover-Mag

and

http://discovermagazine.com/2002/jun/featuniverse/article_view?b_start:int=1&-C=

(There's a problem with the last link. You may need to copy and paste it)

Incidentally, repeating what I noted elsewhere, it appears from my reading that the Planck time is considered by many theorists not to be the smallest possible time interval, only the smallest interval that could, theoretically, be measured. I may have read the wrong things - after all, the internet is a misinformation free-for-all - but all such info obviously needs thorough checking by anyone seriously studying the topic.

That's not just a deep comment, it is at least 3 deep comments. Needs some thought. May take a while though, as I shall want to follow up your links, and I am currently trawling through my Big Bang notes, trying to eradicate errors! Found one typo in which I called it the "Big Bong", my wife said I should not change it as she believes smoking weed is responsible for a lot of scientific theories.

"Found one typo in which I called it the "Big Bong", my wife said I should not change it as she believes smoking weed is responsible for a lot of scientific theories."

That's hilarious...and useful. I think that I'll be finding excuses to recycle that one in the future.

redewenur
Just one note. I'm not really planning any serious comments on this thread. But you said that you don't think spacetime can exist without consciousness. Then where was spacetime before there was consciousness? I prefer to apply Occam's Razor, it is much simpler to assume that spacetime can exist without consciousness unless there is some overwhelming reason to think otherwise.

Bill Gill

Bill,

I was considering posting a similar comment, then I thought: how do we know there has not always been consciousness?

Bill S.
Before the Big Bang and for a long time after there was nothing organized enough to have a consciousness. The only other source of consciousness would be God. But we aren't taking about religion we are talking about science. So we just have to apply Occam's Razor.

Bill Gill

Bill,
I assume from this that you reject the theories of multiple universes, or an eternal cosmos, either of which would not necessarily involve God or William of Ockham.

Bill, while Occam's Razor has a loud and righteous voice in science, there are times when I don't allow it to dictate my hunches. Given the present limited knowledge regarding the nature of spacetime and consciousness, any such speculative notion is almost bound to be cast into the realm of metaphysics and the waste paper basket of science. In that regard, the idea sits comfortably in this fascinating thread.

Nonetheless, your apparently confident remark that there was "nothing organised enough to have a consciousness" before the Big Bang seems to be founded on faith rather than science. I qualify my notion with "I think it most likely"; perhaps you meant to do likewise.

My aim is not to make dogmatic assertions about matters that are unverifiable by current science, nor to advocate blind belief in some metaphysical doctrine or other, but rather to express an open mind regarding what science may yet verify - Occam's Razor notwithstanding.

Well, one last post on this general subject.

In regard to Occam's Razor. As I recall it basically says that if 2 theories explain an observation equally well, choose the simpler. Now this doesn't rule out the more complicated one. If further observation (testing) shows the simpler doesn't work well, then you should go ahead and try the other one. But the requirement of a consciousness for the universe to exist is not a scientific theory, and there is no known way to test for it.

As far as the requirement for a consciousness. I believe this comes from a misunderstanding of a lot of discussions of the quantum theory (QT). An example is Schrodinger's Cat. QT says that until the box is opened the cat is in a superpostion of both possible states (alive and dead). But when the box is opened and we make an observation then the superposition collapses into just one of the states. It is the requirement that an observation be made that confuses people. They assume that an observation requires a consciousness to make it. But lets do a simple thought experiment.

Assume that there exists someplace a quantity of naturally occurring silver iodide.

Immediately above this is a layer of some naturally occurring polarizing crystal.

At some distance from the crystal, and on a line of sight from it, and from the silver iodide, there is a quantity of florescent material which will emit a photon when a beta particle (electron) hits it.

According to QT the polarization of the photon will be in a superposition of all possible polarizations, until it is detected.

If the photon hits the crystal the superposition will collapse into just one polarization.

QT positively defines the probability that the polarization will be the same as the polarization of the crystal.

If the polarization of the collapsed state of the photon is the same as the polarization of the crystal it will pass through the crystal.

If the photon passes through the crystal it will strike the silver iodide and cause one molecule to decay and leave one atom of silver and its other decay products in its place.

Notice that we now have a absolute change that was not observed by a consciousness, and quite probably never will be. But it will make a change in the universe. Therefore I feel that the need for a consciousness to keep the universe running is an unneeded idea.

And that's all I have to say on this subject.

Bill Gill

By the same line of reasoning any superposition in Schrödinger's cat box will have collapsed long before it is opened; right?

In the cat box there is nothing to select among the possible states of the cat until it is opened.

In my thought experiment the crystal initiates the collapse. Then the silver iodide determines if the collapsed state is of the same polarization as the crystal.

Schrodinger was simply attempting to demonstrate how QT does not directly correlate with general reality.

Many QTs rely upon probability and uncertainty. At a macro level they have no value.

I am not saying that it's wrong, but in general it seems that the closer we look, the fuzzier it becomes.

Precision and accuracy are not one and the same.

I believe Niels Bohr maintained that the cat would be either dead or alive long before the box was opened by a conscious observer.