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.