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

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