smallest size a space can occupy

Is this a logic puzzle?

(If a frog climes the side of a well and hops half the distance remaining each day...)

I guess the practical answer is "the smallest amount you can measure" or maybe "the smallest division of space is equal to the smallest particle that could occupy it".

Let's see where that takes us!

Hmmmm if you define space as containing nothing then the smallest size of space must be approaching infinitesmal, or not measureable...

In other words very very very tinnnyyyy, smaller than a very tiny small thing...

John.

OK I"ll bite.

Space would be defined by its limits. either real as in walls or virtual as by measurement. There can be things in a space but if you measure the space you would have to subtract that which is not space. ie any objects in the space. Space can occupy any dimensions you give it or boundries that you build. Space will fill to whatever limits you can describe whether they be large or small. They can be infinite or boundryless. Space doesn't occupy anything. Space is what is left over after you subtract all the objects. Those objects could be cars, the sun, or atoms or a proton. It doesn't matter. Space is what is left over. I guess if you go (0,0,0) from the origin there is no space. As soon as you make any one of those numbers greater than 0 there must be a space. If only one number is greater than 0 then it must be a one dimensional space whatever that is. If two numbers are greater than 0 then you would have a 2 dimensional space and likewise 3 numbers greater than 0 would be a 3 dimensional space. I would guess that 1 nd 2 dimensional spaces are somewhat theoretical.

infinite extension in all directions from a point means that there will always be something called space in any direction unmeasurable or limitless

space (sps)

n. 1. a. Mathematics A set of elements or points satisfying specified geometric postulates: non-Euclidean space. b. The infinite extension of the three-dimensional region in which all matter exists. 2. a. The expanse in which the solar system, stars, and galaxies exist; the universe. b. The region of this expanse beyond Earth's atmosphere. 3. a. An extent or expanse of a surface or three-dimensional area: Water covered a large space at the end of the valley. b. A blank or empty area: the spaces between words. c. An area provided for a particular purpose: a parking space. 4. Reserved or available accommodation on a public transportation vehicle. 5. a. A period or interval of time. b. A little while: Let's rest for a space.

joshua

According to quantum mechanics, I believe that the smallest distance that can exist is Plank's Length, which I am no prepared to give you at this time.

However, prior to reaching Plank's Length, I am assuming vacuum energy will start shaking things up.

http://en.wikipedia.org/wiki/Planck_length

I'm prepared to give it Vermin, the Planck length is 10^-35 m.

Cheers.....Codey

As already noted, much of what lies in the realm of an answer to your question exists in the theoretical world only. And, the theories are continually evolving...

Some authors are better than others at putting theory into the proverbial nutshell for us non-physicists to swallow.

Find a used copy of Brian Greene's "Fabric of the Cosmos"... {http://www.amazon.com/Fabric-Cosmos-Space-Texture-Reality/dp/0375412883}... and you'll be immersed for many hours in a very understandable delineation of the multi-dimensional world of superstring theory.

The angstrom unit has long been eclipsed as the tiniest measurement of consequence! However, I doubt that you'll find the answer that you seek (in the context in which you'd like to hear it) within these here Thread-pages...

"Read On!"

That is, of course, if string theory is ture... It's kind of been having fits and starts lately.

It assumes that the axiom of countability exist for string theory, mirror symmetry and the addition of the 10, 11 or 26 additional dimensions, which all supposes that it is countable and that there are only 26 additional dimensions to count, far to many possibilities that that number will grow as we understand it better, to many additional theories to be added to make it explainable.

joshua

Have you ever been exposed to Quark Theory? In the beginning, the two guys that came up with this thought they had it covered by just three quarks... Do you know how many there are now? And they still need more.

Smell that? that's the stink of a possible dead-end.

Have you ever been exposed to Quark Theory?

Well, I am not sure it was a theory. I was in kindergarten, and Miss Ana was reading to us something and she mentioned something like:

"Three Quarks for master Mark". So this are my $0.02

Wasn't that James Joyce?

'Twas Joyce indeed. The "three quarks for muster mark" refers to three 'quarts' of ale to be counted as present. Sufficient quantities of ale may be required to be present to resolve this 'smallest space' question.

However, what about the corollary - what is the LARGEST space (foregoing the obvious answer of 'the universe itself' of course)? And can it be filled with ale?

ya can't say its not true also, looped back o string theory

Ndt-tom writes: "The angstrom unit has long been eclipsed as the tiniest measurement of consequence!"

-----

What might be regarded as the tiniest unit of measurement depends on whom you talk to. Physicists, for instance, speak of nuclear scattering cross sections in terms of barns and sheds (both being units of area):

barn = 1e-28 m² (the area of a square 1e-14 m on a side) - Said to have been inspired by the phrase "big as a barn."

shed = 1e-24 barn (the area of a square 1e-26 m on a side) - The smaller companion to the barn.

In contrast, a square Ångstrom (the area of a square 1e-10 m on a side, ie, 1e-20 m²) is larger than a barn by 8 orders of magnitude.

Guess which element has the largest barn size (if that's appropriate)... And no looking it up!!!

in response to this (as well as subsequent replies to #6) --- "Thanks" for emphasizing with the numbers, exactly what I said...("eclipsed"). And, I may be doped-up, awaitin the MRI, but I never insinuated that string/superstring theory was THE answer...

... simply that (IMHO) B. Green does a good job of putting many of the associated concepts into clear perspective [without all the spaghetti-math].

And I liked the way he puts into the reader's hands a sequence of magnifiers ... looking at smaller-&-smaller spaces until things get "boiling" and chaotic such that we can't really imagine. ~ The thread HERE should be asking about the predicament that Greene put forth: The reason that we haven't yet SEEN some of those "smaller Dimensions" is because we don't yet know HOW (or have the TOOLS with which) to see them(!) *This-generation's-Leeuwenhoek*, Step Forward!

And, we (here) continue to add-to the evolution of the theories (per #6)...

"As it can not end up with zero , will it end up with a minimum size..."

A presumption that is not necessarily accurate. WHY can it not end up at zero? Back when I studied geometry (somewhat AFTER the Greeks invented formal proofs and theorems, thank you!) we were taught that a plane consisted of space delimited by lines, and lines were a series of points. Points, however, are dimensionless, and thus also sizeless. So, if the X, Y, and Z axes are all at zero, you have a point. What, then, is the least non-zero increment that any axis can display? That may or not be related to Planck's constant... it can't be one point down, though, because the points are still dimensionless.

Ohbytheway, if a truly definitive answer somehow does show up in this thread, do we all get to share in the Nobel for Physics?

"What, then, is the least non-zero increment that any axis can display? That may or not be related to Planck's constant..."

I don't know about a displayed increment, especially if you attempted to display anything at, or below, the Planck scale.

"it can't be one point down, though, because the points are still dimensionless."

How then can a line (axis) have a length if all the points that make it up are dimensionless? Does a dimension consist of non-dimensional components?

Johnjohn,

Please see #42.

A line is simply a collection of locations - and locations in geometry do not have area... Area was not what they were invented for, they were created to define just one specific location, thus their nature.

Geometrically, lines, areas, and three dimensional solids can exist something like fractals... The more detail you want, the more detail you get. But remember, you are asking for locations, and locations do not have any intrinsic area.

However, I can't help but think that if the original question is not oxymoronic, it's at least somewhat linguistically challenged... "The smallest size" THAT "a space can occupy."

That's a little like asking the question "Can God make a rock so big that even he can't lift it?" Of course, we all know the answer is, "No. But he can create a rock so big that his doctor advises him against lifting it."

Yes, but there is a huge gulf between what the OP is speaking of here - physical reality - and its mathematical idealization: geometry. To wit: a physicist and a mathematician are at a blackboard puzzling over a thorny problem. Suddenly the department's drop-dead-gorgeous chief engineer appears at the door. She briskly walks toward them and, in one step, covers half the distance between them and the door. But her next step covers only half that distance, the next one half that, and so on. Exasperated, the mathematician exclaims "She'll never get here!" To which the physicist replies, "She'll get close enough!"

"The Planck constant and the reduced Planck constant are used to describe quantization, a phenomenon occurring in subatomic particles such as electrons and photons in which certain physical properties occur in fixed amounts rather than assuming a continuous range of possible values."

But what are the unfixed amounts of the continuous range of possible values, there comes the rub of renormalization to determine the relationship between the parameters describing large distances as differentiated from small distances, used to make sense of the infinite integrals which means the acceptance of the indefinite integral or antiderivatives leading to limitless or infinite solutions that by definition is arbitrarily closed ended. It is merely an acceptable closure to all the possibilities to allow a means of construct of an acceptable solution to view the interaction at one point while ignoring any other where the interaction might be far more complicated.

A beam of light can be focused to a point in space but beyond that point it becomes defused, scatters, to say that a measure at the point of focus is the only interaction excludes the actions beyond that point.

A point on a line has more than one area of interaction it is not a flat limited point on a single line of reference but a point on many lines of reference, surrounded by a sphere of intersecting lines, it is placed on more than one line of measure and thus endlessly open ended.

joshua

Of course, there is the possibility that if you go down small enough, you lose spatial resolution - and because of that could potentially wind up anywhere in the Universe.

If one accepts the BB theory, then all space in the observable universe arose from a single infinitesimally small point. Therefore space, at one time, was infinitely small.

See that rectangle with the small diamond in it in my previous post? That only started showing up after I switched to Firefox. Any ideas where it's coming from? How would Firefox be interacting with a CR4 editor anyway?

I don't see it while I'm typing a reply, but only after I preview the message. If I go back to "Edit this message" I can see it and delete it. I'm puzzled (as usual).

-John

That's an image placeholder. CR4 balks at really large image files. Is that what you sent?

Hi e,

No, I didn't send an image. The placeholder seems to show up anyway.

One thing I did notice about using the editor since I've switched to Firefox is that if I insert one of the toolbar emotions, my cursor disappears! I can preview the message then go back to editor and the cursor is back. Let's see if the placeholder shows up with this message. I'm not sending any images.

-John

That what you call a rectangle and a diamond is a broken picture link to me as it is a small cross in a rectangle from where I am sitting. Maybe your firefox is sending a picture with the message that does not come through somehow like those annoying adverts from smiley central do when you use them.

Anyway, the bb does indeed specify that it all came from a single point but what was the size of that point and could you split it again? What was outside of that point and what is outside of the "space" our space occupies. If it comes from this point it is finite, or not? Where was it all before it occupied the point?

If it came to be in that point through the big contraction that went before it, up to how small did it go before it reversed and expanded again?

I do support the bb on most points but questions that keep the big brains busy should be good enough for us

My two pesos' worth re: The BB.

A lot of folks here and elsewhere parrot the current party line and say "The BB, the Universe, and all that began with a 'quantum fluctuation.'" A 'quantum fluctuation' in what, exactly? A fluctuation in non-existence? If not, then why do we speak of the Universe and, more generally, of existence, as having originated with the BB? Sure sounds like a leap of blind faith to me. One which pleads for a good dose of critical thinking.

If something came before, a Something in which Something Else could 'fluctuate,' then this Universe didn't originate with the BB; it originated with that Something Else, whatever it is.

Then there's the Cyclic Universe camp. You know: the ...BB, BC, BB, BC, ... ad infinitum crowd. That theory's a cop-out, IMHO. For one thing, there's no evidence for it whatsoever. Doesn't mean it didn't/doesn't happen; there's just no evidence to support this theory. Its proponents take it on faith. They have no other choice.

Interestingly, many of these same folk decry others' faith; faith in such things as the existence of God and so forth. Often in the name of 'tolerance.' What a crock.

Concur on the crock. This is a topic that clearly requires much more discussion (and probably some cussin').

My take on BB is that it is an approximation - not "the" solution, but a straw man that can be hanged up there for all to take shots at until something more useful (or - take your choice - elegant, relevant, comprehensive, etc.) falls out of it all.

Now come to think of it, why couldn't there be a fluctuation in non-existence? Admittedly it's not easy to see what would be flexing, but then none of this is intuitively obvious anyway. Some of the newer theories such as "branes" and "foam" are actually a bit more persuasive (to me, anyway) than BB, Grand Cycles, strings, blind faith, or any of the rest.

Now come to think of it, why couldn't there be a fluctuation in non-existence?

-----

...in non-existence...

Even our words trip us up: does not 'in' silently imply containment within a greater something? I don't know about you, but I simply cannot imagine non-existence. If I'm like most people (I tend to think I'm not, but what the hell do I know?), the best image I can conjure up is one of completely empty space. But this image is completely inaccurate. Space is far from being nothing. It can be measured, filled, ignored, taken for granted, modeled, moved through. But non-existence it is not. That word 'in' presupposes existence.

"Then there's the Cyclic Universe camp. You know: the ...BB, BC, BB, BC, ... ad infinitum crowd. That theory's a cop-out, IMHO. For one thing, there's no evidence for it whatsoever. Doesn't mean it didn't/doesn't happen; there's just no evidence to support this theory."

It seems to me that the Big Bounce makes more sense than the BB, because it, at least, doesn't require something to emerge from nothing. Plus it tends to give the universe a certain sense of continuity (more soothing to the ego or something like that).

I flatly refuse to bring God into the discussion because it brings out all the full moon loonies. That said, the Bounce gives the idea of existence a more solid footing (IMHO). We aren't flowers that sprang up from an infinitely small garden. I'm including an emoticon just to test the editor:

After I inserted it I pressed "Enter" and the cursor disappeared however when I started typing it reappeared! Weird!

-John

"It seems to me that the Big Bounce makes more sense than the BB, because it, at least, doesn't require something to emerge from nothing. Plus it tends to give the universe a certain sense of continuity"

The Big Bounce had to start somewhere and somewhen, did it not?

This reminds me of the Buddhist parable of the turtles - what supports the universe? It sits on the back of a tortoise. What supports the tortoise? It sits on the back of a larger tortoise. What supports...answer - it's turtles all the way down...

If there's to be a sense of continuity, I'll go ask a tortoise.

The human mind really does have an annoying inability to deal with the concept of nothing!

Quantum physics provides the alternative that while nothing is "really" nothing, things can come into being within the nothing through charged vacuum envoidments (look that up in your Funk & Wagnell). It's this ability that brought on the concept that our Universe might not be the only one. In fact, someday we may interact with another one...

Meanwhile, here, back in space, I'm surprised that people are not more blown away by the concept of Boltzmann Brains! Same thing, it just takes place in empty space.

"what supports the universe? It sits on the back of a tortoise. What supports the tortoise?"

Or Atlas, holding the world on his shoulders. What I'm wondering is who took the photo of Atlas holding up the world?

Woof!!! And how many times did you have to take geometry?

A point is not an area. This is like arguing apples and oranges. A point is simply a location. It has absolutely nothing to do with area... Yes, you can say, "I'm on Maggie's farm," but that is not a point. A point (to reiterate) is just the simplest of simplest locations.

infinitely small by definition

A mathematician would agree. A physicist would not.

Not sure what the size is, but reportedly, all politician's brains can fit in with room to spare...

Will it have enough room left for their egos to pack in as well?

Not even close!

From what I have read, the smallest space would be a Planck Volume, which is 1x1x1 Planck Length. To get a grasp of this (as if anyone can), there are as many Planck Volumes in one square centimeter as there are square centimeters in the visible universe. See the cover story on Loop Quantum Gravity in Scientific American from a couple of years ago - the theory proposes a quanta unit of time, ie: a smallest time unit possible.

"But what will happen if we divide space? As it can not end up with zero , will it end up with a minimum size space particle?"

You can cut the space in half and then I can halve that ad infinitum.

You say it is to small to divide again but you can't prove that but as long as it exists and is smaller than ever before it is still of a finite size and I can halve that!

If you are talking about particles then it becomes a discussion of smallest particles.

Now how do you know that there isn't one still smaller that the smallest?

"Now how do you know that there isn't one still smaller that the smallest?"

As someone has posted earlier, a line (axis) is made up of a series of points that are dimensionless, thus no particle can be smaller than a point in a line.

Because Horton heard a Who!!!

All Whovians are now wondering which Who heard a Horton hear a Who?

How small can that point be, and is it a single dimension or spherical intersection of multiple dimensions?

Horton heard the who but only because he was listening!

joshua

WHAT ABOUT SINGLE DIMENSION AREA...... ??? IF THIS EXIST THEN THIS WOULD BE SMALLEST AREA !!!

By definition, area is 2 dimensional. The OP asked about space (implying volume) requiring 3 dimensions, by definition.

I've read all of the "answers" and tangents to the initial question of "what is the smallest size "space" can occupy and I'm just going to interject my own nickel's worth and then I'm going to bed because my puny brain hurts. Any and all backlash is most certainly acceptable and expected.

I do not believe that we can currently answer the question.

1) We don't know the number of particles that make up an atom nor their size, shape or placement within the atom. Any number, size, shape or placement is purely speculation at this point.

2) Since, theoretically, space is a lack of matter, for all practical purposes, and if the statements in #1 above are true then it is not possible to know the smallest size space can occupy.

3) Zero is only a theory used by mathematicians as a starting point to save miles of other math to "approximate" its place in space. I do not believe that there is such a thing as "absolute" zero because all measurements are infintely divisible using our current knowledge and therefore absolute zero is not acheivable.

4) If multiple axis lines converge on a point that we can call zero "point" and a point has no dimensions or mass then the axis lines cannot have dimension or mass either and are not divisible in any way which is not possible and the statement in #3 applies.

5) If anything is divisible down to a point where dimesionability "dissolves" and we possibly end up in another part of the universe; would it still be "our" universe or another co-existing universe? Would it be infinitesimally tiny to be further dimensionalized or would it be like breaking through a doorway into a universe like our own where we would have to start all over again splitting hairs ad infinitum to again cross another boundary and start all over again, ad nauseum..

I LOVE infinity because it messes with our poor little brains as we try to wrap ourselves around the concept. Maybe one day we might even understand that concept but, not at this time.

I go sleepy now.

Wake up, wake up, your subjects are waiting!

"it is not possible to know the smallest size space can occupy."

Well, I still think space is occupied, it doesn't occupy, thus the original question is meaningless. However, if we get into the "anti" thing, i.e., antimatter, etc., we might consider anti-space to be matter and thus it all makes sense. But that gets us down to the same old questions- what's the smallest anti-space there is? We're right back down into all those quarks, muons, bosons, fermions, ad nauseam.

But then what happens when space collides with anti-space? They don't annihilate each other because we observe coexistence everywhere, so that violates the whole annihilation of opposites thing.

Now see what a hell hole you've caused me to dig myself into? For shame...

Well, I still think space is occupied, it doesn't occupy, thus the original question is meaningless.

-----

Ah, but a smaller empty space can occupy a larger empty space!

"Ah, but a smaller empty space can occupy a larger empty space!"

Excellent point!

Since by definition space is not a particle there is no limits to how many times it can be divided. Half of nothing is still nothing!!!

Space and time are but perceptions so the "smallest size space can occupy" would be what we perceive it to be.

joshua

Space and time are but perceptions of what?

perceptions of what we make them to be.

joshua

Cannot resist, (try as I might.)

These ideas are all tared with the same, unanswerable, brush.
(and, yes, they do my head in also.)

i.e. irresistable force meets immoveable post, etc. etc.

One that really gets to me is the the "edge" of the universe.
(because if you go "outside" you are still "in" ...somewhere!)

Similarly, as others have stated nothing divided is nothing!
(that is, we cannot conceive what it is, at this time)

Put in another way; I'm the urban spaceman baby....I don't exist!

jt.

Need a free web page? have one in 30 seconds http://www.mfnb.at

One that really gets to me is the the "edge" of the universe.
(because if you go "outside" you are still "in" ...somewhere!)

-----

Agreed. Please see An Ellipsoidal Universe? Part II for my take on this.

"An Ellipsoidal Universe? Part II"

Great thread e. I had not read it until now. Great insights.

-John

So, conversely: "What is the smallest space a size can occupy?" I think quantum physicists would be far more comfortable with this question.

The next universe.

And once again, Horton hears a Who!!!

I'm slow vermin. I finally caught on. I too heard a who.

Who's on first, so who's on second?

Because you asked:

• First Base: Who
• Second Base: What
• Third base: I Don't Know
• Left field: Why
• Center Field: Because
• Pitcher: Tomorrow
• Catcher: Today
• Shortstop: I Don't Give a Darn!

No! What's on second who is on third. Except in a Minkowski space where he or she could be on both I suppose.

I use to work as a metrologist and I thought I had a good understanding of dimensions. Then I got introduced to Alberts work and that changed the possibilities.

Just to rattle my nice three dimensional concept of things there was this guy called Paul (Also Know As Saul of Tarsus) who was usually a nice sensible writer who in one of his letters wrote "I have known a man in Christ, fourteen years ago – whether in the body I have not known, whether out of the body I have not known, God hath known -- such an one being caught away unto the third heaven;" 2 Corinthians Chapter 12 verse 2.

Is there some connection between the physical and the metaphysical/spiritual or is it all just physics that we don't understand yet?

Hi e,

Your signature reminds me of a joke I heard not too long ago.

A man was standing in his field pondering his situation. He asked God "Why did you give me such a beautiful wife God"?

And God answered: "So you can love her my son".

The man said "Well God, why did you make her such a wonderful cook"?

"So you can love her my son" the Lord replied.

The man said "Well God, "why did you make her so caring and thoughtful?"

And God again answered: "So you can love her my son".

The man said "Lord, I don't want to seem ungrateful, but why did you make her so incredibly dumb"?

And God answered: "So she can love you my son".

Thank you all for responding to my question.Though some answers are very thought provoking , yet I have not got any satisfying answer.

what were you looking to hear as a responce? "yet I have not got any satisfying answer"

joshua

Odd, I would have thought that the Plank volume would be exactly the type of answer you were looking for. Maybe you could rephrase the question?

Ah! <smacking head> Now I get it! You're asking about the smallest size a space can occupy! Well then, I'd have to say that the answer to that one is clearly 409.6 units, given that the minimum value is defined to be no less than 1/5 the em, a value much less than Stephenson Blake's Wide Latin. (Sorry, Steve. Close, but no cigar.)

To wit:

• Space
  Unicode: U+0020
  Advance width rule : The space's advance width is set by visually selecting a value that is appropriate for the current font. The general guidelines for the advance widths are:
• The minimum value should be no less than 1/5 the em, which is equivalent to the value of a thin space in traditional typesetting.
• For an average width font a good value is ~1/4 the em.

Example

: In Monotype's font

Times New Roman-regular

the space is 512 units, the em is 2048.
• For a wide width font a good value is ~1/3 the em.

Example

: in Microsoft's

Verdana

the space is 720 units,

Tahoma

is 640 units. In Stephenson Blake's

Wide Latin

the space is 612 units. In all fonts the em is 2048 units.
• The maximum width should be no greater than 1/2 the em, which is equivalent to the en space of a typeface.

Moral: Ask an engineer the time and he'll tell you how to build a watch.

"Great fleas have little fleas upon their backs to bite 'em,
And little fleas have lesser fleas, and ad infinitum.
And the great fleas themselves, in turn, have greater fleas to go on;
While these again have greater still, and greater still, and so on."

— Augustus de Morgan, noting the expanding scales of life and their connections.

But I still personally think the Buddhist parable is most likely to be correct - it's turtles all the way down.

Your second conclusion is reasonably correct. The minimum space occupied should be the szie of the smallest particle in the space.

"Or its probabilistic approximation!"

Down, Niels! Down, boy!

Cannot define an abstraction by a concrete.

What is the largest space a size can occupy?

Are we talking Spandex?

That's why I use stucco!

are you talking, fresco?