The other day I was watching a program about the Mandelbrot set. One of the characteristics of the set is that it’s truely infinite: you can “zoom” into it infinitely; there’s no limit at which you stop.
Now that’s the case for a mathematical function, but is it the same case in the physical world? Just imagine you can “zoom” into any object (like in a graphics viewer, for example). Suppose you zoom past into an atom, into the nucleus, into a proton, into a quark, into a gluon(?)…
Where does this stop, if ever? Is there a theoretic limit for this? Is there a unit beyond which you cannot go (like a “pixel” in an image)? Or can you keep on doing that infinitely?
Space, as we know it, cannot possibly be infinite. A simple thought problem will suffice:
If space was infinite, even the slightest concentration of matter within it would mean that there would also be an infinite amount of matter.
If there was an infinite amount of matter, then the expansion of big bang would not have occured. An infinite amount of matter would have remained under infinite compression.
There is the remote possibility that there is a finite amount of matter expanding into an infinite amount of space but this is highly questionable. The energy that is distributed throughout space would have to be infinite as well and that is unlikely.
That’s my story and I’m sticking to it.
There is a limit to how far you can ‘zoom’ into something. It’s called the Planck Length and is the smallest unit possible. Planck Length is something like 10[sup]-35[/sup] meters. This is really small. For comparison a proton is around 10[sup]-15[/sup] meters in diameter.
There is also a minimum amount of time you can measure called (you guessed it) Planck Time which is the amount of time light takes to travel the Planck Length (or about 10[sup]-43[/sup] seconds).
In math you can write down most any arbitrarily small number you can think of far in excess of the Planck limits but the Planck limits are as far as we can go in the physical world.
I presume that you were watching “The Color of Infinity” narrated by Arthur C. Clark?
Quite an excellent program. The nature of the universe does indeed seem to be fractal. The only downward limit being the “graininess” of the “Plank Factors”.
One thing that has always made me stop and think is, if Space is not infinite, but is expanding, what is it expanding into? What is outside of the universe?
I’m afraid I never quite got the grasp of ‘nothingness’.
I guess it is somewhat theoretical. Basically the Planck Length is the point at which the known laws of physics break down. There is no way to describe the structure of what you see or make any predictions about what will happen. It is at this point that the quantized nature of gravity is supposed to show itself.
How could you get smaller than that? Nothing you do would make any sense any more at that level hence we, as humans, can’t see beyond it.
If you’re interested the calculation for Planck Length was arrived at by:
If you could somehow see down to the Planck Length then I’ve heard that it would look foamy (hence the term quantum foam). Others have described it differently though such as similar to a bucket of dust (Wheeler) or a never-ending procession of virtual black holes (Hawking).
Not to worry though…it’ll likely be a LONG time before we could probe down to the Planck level. At around 625 million trillion trillion times smaller than a centimeter it is MIGHTY small. I’ve heard a particle accelerator the circumference of earth’s orbit around the sun (or bigger) would be needed to get the energy required to probe this deep. You’d also need to convert the equivalent of the mass of Jupiter to energy to power the thing. A tall order in anyone’s book.
In the end it’d be kinda like throwing bowling balls at a BB to see what the BB looks like (only worse).
on the question of is space infinite, I think that I read somewhere that Einstein said : if you were in space traveling in a straight line,and you traveled long enough, assuming that you didnt run into anything, you would eventually end up where you started. This would mean that space is finite.
What lies outside of the four dimensional curve of timespace has always intrigued me too. Sadly, terms like “outside” do not apply sufficiently to use that concept. So far, it appears that space is “creating” itself. Not much of an explanation, but there it is.
What is most likely to exist “out there” are alternate probability, or “parallel” universes. There are also antimatter structures and other dimensional oddities that might inhabit such a place. Since the only mode of conveyance there currently requires transiting through a black hole, don’t expect any answers in the near future.
Thanks for the clarification, you obviously know a lot about this.
Correct me if I’m wrong, but it seems that Planck’s Length is the smallest unit which our laws can describe. Not that nothing smaller is possible, but rather nothing smaller makes sense?
Another question (I think everyone would have expected this one). If space has a “smallest unit”, i.e. is finite “inwards”, does it follow that it also have a “largest unit”, i.e. is finite “outwards” too?
I’m not talking about the supposed size of the universe, but rather about a theoretical upper limit to space as a concept.
The current theory on space,as highlighted by other posted messages, is that it is expanding.
Hence specific limits are hard to visualise. The question was then posed what is the universe expanding into? To answer this is to discover the very function of life.
All modes of life ranging from sound to mesons and the basic elements of matter matter can be measured as waves. When looking at the universe as an expanding enigma, nature suggests that this too appears as a wave. All other waves including historical shaping of earth possibly dictate the frequency of the expanding wave of space. At the very least it contributes to it. If this is true it is likely that whatever the universe expands into makes use of the universe as a form of energy.
keeping this in mind it is important that we look at the shapes of history and recognise the trend that human theory are eventually discovered as wrong or incomplete.
Strictly speaking, you’re right, Lightkeeper. There might be something smaller than the Planck scale, but we can’t describe it. Of course, it’s also quite possible that there isn’t anything smaller, either. There is no known upper limit on the possible size of space, though. There are theoretical arguments similar to that presented by Zenster saying that space should be finite, but they’re not absolutly proven, and they don’t say just how big it can be.
As for “outside the Universe”, the only answer that can be given to that is that there is no “outside”, and even if there were, it wouldn’t matter. Even a black hole can’t get you outside fo the Universe: If you can get there, then it is, by definition, part of this universe.
The message of my first teacher who introduced the concept of infinity was:
We are unable to imagine an infinite universe.
We are also unable to imagine a universe that is not infinite.
I’ve always believed both statements.