What ramifications will my scientific breakthrough have?

Factual Questions
1

A thought occurred to me today, and I did a quick bit of Googling but couldn’t find anything on the subject. I am wondering if my hypothesis has already been suggested and dismissed by physicists.

I propose that space is not infinitely divisible. Any given chunk of space is composed of a finite number of “space units”, nothing can be smaller than 1 space unit. In terms of matter that occupies a space unit, it’s all or nothing. Either the space unit is occupied by matter or it’s empty. Think of it like bytes in computer memory. A space unit is either full (1) or empty (0). There is no “half a byte”, and there is no “half a space unit”.

Here is my proof that space is indivisible:

Given that the following statement is true: If something could only be achieved “after” an infinite number of steps, and each step must be completed sequentially (ie, one step at a time), and each step takes up at least some time, the “result” is unachievable.

That statement is true, yes?

Now let’s apply this to space and distance. Let’s say there is an apple sitting arm’s length away from me. I intend to reach over and grab the apple. Now, in order for my arm to reach the apple, it must first traverse half of whatever the remaining distance is, and this will take some time. Once there, my arm must now travel to the new half-distance, and this again will take time. My arm, as it turns out, needs to traverse an infinite number of “half distances” to reach the apple, which is of course impossible. Clearly, if I go to grab the apple, I won’t reach it.

Unless…

My arm only needs to traverse the finite number of space units between it and the apple.

Where can I get my Nobel?

2
3

Based on articles I have read in Scientific American, it’s an open question that gets studied regularly. If I remember right, loop quantum gravity is one of the theories of non-continuous space.

4

So I guess that means straggler can walk the Planck …

The last step is a doozy.

5

Then there’s also Planck time, the unit of time necessary for a photon to travel the Planck Length.

6

Zeno of Elea! You finally got your NetZero account!

Please, this is like 2500 years old. Now I am going to read the “Engineers are so s-m-r-t, unlike humanties majors” thread and choke on some irony.

7

Two hetero males are standing on one end of a long corridor. One is a mathematician and the other is an engineer. A stunningly attractive naked woman who is at the other end offers herself to them to do with what they will. The mathematician thinks about it but hesitates because Zeno’s Paradox tells him that he will never get to her. The engineer promptly starts in her direction, figuring that he can get close enough for all practical purposes.

8

Nominated for match of OP’s handle and OP query.

9

beowulff gave the answer that I was thinking of.

Kimmy_Gibbler and Dewey Finn also gave perfect answers, but their link is http://en.wikipedia.org/wiki/Zeno%27s_Paradox.

10

That statement is false.

In Zeno’s time this was fully plausible - possibly even obvious - to nearly everyone. But it’s now well understood that the sum of an infinite series of positive values can in fact be finite.

11

Only if I can judge the current state of English Ph.D. courses by reading High School “Huckleberry Finn” papers.

12

This is neither a proof nor true nor original.

No Nobel for you!

13

Here’s some food for thought: Suppose there were a minimum possible length. Suppose now that I have a right triangle, two of whose legs are this minimum possible length. What is the length of the hypotenuse?

14

It is perfectly consistent to say that no length of material of that precise distance would exist in this world with a fundamental minimum length. We suffer all sorts of mathematical entities whose real world bases are less than readily apparent: irrationals, imaginaries, etc.

After all, to say that you have a rope whose length is an irrational number is to say that if you held your rope up against an infinitely zoomable yardstick, you would find, however much you zoomed in, it always terminated between two of the ruler’s tick marks. I don’t think this is any more satisfying on an intuitive level than a world where we cannot cut a line of rope to perfectly fit a right triangle composed of even integer length legs.

15

(This post may or may not contain the same ideas as Kimmy_Gibbler’s post. My apologies in advance, Kimmy; I’m not trying to steal your thunder.)

Before I respond to Chronos’ question, let me talk about other things: Let’s start with a circle. I don’t care how big the circle is. But if we accept the idea of “a minimum possible length” (i.e. Planck length), then the radius of that circle will be a precise and finite number of those units. In addition, circumference of that circle will be a precise and finite number of those units. That is, there will be an integer which tells us the radius, and another integer which tells us the circumference. Given that pi is an irrational number, this is clearly impossible.

We are entering into the realm of ridiculous impossibilities. Let’s zoom in on this circle, all the way to the scale where we can see these Planck lengths. Is the edge of the circle smooth? Or is it made of pixels, like on a computer monitor, or a piece of graph paper? If there is a “minimum possible length”, then a square is an integer, and it cannot be filled in halfway. But then we can ask how far it is from one corner of each square to the corner diagonally opposite, and that will have to be either 1 or 2. There is no longer any room for 1.4141.

One might suggest that we’re not dealing with squares on graph paper; maybe it’s all a bunch of dots. That won’t help us, because we will still ask how those dots are arranged.

And that brings us to the conundrum of Chronos’ Triangle. Is it truly a right triangle? It can’t possibly be a right triangle, because, as Chronos asks, “What is the length of the hypotenuse?” If it is longer than the other sides, then (since fractions are not an option) it must be twice as long as each of the other sides, which is the same thing as both of the other sides put together, which means we have a line not a triangle. But if it is not twice as long as the other sides, then it is equal to the other sides, and we don’t have a right triangle any more - we have an equilateral! What the hell is going on – is a right angle really only sixty degrees?

The answer to all these questions, and to Chronos’ question, is that – as Kimmy_Gibbler wrote – any tangible circle will be imperfect, and all its dimensions can be counted in finite integers of Planck units. It is only the conceptual circle whose precise circumference, divided by its precise diameter, will yield precisely pi.

(I was tempted to phrase that last paragraph in romantic terms about “the world of the infinitely small.” But the truth is that although Planck units are ridiculously small, they are not infinitely so. They have very real and specific sizes. It is very easy to talk about lengths which are half of a Planck length, or even a millionth of a Planck length; they’re just not real in the physical world.

16

True, although there’s a catch to it.

1/2 + 1/4 + 1/8 + 1/16 … is certainly equal to 1. But if each step took the same amount of time to realize, we would never reach 1 in a finite universe. We get to one only because time as well as distance decreases for each step.

Given that every other statement in straggler’s OP is wrong, he probably was thinking of each step taking an equal time. And in that case it would be true that the result was be unachievable. But since each step takes only half the time as well as half the distance of the one before, the result is quite achievable.

The real question is: does straggler really not know of Zeno’s paradox or have we been whooshed?

17

His statement was “each step takes up at least some time…” which I (perhaps naively) took to imply that he was not thinking the time was the same for each step.

18

Yes, I’m also making a guess since the original statement was itself unclear, although that’s probably the heart of the OP’s confusion.

19

Thank you, beowulff, for the link to the article on Planck length.

Keeve, Zeno’s Paradox is only a paradox if space is infinitely divisible, or if motion can be made in infinitely smaller increments.

Xema and Panache45, I’d like to know why you think this statement is false: “If something could only be achieved “after” an infinite number of steps, and each step must be completed sequentially (ie, one step at a time), and each step takes up at least some time, the “result” is unachievable”.

Chronos, your triangle would be impossible to construct in a universe consisting of a minimum possible length, or “space unit”. It would be akin to challenging someone to draw a triangle within the grid below, using only horizontal and straight lines that connect between dots:

. . .
. . .
. . .
Exapno Mapcase, you said “he probably was thinking of each step taking an equal time”. It doesn’t matter whether each step takes an equal amount of time, or different amounts of time. The important thing is, does each step take some time, each step be taken sequentially (ie, no two or more steps at the same time), and there being an infinite number of steps.

20

Should be…