# Distances between his hand and the table

• aguycalledwil
In summary, the boy argues that if there are an infinite number of distances between his hand and the table, then surely, as he brings his hand to touch the table, it passes through an infinate number of distances. He then concludes that time and space are not infinately divisible and that this might show that the universe is quantized.

#### aguycalledwil

Hi everyone, I am new here, and I am thirteen, but I am really into this and I have recently grasped (only on a basic level) quantum theory. I understand relativity and I am looking into many fields, such as cosmology.

So, me and my dad were talking the other day, and he proposed the following... If there is an infinate number of possible distances between my hand and this table, then surely, as I bring my hand to touch the table, it passes through an infinate number of distances, so how is it that i can touch the table?

After quite some thinking, I concluded that this must indicate that there isn't an infinate number of distances between his hand and the table, and that infact "distance" is not infinately divisable, that is, that there is a distance (smaller than any sub-atomic particle) whereby there can be no smaller distance.

And, I thought, if this is so for distances, then surely (since time and space are relative) it is so for time too. So, I concluded, does this show that time and space are not infinately divisable?

I appreciate any comments on this. I am probably wrong in every possible corner here (lol), but I think it makes sense.

There is only one distance (at a time), though there are an infinite number of points between your hand and the table. But this doesn't really have anything to do with whether the universe is quantized or granular - that's a basic property of math (that you probably haven't gotten to yet).

Woah there fella, you're in a bit over your head! The proper answers to those questions are far above your ability to understand, and I can assure you, Relativity and QM are out of your ability to grasp.

I'm not going to answer your infinity question, persay, but I will show you why the logic breaks down:

If you're traveling at 1 meter per second, it will take you 1/2 a second to travel 1/2 a meter. You're half way there, now! Traveling half of THAT remaining distance of 1/4 meters will take you 1/4 of a second. Now traveling half of THAT remaining distance of 1/8 will take 1/8 seconds. Half of 1/8 (which is 1/16) will take you 1/16 seconds.

The smaller the distance you have left to travel, the faster you cover the remaining distance. By the time you have an "infinitely small ways to go" you'll do it infinitely fast!

If you really find this stuff interesting, stay at it, but keep in mind that you don't understand any of it (yet.) You might THINK you understand it, but trust me, you don't. Also, keep working on your math -- you won't get far without it!

Oh, thanks for the help!
Yeh, I know I don't understand much, but I do get that electrons etc travel in waves, and that the size of the waves determine the probability of that electron etc being at that point.
I see what you mean, now, with the table conundrum. Thanks!

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aguycalledwil said:
Lol, okay then. So does that mean that you hand passes through an infinate number of distances when you touch the table? If so, then I am confused, because surely to do an infinate numer of things, you need an infinate number of time, so you can't touch the table? Anyway, thanks for the help!

But like I said -- you cover the remaining distance infinitely fast. Instead of thinking in terms of "speed" think in terms of how fast you're getting the job done. It takes you 1/2 seconds to cover the first half meter. It takes you 1/4 seconds for the next remaining half. 1/8 seconds to cover the third, 1/16 for the fourth, 1/32 for the fifth, etc. Each remaining half takes half as long -- in otherwords, when your remaining halves are "infinitely small" it will take zero seconds to travel that distance.

It's like this: 1/x is how long it takes to cover the remaining distance. When x is really REALLY huge, 1/x is REALLY REALLY SMALL. When x is "infinitely large," then 1/x is basically zero.

So the first half takes 1/2, the second half takes 1/4, the third takes 1/8, and the infinitely small one takes 1/x, where x is so dang huge that 1/x is zero (and when we realize 1/x is how LONG it takes to cover the remaining distance, that tells us it "takes no time" to travel it.)

Yeh, I see now, thanks.
I have since edited my other post, lol.