Here's something that I've been thinking of, has to do with infinite space?

Question

If objects can be infinitely large, doesn't it follow that they can be infinitely small? If that's true, then isn't every space, no matter how small, also infinite in it's proportions when seen from the correct perspective? Lets say I had a spaceship in my living room and had the ability to shrink myself as small as I wanted to. If I continued to shrink and accelerated forward (towards the wall) at the same rate as I was shrinking, wouldn't I simply go on forever without ever reaching the wall? Is there a point where if something is so small it simply pops out of existence?

Answer 1

You're talking about asymptotic curves.

Problem is whether you realise it or not your statements are based in classical theory and the Universe is quantum mechanical. I've never seen anything to say shrinking is possible even theoretically and at the quantum level you'd be at the mercy of quantum effects, at the planck length you might fall through a tiny wormhole and vanish from this dimension or as someone else said, pass through to another brane.

You ask if there's something so small it pops out of existence - in a way the current theory of black holes is like this - a large star collapses to a point (not a couple of inches as people sometimes say on here) but black holes themselves may not exist. Gravastars and black branes may be modern descriptions of what a black hole really is. Also whether its quarks, strings or something else - there will be a smallest particle - it wouldnt make sense to exist if you were smaller than one of those.

Since the universe isnt infinite (you must have heard that its expanding?) then I guess its all hypothetical anyway. You're definitely implying that units of space could be further and further divided without limit and this is not what quantum mechanics tells us - its about discrete jumps in energy where its not possible to have an intermediate level.

Answer 2

It was proved two centuries ago that the Universe is finite. If there was an infinite Universe, and infinite Mass, there would be infinite stars and the sky would be infinitely bright. This is not the case. Also, yes, the universe is expanding. The solar system, for instance, is whizzing through space at an extremely high speed from the power of the big bang. Where or how is it expanding to is a mystery as we can not see the 'edge' of the universe; it may be an area where time breaks down.

Answer 3

First, why does the existance of the infinitely large (which we don't know exists) imply the existance of the infinitely small?

Second, if you consider the point at your very center, this point will be inside of you no matter how small you get. Assume you accellerate towards the wall. Your velocity towards the wall will increase. This means that there is some positive velocity which, after some amount of time, is smaller than the velocity at which you will travel for the rest of your trip.

v = at, and x = vt + (1/2)at^2. If x is your position.

I have chosen the initial position and the initial velocity to be zero, not that it matters.

Let's say the door is some distance, d, away.

We want to know if there is a time at which you will have gone a total distance, d.

Let's let time go by until your velocity is positive and call this time T. Let's call the velocity at this time V. After this time, the velocity will be larger than V, so

vt + (1/2)at^2 is larger than vt, since time and acceleration are always positive.

Also, vt, after time T, is larger than Vt.

If we solve d = Vt for t, we get t = d/V

this time, however, is greater than the time it would have taken under positive accelleration, which means that the point would have crossed the wall at an earlier time. This means that you will reach the wall in a finite amount of time. You would have to be accellerating away from the wall, or start out with zero accelleration and zero velocity for this to work out.

Answer 4

First, quantum mechanics places a lower limit on any meaningful length, the Planck length (see reference). To the best of our understanding, it's simply not meaningful to talk about something smaller than that. There's no theoretical upper limit to a linear dimension, but there is a lower limit.

Second, the shrinking you describe exists only in fiction. If you take a mass (like a sponge) and force it to occupy a smaller space, you are compressing it. If you 'shrink' an apple by drying it, you are removing matter (water) from it. Does the magic shrinking machine remove half your molecules? If so, at some point your organs and cells would cease to function.

Answer 5

Right! What if you accelerated at a higher rate, would you overshoot the wall? Then are you in another dimension?

Answer 6

If you subscribe to M theory then it seems to me that you would become small enough that you would just pass into one of the 11 dimesions that makes one of the two membranes that is what makes up our universe.

Answer 7

that's a good hypothetical question.
actually, space is not infinite, it is finite but expanding.
go read stephen hawking again.

Answer 8

DUDE. WTF

Have you been watching innerspace again while toking the pipe. I thought we talked about that.

Now you go to your room while I figure out what I'm gonna do with you.

Answer 9

Too deep for this time in the day but I guess you're right in a way

Answer 10

Good question. I'm going to pee now.