Do You Believe in Infinitely Small? I Don't.

[Luminal]

I have recently begun to question whether there is such a thing as "infinitely small" values. Infinitely large, I can accept, for reasons I am about to explain.

 

Look at the function f(x) = xsin(1/x). You'll notice that it oscillates an infinite amount of times in smaller and smaller waves as it gets closer to the y-axis.

 

Now, imagine running your hand over the function. You cross the y-axis, as well as all function values in that range, with no problem. But what was the last oscillation you passed, was it an up or down oscillation? Impossible to know.

 

Now, imagine doing the same with f(x) = 1/x. You pass the y-axis (or x-axis) and pass by all of those infinitely large values as the function approaches the vertical asymptotes, but the important difference, your finger never actually touches (or can) the function's curve at the reletively infinite values, whereas your finger covers all possible values at the same time in the first function.

 

I believe that energy (or particles) have a limit to their smallest size. This may be strings, but I don't know. Either way, whatever limit this is, all other energy or matter is built upon these, and this is why we can move in the physical universe.

 

Otherwise, we'd be constantly struggling with the paradox of nearing limits and never passing them.

 

There must be a miminum size to energy and matter. And I believe the answer lies with neutron stars and black holes. As gravity forces matter past that limit, all current rules are thrown out the window.

 

But in normal space and normal gravity, those rules do apply, and thus there most likely is a miminum size.

[ecoli]

I think that the concept of infintely large is also theoretical. I believe that most physicists agree that there is an finite amount of matter in the universe.

 

However, infinity would still exist as a mathematical idea, both in it's "large" sense (the number line extending forever) and in it's "small" sense (there are an infinite number of points between any two real numbers on a number line.)

 

According to string theory, the string is the smallest indivisible part of the universe, but that doesn't mean you wouldn't (theoretically) 'see' the halfway point on the string - or a quarter or an eight, etc.

 

Although I must admit, I haven't studied these things in great detail, and especially not the mathematics portion of it.

[Sisyphus]

It's been generally assumed there is a smallest size to objects for a long time (hence "atoms" and "quantum" physics). Pretty much since we saw that "things" in general are not continuous, but made up of more or less uniform building blocks. As it turns out, those building blocks are themselves made up of smaller building blocks, and those even smaller, etc. We're not sure if we've reached the "bottom" yet, but it may well be the case that even if the smallest blocks we can see are made up of smaller ones, we have no theoretical way of detecting them or separating them, so it's a purely speculative and inconsequential matter (no pun intended).

 

This doesn't have anything to do with mathematics, though - it's all empirical. As far as pure geometry is concerned, "infinitely" large and small have the same amount of validity.

[foodchain]

I have recently begun to question whether there is such a thing as "infinitely small" values. Infinitely large, I can accept, for reasons I am about to explain.

 

Look at the function f(x) = xsin(1/x). You'll notice that it oscillates an infinite amount of times in smaller and smaller waves as it gets closer to the y-axis.

 

Now, imagine running your hand over the function. You cross the y-axis, as well as all function values in that range, with no problem. But what was the last oscillation you passed, was it an up or down oscillation? Impossible to know.

 

Now, imagine doing the same with f(x) = 1/x. You pass the y-axis (or x-axis) and pass by all of those infinitely large values as the function approaches the vertical asymptotes, but the important difference, your finger never actually touches (or can) the function's curve at the reletively infinite values, whereas your finger covers all possible values at the same time in the first function.

 

I believe that energy (or particles) have a limit to their smallest size. This may be strings, but I don't know. Either way, whatever limit this is, all other energy or matter is built upon these, and this is why we can move in the physical universe.

 

Otherwise, we'd be constantly struggling with the paradox of nearing limits and never passing them.

 

There must be a miminum size to energy and matter. And I believe the answer lies with neutron stars and black holes. As gravity forces matter past that limit, all current rules are thrown out the window.

 

But in normal space and normal gravity, those rules do apply, and thus there most likely is a miminum size.

 

What I don’t understand nearly good enough really is the evolution of such or the universe really. For instance in nucleosynthesis, do you have to have hydrogen before such a process can take effect? Where did the more fundamental subatomic particles themselves come into play? What I mean is the electron for instance, how did it come about overall?

 

Sometimes I think its just a matter that deals with time I guess. In that if you look at a human beings lifespan, its just a little spike of activity that’s almost meaningless in regards to lifetimes of other objects or even the universe, its just a possible product of matter and energy interacting right? Is it the same for all the particles then. Is the environment that spawned such an environment that holds out the ability for other random particles to exist? I Think such would be interesting to study in an atom smasher or particle accelerator as anomalies do come to exist, maybe some benign particle that could not persist.

 

I don’t fully understand the definition of energy either. For instance if all matter or mass is energy, does energy have to have a definite shape, or is the same issue of entropy leading to patterns to reasons we have a certain spectrum of particles and related larger elements of such that spawn off associated physical realities of the universe?

 

It makes the idea of weighing something weird, I mean I can put a pound of bananas on a scale, or a pound of gold, but what am I really weighing and is that proportion truly finite.

[Luminal]

I think that the concept of infintely large is also theoretical. I believe that most physicists agree that there is an finite amount of matter in the universe.

 

However, infinity would still exist as a mathematical idea, both in it's "large" sense (the number line extending forever) and in it's "small" sense (there are an infinite number of points between any two real numbers on a number line.)

 

According to string theory, the string is the smallest indivisible part of the universe, but that doesn't mean you wouldn't (theoretically) 'see' the halfway point on the string - or a quarter or an eight, etc.

 

Although I must admit, I haven't studied these things in great detail, and especially not the mathematics portion of it.

 

No, the theorized smallest subunit of reality couldn't be 'seen' at smaller fractions... at least in my opinion. After you've reached this point, the only way to analyze it (since reductionism is thrown out the window at this point) is to study the forces it interacts with, and the larger entities it goes on to create with the combination of other minimally (not infinitely small, mind you) particles, strings, etc.

 

Infinitely large and infinitely small are very different ideas. Think of it this way: what's the maximum and minimum number of atoms that could exist in any imaginable unbounded space, with a given that at least some do exist? For minimum, one of course. For maximum, infinite of course. And even if you removed the given that at least some must exist, then you have zero for minimum. Atoms have specific requirements that must be met to exist: at least 1 proton and 1 electron.

 

Think of any object, either living or nonliving, and you come to the realization that it has requirements that must be met to exist and/or function (if it has a function). A human: oxygen to breath, environment with plenty of carbon to synthesize organic molecules, water for hydrolysis and dehydration synthesis, and so on. A rock: atoms with covalent bonds, enough strength to remain in one piece, and so on.

 

Why would we think that if you kept getting smaller and smaller, than you would eventually reach a point where things didn't have requirements that must be met to exist? See the above function, xsin(1/x); is the last oscillation postive or negative? Infinitely small just doesn't work, unless all logic and laws completely morph into something else entirely at infinitely small degrees. Even then, the reality that we know does have an minimum size: the size where the aforementioned logic and laws fail.

 

On the other hand, with infinitely large, laws and logic work perfectly fine. However, we are finite beings, and can't interact with or even understand infinitely expanding values. But never do those values break rules, laws, logic, or simple common sense. Think of f(x) = sinx. With infinitely large, we can confidentally say that it has no final oscillation, because we never cross it or reach it or see it. Not so with xsin(1/x). We can see and cross the whole range of oscillations within a finite time and finite space.

 

In short, infinitely small = infinite trapped within finite values. *shakes head* Infinitely large = infinite at infinite values. *nods head*

 

Hopefully, I've made myself understood.