Does infinite small exist?

[jeftones]

This is a very old thought that troubled me when I was about 10 years old.

Today it suddeltly popped in my head again, and I thought it would be funny to hear any reactions on the topic.

 

It goes like this...

The 3 dimensions of space that the universe is expanding in, seems to be infinite in lenght.. This indicates that even though matter in the universe only has travelled as far as it has (our measurement of it's size), the universe is infact infinite in size...

If the universe is infinite big, does that not make everything that reside in it infinite small ? Something thats infinite small could that equal none existant?

[Jake712]

there is a theory that the very center of a black hole is an enormous amount of matter packed into a point with no volume...

is that what you are talking about?

[jeftones]

No not singularities, although they cannot mathematically exist... It was more the term "infinite"... Like if you say... this object is infinite small... does that mean that the object does not exist? And what I meant was if you put any object (regardless of their size) inside something thats infinite big, would that make them infinite small? And if they are infinite small, does they exist?

 

Pardon my english... it's not my mother tongue... hope you understand my point...

[Callipygous]

No not singularities' date=' although they cannot mathematically exist... It was more the term "infinie"... Like if you say... this object is infinite small... does that mean that the object does not exist? And what I meant was if you put any object (regardless of their size) inside something thats infinite big, would that make them infinite small? And if they are infinite small, does they exist?

 

Pardon my english... it's not my mother tongue... hope you understand my point...[/quote']

 

 

you mean if something is inside something that is infinitely large does that make the item infinitely small by comparison?

[jeftones]

you mean if something is inside something that is infinitely large does that make the item infinitely small by comparison?

 

Yes something like that... And because we reside inside this infinite universe, it makes us infinite small in comparison... And the question is, something thats infinite small... does that exist?

[Sorcerer]

The planck length is the smallest anything can be.

 

Ok, so IF the universe is infinite, then anything inside of it which is finite is in comparison infinitely small.

 

To answer this I would say that an infinite entity is required to be made up of an infinite amount of finite parts, thus in order for the universe (if it is infinite) to be infinite the finite parts which make it up must have size, even if this size is infintesimal.

 

I.E. and infinite ammount of parts with infintesimal size is still an infinite size itself.

 

Yes, infintesimal things do exist, infinitely small is an assymtote with 0.

[swansont]

The planck length is the smallest anything can be.

 

It's the smallest anything could be and be explained by currently understood physics.

[Severian]

The planck length is the smallest anything can be.

 

OK' date=' I'm going to be picky. Apologies in advance...

 

Do you have any evidence for that statement? At all? The Planck length is the distance scale at which we [i']think[/i] gravity becomes strong, and will tear holes in space time. But this is conjecture over many orders of magnitude. We have never probed this small in experiment, and don't even know how to explain gravity quantum mechanically! The Plank energy scale is 10¹⁹GeV, while we have probed only up to 10²GeV. I would be very surprised if our description of the three forces we do understand held up to an extrapolation of 100000000000000000 times in energy, nevermind gravity, the one we do not understand.

 

I think it is time we stopped taking string theorists' comments as reality, without experimental data to back them up....

[Sorcerer]

Well ok, scratch that, but what about the rest of the argument then?

[Severian]

I'm afraid not. If the size of the universe was your only length scale and that length scale was infinite, then you would not be able to meaningfully measure distance at all. All measurements are in comparison to something else.

 

In reality that 'something else' is set, in fundamental physics, by some other distance scale in the theory. For example, QCD has a fundamental energy scale of 1GeV (think of an energy as 1/distance), the energy where the force becomes strong enough to form condensates, binding quarks into hadrons (like the proton). It is interesting to note that it is the quantum corrections to the theory which introduce this energy scale - in the classical limit, QCD would have no associated distance scale....

 

Any theory which does not involve a distance scale, such as string theory, is termed 'conformal', but even then there is always some mechanism for generating a distance scale in some way (eg. in string theory, one has the string scale).

[Sorcerer]

Well, so? We cannot use any meaningful distance scale at all, but we can assign an arbitrary scale. I don't think infintesimal is really a meaningful unit for a scale anyway.

 

If you wanted to argue against it I wouldve started with infintesimal being 1/infinity, I said that this would be a unit in an infinite universe, you could have said that since I was assigning 1 to the universe, which is actually infinite, then it would be infinity/infinity which is 1.

 

Also an infinite ammount of infintesimal parts is only 1.

 

So basically I come to the new argument that the if the universe is infinite it is made up made of an infinite number of finite parts (whatever scale you choose to assign to those parts is arbitrary).

 

Edited for a blatant error which nobody picked up on: thank god.

[Severian]

No, there are other scales in the universe set by the fundamental theories, so the scale is not arbitrary.

[Sorcerer]

No, I was commenting on you point that we cannot make a scale if the universe is infinite, then saying that we could if we just used an arbitrary scale, eg assigning the hubble volume as the boundary even if its not.

 

So what are these scales then set by these fundamental theories?? And what is the smallest possible unit under these fundamental theories?? Could it be the planck length? If so, see the first post, then repeat endless loop.

[ed84c]

Singularities DO have a QUANTIZED volume, or so I read. Its very small though. I personalyl beleive that infinities are just inacuraccies in trying to divide by small numbers and people divide by 0.