How small can objects truly be?

[uperkurk]

Can an object be infinitely small? IE if I took the smallest thing known to man (quark) I think, it may not be possible today but in theory, a quark could be split in half, and then in half again an infinite amount of times?

Or is there a proven fact that states the smallest size an object can be until it's literally so small it'll just vanish and that particular object no longer exists.

I read somewhere that there's actually the smallest distance which something can move. Because everything moves in frames... kinda like a slide show? Obviously though the amount of movement from one distance to another is so tiny you couldn't possibly notice it.

 

[Hurkyl]

The question you're asking is more about physics than about math.

Physically, the notion of "size of an object" gradually breaks down as you look at smaller scales; at some point the notion (as you understand it from everyday experience) simply doesn't make sense anymore.

 

[uperkurk]

But that doesn't mean to say that you can't just keep halving the size of an object infinitely? Just as you can half the speed of an object infinitely?

 

[phinds]

But that doesn't mean to say that you can't just keep halving the size of an object infinitely?

Yes, actually it does. There is no evidence yet that there is a smallest physical size, but it is most likely that there is one, as far as actual physical things go. Mathematically, you can always say "half" of something but that does not mean you can realize it physically.

Just as you can half the speed of an object infinitely?

Maybe. Maybe not. Unknown. It seems to be an open question whether or not time is quantized and speed depends on time as well as space.

 

[Greg-ulate]

Some sub-atomic particles, like electrons, are treated as "point-like" particles, and no attempt to measure or calculate a "radius" or "size" has been successful. As far as we can tell with our limited information at this time, electrons behave as if they are infinitely small. We have never encountered anything that could be considered half an electron, or any constituent particles "inside".

The space we live in appears to have a minimum distance and time interval, called the Planck length and time. The scale of the length is smaller to a proton than a proton is to a human, so its incredibly tiny (~10^-35 m). The time interval is the time it takes light to travel that distance (~10^-44 s).

I think its pretty safe to say that there is some indivisible bits that make up all matter that can't be split. "Splitting" objects would then represent simply separating the bits of the object from each other... nothing is really divided, just moved. In the case of the quark, due to the strong force it takes so much energy to separate the quarks that the potential energy is larger than the rest mass of additional pairs of quark-antiquark pairs... but nothing is being divided really. I don't know if quarks are indivisible, perhaps they are made of smaller bits.

In this frame of mind, halving the size of an object has no meaning. Cutting a piece of cheese in half is just separating the molecules of one half from the other. Cutting a molecule in half is separating the atoms of one half from the other. Cutting a nucleus in half is separating the quarks and gluons of one half from the other. Cutting a quark in half would just be separating whatever its made of from each other and so on. In each case, the "object" was just a label that your mind puts on the collection of the parts.

 

[Vanadium 50]

The space we live in appears to have a minimum distance and time interval, called the Planck length and time.

There is no evidence for this.

 

[mfb]

There is no evidence for this.

To extend this answer:
It is expected that some new physics appears at processes of that length/time scale - which also corresponds to an energy scale of ~10¹⁹ GeV, or 15 orders of magnitude above the reach of the LHC. This does not mean that higher energies (and smaller lengths/times) are impossible - we just have no idea how physics there looks like.

 

[Crazymechanic]

This thread got me interested.
I'll try to give some questions I have been thinking on the lines of this myself.

In a singularity we say atleast to our current knowledge that it is a point infinitely small.But how come .Ok I understand that under that huge gravitational pressure the electrostatic repulsion is no more powerful enough to keep protons apart and so on and particles being squeezed together but if particles have finite sizes , then there should be a point at which no further compression is possible and that means that every black hole has all that matter "winrar archived" inside but the huge gravity is keeping us from seeking it and out mathematics fail at predicting it am I right on this one?, so as the OP asked "Can an object be infinitely small?" from what I know it can't.

 

[Greg-ulate]

There is no evidence for this.

Its true that direct evidence for this has not been observed, but the current (unconfirmed) theory to which I subscribe states that you can't compress any object that has a non-zero number of microstates (entropy) into a volume bounded by a surface with less area than 4 square Planck-lengths/bit, where bit is the amount of information required to describe the quantum state of the object in bits, without irreversibly removing the information of the state of that object/system from our causal domain.

I shouldn't try to rephrase this stuff because I know that the subtleties are beyond me.

 

[mfb]

The center of black holes needs new physics for a proper description anyway. Even particles with a finite size (if they exist) might end there - maybe in a very small area instead of a singularity, or whatever.

so as the OP asked "Can an object be infinitely small?" from what I know it can't.

I don't see the argument for this in your post.

 

[Crazymechanic]

Yes your right "mfb" I should have said from what I believe based on what I have read and heard and thought it shouldn't be infinitely small.
Firstly because of what I said earlier in my post of the black holes containing particles that are physical entities themselves and must have a certain size even under the huge pressure they must have atleast some "survival" size as "Greg-ulate" mentioned too in his post.

And if those particles conserve atleast part of their physical size that means with all the trillions of them in a black hole that point called the singularity must have some size that isn't just a infinitely small point.


P.S. I think even under those extreme conditions particles merge into different new ones and some get radiated away as hawking radiation and probably there is more that I'm missing but in any way I believe there is a point where you just can't get any smaller and if you could wouldn't there be a chance for the black hole to just disappear? But something like that doesn't sound logic.

 

[uperkurk]

With regards to splitting quarks, I don't meant splitting it into another object. I mean splitting that quark in half, so you have to bits of a quark that by themselves are nothing..

Just like you take a stone, split it in half and you get 2 smaller stones, split those stones in half, and now you have 4 stones ect ect.

In theory, you could keep on going and going and going because in mathematics, you can always reduce something by half an infinite amount of times.

But in practical terms, is this theory correct? Even if not feasible with todays technology.

 

[Vanadium 50]

There is no evidence for either Crazymechanic's nor Uperkirk's suppositions.

 

[phinds]

P.S. I think even under those extreme conditions particles merge into different new ones and some get radiated away as hawking radiation

You completely misunderstand Hawking radiation. It happens OUTSIDE the event horizon and you are talking about things inside.

 

[MikeGomez]

In theory, you could keep on going and going and going because in mathematics, you can always reduce something by half an infinite amount of times.

But in practical terms, is this theory correct? Even if not feasible with todays technology.

Sure, we can theorize about cutting a quark in half, but you need to understand the current state of modern physics regarding this. The problem is deeper than trying to split a quark. The problem is even being able separate a pair of quarks (quark/anti-quark pair) from each other. This has to do with what is called confinement, and the strong force.

Quote from Wikipedia article on color confinement

“confinement, is the physics phenomenon that color charged particles (such as quarks) cannot be isolated singularly, and therefore cannot be directly observed”

Check out these Wikipedia articles on color confinement and the strong force.

http://en.wikipedia.org/wiki/Color_confinement

http://en.wikipedia.org/wiki/Strong_interaction