Jarlaxle

I have always thought that the only thing stopping one from getting something smaller than the smallest known particle, is the lack of precise enough instruments. If it is true that between two points there are an infinite number of individual points, then why couldn’t the “smallest” particle be cut in half to make yet a smaller “smallest” particle, and then cut that half in two to make yet an even smaller one. If the instruments could be created infinitely precise enough, then we could continue for infinity.

After we have cut the particle in two, and then cut that half in two, and then… until infinity, we would then have the smallest particle. But how big would it be? To still be a particle, it would have to have some volume greater than zero, or it would not be a particle at all. Yet if it had a volume greater than zero, and we added an infinite number of them together, we would have infinite volume! We would have more than we started with! Not just more, but more infinitely more! This is an absurdity. So wouldn’t that prove that there really must be a smallest particle such that it can not be cut in half, or even “chipped” at whatsoever?
<img src="confused.gif" border="0">

Kenny

Actually, that’s false. According to the standard model at least, fundamental particles such as quarks or electrons are point masses; they have zero volume.

Not necessarily, infinite series can and often do converge to a finite value. As long as the volumes which you are adding decrease rapidly enough, you could add an infinite number of finite volumes together and still get a finite volume when you’re done

No, but according to the standard model, there are such particles and these particles are point masses which occupy zero volume. Also, there is not just one kind of such particles but several different varieties.

God Bless,
Kenny

[ May 07, 2002: Message edited by: Kenny ]</p>

Jarlaxle

Is all matter made up of these zero volume particles??

Jarlaxle

Wizardry

Presumably.

Kenny

According to the standard model, yes. Of course, who knows exactly what’s up with all that dark matter out there, which constitutes about 99% of the matter in the universe.

God Bless,
Kenny

Ender

What about the recent findings on that "quintessential energy" the anti-gravity force that presumably has been accelerating the expansion of the universe?

It could account for upwards to 70 percent of the mass in the universe, while dark matter and visible matter account for the rest. This is predicated by the "flat" model of the universe.

~WiGGiN~

eh

Well if string theory is correct, then all particles are actual vibrating strings. They are said to be 1 dimension strings though, so it's not exactly easy to imagine. But yeah, under the standard model particles are zero size, point objects, much like a mathematical point.

And that would mean that even dark matter would be made up of particles. The choice between 1D strings and 0D points is not that great, but it's all we've been able to come up with so far.

Bill

Kenny:

The "Standard Model" may treat an electron as a "point particle," but I don't know of any physicist who actually believes that an electron has "zero volume." And the same goes for quarks.

After all, most of particle physics experimentation concentrates on studying what happens when two particles collide at a high velocity, and it makes no sense at all to speak of particles with "zero volume" actually colliding!

For more on the scale of atomic dimensions, you can read <a href="http://www.newtonphysics.on.ca/EINSTEIN/Appendix1.html" target="_blank">The Dependence of the Size of Matter on Electron Mass</a>, which shows that it is necessary to apply relativistic corrections to atomic models, again demonstrating that particles like electrons cannot be dealt with as simple "zero volume" points of matter!

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Frankly, the idea of "zero volume" point particles leads to certain absurdities in current theory, and it is those very absurdities which leads many physicists to believe that a better theory is required. The best candidate to replace the "Standard Model" is string theory. In string theory, the smallest possible particle is a one dimensional string which (for certain theoretical reasons) cannot get smaller than the Planck size (about 10^-45 meters). In his book <a href="http://www.secweb.org/bookstore/bookdetail.asp?BookID=186" target="_blank">The Elegant Universe</a>, Brian Greene discusses how string theory reacts to compression beyond the Planck scale: it exactly mimics what happens if you get larger than the Planck scale! Thus, the Planck scale defines the minimum "quanta" of distance.

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There is clearly a minimum "quanta" of energy (at least, there is according to quantum mechanics), and there appears to be a minimum "quanta" of distance. There is some speculation that there is also a minimum "quanta" of time. So, the idea that there is a minimum "quanta" of matter which has a minimum "quanta" of size isn't such a strange idea after all.

What is a surprise (at least, to the physicists of several decades ago) is the extremely small scale of these various "quanta" sizes. The size of the "string" in string theory is many orders of magnitude smaller than the size of the electron or quark. (The standard definition of the bohr unit is about 5.29177×10-11 m, versus about 10-45 m for the size of strings.)

In any case, this is actually a controversial idea in physics. On the one hand, we do seem to be ever able to split matter into smaller and smaller "chunks." And quantum mechanics seems to suggest that there is no realistic lower limit of size. However, very weird things occur in quantum mechanics around the Planck length, so many people would prefer to see the Planck length imposed as a lower limit on size. This seems to be a limit that emerges "naturally" from string theory, so that is one of the reasons that continuing research into string theory is attractive to scientists.

But string theory, in turn, is totally incomplete (the equations for string theory haven't even been discovered yet; up until the present, we have only been dealing with substitute equations that are gross approximations of certain subsets of the "actual string theory"), and it hasn't been used to make any predictions that have subsequently been subjected to experimental verification (a la the verifications made for quantum mechanics and relativity).

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But to flatly state that all fundamental particles are "zero volume" is to flatly misstate what most physicists believe.

== Bill

Kenny

Bill,

I am aware of string theory, the possibility that space-time may be quantized and all the rest, which is why I qualified my posts with "according to the standard model." But, I see no philosophical difficulties in conceiving of fundamental particles as point masses, nor is there any difficulty in the idea of two zero volume particles “colliding” with one another. As far as what physicists actually believe, and I never said anywhere that they all believed the standard model (the standard model is nothing more than a convenient way of looking at things until fundamental issues are resolved) , I’m sure it varies from physicist to physicist, but the truth of the matter is that no one really knows yet. There are still a lot of unresolved issues. Of course, that’s what makes things fun, no?

God Bless,
Kenny

[ May 07, 2002: Message edited by: Kenny ]</p>

owleye

Jarlaxle...

You make a good point with respect to particle physics if you hold the view that particles are what used to be called atoms (indivisible particles) in the atomic theory of matter. Atoms used to be thought of as something like billiard balls, but of very small size. Indeed, we even see this in models used by chemists and biochemists. For the reasons you give, Kant concluded that atomic (corpuscular) theory cannot be true.

However, in the modern era, the dimensions of particles, even if they are not elementary, are associated with their wave-length, and only indirectly with some physical volume. We would generally regard the boundary of an entity as the size of a "hole" or "slot" that allows its wave to pass through. Of course, quantum physics tells us that such a boundary is a bit fuzzy and tunneling is not precluded.

But your question is still relevant. But I think it must be asked of wave lengths. Can there be a shortest wave length? The electromagnetic spectrum itself does not preclude it. As far as I'm aware, there is no theoretical limit to how short a wave length can be. A zero wave-length, however, is probably ruled out.

Fell