CALLING ALL PHYSICISTS: Is atomic theory almost wrong?

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Let x be the smallest positive real number.

Divide by 2.

0 < x/2 < x.

Therefore, there is no smallest real number > 0.

I'm a neuroscientist, not a physicist, but atomic theory fascinates me. I mean, how "far" will we have to go to find the smallest subparticle? And while I agree that there HAS to be some finite end, what makes that unknown something ABLE to be the finite end? And of more interest to my field, what makes these mere particles capable of creating THOUGHT?! That really baffles me. Cardiac cells conduct electricity, too, but they don't make consciousness. And neurons have mitochondria and Golgi complexes and the like just like all other cells. They don't have some special organelle that must be the answer to creation of thought. And then that leads into how can a dopamine molecule create ABNORMAL thought in schizophrenia and psychosis? I honestly don't know if we'll ever figure out these questions. Certainly not during MY lifetime!

Reading this was a pleasant surprise, as I was prepared to say something similar.

Yes, this ^^^. There is a fine philosopher of science named Bastian Van Fraassen who has held this view for some time.

But my idea of a set of zeroes and ones, with a multiplier of some least real number > 0 (a concept of set theory) was just my way of establishing the limit of a possible formality for the material order which, since such a tiny number ~ 0, would essentially allow the fundamental "atom" (by this I mean particle) underlying all particles) to practically be infinitesimal. It's merely a thought hypothesis not grounded in any empirical data.

conversely, the same could be applied to the largest


hell, if you want to ask a madman, they just might be the same thing.

I am not a physicist (in this life, heh) but I have observed that what you call the smallest particle is basically movement or oscillation of the order of magnitude such that it appears like matter to (y)our perceptive abilities.

Please read: http://en.wikipedia.org/wiki/Hyper_real_number

The theory of infinitesimals was revived by A. Robinson in 1966 and placed on a modern rigorous foundation. Yes there are hypereals smaller than any real number and not equal to zero.

And this has nothing to do with physical atoms which were known to consist of even small particles. The latest degree of smallness is the electron and the quark.

Atomic theory aka the Standard Model of Particles a Fields is correct to 12 decimal places to the right of the decimal point.

ruveyn

Thank you. I found the article on hyper-real numbers to be very useful.

What I have proposed is therefor possible philosophically, but has no pragmatic application to empirical data.

As for the Standard Model, I am not objecting to its accuracy. The hypothesis is that there must be a deeper theory to relate the particular masses, spins, colors, and charges of the various particles, along with other constants.

Bachlover:

Look up the "Planck Length" online, or in your encyclopedia.

It might be that what you're gropping around in the dark for- was already thought of (and mathematically illuminated) by Max Planck in 1912- that being: a theory that there is a limit to how small things can get.

The planck length is about 1/100,000,000,000,000,000,000 the diameter of a proton. According to Planck: below that size: size itsself, and length cease to have meaning.

Its not proven. But my sense is that something like it (a limit to smallness) must exist. Nowadays theyre talking about "other universes" stacked next to our own (like eggs in cartons). So 'bigness' may go on forever. But smallness may have a limit, and not go on forever. As particles get smaller they act more like waves and less and less like little objects. So at some point its all fields of energy without physical dimension. Or thats my sense.

JSBachlover, here is a study that's related. NASA is making 'the coldest spot in the known universe':
clicky

Thank you, Alpine. That's quite remarkable. There's no telling what such experiments will tell us about the deep structure of matter.

Also, thanks to naturalplastic. It's been a long time since I dealt with Planck's constant. It's interesting that I've never heard anyone speak of the "size" of a quark, and now I know why.

I am quite sure there is a deeper theory but the Standard Model will do fine until it is found.

Whatever replaces it has to be as empirically valid as the Standard Model.

ruveyn

As the density of a particle approaches zero, so does its entropy and any information about its place, time, mass, or momentum. It may follow that particles exist in Reality whose nature is unattainable to us.

so, according to your reasoning, what does that tell us about the photon?

A photon has information about its momentum even though it is massless. A different way to understand my reasoning is to consider the entropy available in an imaginary brain the size of the universe with the density of a black hole would contain less information than that required to imagine all finite lengths, e.g. (Plank length)/(Graham's number). If we accept that length is continuous, we must accept that not all lengths are imaginable. Particles suitably small in size cannot be proven to exist even if they do.

Observable universe (~46 billion light years in radius) ... my mistake for omitting "observable".