The uncertainty principle.

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I vaguely understand that the measures necessary to determine a particles location change its speed and vice versa or something close to that, but what i dont understand is why it is impossible to determine a particles usual speed and direction by comparing all the measurements of its speed and direction and comparing for consistent differences.

Shouldn't there be a formula that explains the motion of particles in an atom? A frightfully complex one, but moving as fast as the particle does, and considering there is a limited amount of space it travels it, it seems there should be some pattern to its movement over the course of infinite time.

My understanding of this field is very limited, and I may be wrong in many ways, if I am then I apologize, and don't hesitate to correct me.
At any rate, the way I undrstand it is that a particle may be in any number of places at a given time, and it only appears to be in one place when we choose to observe/measure it in that place, or something like that. So also in a sense a particle has no speed until we measure its speed. Again, my understanding is very limited, but I don't think it's entirely appropraite to think of sub-atomic particles as moving directly from point A to point B, there is just a probability that they will exist in a given place at a given time. And yes, I believe there are patterns to be found there.
There is the picture of the atom that many of us are familier with that shows electrons in orbit around the nucleus, very similar to our solar system. But this picture is not really correct. When I was in high-school I saw a different picture which showed an enclosed volume of space around the nucleus, a little bit like fog, and the density of the volume in a given area corresponded to the probability that an electron would be there. This volume of space can of course be described mathematically, but I think that's about the best most general mathematical description of sub-atomic particle motion you're going to get, at least out of me.

Of course this might all be old news, what with the advent of string theory. And don't ask me to try and explain that, because I can't.

It's probably best to forget about that, as phrased. The problem is not really with a too-hefty measuring device. The uncertainty is much more fundamental, at the level of electrons.



Given enough particles, an average value can easily be obtained. but this does not give a nice precise answer for each single case.



There is, but it comes in terms of probability, and at this scale of an electron round a nucleus "motion" and "travel" and "orbit" are somewhat misleading words. We are looking at something that has the properties of both a wave and a particle. "Packets of wave". That's awkward enough, but there's the actual quantum leap effect, where a particle is in position a, then position b, but cannot have travelled between the two positions as it cannot exist in the zone between.

Perhaps the most readily seen fundamental mysterious result wich demonstrates this is the two slit experiment for single particles, where ONE electron or photon appears to go through TWO slits at the same time. It is not just that we are not sure where the electron is. It isn't sure where it is either!

http://en.wikipedia.org/wiki/Double-slit_experiment

"Under the Copenhagen Interpretation of quantum theory, an individual photon is seen as passing through both slits at once, and interfering with itself, producing the interference pattern."


See if that helps, or makes things worse, and if you come back I will try and explain the difficulties.
The basic thing is, at that scale, our standard ideas of how things work simply don't fit.

Physics at this point is split into three different major areas:
1. General Relativity discovered by Einstein describing the motion of stars, galaxies, and larger
2. Classical or Newtonian Mechanics that describes the world we can see from about the size of a galaxy to about the size of a molecule
3. Quantum Mechanics that describes the world from about the size of an atom and smaller

The problem is that there is no unified theory of everything and string theory is not understood enough to solve the problem. But back to your problem, you naturally think in terms of Classical Mechanics (F=ma and the like) but that breaks down when you get to the size of an electron. It just stops giving answers that make sense. The best alternative is Quantum Mechanics (which I have not learned much of yet) which can only give you a probability of anything. Heisenburg's uncertainty priciple (which is derived from something -- again, not there yet) says that delta p times delta x >= h /4pi where delta p is the uncertainty in momentum, delta x is the uncertainty in position and h is Planck's constant. Basically, it says that if you want to know the absolute position of any particle, it would be impossible to know how fast it was going at the time (what its momentum was). I think that some of the problem is that to observe a particle, you have to shoot another particle at it. Imagine that we want to know where an electron is and how fast it is going by shooting a photon at it whose initial position and momentum we know. The problem is that we don't really know the photon's initial position and its momentum absolutely anyway, so we couldn't know the electron's position or momentum any more accurately than we know of the photon anyway.

About electrons orbiting a nucleus, it appears that electrons don't actually orbit but set up a wave pattern around the nucleus. It is as if each electron was on a vibrating violin string on the nucleus. But what is vibrating is actually the probability that the electron will be in any particular spot. This is not that good of an analogy, but I hope you get the idea. I imagine that string theory extends this idea a bit more (like with real equations!).

Anyway, I'm a sophomore physics/computer science dual major at NJIT. I'm learning thermal physics right now and it is really crazy because it is basically how they came up with quantum mechanics.

Here's an excellent zero-maths introduction to string theory, in a couple of hours of downloadable video. It also covers quantum uncertainty while it's at it.

http://www.pbs.org/wgbh/nova/elegant/program.html

Although newtonian mechanics are used for almost everything these days, excepting microelectronics, deep space astronomy and other extreme fields where it's too innacurate or just plain wrong, it's not really a part of the standard model in the same sense as general relativity and quantum mechanics. GR and QM together, while unable to cover absolutely everything, do cover more than NM does, so in a theoretical sense, NM has been obsolete for many years.

The reason NM's still used for almost everything in the engineering world is that it's simple, works well enough for most things as long as you're not building a particle accelerator or nuclear reactor, and to calculate the behaviour of a bridge, for example, by a mixture of GR and QM would be prohibitively difficult and wouldn't make any difference to how you actually built the thing in the end (how many bridges have been accelerated to near-lightspeed and dropped into a black hole recently?).

As soon as you're thinking of the electron as a "particle", and want to locate it, you're thinking in Newtonian terms and have it wrong. It's not something you can locate because that implies that you could somehow "catch" it, which just isn't possible. Boothinator's description is more to the point.

The reason I separate physics into three disciplines is because you can't mix GR and QM, but can average both and get Newtonian mechanics. On large scales (quantum mechanically), all the quantum equations turn into newtonian ones, and on a small scale (in a general relativity way) general relativity is the same as newtonian mechanics. Besides, on massive, galactic scales, the only force that matters is gravity, and on solar scales, you can use newtonian mechanics to get a good enough answer (except for mercury) and still ignore everything but gravity. E&M only plays a part if you worry about earth's magnetic field, but you can use Faraday's laws for that. I'm not sure if you can use Classical E&M for molecules (maybe for molecules, but not for stuff like protein folding where as the molecule changes shape the electric fields change quantum mechanically, unless you model it semi-classically). Remember, newtonian mechanics is still more fundamental than quantum mechanics since it begins from first principles (derivatves, conservation of mass, momentum, energy) while QM is rather empirical (afaik) and messy. Sure you could say we just have quantum mechanics and general relativity as our fundamental theories, but then you don't have the relation between them that newtonian mechanics provides. But it's not even that big of a deal, and I should probably learn a bit more before making a final judgement.

I say we should scrap the whole thing and get ourselves a real universe, where the billiard ball is king and there's none of this upstart wave nonsense. When I was a boy, cats bloody well knew when they were dead, and we didn't have to observe them to find out either; we knew from the smell even while the box was still closed.

Speed of light, 100 mph, tops.
Wouldn't that make being a train driver an interesting job?
Though rather hard on long-term relationships, and murder on the wages clerk...

Plus the earth would be a black hole (though a very un-crushy one; we'd just be unable to leave). It could get a bit chilly also, since the sun would retain all it's photons too, though if you looked up, you'd be able to see light curving back from down girl's cleavages, which might make it worth the chill.