With my.. horrible understanding of physics

[MetKiller Joe]

Since every particle has a set of equations governing it, no matter how complicated. And every particle's collisions and interactions with other particles could also, in theory, be put into functions.

Given a time, couldn't one, with these equations, find the location of all of these particles and using those locations, in theory figure out what has happened and what will happen?

I know it is impossible to do, but according to this, couldn't you make an argument for fate?

[Mass]

Since every particle has a set of equations governing it, no matter how complicated. And every particle's collisions and interactions with other particles could also, in theory, be put into functions.

Given a time, couldn't one, with these equations, find the location of all of these particles and using those locations, in theory figure out what has happened and what will happen?

I know it is impossible to do, but according to this, couldn't you make an argument for fate?
Yes, if you understood enough about the laws of physics and possessed infinite calculation abilities you would be able to predict the entire course of the universe based on data from one specific point in time.

Because of the specific way the Big Bang occurred specific things happened. The creation of life and everything else is like two planks banging together in an explosion--Because particles interact based on rules the outcome is generated at detonation and everything that follows occurs in a specific manner which corresponds to the initial event.

[itszutak]

Except that you get into quantum physics and essentially random events (you can only predict half of the properties of a particle, etc.) that make the universe essentially unpredictable, even with an infinite capacity for calculation.

[ExAm]

Plus we decide where the molecules in our bodies go, so really you can't predict what people will do, and therefore you can't predict what will happen to the world we affect.

[itszutak]

Plus we decide where the molecules in our bodies go, so really you can't predict what people will do, and therefore you can't predict what will happen to the world we affect.
Technically, if everything in the universe was the result of predetermined formulas, any semblance of free will would be an illusion-- everything that we do would be the result of predictable formulas.

Anyhow, this is getting into weird philosophical stuff I don't feel like dealing with right now.

[Con]

As wiki says, our formulas are really only approximations when you get to quantum stuff.

[Warsaw]

Sounds like Herbert's Dune meets Asimov's Foundation series...

I have often wondered about this, and have come to the conclusion that humans and life are exempt from the general rule because they convert energy and matter readily, which adds chaos to an otherwise orderly chain of reactions. I've also come to the conclusion that you can't predict individual people, but you can predict masses of them.

[Phopojijo]

Since every particle has a set of equations governing it, no matter how complicated. And every particle's collisions and interactions with other particles could also, in theory, be put into functions.

Given a time, couldn't one, with these equations, find the location of all of these particles and using those locations, in theory figure out what has happened and what will happen?

I know it is impossible to do, but according to this, couldn't you make an argument for fate?Not really.

Firstly... if two bosons get near to each other... you physically are incapable of determining which boson is which. In fact... just about all of Quantum Physics (if not **all** of Quantum Physics) involves finding equations which determine the probability of an event occurring... even passing through locations which are physically impossible to pass (as long as they're close enough to locations which aren't physically impossible to pass). Heisenberg's Uncertainty Principle... check it.

[Rob Oplawar]

Here's my opinion, although it isn't strictly well grounded (just seems to be consistent with my observations):


In order to perfectly predict the outcome of an event, you have to know all the states involved, as well as the relationship between the states. So to know exactly how an electron will behave, you have to know its position, velocity, spin, charge, etc, and you have to know all the forces acting on it, etc.

Modern physics seems to agree that, while forces such as gravity drop off exponentially, their effects do not disappear completely over any distance. Therefore, to truly know all of the forces acting on a particle, you have to know the summation of the forces of the rest of the universe at that time and for the duration of the period you want to predict. Since the electron itself affects the rest of the universe, and the rest of the universe affects itself, in order to predict with 100% certainty what will happen to it you have to know the state of the entire universe.


If we think about what the universe is, all we really know that the universe truly consists of is information- position, velocity, charge, mass, etc. So by containing all the information that the universe contains, in addition to knowing the equations that perfectly describe all interactions therein, you have effectively duplicated the entire universe.


Since we can't duplicate the universe inside our own universe, and since what can be accomplished in our universe is what's defined as physically possible, it is physically impossible to predict any outcome in the universe with 100% certainty.

I don't know the first thing about quantum physics, but it wouldn't surprise me if that's where the uncertainty comes from.


Of course, we might be able to predict with 1 - 10^-200 probability, which is good enough for us. Hell, .9 probability is often just fine.

[Phopojijo]

Nah, the uncertainty comes from matter behaving like waves.

***

Edit... Basically matter is this: http://en.wikipedia.org/wiki/Wave_packet

The Wave Packet's group velocity (the velocity the bulge moves) is what's limited by the speed of light... the phase velocity (velocity of individual waves) is not even bound by the speed of light... (no you cannot use it to transmit data). Everything can be reduced to a sum of sine and cosine waves... even if they're not periodic ("they're periodic every infinity") see: http://en.wikipedia.org/wiki/Fourier_series


http://upload.wikimedia.org/wikipedia/commons/e/e8/Periodic_identity_function.gif

Interesting things happen though when two wavepackets interact on length scales that are smaller than the wave packet (basically)... if they were identical wave packets -- you physically cannot be sure which wave packets entering were the ones entering. Etc.

We however know what happens when two identical cueballs bump into each other though... because they're MUCH LARGER than their "quantum box". Fast moving electrons and light, for examples, are not though...

[Rob Oplawar]

Ok, so I lied, I did take physics 3 a couple of semesters back, and I do know the whole wave thing. I'm not sure why you brought Fourier series into it...
But what I'm really saying is that I've never really thought quantum mechanics was right, as I'm a firm believer in the deterministic universe. I'll buy that particles behave as waves and that we can use a wave function to describe the probability of the location of a particle, but I will not buy that it is impossible to calculate the exact location because the exact location is not deterministic.
Somewhere the information exists; the location is coming from somewhere; it is not pure chance. Saying it's impossible to know because it's so small is like saying it's impossible to know the composition of stars because they're so far away. We just haven't found a way yet.

"God does not play dice with the universe."

[Phopojijo]

Oh you can determine its precision REALLY accurately... however the more accurate you become, the less accurate your measurement of its momentum becomes.

Also... if you take a collection of particles... eliminate all spin-x-up (or down) particles... then you eliminate all spin-y-up (or down) particles... all of a sudden both flavours of spin-x re-appear.

It all has to do with what observable is "compatible" with another... unless it's an eigenvalue in which case it's exact.

[Rob Oplawar]

I'm not talking about the Heisenberg Uncertainty Principle, I'm talking about that core claim of quantum physics that a particle eventually does have a definite position but that definite position is determined by a naturally indefinite function. I don't like the term "indefinite" when it comes to describing how the universe actually works, although it's a fact of life when it comes to predicting an event. My beef with quantum physics is that they don't say "we can't know with certainty because we can't measure it well enough" but instead say "we can't know with certainty because that certainty doesn't exist in the first place." Bullshit.

[Phopojijo]

Nah, not bullshit, the specific uncertainty is derived from mathematics.

In order for you to calculate the value of an observable (position, momentum, energy, etc), you need to multiply the operator into the wave function, then multiply that by the wavefunction's complex conjugate, then do the integral over all space. (WaveFunctionCC * Operator * WaveFunction)

Mathematically:

A) The integral of a wave function multiplied by its complex conjugate over all space is 1. (100%)
B) Multiplying an operator (position operator, spin operator, energy operator, momentum operator) in the middle, before integration, determines how much any portion of the wave function contributes to your observable.
C) Integrating after you modify the wave function tells you the expected value of the observable over all space. (The total energy of the wave function is 20 Joules... its expected value is 20 microns along the x-axis, etc)

Okay.

Now here's where the uncertainty principle arises... since these operators involve derivatives of the wave function, etc... the order you USE these operators matters. (think about what'd happen if you change the order of a division... 5/2 is not 2/5)

***Since measuring the position then the momentum is different than measuring the momentum then the position it follows that you cannot measure one than the other and know the result is true... because if you would have measured them in reverse, you would have gotten a different result.*** (How different the results are becomes the "edges of the quantum box")


As a matter of fact... the Uncertainty Principle is actually just Linear Algebra



(UncertaintyInPosition)(UncertaintyInMomentum) = i*h-bar

... is mathematically just the result of the commutator of the two operators acting on the wave function... the commutator being a well known and mathematically rigerously proven operation to quantify "how well" two things commute (in ALL of math, not just physics). It applies to all observables.

However if an observable is an eigenvalue of the wavefunction... it acts as if it is simply a constant multiplied to the wavefunction. Since constants ALWAYS commute in multiplication... an Eigenvalue of the wavefunction has ZERO uncertainty regardless of what other measurement you did.

[Rentafence]

This stuff is so interesting. I wish my high school would teach quantum physics.

[Disaster]

I'm so confused :(

[Phopojijo]

This stuff is so interesting. I wish my high school would teach quantum physics.Yeah to get anywhere beyond the philosophical... you would need University Calculus II at the very minimum... preferably University Linear Algebra as well.

[MetKiller Joe]

This stuff is so interesting. I wish my high school would teach quantum physics.

Math started really getting interesting for me this year; I was really fortunate to have a teacher that knew how to keep it interesting every second.

Most interesting thing we've done this year (and will keep doing) is laying proofs for finding things like the infinite sum which equals the arctan.

Cool stuff. I will definitely take physics and calc in college.

[Rob Oplawar]

Yeah, that's the uncertainty principle, and I'm fine with that, because it says you can't measure it, but elsewhere quantum physics actually goes ahead and suggests that even if you did know everything there is to know a particle would still have uncertainty because its behavior is essentially random. It says that even the universe can't tell how a particle is going to behave and that if the universe were played out from exactly the same starting point it might behave differently. That's what kills me.

[Phopojijo]

May kill you but it's a mathematical artifact that follows experiment.

[Mr Buckshot]

This stuff is so interesting. I wish my high school would teach quantum physics.

I heard AP Chem (yes, chem) does teach a bit of this heisenberg uncertainty principle and schrodinger wave function stuff. Really cool.

[Phopojijo]

Yeah they teach a little bit to explain the electron orbitals (which are the spherical harmonics of the Schrodinger Wave Equations...)

Explaination: Spherical harmonics being separable solutions to the differential wave equation that are single-valued.

Explaination of Separable Differential Equations
Most of you are used to algebra which is simply isolating one or more variables. A differential equation is an equation that also has terms which refer to how quickly one variable changes as another variable is changed.

Differential equations are easy to model but often hard to solve. The easiest differential equation that's non-trivial I can think of is simply


dx/dt = x

Or in plain English... the speed "the object", whatever it is, travels is its position. IE: An object 3m away from the origin goes 3 meters per second away from the origin.

What we want to do is find out what function does X represent... as a function of time... from practice I know that


e^t

Works. The derivative (how fast something changes compared to something else) of e^t is e^t. Therefore -- dx/dt = e^t and x = e^t... and therefore dx/dt = x.

Unfortunately, Schrodinger's Equation involves different types of derivatives... both time and position as a result... You need solutions that are not dependent on each other. You don't want time to change your solution for position... just uniformly scale (multiply by a constant) it... so that you can solve (or look up) them separately and multiply them later (separable differential equations)

Single Valued Explanation:
A single-valued problem simply means that getting to a point has the same result regardless of how you get there.

An example of a single valued problem: The elevation of a point on the earth. It would be very very very bad if flying around the world suddenly made a mountain appear where there was a valley.

An example of a non-single valued problem: The elevation of a spring. If you go a full circle around a spring... you're not at the same height you once were.

The Spherical Harmonics are single valued functions because the wave has the same value at a given point... regardless of how many times you go around the (in this case, atom).

The Electron Shells follow both conditions... they satisfy the wave equation for the electron... and they don't care how many times you spin around that sphere.

Since you can simply multiply that solution into the radial solution... all that's left to understand the probability of finding an electron in any shell is simply solving the equation that depends on how far away the electron is from the nucleus... which chemistry also takes care of with the first quantum number. (Which shell is it in)... again... the Spherical Harmonics are the orbitals IN the shell.