Understand Uncertainty Principle in Computer Simulations

[cam875]

ok so i sort of understand this principle and how to visibly identify an electrons exact location in the space it occupies you have to shoot a photon off it that has a wavelength the same as or less than the electrons wavelength or something and how that alone moves the electron to a new location. But in computer simulations since the electrons co-ordinates are defined in computer memory and to view the value of computer memory locations you don't need to change the value lol thankfully, so does this mean that in computer simulations you can make an electron become a nice defined co-ordinate particle or does it still not matter.

 

[DrChinese]

Keep in mind that the Heisenberg Uncertainty Principle is NOT a result of the physical disturbance of one particle by another... although this does happen. This is usually easier to see if you consider the electron's spin components x, y and z. According to the HUP: Knowledge of x makes y and z fully indeterminate (i.e. random). Yet you can re-measure x all day long and always get the same answer.

So obviously the observation does not change x, and yet y and z follow the HUP perfectly. So this should be your first clue that the HUP is not a function of a physical disturbance by the observing apparatus.

The second clue would come from experiments involving 2 entangled particles (usually called Alice and Bob). Such particles jointly obey the HUP, even when separated. An observation on Alice acts like it causes a matching observation on Bob. And yet the measurement apparatus never touches Bob.

 

[0xDEADBEEF]

Keep in mind that the Heisenberg Uncertainty Principle is NOT a result of the physical disturbance of one particle by another... although this does happen. ...

Well as much as I dislike this view, because it encourages people to think classicly and missing the whole point of QM. AFAIK the pertubation by measurement view is aequivalent to the HUP. It is one of these cases where it seems like quantum mechanics actively seems to pretend that things happen classicly, which is the reason why the Bell inequality is so important. There we could finally catch nature in the act and prove that she is cheating.

 

[IPart]

You know, for a minute I thought you were asking about the electrons that light up CRT screens and how it is that they don't form interference patterns on the screen and I thought wow, that's an interesting question! I know that's not what you are asking about but if you clarify whether you are talking about real electrons or the simulation of an electron, then maybe I can add something pertinent.

 

[edguy99]

ok so i sort of understand this principle and how to visibly identify an electrons exact location in the space it occupies you have to shoot a photon off it that has a wavelength the same as or less than the electrons wavelength or something and how that alone moves the electron to a new location. But in computer simulations since the electrons co-ordinates are defined in computer memory and to view the value of computer memory locations you don't need to change the value lol thankfully, so does this mean that in computer simulations you can make an electron become a nice defined co-ordinate particle or does it still not matter.

The computer simulation breaks down if say an electron and a proton are assumed to be point charges and you try and track them over time. You cannot track or calculate the exact positions and speeds (momentum) of even one electon and one proton that start out at rest with respect to each other over time by paper, computer or any other way in a classical sense. The problem is that the more accuracy you apply in tracking the particles when they are close together, the more "erratic" the electron path becomes as the electron passes over the proton (the attractive force gets very high as they get close).

Computer gravity simulations work since the particles have a radius and if they get too close together they "crash". Assuming either the electron or the proton or both have "size" or "radius" is one way of allowing them to be simulated and tracked in computer animations.

 

[intervoxel]

... But in computer simulations since the electrons co-ordinates are defined in computer memory and to view the value of computer memory locations you don't need to change the value lol thankfully, so does this mean that in computer simulations you can make an electron become a nice defined co-ordinate particle or does it still not matter.

Actualy nobody knows what those naughty particles are doing between observations. Feynman was able to create a formulation about this (please google "Feynman path integral").
What I would do to illustrate (SIC) a quantum system using the computer is as follows:

1 - Assemble the Schroedinger equation
2 - Discretize it
3 - Create a routine for the time evolution of the discretized equation
4 - Create a visualization thread which would generate a random number between 0 and 1; use this number and the squared amplitudes to determine the instantaneous position of the particles

Clearly, many-particles systems explode "tensorialy" in complexity.

I wonder if the resulting clouds would really help? Honestly, I don't know.

 

[ZapperZ]

ok so i sort of understand this principle and how to visibly identify an electrons exact location in the space it occupies you have to shoot a photon off it that has a wavelength the same as or less than the electrons wavelength or something and how that alone moves the electron to a new location. But in computer simulations since the electrons co-ordinates are defined in computer memory and to view the value of computer memory locations you don't need to change the value lol thankfully, so does this mean that in computer simulations you can make an electron become a nice defined co-ordinate particle or does it still not matter.

The problem with your question here is that there are several different issues going on in different directions. Let's address this from the issue brought up at the END of your post.

1. Electrons can be described classically under many circumstances! Look at the simulation that is used in particle accelerators (example: the PAMELA code for particle tracking). This is purely classical E&M. We use PAMELA in many cases to design particle accelerator components, such as magnet settings, where to place various accelerating components, etc. So we know such codes work.

2. Shining light onto an electron as the 'detector' to make such measurement is a very poor illustration for the relevance of the HUP. The HUP has nothing to do with that, nor does it have anything to do with the accuracy of a single measurement of two non-commuting observable. Do a search on here. I've described many times why the HUP has nothing to do with instrumentation accuracy via the example of a single-slit measurement.

3. In a computer simulation, you can do anything you want. It depends on what you are trying to simulate, which you never described. It would be silly to use QM to simulate something that can easily be described via classical means. Unless you have a definite goal and system in mind, that part of your question is rather vague, and it is meaningless for anyone to try to address it without any further elaboration.

Zz,.

 

[Naty1]

Well as far as I can figure neither post 2 nor 3 is complete by itself; ...taken together they provide an overall desription I like...

... so does this mean that in computer simulations you can make an electron become a nice defined co-ordinate particle or does it still not matter.

Of course you can..likely you already know that.

The important question is whether such a simulation will be useful and that depends on what you are trying to accomlish...

 

[cam875]

well i was trying to make it an accurate simulation of electrons orbiting the nucleus in a 2D environment, and yes i have the programming experience but I am wondering how daunting it is mathematically, should I just describe every electron using the four quantum numbers to differentiate between all the electrons in the atom. I mean I didnt really understand the above posts, you said that my idea of HUP isn't correct because its not to do with the measurement affecting the location of the electron but something else, and that's fine but I don't understand what you meant by that something else affecting it, an elaboration on it would be great if someone doesn't mind.

 

[ZapperZ]

well i was trying to make it an accurate simulation of electrons orbiting the nucleus in a 2D environment,

Er... whaaaaaat?!

Is this simply a toy model that you want to play with, or are you trying to simulate something realistic? If you're doing the latter, your starting point isn't.

Zz.

 

[malawi_glenn]

you can not simulate how the electron is moving, what you can do is to graphically draw the wavefunctions or their modulus square.

 

[edguy99]

Actualy nobody knows what those naughty particles are doing between observations. Feynman was able to create a formulation about this (please google "Feynman path integral").
What I would do to illustrate (SIC) a quantum system using the computer is as follows:

1 - Assemble the Schroedinger equation
2 - Discretize it
3 - Create a routine for the time evolution of the discretized equation
4 - Create a visualization thread which would generate a random number between 0 and 1; use this number and the squared amplitudes to determine the instantaneous position of the particles

Clearly, many-particles systems explode "tensorialy" in complexity.

I wonder if the resulting clouds would really help? Honestly, I don't know.

Cool. Any chance of a sample (or link) of what 2 hydrogen protons and 2 electrons (normal H2 orthohydrogen) "look" like in your drawing?

 

[edguy99]

you can not simulate how the electron is moving, what you can do is to graphically draw the wavefunctions or their modulus square.

Do you have a link or picture of this for something simple? What happens over time to this type of drawing - do things move around?

 

[cam875]

ive seen a model of this before done in a java applet of the different wavefunctions and its just a graphic of the different s,p,d,f orbitals and stuff, so basically its only probability and you can only draw the area where the electron is expected to be?, I think I once read an article somewhere about why einstein hated all this probability stuff lol, since it defies the abilitity to accurately predict which was basically his life devotion. Could it be we just don't understand enough about the subatomic that we rely on probability as the current theory, not meaning it as offense or anything just that I can see it being one of those things that in 1000 years they look back and laugh at us just like we laugh at the different old metaphysical ideas of our universe.

 

[ZapperZ]

ive seen a model of this before done in a java applet of the different wavefunctions and its just a graphic of the different s,p,d,f orbitals and stuff, so basically its only probability and you can only draw the area where the electron is expected to be?, I think I once read an article somewhere about why einstein hated all this probability stuff lol, since it defies the abilitity to accurately predict which was basically his life devotion. Could it be we just don't understand enough about the subatomic that we rely on probability as the current theory, not meaning it as offense or anything just that I can see it being one of those things that in 1000 years they look back and laugh at us just like we laugh at the different old metaphysical ideas of our universe.

Now you are completely changing the subject and going off your own topic. If you want to ask about the physics of deriving the orbital wavefunction, then to mix it with your own view of whether QM is complete or not. Einstein could easily be wrong on this, especially when he didn't live long enough to see what QM has accomplished.

Those sketches of atomic orbitals were derived out of a 3D schrodinger equation, probably using a Hydrogen atom solution. These are not 2D systems! A 2D system will give you completely different solutions.

Look up any QM text on the derivation of the wavefunction for the hydrogen atom. These do not require "simulation".

Edit: not that I expect you to be able to understand this, but this is the full derivation of the wavefunction for a hydrogen atom.

http://galileo.phys.virginia.edu/classes/751.mf1i.fall02/HydrogenAtom.htm

As daunting as this looks, every single undergraduate physics major has to know this derivation COLD. It is probably in all intro QM text.

Zz.

 

[edguy99]

ive seen a model of this before done in a java applet of the different wavefunctions and its just a graphic of the different s,p,d,f orbitals and stuff, so basically its only probability and you can only draw the area where the electron is expected to be?, I think I once read an article somewhere about why einstein hated all this probability stuff lol, since it defies the abilitity to accurately predict which was basically his life devotion. Could it be we just don't understand enough about the subatomic that we rely on probability as the current theory, not meaning it as offense or anything just that I can see it being one of those things that in 1000 years they look back and laugh at us just like we laugh at the different old metaphysical ideas of our universe.

As Zz has pointed out, these are generally calculated for a single atom (usally hydrogen), they look very different if you are talking about 2 hydrogens joined in say an ortho bond. I don't know of many places that show these type of drawings for more complex molecules but would be happy to find them. I think they would probably look pretty neat, I was hoping we would get a few links.

 

[intervoxel]

Cool. Any chance of a sample (or link) of what 2 hydrogen protons and 2 electrons (normal H2 orthohydrogen) "look" like in your drawing?

As I said

Clearly, many-particles systems explode "tensorialy" in complexity.

This means that quantum simulation is a class of problems known as NP-Complete, like the famous traveling salesman problem.
Simulating your 4 particle system might require a supercomputer.

Using my humble 950MHz PC what I got was a one electron, one dimensional cloud.

The cloud is represented by red dots above the probability curve.

http://www.intervoxel.com/physics/wavefunction.html

 

[cam875]

yes youre correct, it was for a hydrogen atom, for the one i looked at. And that math is beyond me by a mile lol. Ill just wait for calculus next year and maybe I will be able to begin understanding something on this forum haha. But is the reason that electrons don't have co-ordinates also because you can't localize a point on a wave because there are so many or something. It was somewhere in my particle physics book.