[pdmunro]

I enjoyed doing numerical simulations, but I found there were a few traps for young players.

From my limited experience:

1) Make sure the problem is clearly defined: I once spent 3 months solving the wrong problem. My flatmate asked for my help regarding a polymer flow problem, and I spent 3 months trying to solve his problem when I should have working on my own PhD. I misinterpreted the diagram he drew and spent all that time thinking about polymers falling through air, rather than being squeezed through a funnel. A painful memory.

2) If possible have two mathematical methods of arriving at an answer: I solved a blood-clotting problem using (1) a monte-carlo simulation of the final equilibrium position, and (2) numerical solution - using algorithms - of a set of kinetic equations till they reached equilibrium. When I didn't get the same answer, I knew something was wrong. I asked for help and someone showed me how they would use the Monte Carlo approach in method 1. Their code was computationally simpler and, importantly, it gave the same answer as method 2.

3) Find out what simplifying assumptions can be made: I once got engrossed in trying to write a model of gene transcription control that was 10 times more complex than it needed to be. I presented my work a number of times at group meetings, but everyone was too concentrated on their own presentations to really listen to what I was doing. One day I overheard a lab member talking about a simplifiying assumption that they were using to analyse their observed data, and I immediately knew the assumption was both valid and useful for my model. My slimmed down model worked beautifully.

I guess you know all this, and a whole lot more, Helene. I just wanted to put a few somewhat painful thoughts on paper.

[helene_t]

Al_U_Card, on Jun 19 2007, 10:29 PM, said:

Well, those certainly are of interest......to people for whom consciousness is unimportant or irrelevant...

In that respect, perhaps quite a few in fact .....

How does (for example)

"I don't interpret the oberserver-object interaction as consciousness (per se) in action, I think a non-conscious observer could play the same role"

translate into

"consciousness is unimportant" ?

Even if consciousness is unimportant in quantum mechanics it could be important in other areas (like psychology, ethics, fine arts, evolutionary biology, microeconomics and artificial intelligence, to name a few)

I'll start another thread about this, though .....

[Quantumcat]

I thought I might provide a small amount of info to those who are unfamiliar with quantum mechanics, perhaps it may help.

Particles can be described as waves as well as particles, and waves can be described as particles. In order to observe wave-like properties however, the arpetures need to be on the order of the wavelength of the objects, and the size of the wavelength is disproportional to the size of the object, which is why we can only see wavelike properties for particles up to the size of small atoms (and only relatively recently, at the beginning electrons, or "cathode rays", were as big as we could go) and not for macroscopic objects.

Quantum mechanics is about studying wavefunctions of particles. Wavefunctions describe the wave that a particle is. A particle is located at one specific point in space, but a wave is spread out through space, so this doesn't seem to make sense. But what a wavefunction describes is the probability of finding a particle somewhere, were a measurement to be made. Often wavefunctions look like standing waves on a string (if it is prevented from going outside certain boundaries: this is the infinite square well) or like a bell curve. The thing that determines what the wavefunction looks like, is the potential the particle is in. When you insert this potential into the schrodinger equation and solve it (it is a differential equation) it gives you the wave function.

When you measure a particle's position, and you find it to be some value, the particle no longer has a 20% or 5% chance of being there, that wouldn't make any sense. It has to have a 100% probability. So what the act of measurement does, is "collapse" the wavefunction into a specific point: it becomes a large spike around that point (since the measuring instrument has certain error margins) instead of being the shape it was prior to the measurement.

We cannot know what the particle was doing prior to the measurement, since we would obviously have to measure the position to find out. There are three interpretations of this:

• The realist postion
  
  The interpretation is that the particle really was at the measured point, yet quantum mechanics is incomplete and counldn't tell us. This interpretation says it was only our ignorance that led us to believe it had less than 100% probability of being there. But not many subscribe to this view since the mathematics of quantum mechanics is pretty solid.
  
  
• The orthodox view (the Copenhagen interpretation)
  
  This view, which most physicists subscribe to, is that the very act of measurement forced the particle to "take a stand" and decide upon the point we found it in. It's this view that led to Schrodinger's thought experiment about the cat, that it is both alive and dead prior to the measurement, but then decides which it wants to be when we do measure it.
  
  
• The agnostic position
  
  This position refuses to answer. It claims it is pure metaphysics to try to know what something is doing before a measurement, and that it makes no sense to try to speculate. There is a quote from Pauli (author of the Pauli exclusion principle you might have heard of?) "One should no more rack one's brains about the problem of whether something one cannot know anything about exists all the same, than the ancient question of how many angels are able to sit on the point of a needle".

So, anyway, hope that might have helped some people with their debates

[DrTodd13]

The problem is the concept of "measurement." A measurement device is one that is effected by its environment and that somehow displays how it is being affected by its environment. Surely, the "displaying" part does not have some magical property by which the wavefunction is forced to collapse. The effected by its environment part is likewise impotent to collapse the wavefunction because everything is effected by its environment. There are those that claim that a consciousness observing the measurement device is what collapses the wavefunction. So, it is never the act of some measurement device that causes the collapse but the observation of that device by a consciousness. This is a classic interpretation but one with which I totally disagree. My preferential interpretation is that as the size of the superimposed system increases, the time that you can remain superimposed decreases. This time is so small at macroscopic scales as to be unnoticeable. I think that quantum computers may shed some light on this phenomenon. If they reach a limit at which they cannot further increase the size of a quantum computer in a superimposed state then the consciousness interpretation may be proven false.

[Al_U_Card]

Perhaps that is where the meaning of intention comes into play. Conscious intention causes the collapse because it affects the quantum dynamical field in an as yet understood but observable way.....

[helene_t]

DrTodd13, on Jun 21 2007, 10:19 PM, said:

My preferential interpretation is that as the size of the superimposed system increases, the time that you can remain superimposed decreases.  This time is so small at macroscopic scales as to be unnoticeable.  I think that quantum computers may shed some light on this phenomenon.  If they reach a limit at which they cannot further increase the size of a quantum computer in a superimposed state then the consciousness interpretation may be proven false.

This is interesting. Would you say that Schoedinger's Cat would, given its complexity, only stays in its undetermined (=superimposed?) state for a short time, even if it is not observed?

(In the classical interpretation it may be a relevant question if the cat is conscious, but that could be avoided by replacing "cat" with "grandfather clock" or some such).

[DrTodd13]

Yes. For Schroedinger's cat, the mass of the Geiger counter itself is probably sufficiently large to cause the wavefunction to collapse. The cat would never be alive and dead simultaneously. It wouldn't matter if a conscious observer were anywhere nearby.

[slothy]

As cats are rather horrible clingy creatures who never piss in the litter-tray provided, could not we speed up the simulation so they all perish simultaneously?

[helene_t]

slothy, on Jun 22 2007, 02:02 PM, said:

As cats are rather horrible clingy creatures who never piss in the litter-tray provided, could not we speed up the simulation so they all perish simultaneously?

There is currently a bug in my software which makes the cat's probability of being alive explode to several hundred percents after a few iterations, which seems realistic given that my laptop bag is full of cat hairs. So you may prefer some other plan, say reformatting my harddisk.

[Al_U_Card]

But at the quantum level, the cat is irrelevent (which may help to explain their aloofness....) as it is the consciousness (awareness of intention) of each particle that impinges on the wave functions of the others, causing them to condense into one state or the other.