Re: Probabilities in nature or imperfections in human measuring methods

Hello Pierre, that's a good question! Perhaps the best way to answer would be with a lot of math, but I will try to use words instead ...

Quantum mechanics revolves around "Schrodinger's equation": Schrodinger's equation takes "wavefunctions" (which describe, e.g., electrons, or baseballs, or whatever) and "potentials" (which describe forces), and tells you how the wavefunction will move in relation to the forces. It gives an "equation of motion", just like the equation of motion you'd use for the trajectory of a baseball or the orbit of a planet.

Schrodinger's equation is exact - it's not an approximation, it's not fuzzy or probabilistic. It tells you exactly how the wavefunction evolves and changes over time, no matter how small or complicated it is. The strange thing - and the uncertain thing - is that the "wavefunction" does not tell you the location (or momentum) of the particle ... it only tells you the probability of the particle having a particular location or momentum.

Heisenberg's uncertainty comes from this "wavefunction" method of describing things. As soon as we attempt to describe both the particle-like and wavelike aspects of an object using a single wavefunction, we run into something interesting: mathematics itself. A branch of math called "linear algebra" allows us to describe a particle as a combination of many waves; we can also describe a wave as a combination of many particles; but the resulting equations result in Heisenberg's Uncertainty Principle. So, this uncertainty is a fundamental aspect of the wave/particle duality of quantum mechanics ... it is not a defect of our measuring devices!! Since the wavefunction is described, using linear algebra, as a combination of several waves (with a range of momenta) or different particles (with a range of positions), it follows that measurements of it will get a range of answers. (The example of "when you hit the particle with a photon to measure it, you make it move" is very misleading, in my opinion ... it does NOT tell you much about Heisenberg.) I found a web page about this here with some videos, or here in mathematical form.

Perhaps the more useful word is "superposition" rather than "uncertainty". When dealing with wavefunctions, we have to "superimpose" many different waves in order to get something that is well-localized like a particle. The more localized the particle, the greater the range of momenta we need to add up, to define that localized wavefunction. When we then look at this well-localized particle an ask "what is its momentum?", there is a larger range of answers.

So there's no randomness there. Schrodinger's Equation tells you exactly how a given wavefunction moves around, and linear algebra tells you what positions and momenta will be found when measuring a given wavefunction. The randomness emerges because our "measuring devices" can't give us a "superposition of many answers", but only a single answer. This answer is picked - randomly - out of the possibilities available in the wavefunction.

There has always been debate among physicists and philosophers about what quantum mechanics "really means". The way I understand it, "wavefunctions" are reality; Nature deals with wavefunctions, moves them around, and interferes them, all according to Schrodinger's Equation. If you want to observe a localized particle, you have to pick it out from the probabilities available in the wavefunction, but nature doesn't know or care where the particle is. Nature only cares about the wavefunctions. There's a sensible way of understanding this, called the "many worlds" interpretation. In this way of thinking, you have to consider your mind itself as being a wavefunction, itself being a superposition of many waves and particles that make up the brain. Now, all of the linear-algebra of any quantum system that you are observing - for example if you are doing the double-slit experiment - gives sensible results when you consider the whole quantum brain's wavefunction interacting with the wavefunction of the experiment!!! It sounds a little crazy, but it makes sense to a lot of physicists. You can read more about it at the Stanford department of philosophy page.

To sum up: yes, quantum mechanics really is a set of exact laws. The laws themselves only attempt to describe a wavefunction; the wavefunction is basically a collection of probababilities. Interpreting these probabilities sometimes appears to yield "random" results, but that depends on your philisophical approach to the situation!

Hope this is helpful! Good luck!

Sincerely,

-Ben Monreal