Tuesday, April 5, 2011

Wave function build-up and the skier of Charles Addams: background

Everyone knows about wave function collapse. (If you don't want to read about it, skip to the quote from Martin Gardner.)

In short, imagine you wanted to determine where I am right now. Without knowing my exact location, but knowing where I might be, you can assign probabilities to a number of locations. I can be at my home. I can be at work. I can be on my way in between. I can be in a grocery store. I can be shopping for a new pair of headphones at BestBuy. And so on. I can also be in Maryland — but with much lower probability than in the above places, although probability greater than zero. Probability of me being on the moon right now is very-very close to zero. Probability of me being in Alpha Centaura solar system is zero.

So, you can draw a "probability cloud", with each location's density proportional to the probability of my being there.



At different times, my probability cloud changes shape. For instance, on Shabbos, it becomes restricted to the walking distance around my house, and it's densest at my house, my shull, and the homes of the few people that I go to lunch to on Shabbos with my wife. Around Peisach time, my probability wave will shift to Skokie, when I will be visiting my in-laws. And so on.

The interpretation of the probability cloud regarding me is that I may be found in any of the locations on the cloud. In reality, however, at any given moment of time, I am at only one of those locations. It's not like 50% of me is at my work, 40% is at home, and 10% on the highway in between. The probability cloud is a result of your lack of precise knowledge about my location. If you put a GPS device on me, my probability cloud in your measurement will shrink to whatever the limitations of the device's accuracy are (e.g., plus-minus ten meters).

Well, in the quantum world, it's different. An electron's probability cloud has reality. The electron really exists at the same time in all the places represented by its probability cloud — the greater the probability, the more it exists there. It's as if the electron's metzius was smeared over the space.


(different shapes of electron's orbitals)


Well, if you make an experiment of shooting an electron (or any other quantum "particle") through two slots many times, as everyone knows, the collection of the marks on the screen where the electron hits will have interference pattern — a pattern similar to what you would see if you sent two waves of any kind through two slots (e.g., waves of water or a wave of light).

As waves go through space, they interfere with each other, partially cancelling each other in some places and super-imposing on each other in others, forming this pattern in the end:



In contrast, if you shoot a bunch of pellets through two slots, those pellets that pass through will form two parallel bars of marks on the screen — since the pellets don't interfere with each other (as waves do) when they fly.



(Watch this cartoon for a description of the whole experiment.)

Now, if you shoot a bunch of electrons at the screen, they will form wave-like interference patterns seen above. This suggests that electrons interfere with each other as waves when they fly through space. But, even more shockingly, if you shoot electrons one at a time, the interference pattern will be the same (with each bright bar representing places of greater probability for the electrons to hit the screen). It's as if the electron is interfering with itself when flying through space — which means that it doesn't fly as a particle, but as a probability wave, a wave of metzius, if you will, which interferes with itself just like a water wave passing through two slits.



In the last part of the experiment, if you put a detector next to one of the slits, to see if the electron "really" passes through the slit, the interference pattern forming on the screen will be only two bars. It's as if when you observe the electron, you force it to pick a slit. While flying unobserved, the electron is free to be as "scatter-brained" and indecisive as it wants (or as its wave function dictates). But, when meeting a detector (and, whatever Tzvi Freeman tells you, it's not the human consciousness that the electron meets, but simply a piece of macro-world, a detector, which will work even if the human being with his consciousness went to lunch), the electron has to make a decision, and it will decide for sure that it wants to fly through the one slot only or through the other.

This is known as wave function collapse.

[Continued in the next post.]

5 comments:

e said...

I was wondering how consciousness effects (or doesn't effect)the wave function collapse. Can you shed some light on this?

e said...

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Barzilai said...

Thank you for your explanation. It is very helpful to clarify what I was trying to say on my website, and I linked to your post here:
http://havolim.blogspot.com/2011/04/metzora-vayikra-1435-saying-its-so.html

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