This post is aimed at someone on the Chess site www.chess.com who told me I don't know the Uncertainty Principle.
In short it is this:
Dp.Dx >= h/(2*pi)
where
Dx is the uncertainty in the position of a particle
Dp is the uncertainty in the momentum of it
h is Planck's constant which is:
6.626068 × 10-34 m2 kg / s
pi = 3.1415926.......
and ">=" means "greater than or equal to"
The Uncertainty here is best explained with reference to my car example in the Calculus post. If the car is travelling at 30 kph, it is not travelling at EXACTLY 30 kph because of bumps in the road, uneven tire pressures, wind, etc. A more accurate statement would be "approximately 30kph", or better still, "somewhere between" 29kph and 31 kph. The speed would then be 30kph "give or take" 1 kph. The "1kph" is called the "uncertainty".
Thus Heisenberg's Uncertainty Principle says that the uncertainty in position, multiplied by the corresponding uncertainty in momentum, can be no less, even in principle, than a certain number (h/(2*pi).
The astounding thing to come out of this is that there is even a number.
Ok, so the number is very small, and has often been quoted as the "measurement" of how small quantum mechanics has to be in order to effective.
This is deeply related to the double slit video posted earlier. If you see the electron then the photon's momentum in order to see it, and it's uncertainty, is enough to raise the uncertainty in the position of the electron so as to destroy the diffraction pattern .
The uncertainty relation has its roots in wave theory, where a wave "packet", caused by many waves of similar wavelengths superimposed, results in a bunch of waves, travelling at a particle's speed (the group velocity), but the waves themselves (the phase velocity) travel at a speed much greater than that of light. It's dealt with here:
http://gnabgib.blogspot.com/2005/06/groupie-or-just-phase.html
The uncertainty in the wavelength is equivalent to the uncertainty in momentum, according to the De Broglie formula (wavelength of "particle" equals "h" divided by momentum), and the uncertainty in the position is equivalent to how "big" the "bunch of waves" is.
What does it teach us? It teaches us that we cannot measure everything.
This is something that the books don't teach, and is a piece of knowledge only available through complete understanding. That means, you can find it nowhere on the web either, unless you ask Mr Feyman, who would probably say the same, but unfortunately he is rather indisposed at this time.
The fundamental obstacle that faces us all in quantum mechanics is trying to envisage "particles" as "waves". It did in 1924 and still does now.
4 comments:
Morticia, you are so lovely and invigorating when you get scientific! You make me want to howl at the moon. (Sorry, could not help myself. All I could think of was the Addams Family after reading this.)
I am no expert, nor close to it, but I would say that blog could be cited as a reference for explaining Uncertainty, if one were doing a paper in need of such a reference. I am sure I will make use of it in connection with some of my own readings.
What I find both sad and interesting about Uncertainty is it seems to derive as a natural consequence from Quantum Mechanics. You can't seem to have QM without Uncertainty. Heisenberg to his credit saw this before others did although I think they could not have avoided comprehending this at some point in those early years of QM.
;-) I would love to get rid of Uncertainty, but it will take quite an explanation to do this, if this can ever be done. I have said too much, but this is quite a subject!
Actually, it is a natural consequence of something called Fourier Transforms in wave mechanics. QM just used this piece of math to explain uncertainty in terms of particles.
you know you cannot mesure the size of an electron not because it's too small or too fast mainly because there is nothing to reflect of it! I figured it out in my head also you cannot weigh atoms because there is nothing small enough to weigh them I'm just wondering if this is right....
Well, you can weigh things smaller than atoms by looking at how much you have to bend their paths in a magnet. It's called a spectrometer.
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