I appreciate it! : )
So you claim to be unable to visualize the seemingly paradoxical vector state of an elementary particle, as described by quantum theory?
JOIN THE CLUB MY FRIEND! This puts you in the same category as some of the world's greatest physicists that ever lived; so your not at much a loss. The particle/wave dual nature of matter caused an uprorar in the physics community when it was first studied and the theory bagan to take shape. It forced many physicists to start to wonder if our LANGUAGE was even capable of describing the odd, "unreal" phenomena of quantum theory. How does one begin to imagine particles which somehow have a defined location and yet can constructively or destructively interfere with the trajectory of other particles, as if they were all "chunks" of a wave (with no defined location mind you). Doesn't this seem like a complete contradiction? It's a wave when we don't look at it... but as soon as we set up a detection apparatus, it has a more definite position as if it were a particle; like it knew how to behave while being watched but could go beserk out of view. I believe it was Bohr (but I'm not 100% sure it was him) who said, "Anybody who believes that they have fully understood quantum theory, doesn't in the least bit understand quantum theory."
As for your momentum/position uncertainty delima, consider this... If matter is to be considerred simultaneously as a particle and a wave, then whatever detection apparatus we choose to view particles of matter, obviously has to "emit" something to "reflect" off of the matter so we can "see" it. Just like how light opperates...so let's use this for the discussion.
Now say I want to "look" at an electron with position x and momentum p. If I send a wave of light, I must first consider how high a wavelength I choose to emit. (Shorter wavelength means higher resolution in position...think of wavelength as the "tick marks" on a ruler...shorter = higher measurement accuracy). So wavelength determines accuracy, and its wavelength is presicely inversly proportional to its frequency...evident in the equation f = wc (w is a crude symbol for "wavelength" and c is the is the speed of light, a constant). Frequency is related to the energy of a particle by the following equation: E = fh, where E is energy, f is frequency, and h is planck's constant. So you can interpret the equations as saying that, as a light wave increases in energy, so too does its accuracy in determining position. But now that we brought the word Energy into the picture, and light is also a particle, we can now also state the relationship between energy and momentum; p = E/c, where E once again is energy, c is constant, and p is momentum. As you can see, if we increase the energy, then the fraction increases in value, which is greater momentum.
So if light is a wave, greater energy means greater precision in measuring postion. If light is a particle, greater energy means greater momentum. Since momentum can be exchanged between particles, and we don't know the initial momentum of a particle of light (afterall its the other object we measure... not the light), we would be hard pressed to give an accurate account of the total momentum transfer between the two particles at the time of interaction. So when the light reflects back to our eye, the inforamtion it carries has been adalterated with uncertainty. We could send a less energetic photon, then we could be CERTAIN that less momentum was transferred. But this comes at a price.... remember that lower energy means longer wavelength means less precision in determining postion. So no matter what there will always be uncertainty, regardless of how technologicly precise your detection apparatus. It is an inherent property of particle interaction.
So you cant detect the precise trajectory and hence momentum of a particle (it has many possibilities) but you can determine its position. You can't detect the positin of a wave (smeared out and many places at once) but you can detect it's momentum (approaches the definite value of zero as wavelength gets smeared out ever increasingly). That's uncertainty in a nutshell. |