Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: neilep on 07/11/2005 21:32:40
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In my never ending quest to join the elite amongst you so that I may attempt to converse with more than just one sentence, I have actually splurged out on a few books recently. A couple of them are about that 'middle-of-the-road-easy-to-understand-pre-school ' subject of Quantum Theory/Mechanics.
As curious as I am about this, is there any way to explain in the simplest terms possible what a ' wavefunction' is ?...pretty please ?
Please advise..I am waiting here, and there...at the same time !!
Men are the same as women.... just inside out !! (https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Fwww.world-of-smilies.com%2Fhtml%2Fimages%2Fsmilies%2Fparty%2Fballoons.gif&hash=f9f40e7ab655ca9089398c3f3719f593)
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I feel that if I ventured any kind of definition, it would indicate my true lack in understanding quantum theory while remaining silent, I'll still have a bit of such an interpretation. I think Feynman stated that no one really understands quantum mech. Perhaps one could say that a wavefunction is an expression describing a single particle's motion to all parallel universes in existence.
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Hi Neil.
So you wish to learn about quantum theory. HE HE HE HE[:D]
I've been there tried that, and still only a little bit wiser.
I agree it would be nice to be able to converse with the elite of this forum on occasions.
I try every now again but allas i'm still uncertain as to the priciple's of quantum machanics.[:)]
Good luck though.Hope you do better than me [:)]
Michael (https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Fi11.photobucket.com%2Falbums%2Fa186%2Fukmicky%2Frofl.gif&hash=481319b762ee9d57cda15e90d2e83ee6)
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Wavefunctions - nice easy one for the morning then ;)
You have probably heard a load of stuff about uncertainty in quantum mechanics. This means that we can't work out where or how much momentum any particle has exactly. That doesn't mean we don't know anything about it though. We can work out how likely it is to be in any place/momentum/energy, this is a bit annoying if you are dealing with individual particles but not so bad when you are dealing with statistical numbers of them.
Now this probability of where the particles end up seems to behave a bit like a wave. Lets call it a wavefunction. Now where there are standing wave peaks in this wavefunction you are very likely to find your particle and where there are nodes (points of no amplitude) you are not going to find the particle. If you have two of these wavefunctions they will interfere like waves causing cool interference patterns. Hence although particles appear to arrive places as lumps, their wavefuntions make them behave a lot like waves - hence wave-particle duality stuff...
dunno if that helped, good luck
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THANK YOU LARS, DAVID and MICHAEL for your encouragment. I am getting there and your explanations help a lot. I am indeed fascinated by all of this and you can imagine how frustrating it must be for a novices novice like myself who wants to know but needs to understand....well, I presume that applies to anyone researching anything...but thank you all agin for your responses.
DOUGHNUT ! Everything was going fine until your last paragraph....I gather I need to understand Quantum before I can comprehend your last few lines but I thank you for your first paragragh....errhm...why am I called ' Yan ' after my name ?
Men are the same as women.... just inside out !! (https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Fwww.world-of-smilies.com%2Fhtml%2Fimages%2Fsmilies%2Fparty%2Fballoons.gif&hash=f9f40e7ab655ca9089398c3f3719f593)
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Neil,
here's my explanation, in case it's of interest. (If it looks a bit too heavy, just jump to the ANALOGY at the bottom, which might be more helpful.)
A wavefunction is just an abstract mathematical function. Like y=x^2 or y=2x (which are both "functions of the variable x"). But in quantum mechanics the wavefunction is normally a complicated function of several variables (e.g. the position variables in 3 dimensions, x, y & z, plus time t). It's also a "complex" function, with real and imaginary numbers. (Don't worry if you don't understand what that means.)
A particle can have different wavefunctions depending on what physical attribute you're interested in / what it is you want to track and measure. You can have a wavefunction for its position, or momentum, or energy, or ...
At any instant in time, the wavefunction gives you a number for each point in space (for a position wavefunction) or for each combination of momentum in each direction (if it's a momentum wavefunction), etc. The number at that point in space and time is just an abstract number, but if you square that number you get the probability of finding the particle at that position (or momentum or ...) at that time.
And finally, the way the wavefunction spreads out over time and space is governed by the Schroedinger Wave Equation.
ANALOGY:
There's a really good analogy in the book "Quantum" by Jim Al Khalili which might help you understand what a wavefunction is. To paraphrase it slightly (to ensure I don't breach any copyright laws):
Imagine a burglar is out on a crime spree one night (a one-man crime wave, you might say). You know he's just burgled 101 Station Road a couple of minutes ago. But you don't know where he is now. So you get out a map of the town and assign probabilities to where he might be now. To start with, houses around Station Road are most at risk of being burgled next. But as time passes, the area he's likely to be in grows over time. (His "position wavefunction" spreads out.) And it might not spread out uniformly - perhaps he's more attracted to posh streets but less interested in houses around the police station.
This "crime wave", like any wavefunction, isn't something physically real, it's just a set of abstract numbers assigned to each position on the map.
And also, when you hear a report that he's just burgled another house, you have to re-do your figures (the wavefunction "collapses" to a small area around this new house) - but over time the wavefunction spreads out yet again.
Hope that helps.
Solvay.
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Paul...thats brill, thank you very much indeed....and guess what ? "Quantum" by Jim Al Khalili is the very book I'm reading.
I really appreciate all your attempts to help me understand.....and if I may also use a quote from the back cover of that book ' Anyone who is not shocked by quantum theory has not understood it'..Niels Bohr....so, I'm happy in my state of confusion !
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Glad to be of help, Neil. (I told you it was a good book, didn't I.)
And something I've just noticed - this will be my 100th post! Yay! (cue fanfare and balloons)
At this rate I'll have overtaken your record in ... er ... about 20 years.
"Eagles may soar, but weasels don't get sucked into jet engines."
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There have been many attempts to understand the wavefunction. Some get really weird, such as Feynemans sum-of-histories. My favorite is probably Schroedinger's, who was not comfortable with QM. This is really a classical explanation, trying to breach the gulf between our intuitive macro-world, and the pico-world of QM. This is simple: The relationship between the wave and the particle is the energy-mass relationship. The energy has a wavelength, and the particle has a mass. There is uncertainty about both, so the massive particle can't be localized exactly, and the energy wavelength can't be measured exactly either. The less massive the particle, and the less energetic the wavelength, the greater the uncertainty, and the larger the wavelength. Einstein's and Max Planck's equations fit this nicely.
Unfortunately, it isn't this simple, and you would have to try to understand more of the meaning, but this is a good point-of-departure for a classical guy.
"F = ma, E = mc^2, and you can't push a string."
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Solvay - I agree with you about Al Khalili. That burglar analogy is fabulous. But, of course, a burglar can't move backwards in time! [:D]
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A burglar can't move backwards in time? Yes they can - it's called "coming up with an alibi"![:o)]
"Eagles may soar, but weasels don't get sucked into jet engines."
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Very good, Solvay - I like that about an alibi!
Oh, & weasels can get sucked into jet engines if you catapult them high enough
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quote:
Originally posted by Solvay_1927
ANALOGY:
There's a really good analogy in the book "Quantum" by Jim Al Khalili which might help you understand what a wavefunction is. To paraphrase it slightly (to ensure I don't breach any copyright laws):
Imagine a burglar is out on a crime spree one night (a one-man crime wave, you might say). You know he's just burgled 101 Station Road a couple of minutes ago. But you don't know where he is now. So you get out a map of the town and assign probabilities to where he might be now. To start with, houses around Station Road are most at risk of being burgled next. But as time passes, the area he's likely to be in grows over time. (His "position wavefunction" spreads out.) And it might not spread out uniformly - perhaps he's more attracted to posh streets but less interested in houses around the police station.
This "crime wave", like any wavefunction, isn't something physically real, it's just a set of abstract numbers assigned to each position on the map.
And also, when you hear a report that he's just burgled another house, you have to re-do your figures (the wavefunction "collapses" to a small area around this new house) - but over time the wavefunction spreads out yet again.
Hope that helps.
Solvay.
All of which is very interesting (and I'm not being sarcastic), but it would be interesting to know how you explain the double slit experiment using your single burglar analogy?
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Another_someone.
That's easily explained. He needs 2 slits in his mask - 1 for each eye
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No DrB, you're just being silly now aren't you!
Someone - the two slits are like the two poshest streets (areas of high probability where you're likely to find him) and the screen represents the police cordon (where you almost certainly won't find him). And this cordon crosses his entire route apart from the entrances to the 2 posh streets, say.
Then, when he's passed through the cordon into one of the 2 streets (but you don't know which one), he continues going forward past these streets, and his probability wave fans out again from these two streets. And where the probability waves from each street overlap (say, at a third street inbetween the two) the probability is higher.
As for why the probability wave ends up with an interference pattern (of several alternating peaks and troughs) beyond the two slits ... er ... I don't know. The analogy falls down there. (It's only a simple analogy, it's not designed to cover every quantum phenomenon.)
Or maybe he's not only a burglar, but he also does a sideline in "flashing", so he's just "interfering with himself". (Sorry, couldn't resist it. [:D])
"Eagles may soar, but weasels don't get sucked into jet engines."
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So would there be a virtual burglar to carry away the loot? Or what about an anti-burglar? [:p]
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Hmmm, I suppose a virtual burglar would be an opportunistic thief - someone who wasn't planning to be a thief, but gets tempted when an opportunity falls into their lap, so they just "pop up out of nowhere" and then disappear again!
And an anti-burglar is something that, when it collides with a burglar, explodes into heat and energy. So that must be a copper then! [:D]
(This analogy just gets better and better, doesn't it.)
FOOTBALLERS’ QUOTES #2 : "Argentina are the second-best team in the world, and there's no higher praise than that." - Kevin Keegan
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quote:
Originally posted by Solvay_1927
Hmmm, I suppose a virtual burglar would be an opportunistic thief - someone who wasn't planning to be a thief, but gets tempted when an opportunity falls into their lap, so they just "pop up out of nowhere" and then disappear again!
And an anti-burglar is something that, when it collides with a burglar, explodes into heat and energy. So that must be a copper then! [:D]
(This analogy just gets better and better, doesn't it.)
FOOTBALLERS’ QUOTES #2 : "Argentina are the second-best team in the world, and there's no higher praise than that." - Kevin Keegan
But does not anti-matter, when in a world of anti-matter, behave almost exactly like matter does in a world of matter.
Does this mean that a copper inhabiting a world only inhabited by other coppers, would behave almost indistinguishably from a burglar inhabiting a world only of burglars?
Ofcourse, we then get to the interesting issue of Hawkins radiation, where matter and antimatter can be created simultaneously out of nothing, and one part dragged into a black hole, and the to remain outside of the black hole. So is this where we have two brothers, where one decides to be a burglar and the other a policeman, and one goes to prison and the other stays outside. Ofcourse, one has to remember that if this analogy is to remain true, it is not always the burglar who goes to prison, it may be the brother who became a policeman. But then, given we have already said that (in our world of analogies) policemen, in a world without burglars, would behave as if they were burglars, maybe this is apt.
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The Home Office would love the Hawkings policeman/burglar thing. For every burglar that appears, a policeman appears too. Then, when the burglar has been dispatched, the copper disappears thus saving on the wage bill!
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The force acting between them would be handcuffs?
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I've been silly again, haven't I. The copper wouldn't disappear. He'd either end up in prison (the black hole) or wander around looking for a friend (or another burglar). We could end up having an infinite number of coppers wandering around [:0]
*rushes out to get an up-to-date tax disc*
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quote:
The force acting between them would be handcuffs?
So photons are handcuffs in this analogy, then. (Obviously, the handcuffs would have to be a modern design - i.e. they need to be virtually weightless.)
quote:
Does this mean that a copper inhabiting a world only inhabited by other coppers, would behave almost indistinguishably from a burglar inhabiting a world only of burglars?
But for that analogy to work, you'd have to assume that the police are capable of dodgy dealings and, within their own community (the police force), they would conspire together to cover up their misdemeanours. Obviously, that would never happen in real life ...
(Maybe I'd better stop there before I provoke another one of those trendy-lefty-liberal-versus-the-establishment debates![:)])
FOOTBALLERS’ QUOTES #3 : 'I couldn't settle in Italy - it was like living in a foreign country.' - Ian Rush
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Indeed, Solvay - the handcuffs would need to be very "light"
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Would remote entanglement mean the policeman could arrest the burglar at a distance? Or would that equate to speed cameras?
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Speed cameras? I feel a new thread approaching...
[:p]