Seasons
This is a forum or general chit-chat, small talk, a "hey, how ya doing?" and such. Or hell, get crazy deep on something. Whatever you like.
Posts 4,088 - 4,099 of 6,170
Psimagus, you told Irina,"And I must repeat that you are failing to differentiate a wave from a wave function - they are not synonymous,..."
Oh Great. Just when I thought I had something with "physical waves" vs. "mathematical waves". Please to elaborate now?
Okay, I am going to grossly simplify the explanation of this, but attempt not to oversimplify it. It's 5 in the morning, and not an easy thing to describe plainly even with a brain that's awake. And I admit - I'm no mathematician. If any mathematicians or physicists out there would like to improve or refute any or all of this description, please do.
A wave itself is a wave - rippling water, sound, concussion, in this case electromagnetic (ie: light.) A regular pattern of amplitudes that range from a positive to a negative boundary that (largely for convenience I suspect,) is normalized to 1. So the amplitude may fluctuate from -1 to +1. The wave may propagate or not (there are "standing waves" that don't.) It is characterised by the ability to interfere with other like waves by a destructive process whereby positive and negative amplitudes cancel out.
If you want me to get really metaphysical, I will when I'm more awake, but I think that's enough on waves.
A wave equation is a set of solutions to a differential equation that plots the values of those amplitudes, and thus define the state of a wave at one instant.
A wave function is a linear combination of such solutions superimposed, that defines the wave-state over time.
The wave function isn't the wave it describes - it's a description of it. The map is not the territory. That is the only really important thing to recognize.
How real is the map? There are some profound implications to that question - but I'm not going there now! I'm going to bed.
The term "Coulomb" is a tip-ff that it has something to do with electric charge.
Yes - it is an electrical wave function. Not a probability wave function.
Electricity is not probability.
A wave equation is a set of solutions to a differential equation that plots the values of those amplitudes, and thus define the state of a wave at one instant.
A wave function is a linear combination of such solutions superimposed, that defines the wave-state over time.
Thanks for staying awake for this.
So what I was calling "mathematical wave" is a wave equation, and the set of all wave equations for a given probability of instance (photon/quantum) at a certain time is a wave function and looks like a line. Psi is the wave function the applies to quantum/photons. It will share the characteristics of all wave functions by definition. It will also have it's own unique characteristics that make it psi. Then wave function psi for a given quantum should not move or change, because it already includes all possible wave equations for that quantum, right? But once that quantum is measured again we have a whole new set of wave equations and one could say that the psi has changed, relative to the last time we calculated it.
How real is the map? There are some profound implications to that question - but I'm not going there now!
Oh yes I am.
Irina, you have created a wonderful thing, without even knowing it. It's crazier than a box of frogs, but it's very beautiful nonetheless.
I believe the Irinaverse contains nothing but the most concise practical proof of its own non-existence that it is possible to construct.
By conflating every last quantum into psi, you have produced a perfectly self-referential description of itself to the exclusion of anything else. A map of that same map, with no terrain.
The more I think about it, the more beautiful I think the paradox is. And if I can ever figure out the math to hide the illegal operations neatly, like Escher hides his violated perspectives, I am going to print the equations on a T-shirt and wear it with pride!
I can't say what 'it' would look like, because there are many different wave functions.
You accept this now? Oh no - that will ruin the Irinaverse's perfect self-reference!
Posts 4,088 - 4,099 of 6,170
Oh Great. Just when I thought I had something with "physical waves" vs. "mathematical waves". Please to elaborate now?
Okay, I am going to grossly simplify the explanation of this, but attempt not to oversimplify it. It's 5 in the morning, and not an easy thing to describe plainly even with a brain that's awake. And I admit - I'm no mathematician. If any mathematicians or physicists out there would like to improve or refute any or all of this description, please do.
A wave itself is a wave - rippling water, sound, concussion, in this case electromagnetic (ie: light.) A regular pattern of amplitudes that range from a positive to a negative boundary that (largely for convenience I suspect,) is normalized to 1. So the amplitude may fluctuate from -1 to +1. The wave may propagate or not (there are "standing waves" that don't.) It is characterised by the ability to interfere with other like waves by a destructive process whereby positive and negative amplitudes cancel out.
If you want me to get really metaphysical, I will when I'm more awake, but I think that's enough on waves.
A wave equation is a set of solutions to a differential equation that plots the values of those amplitudes, and thus define the state of a wave at one instant.
A wave function is a linear combination of such solutions superimposed, that defines the wave-state over time.
The wave function isn't the wave it describes - it's a description of it. The map is not the territory. That is the only really important thing to recognize.
How real is the map? There are some profound implications to that question - but I'm not going there now! I'm going to bed.
Dear Psimagus:
I tell you what: give me a reference for the claims you say that Penrose is making: book and page numbers. That way I can get the book, see them in context, and then respond to them. In this way I can, for example, satisfy myself about whether he might be using words in a different sense thatn I am used to. I can also see whether he is talking about mainstream QM or about one of his far-out theories like quantum Gravity, etc..
Walk in Beauty, Irina
I tell you what: give me a reference for the claims you say that Penrose is making: book and page numbers. That way I can get the book, see them in context, and then respond to them. In this way I can, for example, satisfy myself about whether he might be using words in a different sense thatn I am used to. I can also see whether he is talking about mainstream QM or about one of his far-out theories like quantum Gravity, etc..
Walk in Beauty, Irina
Yes - it is an electrical wave function. Not a probability wave function.
Electricity is not probability.
Hey Irnia. A basic question first. In
(Psi)*(r, t) (Psi)(r, t) d(tau),
What does the asterisk stand for again?
(Psi)* means the complex conjugate of (Psi). (psi) is a complex number, say (2 + 3i) , where i is the square root of -1. In general,
complex numbers can be put in the form (a + bi). Here a=2 and b=3. The complex conjugate of (a + bi) is (a - bi). That is,
(a + bi)* = (a - bi). Just change the sign of the imaginary part.
When you multiply a number by its complex conjugate, you always get a real number.
Proof: (a +bi)(a - bi) = a^2 + abi - abi + b^2i^2. But the two abi terms will cancel each other out, giving a^2 + b^2i^2. But i is by definition the square root of -1, so i^2 = -1. So we get a^2 - b^2. But since both a and b are real numbers, so is
(a^2 + b^2).
This function
(Psi)(r, t)
can be
visualized as a wave when we plot it on a graph,
So what does the whole enchilada look like on a graph? Do I do I have to get Prob123’s site to work?
I don't know what Prob123's site is. I can't say what 'it' would look like, because there are many different wave functions. The wave function for a free electron would look different from the wave function for an electron bound to an atom. Furthermore, its a function of four variables, so you couldn't graph it on two axes. I sympathize with your desire to 'see what it looks like,' though. Let me think about it and hunt for nice sites; there must be some with nice graphics.
Do you know the trig functions, sine, cosine, and tangent? That would be helpful.
>
but has
nothing to do with wave-like behavior of the quantum itself.
I'll agree to the first clause, but the clause after the "but" I cannot agree with.
I phrased that badly. I was trying to distinguish between mathematical waves and physical waves, but I didn’t pull my thoughts together say it correctly.
OK, I see, and I agree; as indeed I say below.
For one thing, I don't really understand what "the quantum" is. But I suppose it means
something like a photon;
But, but but…a few posts back when I started talking about photons Psimagus said to use “quantum”. *pouts*
I sympathize with your frustration. It's bad enough that Psimagus and I disagree, but it is really confusing that our terminolgical preferences also differ. If you prefer to use "quantum," on the understanding that it means some particle like a photon, that's OK with me.
Yes! these things are all related, since they all come out of the wave function.
Why do they come out of the wave function instead of feeding into the wave function? I understand that the wave function was developed based on observations of some real world phenomena, but the change in the photon/quantum/horse produce a change in the state, it’s not as if the change in state of the mathematical wave produces a change in the quantum/photon/horse.
You're right, the mathematical function has no power to reach out and change the material world. But it describes the material world. When we say that the Earth is (roughly) a sphere, we are using the mathematical notion of sphere to (partially) describe a material object. The mathematical wave function describes the physical wave-function, which in turn determines the probabilities of specific, concrete events. The physical wave-function is not something that is visible, but it is nevertheless real. A coin is either fair or biased; that is a real feature of the coin. It is also a matter of probabilities. Probabilities aren't something you can see or touch, but they are still real. If you play Russian Roulette often enough, you will die. In my "Quantum Theory" bot, Elena uses the metaphor that the physical wave function is an inaudible song to which the universe dances.
This momentum is "part" of the probability,
More precisely: implicit in the wave function.
implicit meaning it’s a factor used in the formula (or a characteristic of a factor)? Or implicit in that momentum is a characteristic of the wave function itself?
Well, given the wave function, you can calculate the probabilities of the various possible momenta.
They are not following Dobbin around the track, no. They may change, however. As Dobbin gets older, for example, his chances of winning the Derby may shrink.
Yes, but it’s the real world conditions of Dobbin that cause these changes (new values for specific factors) so the wave changes when Dobbin changes, but does not move on its own. Right?
Good question, very profound... I will have to think about it, but right off the bat I'd say that Dobbin dances to the song of the physical wave function. But there's a little freedom in the dance - the song does not determine his every move, it just says, "these are the probabilites." Even if there is a probability of .9999 that something will happen, it still may not happen. So things in the world are improvisational dancers. The physical wave function, however, is completely determined - it is, so to speak, completely written out in advance.
Of course, all this stuff about music and dance is only a metaphor, but it may be helpful.
On one of those sites I finally got to, http://www.ncsu.edu/felder-public/kenny/papers/psi.html (those were the guys with the M & M’s in their demonstration. I always go to the sites who offer chocolate). They said, “I want to make it clear what we've introduced so far. We've said that 'the magnitude of the wave function squared gives the probability of finding the particle at a particular position.' This is a totally out-of-the-air rule; or, to put it another way, a fundamental postulate of quantum mechanics, that we will not make any attempt to justify." Are they are describing your postulate in other words or am I confusing it with another postulate? I think I have some idea based on this I may want to clarify but first I have to check that this “magnitude” (size of measurement from the very peak of the highest part to the very lowest part of the trough) of the wave function squared is somehow implicit in postulate one or if it comes in later.
It's the same, although they are expressing it a little sloppily, IMHO. What they are calling 'the magnitude of the wave function squared' is actually (Psi)*(Psi) (i'm leaving out the (r,t)'s, as is often done for brevity). In popularizations, people often tell a few white lies in order not to burden the reader with technical complexities that don't bear on the main point.
Walk in Beauty, Irina
complex numbers can be put in the form (a + bi). Here a=2 and b=3. The complex conjugate of (a + bi) is (a - bi). That is,
(a + bi)* = (a - bi). Just change the sign of the imaginary part.
When you multiply a number by its complex conjugate, you always get a real number.
Proof: (a +bi)(a - bi) = a^2 + abi - abi + b^2i^2. But the two abi terms will cancel each other out, giving a^2 + b^2i^2. But i is by definition the square root of -1, so i^2 = -1. So we get a^2 - b^2. But since both a and b are real numbers, so is
(a^2 + b^2).
(Psi)(r, t)
can be
visualized as a wave when we plot it on a graph,
Do you know the trig functions, sine, cosine, and tangent? That would be helpful.
>
nothing to do with wave-like behavior of the quantum itself.
something like a photon;
You're right, the mathematical function has no power to reach out and change the material world. But it describes the material world. When we say that the Earth is (roughly) a sphere, we are using the mathematical notion of sphere to (partially) describe a material object. The mathematical wave function describes the physical wave-function, which in turn determines the probabilities of specific, concrete events. The physical wave-function is not something that is visible, but it is nevertheless real. A coin is either fair or biased; that is a real feature of the coin. It is also a matter of probabilities. Probabilities aren't something you can see or touch, but they are still real. If you play Russian Roulette often enough, you will die. In my "Quantum Theory" bot, Elena uses the metaphor that the physical wave function is an inaudible song to which the universe dances.
implicit meaning it’s a factor used in the formula (or a characteristic of a factor)? Or implicit in that momentum is a characteristic of the wave function itself?
Of course, all this stuff about music and dance is only a metaphor, but it may be helpful.
Walk in Beauty, Irina
A wave function is a linear combination of such solutions superimposed, that defines the wave-state over time.
Thanks for staying awake for this.
So what I was calling "mathematical wave" is a wave equation, and the set of all wave equations for a given probability of instance (photon/quantum) at a certain time is a wave function and looks like a line. Psi is the wave function the applies to quantum/photons. It will share the characteristics of all wave functions by definition. It will also have it's own unique characteristics that make it psi. Then wave function psi for a given quantum should not move or change, because it already includes all possible wave equations for that quantum, right? But once that quantum is measured again we have a whole new set of wave equations and one could say that the psi has changed, relative to the last time we calculated it.
Bev (4092): I think the part you have written in red contains errors. But to tell the truth, I am too tired right now to deal with it! Tomorrow, tomorrow, ...
Oh yes I am.
Irina, you have created a wonderful thing, without even knowing it. It's crazier than a box of frogs, but it's very beautiful nonetheless.
I believe the Irinaverse contains nothing but the most concise practical proof of its own non-existence that it is possible to construct.
By conflating every last quantum into psi, you have produced a perfectly self-referential description of itself to the exclusion of anything else. A map of that same map, with no terrain.
The more I think about it, the more beautiful I think the paradox is. And if I can ever figure out the math to hide the illegal operations neatly, like Escher hides his violated perspectives, I am going to print the equations on a T-shirt and wear it with pride!
You accept this now? Oh no - that will ruin the Irinaverse's perfect self-reference!
Irina,
I tell you what: give me a reference for the claims you say that Penrose is making: book and page numbers. That way I can get the book, see them in context, and then respond to them.
The Road to Reality: A Complete Guide to the Laws of the Universe
http://www.amazon.co.uk/Road-Reality-Complete-Guide-Universe/dp/0099440687/
It was a bargain at £15. At £8.99 on amazon, it's frankly a steal.
In this way I can, for example, satisfy myself about whether he might be using words in a different sense thatn I am used to.
He uses them in the same sense that most other quantum physicists I have read do. How you interpret them is another question, and not one I can answer.
I can also see whether he is talking about mainstream QM or about one of his far-out theories like quantum Gravity, etc..
I believe it was page 516 or 519 I quoted from, but the whole chapter is just as relevant - quantum basics. I think the Quantum Gravity chapter's a few hundred pages further on.
The Road to Reality: A Complete Guide to the Laws of the Universe
It was a bargain at £15. At £8.99 on amazon, it's frankly a steal.
He uses them in the same sense that most other quantum physicists I have read do. How you interpret them is another question, and not one I can answer.
I believe it was page 516 or 519 I quoted from, but the whole chapter is just as relevant - quantum basics. I think the Quantum Gravity chapter's a few hundred pages further on.
Enough to know I wouldn't know enough to dispense with professional representation if I ever got involved in it 
Not much - I think I can tell the difference between contracts and invitations to treat, contracts in law and contracts in fact, and spot a collateral contract without it having to bite me in the butt. That's about it.
Oh yes, and I believe it's all very different in the US, but I don't really know how. Verbal contracts are unenforceable there?
Not much - I think I can tell the difference between contracts and invitations to treat, contracts in law and contracts in fact, and spot a collateral contract without it having to bite me in the butt. That's about it.
Oh yes, and I believe it's all very different in the US, but I don't really know how. Verbal contracts are unenforceable there?
If they can't get next weeks weather right how should I believe that global warming is really happening?
Also here is the truth about ethanol. There's not nearly as much energy in ethanol as there is in gasoline. producing corn and processing it into 1 gallon of ethanol requires 131,000 BTUs of energy; but 1 gallon of ethanol contains only 77,000 BTUs. So producing ethanol actually creates a net energy loss. And since farmers are using fossil-fuel-powered equipment to plant, maintain and harvest the corn and are using fossil-fuel-powered machinery to process that corn into ethanol and then transport that ethanol to collection points (ethanol can't run in underground pipelines because it picks up damaging impurities), the ethanol industry is actually burning large amounts of gasoline to produce ethanol, and that ethanol contains far less energy than the gasoline they consumed to produce it.
To make significant amounts of energy from food crops would deplete the amount of land available for growing actual food for people to eat.
Isn't it better to help out a good cause like saving starving children than something we aren't really sure is happening.
-http://auto.howstuffworks.com/ethanol-facts.htm
To make significant amounts of energy from food crops would deplete the amount of land available for growing actual food for people to eat.
Isn't it better to help out a good cause like saving starving children than something we aren't really sure is happening.
-http://auto.howstuffworks.com/ethanol-facts.htm
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