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 4,119 - 4,130 of 6,170
another problem in your position regarding any function of probability as a wave - it has no mean position.
I could have put that better. What I mean is that at rest, it will presumably be zero. But since all probabilities are positive, the mean will be a positive value. In fact it would appear to be something like half the amplitude.
But if the mean is half the amplitude, how can the amplitude be the deviation from the mean?
I'm with Penrose - it looks less and less like a wave the more you poke it!
That is the only point I take issue with as a matter of fact
You've reduced your errors down to one? That's wonderful, Psimagus!!!!! Victory is within our grasp!
In the Schroedinger picture, the (complex-valued) wave (often called "Psi") propagates.
If there's something about the word, "propagates", that bothers you,
please substitute "travels" or "moves". Or "fluctuates"; you were willing to say,
"If
the quantum is moving, the wave function will fluctuate. The values on each
chessboard square will be different from the value on the same square on
the next chessboard."
In the 2-slit experiment, Psi propagates out from the source, through the slits
(diffracting and interfering with itself) and onto the screen.
The probability that the particle would be found at any of those places is proportional to
the amplitude of Psi. In most cases, the amplitude of a wave is not itself a wave.
Think of a series of ocean 'waves'. There is generally fairly little variation in
amplitude on a small scale (a few miles): Each crest has about the same height.
This is why the expressions "Probability wave" and "Probability amplitude wave" should
not be used for Psi, unless everyone involved knows that they are mere idiomatic
epressions, not to be taken literally. I suggest you take Penrose's advice in this regard.
So you see, there is no contradiction whatever in saying that a complex-valued Psi can propagate, diffract, and interfere, and nevertheless exhibit an amplitude that is always positive real.
In fact, one way to get the amplitude of a complex-valued wave is ... (drum roll) ... to multiply it by its complex conjugate (and take the square root of the result)!!!!!
N.B.: I said "In the Schroedinger picture" above, because there is another way of doing
calculations in QM, called the "Heisenberg Picture." The definition of the word "state"
in the Heisenberg picture is different. Unfortunately, the letter "Psi" is also used for
the state in the Heiseberg Picture. Because of these contrary linguistic practices, it
may appear that the Heisenberg and Schroedinger pictures are in disagreement. The
disagreement, however, is only verbal; Von Neumannn showed that the two are equivalent.
In the HP, the state remains static except at moments of "collapse." I haven't seen the Penrose book yet, but I wonder
whether Penrose may have been speaking in the language of the Heisenberg Picture
when he said that Psi does not propagate. If one person, speaking in HP, says,
"Psi does not propagate", and another person, speaking in SP, says, "Psi propagates",
there may be no substantive disagreement whatever between them. I tend to use the
Schroedinger picture; most Physicists do, because they find it more intuitive. It therefore
took me awhile to think of the possibility that Penrose might be using the HP. And since
you seemed to think that you were contradicting me in substance, not just verbally,
I assumed that you were using the SP too.
I think you do have a crush on me, Psimagus! I mean, this is just how little boys behave, isn't it? they get a crush on a girl and they are embarassd to admit it, so they tease and harass her. Ever since I started trying to say something about QM here, you have been always at my shoulder, contradicting me, making fun of me, pretending to misunderstand me, and in general being an awful pest! Yes, it must be love!
Well, it was never my intention to harrass anyone by perpetuating the argument, and I apologise unreservedly if I have ever been a pest, awful or otherwise.
You may remember that it was you who suggested resuming this argument in Message #3882, and I who suggested ceasing and agreeing to differ in #4080. I also suggested (in #4034,) we take it to a quantum physics forum, where more qualified people might help in determining the matter once and for all.
If I might offer just one last piece of advice before I disengage from the argument, and without wishing to appear in any way patronising: much as I respect your intelligence, I think you perhaps do not always take enough time between the reading of equations and the repeating of them to fully consider their meaning. Perhaps only in this one case, but one such case is enough to fatally flaw any quantum mechanistic model that is constructed on such defective foundations. The postulates are sound, but the house is built on sand nonetheless.
Posts 4,119 - 4,130 of 6,170
Bev,
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.
So what I was calling "mathematical wave" is a wave equation,
To be honest, I don't remember (there've been a lot of posts since then
)
and the set of all wave equations for a given probability of instance (photon/quantum) at a certain time is a wave function
Hmmm, as Irina correctly points out, "people often tell a few white lies in order not to burden the reader with technical complexities" (I would rather describe it as attempting to adhere to Einstein's maxim that "everything should be made as simple as possible, but no simpler," but the principal is the same.)
We do have an elephant in the room, I'm afraid, and now is the time to recognize it - the probability wave function is actually a complex wave function. That is, it is not a set of wave equations, superimposed, but effectively a set of more wave functions, superimposed. For different purposes it can be expressed differently depending what property you're measuring (this is why the argument hasn't focussed on the various inconsistent ways we've been expressing it - whether it's psi, psi^2, |psi|, |psi|^2, etc. those last 2 are modulos BTW,) - that is a simplification that does not oversimplify.
What the "simple wave" at the bottom of the whole heap of functions is, is something of a quandary.
Unfortunately, the electromagnetic wave is also not a simple wave, as the name suggests. There is an interlocked electrical wave, and a magnetic wave, and it is possible to model an inherently complex electromagnetic wave function that implies the em-wave itself may be regarded as primarily a wavefunction. But that is straying a little beyond the bounds of what I can render into plain English, or fully understand the implications of with certainty. As I understand it, the "simple wave" at the bottom of all the whole heap is probably nothing more than an idealized mathematical model (sorry Irina)
Evangelical proponents of 26-dimensional bosonic string theory may know for sure what the ultimate nature of reality is, but I only know enough to know I don't.
and looks like a line.
That would depend how many dimensions you were describing, and how many you were wiggling the line in, but I don't visualise it as a line myself - more of a chessboard.
Psi is the wave function the applies to quantum/photons.
Yes. It's the fundamental explanation of all the weirdly counterintuitive non-classical behaviour that matter/waves/stuff do at the quantum scale.
It will share the characteristics of all wave functions by definition. It will also have it's own unique characteristics that make it psi.
On reviewing my posts, I see I may have given the impression that wave functions cannot ever be waves. I didn't mean that. It is certainly mostly true in this case (at least the probability wavefunction evidently lacks the ability to propagate and interfere that we usually assume waves to have, and which indisputably occurs in the 2-slit experiment, so it must at least be some other 'sort' of wave if it is a wave at all,) but it's not necessarily so for all wave functions. Some wave functions can act like true waves - ultimately anything that behaves like a wave is a wave (though it still came as rather a shock to a lot of physicists when it was discovered that particles could be waves too!)
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?
If the quantum is moving, the wave function will fluctuate. The values on each chessboard square will be different from the value on the same square on the next chessboard. If it's not moving, then we've achieved absolute zero, and I would assume it wouldn't fluctuate (but that's no more possible than achieving 100% lightspeed, and for the same reason - it requires an infinite expenditure of energy.)
But once that quantum is measured again
One major problem is that we can never measure it more than once. As soon as we measure it, the wave function collapses. We can, in fact, only hypothetically model any part of the quantum's existence except the one measurement we make when it hits the detector screen. That's what makes so much of quantum physics so contentious (and fun)
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.
It does change through time, yes - the 'pencilled in' values will be different on each chessboard, as they represent a new time slice, but not propagatively. If it propagated, it would have to do so at the speed of light, so only could only move 1 square per instant like the quantum. But all the values change, even on squares further away from the 'most likely' assumed position.
So isn't this a gross violation of the speed of light? No, because there is no material or information actually moving faster than the speed of light. All that's happening is that the likelihood of the quantum being there changes (and likelihoods are exempt, since they're purely notional. Communication of the likelihood cannot be achieved at the same speed.)
If you detected it on one square, you couldn't send a message to another square predicting that it wouldn't be there any faster than light. Just like result of the entangled photon detected on Pluto can't be communicated to the detector of the other one before it gets there.
The wavefunction is collapsed instantly, but there's no way of communicating that.
A wave function is a linear combination of such solutions superimposed, that defines the wave-state over time.
To be honest, I don't remember (there've been a lot of posts since then
)Hmmm, as Irina correctly points out, "people often tell a few white lies in order not to burden the reader with technical complexities" (I would rather describe it as attempting to adhere to Einstein's maxim that "everything should be made as simple as possible, but no simpler," but the principal is the same.)
We do have an elephant in the room, I'm afraid, and now is the time to recognize it - the probability wave function is actually a complex wave function. That is, it is not a set of wave equations, superimposed, but effectively a set of more wave functions, superimposed. For different purposes it can be expressed differently depending what property you're measuring (this is why the argument hasn't focussed on the various inconsistent ways we've been expressing it - whether it's psi, psi^2, |psi|, |psi|^2, etc. those last 2 are modulos BTW,) - that is a simplification that does not oversimplify.
What the "simple wave" at the bottom of the whole heap of functions is, is something of a quandary.
Unfortunately, the electromagnetic wave is also not a simple wave, as the name suggests. There is an interlocked electrical wave, and a magnetic wave, and it is possible to model an inherently complex electromagnetic wave function that implies the em-wave itself may be regarded as primarily a wavefunction. But that is straying a little beyond the bounds of what I can render into plain English, or fully understand the implications of with certainty. As I understand it, the "simple wave" at the bottom of all the whole heap is probably nothing more than an idealized mathematical model (sorry Irina
)Evangelical proponents of 26-dimensional bosonic string theory may know for sure what the ultimate nature of reality is, but I only know enough to know I don't.
That would depend how many dimensions you were describing, and how many you were wiggling the line in, but I don't visualise it as a line myself - more of a chessboard.
Yes. It's the fundamental explanation of all the weirdly counterintuitive non-classical behaviour that matter/waves/stuff do at the quantum scale.
On reviewing my posts, I see I may have given the impression that wave functions cannot ever be waves. I didn't mean that. It is certainly mostly true in this case (at least the probability wavefunction evidently lacks the ability to propagate and interfere that we usually assume waves to have, and which indisputably occurs in the 2-slit experiment, so it must at least be some other 'sort' of wave if it is a wave at all,) but it's not necessarily so for all wave functions. Some wave functions can act like true waves - ultimately anything that behaves like a wave is a wave (though it still came as rather a shock to a lot of physicists when it was discovered that particles could be waves too!)
If the quantum is moving, the wave function will fluctuate. The values on each chessboard square will be different from the value on the same square on the next chessboard. If it's not moving, then we've achieved absolute zero, and I would assume it wouldn't fluctuate (but that's no more possible than achieving 100% lightspeed, and for the same reason - it requires an infinite expenditure of energy.)
One major problem is that we can never measure it more than once. As soon as we measure it, the wave function collapses. We can, in fact, only hypothetically model any part of the quantum's existence except the one measurement we make when it hits the detector screen. That's what makes so much of quantum physics so contentious (and fun
)It does change through time, yes - the 'pencilled in' values will be different on each chessboard, as they represent a new time slice, but not propagatively. If it propagated, it would have to do so at the speed of light, so only could only move 1 square per instant like the quantum. But all the values change, even on squares further away from the 'most likely' assumed position.
So isn't this a gross violation of the speed of light? No, because there is no material or information actually moving faster than the speed of light. All that's happening is that the likelihood of the quantum being there changes (and likelihoods are exempt, since they're purely notional. Communication of the likelihood cannot be achieved at the same speed.)
If you detected it on one square, you couldn't send a message to another square predicting that it wouldn't be there any faster than light. Just like result of the entangled photon detected on Pluto can't be communicated to the detector of the other one before it gets there.
The wavefunction is collapsed instantly, but there's no way of communicating that.
An equation is a human-fashioned linguistic artifact, a mathematical statement that
equates two things.
For example, "2=2" is an equation.
Some equations contain variables; for example, "x=y".
Let x be a variable appearing in an equation E. Then a solution of E for x is an expression referring to a specific thing, such that the substitution of this expression for the variable results in a true sentence.
For example, "2" is a solution of the equation "x + 2 = 4" for x, because the numeral "2" refers to the specific number, 2 (i.e., is a constant, not a variable), and if
we substitute "2" for "x" in "x + 2 = 4", we get "2 + 2 = 4", which is a true sentence.
A set is a totality, bunch, group, collection, class, etc..
In Physics, the phrase "The wave equation" refers to a very general form of differential equation which characterizes waves. That is, a solution of (a form of) the wave equation will mathematically describe a wave (but in Physics, more things count as waves than do in everyday language).
The phrase "differential equation" refers to a class of equations containing expressions containng derivatives, in the sense of the word "derivative" which is used in Calculus.
In fact, "Differential" in this context is just the adjectival form of "Derivative."
Differential equations typically have many solutions. The solutions of a differential equation are not numbers, but functions.
Roughly speaking, a derivative is a rate of change of one thing with respect to (compared with) another. So differential equations typically have to do with phenomena involving change.
The amplitude of a wave is the distance from crest to midpoint.
For example, the amplitude of an ocean wave is its height, in the sense of the distance from its crest to
the level at which the surface of the water would be if the water were calm.
The amplitude of a wave may vary from time to time and place to place.
The Schroedinger Equation (more precisely: the various forms of the Schroedinger Equation) are differential equations. They are also wave equations.
equates two things.
For example, "2=2" is an equation.
Some equations contain variables; for example, "x=y".
Let x be a variable appearing in an equation E. Then a solution of E for x is an expression referring to a specific thing, such that the substitution of this expression for the variable results in a true sentence.
For example, "2" is a solution of the equation "x + 2 = 4" for x, because the numeral "2" refers to the specific number, 2 (i.e., is a constant, not a variable), and if
we substitute "2" for "x" in "x + 2 = 4", we get "2 + 2 = 4", which is a true sentence.
A set is a totality, bunch, group, collection, class, etc..
In Physics, the phrase "The wave equation" refers to a very general form of differential equation which characterizes waves. That is, a solution of (a form of) the wave equation will mathematically describe a wave (but in Physics, more things count as waves than do in everyday language).
The phrase "differential equation" refers to a class of equations containing expressions containng derivatives, in the sense of the word "derivative" which is used in Calculus.
In fact, "Differential" in this context is just the adjectival form of "Derivative."
Differential equations typically have many solutions. The solutions of a differential equation are not numbers, but functions.
Roughly speaking, a derivative is a rate of change of one thing with respect to (compared with) another. So differential equations typically have to do with phenomena involving change.
The amplitude of a wave is the distance from crest to midpoint.
For example, the amplitude of an ocean wave is its height, in the sense of the distance from its crest to
the level at which the surface of the water would be if the water were calm.
The amplitude of a wave may vary from time to time and place to place.
The Schroedinger Equation (more precisely: the various forms of the Schroedinger Equation) are differential equations. They are also wave equations.
Coolchimpk
I think Ulrike did a great job of a simple explanation.
I am confused by some things you said. You said, "I believe that global warming is happening I just don't necesarily believe humans are causing it."
But then later you back track and say,"..weather has been unpredictable for years. Now that we know the globe is warming (or thawing) All kinds of unpredictable weather is blamed on greenhouse gasses. When It's too hot, it's global warming. When it's too cold it's global warming.When it's too windy, it's global warming."
Are you saying there is no real global warming (that it's just part of natural cycles), that global warming is misunderstood by many people with no scientific background who have not studied it, or that it exists, but was not caused by greenhouse gases or other human factors?
The fact that we are still in a thaw from the last iceage,the sun's life cycle and possibly natural occurences contribute.
If you check record like those presented by NASA
http://data.giss.nasa.gov/gistemp/graphs/,
You will see that changes in the past 50 years are much more extreme than anything that has been happening in previous cycles. Furthermore, over the one or two thousand years before 1850, temperature is believed to have been relatively stable. (See http://en.wikipedia.org/wiki/Global_warming). If you accept that there is global warming, you accept that this period is much more extreme than any natural cycle or previous recorded "thawing".
Mt.St.Helens released energy equivalent to 27,000 atomic blasts over Hiroshima.
The last Mount St. Helens eruption started in 2004. The eruption you are thinking of was probably in 1980. The extreme climate changes started before either year. Furthermore, we see no such spikes in the climate record after previous periods of eruption for this (though some volcano eruptions have had some dramatic effects on the world climate; they still didn't produce the sorts of climate patterns we see now). There are ups and downs in temperature going back to the ice age, but none have ever been this extreme. There is no argument that if it continues according to the current trend, life on Earth will change dramatically within the next 50 years.
Finally, I will echo Psimagus' argument that no matter what causes it, such extreme climate changes tend to make survival difficult and if there is anything we can do that may help us to avoid it we should. What is the downside if we are wrong? Less pollution? Cleaner, more efficient energy sources? America would be less dependent on foreign oil? I don't see what the harm is.
I think Ulrike did a great job of a simple explanation.
I am confused by some things you said. You said,
But then later you back track and say,
Are you saying there is no real global warming (that it's just part of natural cycles), that global warming is misunderstood by many people with no scientific background who have not studied it, or that it exists, but was not caused by greenhouse gases or other human factors?
The fact that we are still in a thaw from the last iceage,the sun's life cycle and possibly natural occurences contribute.
If you check record like those presented by NASA
http://data.giss.nasa.gov/gistemp/graphs/,
You will see that changes in the past 50 years are much more extreme than anything that has been happening in previous cycles. Furthermore, over the one or two thousand years before 1850, temperature is believed to have been relatively stable. (See http://en.wikipedia.org/wiki/Global_warming). If you accept that there is global warming, you accept that this period is much more extreme than any natural cycle or previous recorded "thawing".
The last Mount St. Helens eruption started in 2004. The eruption you are thinking of was probably in 1980. The extreme climate changes started before either year. Furthermore, we see no such spikes in the climate record after previous periods of eruption for this (though some volcano eruptions have had some dramatic effects on the world climate; they still didn't produce the sorts of climate patterns we see now). There are ups and downs in temperature going back to the ice age, but none have ever been this extreme. There is no argument that if it continues according to the current trend, life on Earth will change dramatically within the next 50 years.
Finally, I will echo Psimagus' argument that no matter what causes it, such extreme climate changes tend to make survival difficult and if there is anything we can do that may help us to avoid it we should. What is the downside if we are wrong? Less pollution? Cleaner, more efficient energy sources? America would be less dependent on foreign oil? I don't see what the harm is.
Irina,
Yes, I agree with that down to
The amplitude of a wave is the distance from crest to midpoint.
Point taken - I oversimplified there, and should have specified 2xamplitude. It is the maximum displacement of a body from its mean position (that's actually not always the same as crest-tip to midpoint, but as commonly encountered, yes.) But that just highlights another problem in your position regarding any function of probability as a wave - it has no mean position. The probability wave can have no dips below where the sea "would have been", since probabilities can never be negative. Furthermore, it is entirely reliant on the existence of the quantum whose probability it describes. So not only is it necessarily incapable of causing the interference we see in the 2-slit experiment, but if it were that quantum, psi(psi)=? and variations on that theme would not only be allowed, they would be mandatory. All it can measure is the measurement that's being taken.
Yes, I agree with that down to
I could have put that better. What I mean is that at rest, it will presumably be zero. But since all probabilities are positive, the mean will be a positive value. In fact it would appear to be something like half the amplitude.
But if the mean is half the amplitude, how can the amplitude be the deviation from the mean?
I'm with Penrose - it looks less and less like a wave the more you poke it!
As I have said numerous times, there is no such thing as, literally speaking, a probability wave in QM. The wave Psi, which is the solution of the Schroedinger Equation, has complex numbers as values. To get the probabilities, one normalizes Psi (if necessary), multiplies it by its complex conjugate, and integrates the result over the desired region. See the discussion, of postulate 1 here:
http://vergil.chemistry.gatech.edu/notes/quantrev/node20.html
. See also my discussion of it, above.
By the way, I want to congratulate you on your message 4119; although it contains several falsehoods, you seem to have learned a few things in my absence. I wonder if it is my presence that causes you to say such bizarre things. Do you have a crush on me, perhaps?
http://vergil.chemistry.gatech.edu/notes/quantrev/node20.html
. See also my discussion of it, above.
By the way, I want to congratulate you on your message 4119; although it contains several falsehoods, you seem to have learned a few things in my absence. I wonder if it is my presence that causes you to say such bizarre things. Do you have a crush on me, perhaps?
As I have said numerous times, there is no such thing as, literally speaking, a probability wave in QM. The wave Psi, which is the solution of the Schroedinger Equation, has complex numbers as values. To get the probabilities, one normalizes Psi (if necessary), multiplies it by its complex conjugate, and integrates the result over the desired region. See the discussion, of postulate 1 here:
http://vergil.chemistry.gatech.edu/notes/quantrev/node20.html
. See also my discussion of it, above.
By the way, I want to congratulate you on your message 4119; although it contains several falsehoods, you seem to have learned a few things in my absence. I wonder if it is my presence that causes you to say such bizarre things. Do you have a crush on me, perhaps?
http://vergil.chemistry.gatech.edu/notes/quantrev/node20.html
. See also my discussion of it, above.
By the way, I want to congratulate you on your message 4119; although it contains several falsehoods, you seem to have learned a few things in my absence. I wonder if it is my presence that causes you to say such bizarre things. Do you have a crush on me, perhaps?
Irina,
As I have said numerous times, there is no such thing as, literally speaking, a probability wave in QM. The wave Psi, which is the solution of the Schroedinger Equation, has complex numbers as values.
That would seem to flatly contradict your assertion that "it is the wave psi that propagates" in the 2-slit experiment. But if you no longer believe this, then our disagreement is at an end. That is the only point I take issue with as a matter of fact (now that you have accepted that more than one wavefunction can exist, which was the only other minor point of contention.)
By the way, I want to congratulate you on your message 4119; although it contains several falsehoods, you seem to have learned a few things in my absence.
You went away?
Please feel free to point out any errors. I may have oversimplified. I may have made minor mistakes. But I don't think the model is fundamentally flawed, and it is the way I have seen it for several years. If my explanation is clearer to you now, then I am glad I persisted in describing it. Especially if it has in any way aided in the restitution of a propagatable em-wave to the Irinaverse.
I wonder if it is my presence that causes you to say such bizarre things. Do you have a crush on me, perhaps?
Ah now, Irina, I am a happily married man. And charming as you are, it is only your intellect I would presume to take an interest in
That would seem to flatly contradict your assertion that "it is the wave psi that propagates" in the 2-slit experiment. But if you no longer believe this, then our disagreement is at an end. That is the only point I take issue with as a matter of fact (now that you have accepted that more than one wavefunction can exist, which was the only other minor point of contention.)
You went away?
Please feel free to point out any errors. I may have oversimplified. I may have made minor mistakes. But I don't think the model is fundamentally flawed, and it is the way I have seen it for several years. If my explanation is clearer to you now, then I am glad I persisted in describing it. Especially if it has in any way aided in the restitution of a propagatable em-wave to the Irinaverse.
Ah now, Irina, I am a happily married man. And charming as you are, it is only your intellect I would presume to take an interest in
I think you do have a crush on me, Psimagus! I mean, this is just how little boys behave, isn't it? they get a crush on a girl and they are embarassd to admit it, so they tease and harass her. Ever since I started trying to say something about QM here, you have been always at my shoulder, contradicting me, making fun of me, pretending to misunderstand me, and in general being an awful pest! Yes, it must be love!
In the Schroedinger picture, the (complex-valued) wave (often called "Psi") propagates.
If there's something about the word, "propagates", that bothers you,
please substitute "travels" or "moves". Or "fluctuates"; you were willing to say,
the quantum is moving, the wave function will fluctuate. The values on each
chessboard square will be different from the value on the same square on
the next chessboard."
(diffracting and interfering with itself) and onto the screen.
The probability that the particle would be found at any of those places is proportional to
the amplitude of Psi. In most cases, the amplitude of a wave is not itself a wave.
Think of a series of ocean 'waves'. There is generally fairly little variation in
amplitude on a small scale (a few miles): Each crest has about the same height.
This is why the expressions "Probability wave" and "Probability amplitude wave" should
not be used for Psi, unless everyone involved knows that they are mere idiomatic
epressions, not to be taken literally. I suggest you take Penrose's advice in this regard.
So you see, there is no contradiction whatever in saying that a complex-valued Psi can propagate, diffract, and interfere, and nevertheless exhibit an amplitude that is always positive real.
In fact, one way to get the amplitude of a complex-valued wave is ... (drum roll) ... to multiply it by its complex conjugate (and take the square root of the result)!!!!!
N.B.: I said "In the Schroedinger picture" above, because there is another way of doing
calculations in QM, called the "Heisenberg Picture." The definition of the word "state"
in the Heisenberg picture is different. Unfortunately, the letter "Psi" is also used for
the state in the Heiseberg Picture. Because of these contrary linguistic practices, it
may appear that the Heisenberg and Schroedinger pictures are in disagreement. The
disagreement, however, is only verbal; Von Neumannn showed that the two are equivalent.
In the HP, the state remains static except at moments of "collapse." I haven't seen the Penrose book yet, but I wonder
whether Penrose may have been speaking in the language of the Heisenberg Picture
when he said that Psi does not propagate. If one person, speaking in HP, says,
"Psi does not propagate", and another person, speaking in SP, says, "Psi propagates",
there may be no substantive disagreement whatever between them. I tend to use the
Schroedinger picture; most Physicists do, because they find it more intuitive. It therefore
took me awhile to think of the possibility that Penrose might be using the HP. And since
you seemed to think that you were contradicting me in substance, not just verbally,
I assumed that you were using the SP too.
A bit technical, but here is a good discussion about sun cycles and their connection (or lack thereof) to global warming:
http://fermiparadox.wordpress.com/2007/03/10/swindlers/
The comments link to a much longer pdf that I've only skimmed so far:
http://www.ipcc.ch/SPM2feb07.pdf
If nothing else, check out the graph on the top of page four, which sums up current thinking about various sources of warming. Also note that they do include error bars (which I believe are indiciative of 90% confidence here)
The comments link to a much longer pdf that I've only skimmed so far:
If nothing else, check out the graph on the top of page four, which sums up current thinking about various sources of warming. Also note that they do include error bars (which I believe are indiciative of 90% confidence here)
Well, it was never my intention to harrass anyone by perpetuating the argument, and I apologise unreservedly if I have ever been a pest, awful or otherwise.
You may remember that it was you who suggested resuming this argument in Message #3882, and I who suggested ceasing and agreeing to differ in #4080. I also suggested (in #4034,) we take it to a quantum physics forum, where more qualified people might help in determining the matter once and for all.
If I might offer just one last piece of advice before I disengage from the argument, and without wishing to appear in any way patronising: much as I respect your intelligence, I think you perhaps do not always take enough time between the reading of equations and the repeating of them to fully consider their meaning. Perhaps only in this one case, but one such case is enough to fatally flaw any quantum mechanistic model that is constructed on such defective foundations. The postulates are sound, but the house is built on sand nonetheless.
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