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 4,111 - 4,122 of 6,170
Oh and just to make Irina happy, we should both be saying "oral contract" not "verbal contract" (written contracts involve words too, though I know what you meant and used the same term the same way);
Very true - sorry, sloppy expression.
and I have no doubt you are involved in contracts all the time without legal representation you just don't think about it
True - but I haven't yet found myself needing legal representation in the acceptance of an offer to treat during the purchase of groceries. In this ever more litigious age, of course, that day may yet come
I'll get back to your latest QM post when (if!) I ever get round to getting some sleep - sorry, my brain packed up and shipped out some time ago.
I would only believe this theory if someone told me some science behind it rather than just numbers and data. Try this NASA link nasa.gov/ftp_docs/Global_Warming.pdf
Posts 4,111 - 4,122 of 6,170
Very true - sorry, sloppy expression.
True - but I haven't yet found myself needing legal representation in the acceptance of an offer to treat during the purchase of groceries. In this ever more litigious age, of course, that day may yet come
I'll get back to your latest QM post when (if!) I ever get round to getting some sleep - sorry, my brain packed up and shipped out some time ago.
'Twas only a joke, Bev. I have every confidence in your good judgement, self-control, and general savoir faire.
Oh, and just to make you feel very good, Coolchimpk, I just saw this on a general law site: Is Global Warming the Hot New Litigation Frontier? http://www.law.com/jsp/article.jsp?id=1173625811180&rss=newswire
I should have phraseed that better. By science I mean I want to see how the CO2 reacts with the ozone layer. I lot of times when you see enviromentalists on TV they don't even explain how it works.
Prob123: I believe that global warming is happening I just don't necesarily believe humans are causing it. There are many bigger things that could be a factor; The fact that we are still in a thaw from the last iceage,the sun's life cycle and possibly natural occurences contribute. Mt.St.Helens released energy equivalent to 27,000 atomic blasts over Hiroshima.
Also, 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.
Prob123: I believe that global warming is happening I just don't necesarily believe humans are causing it. There are many bigger things that could be a factor; The fact that we are still in a thaw from the last iceage,the sun's life cycle and possibly natural occurences contribute. Mt.St.Helens released energy equivalent to 27,000 atomic blasts over Hiroshima.
Also, 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.
CO2 does not react with the Ozone layer (that I know of). It traps heat in the earth's atmosphere. i.e. less of the heat radiates back out into space.
CFC's, HCFC's, and some others react with the ozone layer, which is actually on the mend (from what I've read recently). The ozone layer blocks some of the harmful UV from the sun (which causes skin cancer, and tends to bounce back as heat, and then get trapped by extra CO2 and other greenhouse gases).
CFC's, HCFC's, and some others react with the ozone layer, which is actually on the mend (from what I've read recently). The ozone layer blocks some of the harmful UV from the sun (which causes skin cancer, and tends to bounce back as heat, and then get trapped by extra CO2 and other greenhouse gases).
For info on what greenhouse gases are and why they increase heat: http://en.wikipedia.org/wiki/Greenhouse_effect#The_greenhouse_gases
For how CFC's destroy ozone:http://en.wikipedia.org/wiki/Ozone_depletion#Ozone_cycle_overview
For how CFC's destroy ozone:
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
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