Misleading Phrase: Collapse of wave function

[Billy T]

This is "point-particle thinking", and IMHO it's the source of a lot of problems. ...

I certainly do not think of photons as points or very tiny balls of energy. I have measured some, and posted several times how I did that. (With a Mach Zehner interferometer whose two paths were increasingly different and watching the interference pattern “wash out.”) The path difference was 35cm when it first completely did. Crudely: the part of the single photon going the longer path then arrived at the screen too late to interfere with its self going the shorter path.)

I have also noted that when the transition probability is low* they can be much longer. For example the green photons, very prominent in the Northern Lights are several meters long. They come from a first order forbidden transition of the oxygen atom. In the extremly rarified gas they come from, they can "wait around" to radiatively decay from the upper state, without being transfered to the lower state during a collision. They can not thus be produced in the lab with observable intensity - the highly evacuuated "lab" would need to much larger than a foot ball stadium.

I have in essence made a campaign trying to get people here to stop thinking of photons as tiny energy balls.

* When they were emitted is very uncertain. I. e. the “Delta T” is extraordinary large and correspondingly, their “Delta E” is extremely small. Fourier tells you that for an EM wave to have extremely precisely defined energy, it must have a very large number of cycles – I. e. be unusually long.

 

[krash661]

This is "point-particle thinking", and IMHO it's the source of a lot of problems. If you remember that we're dealing with quantum field theory rather than quantum point-particle theory, you can soon start thinking of a photon as something more like a seismic wave than a billiard ball. It doesn't have any surface, it takes many-paths. When you then put it through pair production to create an electron (and a positron) the electron still isn't some little billiard-ball thing. It isn't some little round thing that has a field. It is field, this field has a spherical symmetry, and it doesn't have a surface.

if billiard balls are built up then the billiard balls will build into a field. simply putting the balls in its rack should have shown you that.

 

[QuarkHead]

we're dealing with quantum field theory rather than quantum point-particle theory,

This gibberish shows you have no idea what a field is - no sane person would equate a field with a point-particle any more than thy would equate a field with a wave function. It makes no sense.

the electron ........isn't some little round thing that has a field. It is field,

This makes no sense - tell us what you think a field is

this field has a spherical symmetry, and it doesn't have a surface.

No field has any sort of symmetry or surface. Tell us what you think a field is

 

[Fednis48]

This gibberish shows you have no idea what a field is - no sane person would equate a field with a point-particle any more than thy would equate a field with a wave function.

For what it's worth, Farsight actually does equate the field with the wavefunction.

 

[Farsight]

This gibberish shows you have no idea what a field is - no sane person would equate a field with a point-particle any more than thy would equate a field with a wave function. It makes no sense.This makes no sense - tell us what you think a field is No field has any sort of symmetry or surface. Tell us what you think a field is

I think a field is a state of space. Usually a non-uniform state of space. See this article where Einstein said this:

"This theory having brought together the metric and gravitation would have been completely satisfactory of the world had only gravitational fields and no electro-magnetic fields. Not it is true that the latter can be included within the general theory of relativity by taking over and appropriately modifying Maxwell's equations of the electro-magnetic field, but they do not then appear like the gravitational fields as structural properties of the space - time continuum, but as logically independent constructions. The two types of field are causally linked in this theory, but still not fused to an identity. It can, however, scarcely be imagined that empty space has conditions or states of two essentially different kinds, and it is natural to suspect that this only appears to be so because the structure of the physical continuum is not completely described by the Riemannian metric".

I don't think a field is some abstract thing that has one or more values at every point in space. Instead I think a gravitational field is a region of space that is "neither homogeneous not isotropic", and so on.

 

[Beer w/Straw]

I suck at pool. But what if, assuming we don't sink right in, we play a game of pool on Jupiter?

What difference?

:EDIT:

Maybe this is the wrong thread, I gotta' stop doing that, but the question still intrigues me.

 

[Farsight]

For what it's worth, Farsight actually does equate the field with the wavefunction.

See above. A field is typically some static state of space, whilst a wave is typically some dynamical state of space, propagating at c. However things get hazy in that a standing wave is associated with a standing field, and a Poynting vector. Regardless of that, I take my cue from the likes of Jeff Lundeen and associate the wavefunction with something real that's measureable in the lab. Such as the state of space, not with the square root of a probability density.

 

[Beer w/Straw]

Can you make a post without trying to preach.

There are those that want knowledge, you don't provide it.

 

[QuarkHead]

I think a field is a state of space.

Since the domain of this discussion is Quantum Mechanics, you should perhaps be a little wary of using the term "state" in your own way - in QM a state is extremely well-defined, and cannot be used the way you use it.

Moreover you don't specify what you mean by "space". The space of QM is an Hilbert space of square integrable functions, is this the space you are referring to?

Usually a non-uniform state of space.

Why non-uniform? Do you mean a field "usually" takes on different values at different points in whatever space you are referring to?

See this article where Einstein said this:

No thanks,it's not relevant

I don't think a field is some abstract thing that has one or more values at every point in space.

Neither does anyone else - a field, by definition, assigns a single value (scalar, vector, tensor,......) to each point in some chosen space

Instead I think a gravitational field is a region of space that is "neither homogeneous not isotropic", and so on.

And what has the gravitational field got to do with the present discussion?

PS I will explain your Einstein quote if you want - but you probably won't

 

[PhysBang]

I think a field is a state of space. Usually a non-uniform state of space. See this article where Einstein said this:

"This theory having brought together the metric and gravitation would have been completely satisfactory of the world had only gravitational fields and no electro-magnetic fields. Not it is true that the latter can be included within the general theory of relativity by taking over and appropriately modifying Maxwell's equations of the electro-magnetic field, but they do not then appear like the gravitational fields as structural properties of the space - time continuum, but as logically independent constructions. The two types of field are causally linked in this theory, but still not fused to an identity. It can, however, scarcely be imagined that empty space has conditions or states of two essentially different kinds, and it is natural to suspect that this only appears to be so because the structure of the physical continuum is not completely described by the Riemannian metric".

I don't think a field is some abstract thing that has one or more values at every point in space. Instead I think a gravitational field is a region of space that is "neither homogeneous not isotropic", and so on.

Yes, Farsight can cherry-pick a quotation out of Einstein without any regard for the science Einstein promoted or the science that the evidence supports. He will use this cherry-picked quotation regardless of whether it is correct and regardless of whether it is relevant to the topic at hand. All that matters is whether or not it contains enough words that Farsight can pretend it is relevant.

 

[PhysBang]

See above. A field is typically some static state of space, whilst a wave is typically some dynamical state of space, propagating at c.

No. A field can be static or not. Many people have pointed out to Farsight that "Static" has a specific definition, but Farsight does not care, because Farsight has abandoned learning. Farsight only cares about supporting the per-established conclusions to which Farsight has come. Look at the early versions of Farsight's book and at the later version to see all the errors not removed. The only error removed is one horrible prediction that he made that he cannot figure out how to reconcile, even though he has done nothing to repudiate the line of thinking that makes the prediction.

However things get hazy in that a standing wave is associated with a standing field, and a Poynting vector. Regardless of that, I take my cue from the likes of Jeff Lundeen and associate the wavefunction with something real that's measureable in the lab. Such as the state of space, not with the square root of a probability density.

Any theory of quantum mechanics that does not support the probability density is wrong.

 

[QuarkHead]

I .......... associate the wavefunction with something real that's measureable in the lab.

You are confused, but at least half right - this is a bit back-to-front.

Look, I know you distrust mathematics, but others may be interested.......

The state of a quantum system is described by a state function which, as shown by P.A.M. Dirac, is taken to be an element in a vector space of functions (called an Hilbert space - it's not the only Hilbert space, of course). In other words the state function is a vector. It is called a wave function because it takes on values in the Real interval [-1,1], just like a sine wave (for example). It incidentally takes no genius to see that the square of this function takes on values in the Real interval [0,1], as we might expect for any probability

In QM, the operators that act on this vector space - and all vector spaces admit of operators of one kind or another - I repeat that the operators acting on the QM vector space of functions are taken to be the measurables or observables of the quantum system in question.

And the actual measurements made on the system are the eigenvalues of whatever operator we have chosen. And, again as shown by Dirac (and others), these operators must be Hermitian, which have the property that all their eigenvalues are Real - a comforting fact, don't you think?.

 

[RJBeery]

The idea that the wave function "collapses" violates the conservation of information. It isn't an entropy issue (where information has simply been obfuscated) either; the information is theoretically gone. MWI suffers from the same problem even while denying a collapse. Once a measurement has been made on a quantum system there is simply no way to reverse processes to retrodict the prior state. This should deeply disturb anyone granting a physical relevance to the wave function.

 

[arfa brane]

The idea that the wave function "collapses" violates the conservation of information.

Not really, it's more that there is only half the information we expect.

It isn't an entropy issue (where information has simply been obfuscated) either; the information is theoretically gone.

What information? Send a single photon through a double slit, you see a dot on a screen. What's "gone"?

Once a measurement has been made on a quantum system there is simply no way to reverse processes to retrodict the prior state.

Although, "strangely", all quantum measurements need to be reversible even if you can't actually reverse them (by reversing the direction of time, say).

This should deeply disturb anyone granting a physical relevance to the wave function.

Well, it turns out the wavefunction can be given a physical relevance with the quantum Zeno effect.

 

[Billy T]

The idea that the wave function "collapses" violates the conservation of information. It isn't an entropy issue (where information has simply been obfuscated) either; the information is theoretically gone. MWI suffers from the same problem even while denying a collapse. Once a measurement has been made on a quantum system there is simply no way to reverse processes to retrodict the prior state. ...

No the total informtion remains unchanged. Perhaps this analogy will help you:

A spinning coin is falling towards the floor. Before land it is valid to say the information about it is 0.5 heads + 0.5 tails.
Same total information as after it lands (on the "floor operator" which collapses this mixed state into one of its eigenstates) with total information content of 1.0

 

[Billy T]

... The state of a quantum system is described by a state function which, as shown by P.A.M. Dirac, is taken to be an element in a vector space of functions (called an Hilbert space - it's not the only Hilbert space, of course). In other words the state function is a vector. ... [/B]

Perhaps or perhaps not on final part I made bold. It depends on if "vector" includes a matrix?

My first exposure to QM did not have any wave functions - the state functions were square (as I recall) matrices and the operators were a column matrix, which I grant could be called a "vector."

PS I did not want this all bold, but a change by sciforums more than a year ago, which I hate, no longer shows things like [.b]xyz[/.b], when you edit, so it is very hard to "unbold." I added a one of them at end of your post, and other things tried, but can not make my post not be bold.

 

[RJBeery]

No the total informtion remains unchanged. Perhaps this analogy will help you:

A spinning coin is falling towards the floor. Before land it is valid to say the information about it is 0.5 heads + 0.5 tails.
Same total information as after it lands (on the "floor operator" which collapses this mixed state into one of its eigenstates) with total information content of 1.0

This isn't true. We have information in the heat and noise pattern the coin imparted to the floor and surrounding air that allows us (classically) to reconstruct what came prior. In a classical sense there was no mixed state, ever, and both the future and the past could be calculated as the coin was falling. In QM, if we attribute physical significance to the wave function, then we are unable to reconstruct that wave function by a simple dot on a collector screen, for example. This is not a profound or controversial concept; QM may be fundamentally time-asymmetric in its current form. (Meaning, my assertion that QM is time-asymmetric is not controversial, but the asymmetry certainly should be!)

 

[QuarkHead]

My first exposure to QM did not have any wave functions - the state functions were square (as I recall) matrices and the operators were a column matrix, which I grant could be called a "vector."

Unfortunately, Billy, your recollection has let you down. Any operator has a representation as a square matrix, any vector has a representation as a column matrix.

Suppose A a 1 x n column matrix, and B a n x n square matrix. Then the matrix product AB is not defined, whereas the matrix product BA is another 1 x n column matrix as required and is easily calculated.

Interestingly (and irrelevantly), an early exercise in any linear algebra course is to prove that the set of all operators acting on a finite-dimensional vector space is itself a vector space of the same dimension

 

[RJBeery]

Unfortunately, Billy, your recollection has let you down. Any operator has a representation as a square matrix, any vector has a representation as a column matrix.

Suppose A a 1 x n column matrix, and B a n x n square matrix. Then the matrix product AB is not defined, whereas the matrix product BA is another 1 x n column matrix as required and is easily calculated.

Interestingly (and irrelevantly), an early exercise in any linear algebra course is to prove that the set of all operators acting on a finite-dimensional vector space is itself a vector space of the same dimension

Perhaps Billy is, like, 110 years old and is remembering Matrix Mechanics. https://en.wikipedia.org/wiki/Matrix_mechanics

 

[Schneibster]

The idea that the wave function "collapses" violates the conservation of information. It isn't an entropy issue (where information has simply been obfuscated) either; the information is theoretically gone. MWI suffers from the same problem even while denying a collapse. Once a measurement has been made on a quantum system there is simply no way to reverse processes to retrodict the prior state. This should deeply disturb anyone granting a physical relevance to the wave function.

This, to me, begs the question whether you think that a superposed state is physical or not.

The alternative to superposed states being physical seems to me to be the assertion that a propagating particle has some value for its parameters even when they are Heisenberg uncertain, and this is belied by the three-polarizers experiment, as well as various Bell tests. And if superposed states are physical, then the wavefunction is a description of a real thing; it's not the thing itself, but a representation of the superposed state.

I don't think wavefunction collapse is a real event; but I think it might indicate a real change of state, from the superposed state into a definite state, that is, an interaction causes the particle to take on a definite state rather than the previous superposed state, in the parameter that was superposed; and, of course, the Heisenberg complement of that parameter then enters a superposed state. I think that a particle changes state when it interacts, and I see nothing surprising in that, since interacting particles often change direction, or charge, or other parameters when they interact. I can't figure out why people think that wavefunction collapse doesn't represent a real event, when we can point to a real interaction that caused the phenomenon that wavefunction collapse seems to describe. Perhaps someone can explain this to me, or present a scenario in which wavefunction collapse is thought to occur that does not involve an interaction.

As for retrodiction, isn't that what the Consistent Histories interpretation is all about?

I anticipate controversy on this point.