Wave collapse

**hypnagogue** · Mar10-04, 08:36 AM

Hate to ask another one of these questions, but I've just read something about the collapse of the wave function that does not seem consistent with other accounts I've read about it. From what I understand, the wave function of a system is collapsed automatically by interaction with another, macroscopic system. Would anyone care to comment on the following?

One might assume that this state vector collapse occurs when we disturb the system by having some measuring device interact with it in order to make a measurement on the system-- that is, when the outside world interact with it. But that is not how quantum mechanics works. When a second system interacts with the first system, all that happens is that we get an even more complicated system with more potential states: a bigger $LaTeX Code: \\Psi$ with more little $LaTeX Code: \\Psi_i$ component pictures than before. The measurement device we use to look at quantum mechanical atoms is itself governed by the Schrodinger equation, and, therefore, it cannot give us anything but a more complicated $LaTeX Code: \\Psi$ that is made out of the set of pictures that represents the overall system's potentialities, but now consisting of two parts: one part for the atomic system's state in each picture and one part for the measurement device's corresponding readings.

from The Physics of Consciousness by Evan Harris Walker

**ZapperZ** · Mar10-04, 08:55 AM

Originally posted by hypnagogue
Hate to ask another one of these questions, but I've just read something about the collapse of the wave function that does not seem consistent with other accounts I've read about it. From what I understand, the wave function of a system is collapsed automatically by interaction with another, macroscopic system. Would anyone care to comment on the following?

What you quoted is only valid up to a certain extent. Let's say we have an isolated atom, and we solved for the wavefunction of this atom. If we start having many more of these atoms and they start to WEAKLY interact with each other, then the most general wavefunction for the entire system can be accurately approximated as a sum of each individual atomic wavefunction - the Psi_i's that you quoted. [Note that when you do this, the general wavefunction is no longer orthorgonal. In solid state physics, we now have to construct what is known as the Wannier function to preserve some degree of orthorgonality]. This is because we make very little perturbation to the original individual hamiltonian.

However, once we make them interact even stronger that the modification to the potential part in the hamiltonian can no longer be ignored, then the ORIGINAL, individual wavefunctions are no longer the eigenfunction of the system. You cannot simply assume that the general wavefunction is the sum of all the atomic wavefunctions. One has to re-solve the new hamiltonian and find the new eigenfunctions, and typically, this can't be done analytically. In such cases, this is where many-body physics comes in and provide various models to formulate a new hamiltonian for the many-body system.

As a side note, I am always skeptical of anyone trying to make any connection between a science and a pseudoscience, especially when there are concepts such as "consciousness" that are ambiguously defined. More often than not, those who tried to do such things tend to not be physicists, but think they know enough to interpret and use various physics ideas.

Zz.

**hypnagogue** · Mar10-04, 09:09 AM

Originally posted by ZapperZ
What you quoted is only valid up to a certain extent. Let's say we have an isolated atom, and we solved for the wavefunction of this atom. If we start having many more of these atoms and they start to WEAKLY interact with each other, then the most general wavefunction for the entire system can be accurately approximated as a sum of each individual atomic wavefunction - the Psi_i's that you quoted. [Note that when you do this, the general wavefunction is no longer orthorgonal. In solid state physics, we now have to construct what is known as the Wannier function to preserve some degree of orthorgonality]. This is because we make very little perturbation to the original individual hamiltonian.

However, once we make them interact even stronger that the modification to the potential part in the hamiltonian can no longer be ignored, then the ORIGINAL, individual wavefunctions are no longer the eigenfunction of the system. You cannot simply assume that the general wavefunction is the sum of all the atomic wavefunctions. One has to re-solve the new hamiltonian and find the new eigenfunctions, and typically, this can't be done analytically. In such cases, this is where many-body physics comes in and provide various models to formulate a new hamiltonian for the many-body system.

Thanks for your response. Some of it is beyond my knowledge of physics but I think I have the general idea. However, I don't think Walker's claim here is that we simply do a linear combination of wave functions as much as it is that what we get, ultimately, is still a wave function with a superposition of states rather than just one state-- there is nothing in QM that states that the function has collapsed yet. Do you agree with this general statement?

As a side note, I am always skeptical of anyone trying to make any connection between a science and a pseudoscience, especially when there are concepts such as "consciousness" that are ambiguously defined. More often than not, those who tried to do such things tend to not be physicists, but think they know enough to interpret and use various physics ideas.

I'd like to stay away from this issue, as it is only my intent right now to assess the quoted passage. However, since you brought it up, I might as well list the information about the author given in the book:

Evan Harris Walker is the founder of the Walker Cancer Institute. Since he received his Ph.D. in physics from the University of Maryland in 1964, he has published more than a hundred paper in scientific journals and holds a dozen patents. He lives in Aberdeen, Maryland.

selfAdjoint · Mar10-04, 09:30 AM

It seems to me that the Walker quote is saying that the measurement device is itself a quantum system, and since it is (stongly?) interacting with the given quantum system its state function becomes part of just such a larger nonlinear wavefunction as ZapperZ described. I believe Wigner was the first to state this clearly, and John Bell has also written on it.

**ZapperZ** · Mar10-04, 09:33 AM

Originally posted by hypnagogue
Thanks for your response. Some of it is beyond my knowledge of physics but I think I have the general idea. However, I don't think Walker's claim here is that we simply do a linear combination of wave functions as much as it is that what we get, ultimately, is still a wave function with a superposition of states rather than just one state-- there is nothing in QM that states that the function has collapsed yet. Do you agree with this general statement?

I don't agree with it in general. I think what he was trying to convey is the concept of decoherence whereby the act of measurement simply induces a larger degree of freedom to the whole overall system (which now includes the orginal system and the instrument). This is totally different than the mathematical operation A|psi> or <psi|A|psi> where A is an observable and |psi> is the complete set of basis function. It is where there is a selection of which states "survive" after a measurement (operation with an observable). If all we get after a measurement is just MORE superposition, there wouldn't be any reason for the brouhaha surrounding the Schrodinger Cat in the first place.

I'd like to stay away from this issue, as it is only my intent right now to assess the quoted passage. However, since you brought it up, I might as well list the information about the author given in the book:

Evan Harris Walker is the founder of the Walker Cancer Institute. Since he received his Ph.D. in physics from the University of Maryland in 1964, he has published more than a hundred paper in scientific journals and holds a dozen patents. He lives in Aberdeen, Maryland.

You're right. I was making a general observation and not specifically directed to him. I may have actually heard of him, though I have not read the book you quoted. If it's any consolation, I'm also skepticaly of Stephen Wolfram and his latest book on complexities - or maybe I've made it worse by saying that! :)

Zz.

**hypnagogue** · Mar11-04, 04:21 PM

Originally posted by SelfAdjoint
It seems to me that the Walker quote is saying that the measurement device is itself a quantum system, and since it is (stongly?) interacting with the given quantum system its state function becomes part of just such a larger nonlinear wavefunction as ZapperZ described. I believe Wigner was the first to state this clearly, and John Bell has also written on it.

So the measurement problem is such that we cannot be sure exactly when the wave function collapses, just that by the time we observe the results of the experiment the relevant functions will have been collapsed-- is that correct?

**hypnagogue** · Mar11-04, 04:22 PM

Originally posted by ZapperZ
If all we get after a measurement is just MORE superposition, there wouldn't be any reason for the brouhaha surrounding the Schrodinger Cat in the first place.

OK, but how exactly are you defining 'measurement'?

**ZapperZ** · Mar11-04, 05:18 PM

Originally posted by hypnagogue
OK, but how exactly are you defining 'measurement'?

I define it exactly as it is defined in the postulates of quantum mechanics. See, for example:

http://vergil.chemistry.gatech.edu/n...ev/node20.html

Zz.

**venkat** · Mar13-04, 06:52 AM

hey ZapperZ,
i visited the webpage you mentioned in the link...but where in that page does the author talk about what a measurement IS ?!
i did not find a defenition of measurement there!

**ZapperZ** · Mar13-04, 08:09 AM

Originally posted by venkat
hey ZapperZ,
i visited the webpage you mentioned in the link...but where in that page does the author talk about what a measurement IS ?!
i did not find a defenition of measurement there!

Postulates 3,4, and 5. They define what is meant as an act of measurement on a quantum system.

Zz.