# Wave Function mathematical vs real

• daezy
So I guess one would have to say that the wave function is a function of six variables, but we can't see it in 6D space. In summary, the conversation discusses the concept of wave function and its interpretation in different theories such as Copenhagen Interpretation and Bohmian Mechanics. In Copenhagen Interpretation, the wave function is considered a mathematical tool with no physical reality, while in Bohmian Mechanics it is believed to have objective reality as a field. The question arises as to whether both interpretations can coexist, and what principle prevents a hybrid model. The discussion also delves into the idea of the wave function being a complex function and whether this affects its reality. It is also mentioned that the wave function can describe

#### daezy

Hi,

In Copenhagen Interpretation, the wave function is just a mathematical tool that has no physical reality.

In Bohmian Mechanics, the wave function has objective reality as some kind of field.

Why can't we have both where the wave function has objective reality as some kind of field and yet the particles has no definite properties or physical existence before measurement and they only literally physicalize upon measurements obeying the formula that squaring the wave function gives the probability of its location??

What principle avoid a hybrid model of the two above?

I think the wave function can't be physical in the Copenhagen Interpretation because it is a complex function. Why. In Bohmian, isn't the wave function a complex function too??

I'm sure one can marry the two ideas. In fact, I switch between the two interpretations quite regularly to help me understand difficult quantum systems.

Maybe the question can be rephrased as:

What if in Copenhagen Interpretation, the wave function is not just mathematical but has objective existence although the particles behave just like what Copenhagen says. Is the reason physicists ignored the possibility of the wave function being real is because it doesn't add anything new to quantum theory?

Or is the wave function not real is because it is a complex function?

In Bohmian Mechanics, isn't the wave function also a complex function? Hope someone can clarify. Thanks.

Wave function has to be a description of a real, physical object (field, actual physical wave function, or whatever), because it is objective. Knowing wave function now, I can compute what it's going to be later, assuming I know Hamiltonian of the system. I can then make measurements to prove that my computations are correct.

What it doesn't have to be is observable. But yes, the QM basically just doesn't bother it. All it assumes is that there is a real physical object that the wave function describes and that whatever it is obeys principles of super position. Given that, wave function is sufficient explanation of what's going on, and we need not bother with the actual object it is describing.

Unfortunately, things turn sour with Gravity, which basically throws super position out of the window. And without that, we cannot make such bold claims. So it'd be nice to know what it is that we are actually describing, and unfortunately, the closest thing we have is EM field behaving like wave function of a single photon. But it is enough to throw in a second photon, and EM field no longer corresponds to the relevant wave function.

What would it mean for the wave function to be 'real' when there is more than one particle? Say a system of two particles. The wave functions is a function in six dimensional space! Then, what does it mean to be real?

martinbn said:
What would it mean for the wave function to be 'real' when there is more than one particle? Say a system of two particles. The wave functions is a function in six dimensional space! Then, what does it mean to be real?

How about in Bohmian Mechanics. In a system of two particles. Is its wave function also a function in six dimensional space? If so, how can it be real in Bohmian??

But then the 6 dimensional space formlism is because we model it using Hilbert Space. If we just use the old superposition method.. then it still exists in 3 dimensional space, correct?

daezy said:
How about in Bohmian Mechanics. In a system of two particles. Is its wave function also a function in six dimensional space? If so, how can it be real in Bohmian??

I don't know how it is in Bohmian Mechanics. I am curious to learn. Pretty sure someone will tell us.

But then the 6 dimensional space formlism is because we model it using Hilbert Space. If we just use the old superposition method.. then it still exists in 3 dimensional space, correct?

I don't think so.

The original question seems the same as to ask in classical mechanics if points from the phase space are actually points in the physical space.

martinbn for two particle its not 6-dimensional!
Let me clarify for a particle in 3-D its 3-1 dimensional problem.
for 2 particles it is 3-2 dimensional problem not 6-D one.
you might have read a problem which state for N particles its a 3N dimensional problem not 3 multiplied by N dimensinoal or we wouldn't have had wave functions of H-atom.Instead it is read as a 3-D N particles involved condition.
And my dear daezy wave functions obtained from Schröodinger's equation are diffusion functions.They just define probability waves.

Deric Boyle, I am confused, probably I don't understand something on a very fundamental level. What I meant was not two particles with their two wave functions each of three variables, so that we have what you call 3-2 dimensional problem. I meant two particles with a common wave function. Then it is a function of 6 variables, no?

Both of us may have to check.
What I think here is that in your 2-particle problem those six varibles are spatial and desribing 'interactions' between them. Out of these 6 a set of three is for each as I think so.
And if the particles are identical it's hard to dicern.But if different you may give same treatment to as to an H -atom.(I am considering stationary states here)

I suppose so, but my point was that the function is a function of six variables, so if it represents a field it must live in 6D space.

martinbn said:
I suppose so, but my point was that the function is a function of six variables, so if it represents a field it must live in 6D space.

Look at the hydrogen atom as a simple example. You have two particles, the proton and electron, but the wavefunction is three-dimensional (assuming time-independent).

Where can I see the hydrogen atom? On the other hand here in the subsection on spatial interpretation it says 'six spatial variables'.

Sorry daezy for derailing the thread.
Sir born2bwire I fully agree with you.

Wave-function is defined on configuration space not real 3D space. So 6-dimensional space for two particles translates to probabilistic configurations for the particles in real 3D space which can be depicted by pretty coloured pictures but aren't to be interpreted as the literal particle orbits.

unusualname said:
Wave-function is defined on configuration space not real 3D space. So 6-dimensional space for two particles translates to probabilistic configurations for the particles in real 3D space which can be depicted by pretty coloured pictures but aren't to be interpreted as the literal particle orbits.

but in Bohm Mechanics, wave function is literally real, how is that so?

daezy said:
but in Bohm Mechanics, wave function is literally real, how is that so?

Bohmians are friggin' crazy.

Well maybe not so crazy, but they interpret the wave as an ontologically existing non-local "guiding wave". The physical mechanism enabling the non-locality is of course not known, and may not exist, but the theory is consistent with other interpretations as far as measurements are concerned.

There are many people who will tell you non-local guiding waves are a ridiculous notion, but we can't rule them out experimentally.

unusualname said:
Bohmians are friggin' crazy.

Well maybe not so crazy, but they interpret the wave as an ontologically existing non-local "guiding wave". The physical mechanism enabling the non-locality is of course not known, and may not exist, but the theory is consistent with other interpretations as far as measurements are concerned.

There are many people who will tell you non-local guiding waves are a ridiculous notion, but we can't rule them out experimentally.

But how come the Bohmians can model the wave as an ontologically existing non-local guiding wave as you described while the Copenhagens can't model it as such in spite of them located both in the same configuration space?? What is the mathemtical reason?

Alfrez said:
But how come the Bohmians can model the wave as an ontologically existing non-local guiding wave as you described while the Copenhagens can't model it as such in spite of them located both in the same configuration space?? What is the mathemtical reason?

There isn't any mathematical reason, just as there's no mathematical reason to choose between other interpretations of QM. Copenhagen Interpretation just accepts that the wave is a description of probabilisitic information whereas de Broglie Bohm Interpretation hopes that real particles are being guided by a non-local guiding wave (maybe with complex topological origin).

In any case you can't naively visualise the wave in 3D space, except in the case of a single particle where configuration space happens to be 3D.

unusualname said:
There isn't any mathematical reason, just as there's no mathematical reason to choose between other interpretations of QM. Copenhagen Interpretation just accepts that the wave is a description of probabilisitic information whereas de Broglie Bohm Interpretation hopes that real particles are being guided by a non-local guiding wave (maybe with complex topological origin).

In any case you can't naively visualise the wave in 3D space, except in the case of a single particle where configuration space happens to be 3D.

I see. So the Copenhagens can also model it as real like the Bohmians without any additions to the mathematics but since the Copenhagens focus only on measurement and don't care the physical interpretations then they just treat it as unreal??

This means we can choose to believe the wave function is real or not in Copenhagens dependent on our preference of thought as there is no a priori reason it is not real?

Alfrez said:
I see. So the Copenhagens can also model it as real like the Bohmians without any additions to the mathematics but since the Copenhagens focus only on measurement and don't care the physical interpretations then they just treat it as unreal??

This means we can choose to believe the wave function is real or not in Copenhagens dependent on our preference of thought as there is no a priori reason it is not real?

Yes I would say so. But I can't really claim to know how other people think of the wave or generalise about CI, personally I think it's just a description of probabilistic information which we must measure or "look at" to obtain definite values. Then it's a philosophical question as to whether you call probabilistic waves "real" or "unreal"