Do Pilot Waves of Apple Resemble an Apple in Configuration Space?

[bluecap]

Dear Physicsforums,

Does the pilot waves of apple look like an apple? It was supposed to occur in configuration space and not in spacetime.. but isn't it configuration space is a possible spacetime since the pilot waves are supposed to be not just smokes and mirrors like the wave function in Copenhagen?

Whatever (whether the configuration space of the pilot wave is in some kind of space or not), if the pilot waves of apple would be altered like orange pilot waves fragments were inserted. Would the physical apple become altered too with orange in the middle?

 

[Demystifier]

Does the pilot waves of apple look like an apple? It was supposed to occur in configuration space and not in spacetime

Well, yes and no. If the apple consists of $N\gg 1$ elementary particles, then its pilot wave (at fixed time) is a function of the form $\Psi({\bf x}_1,\ldots, {\bf x}_N)$. It does not look like an apple. But from it you can easily construct something that does look like an apple. Construct first $N$ partial density functions
$$\rho_1({\bf x}_1)=\int d^3x_2 \cdots \int d^3x_N \, |\Psi({\bf x}_1,\ldots, {\bf x}_N)|^2$$
$$...$$
$$\rho_N({\bf x}_N)=\int d^3x_1 \cdots \int d^3x_{N-1} \, |\Psi({\bf x}_1,\ldots, {\bf x}_N)|^2$$
Then the total density function
$$\rho({\bf x})=\rho_1({\bf x})+\ldots +\rho_N({\bf x})$$
looks very much like the apple.

 

[bluecap]

Well, yes and no. If the apple consists of $N\gg 1$ elementary particles, the its pilot wave (at fixed time) is a function of the form $\Psi({\bf x}_1,\ldots, {\bf x}_N)$. It does not look like an apple. But from it you can easily construct something that does look like an apple. Construct first $N$ partial density functions
$$\rho_1({\bf x}_1)=\int dx^3_2 \cdots \int dx^3_N \, |\Psi({\bf x}_1,\ldots, {\bf x}_N)|^2$$
$$...$$
$$\rho_N({\bf x}_N)=\int dx^3_1 \cdots \int dx^3_{N-1} \, |\Psi({\bf x}_1,\ldots, {\bf x}_N)|^2$$
Then the total density function
$$\rho({\bf x})=\rho_1({\bf x})+\ldots +\rho_N({\bf x})$$
looks very much like the apple.

Is the pilot wave in Bohmian more objective than the wave function in Copenhagen or are they both just mathematical entities and just figments of the imagination? If so then why differentiate between Bohmian and Copenhagen since the wave function does't occur in spacetime in either of them?

 

[Ilja]

Is the pilot wave in Bohmian more objective than the wave function in Copenhagen or are they both just mathematical entities and just figments of the imagination? If so then why differentiate between Bohmian and Copenhagen since the wave function does't occur in spacetime in either of them?

The dBB interpretation has the advantage that what we observe - the real apples and oranges - exists in the interpretation too. As the configuration, the not so hidden "hidden" variable.

So, in particular, you will not be too much confused by a wave function of Schrödinger's cat. Because there also exists a real cat, which is what we observe, and the wave function may exist or not, this is something you can leave to philosophers.

 

[Demystifier]

Is the pilot wave in Bohmian more objective than the wave function in Copenhagen or are they both just mathematical entities and just figments of the imagination? If so then why differentiate between Bohmian and Copenhagen since the wave function does't occur in spacetime in either of them?

Perhaps the pilot wave in Bohmian is somewhat more objective than wave function in Copenhagen, but that is not the main reason to distinguish between Bohmian and Copenhagen. The main difference between Bohmian and Copenhagen is in the things which are not the pilot wave or wave function.

This is like a difference between an airplane pilot and a man in uniform looking like a pilot but not being a pilot. The difference is not so much in those two men, but in the fact that in the former case it is understood that there is also a plane (piloted by the pilot).

 

[bluecap]

Perhaps the pilot wave in Bohmian is somewhat more objective than wave function in Copenhagen, but that is not the main reason to distinguish between Bohmian and Copenhagen. The main difference between Bohmian and Copenhagen is in the things which are not the pilot wave or wave function.

This is like a difference between an airplane pilot and a man in uniform looking like a pilot but not being a pilot. The difference is not so much in those two men, but in the fact that in the former case it is understood that there is also a plane (piloted by the pilot).

What do you mean "The main difference between Bohmian and Copenhagen is in the things which are not the pilot wave or wave function."? Are you saying the apples and oranges we can touch are not even similar in Bohmian or Copehagen interpretation? Kindly elaborate.

 

[Demystifier]

Are you saying the apples and oranges we can touch are not even similar in Bohmian or Copehagen interpretation?

Yes. According to the Bohmian interpretation, the apples and oranges we can touch are made of a large number of pointlike particles. Those particles are guided by the wave, but we don't touch the wave itself.

On the other hand, the Copenhagen interpretation is not so specific about what these things we touch are really made of. But even though it is not very specific about that, it definitely denies the existence of those Bohmian pointlike particles.

 

[bluecap]

Perhaps the pilot wave in Bohmian is somewhat more objective than wave function in Copenhagen, but that is not the main reason to distinguish between Bohmian and Copenhagen. The main difference between Bohmian and Copenhagen is in the things which are not the pilot wave or wave function.

This is like a difference between an airplane pilot and a man in uniform looking like a pilot but not being a pilot. The difference is not so much in those two men, but in the fact that in the former case it is understood that there is also a plane (piloted by the pilot).

Is it possible the pilot wave in Bohmian lives in spacetime or some kind of spacetime container that can make you interact with the pilot wave using some form of technology in the future?

 

[Nugatory]

Is it possible the pilot wave in Bohmian lives in spacetime or some kind of spacetime container that can make you interact with the pilot wave using some form of technology in the future?

This might be a good time to mention the Physics Forums rule prohibiting posting personal theories and speculation...

 

[bluecap]

This might be a good time to mention the Physics Forums rule prohibiting posting personal theories and speculation...

Thanks for emphasizing there is really nothing to the pilot waves. I thought prior to the original post they really existed in spacetime.
So Bohmians need pilot wave as calculational aid because these can split in the double slit setup guiding the local particles.. while in Copenhagen, the wave functions are the particles/objects themselves.

But I'm asking (and not speculating or personal theories because I have none) now whether it is possible for pilot waves to be there yet the particles are not local or always particles.. they can also appear and vanish like the wave functions as objects in Copenhagen? These would enable the particles to tunnel or not make them create trajectories causing for example the electrons to lose energy as it literally rotates around the atoms in Bohmian. So is it possible there is pilot wave in the electron in the atom yet the electron doesn't have local and trajectories as Bohmians always wanted us to imagine or visualize?

 

[Ilja]

bluecap, this text sounds like you have not understood what the wave function is. It is not a function in spacetime, but a function on the configuration space changing in time. The configuration space is something much larger that space. Say, for a system of N particles it is a function on some 3N-dimensional space.

The closest thing to such a function in classical physics is energy. It is also defined for every configuration q(t), but can also depend on $\dot{q}$. It essentially does not define the system itself - which is described by the configuration q(t) - but everything else what can influence this system.

 

[Nugatory]

Several posts containing speculations based on pop-sci misunderstandings have been removed from this thread. The thread is open, but please keep posts relevant to the original question about how the Bohmoan interpretations work with macroscopic objects.

 

[bluecap]

After understanding more about the role of wave functions in Bohmian Mechanics. I think in macroscopic objects. Copenhagen and Bohmian Mechanics don't really differ much. Why. Because in the electrons in the atoms for example... both Copenhagen And BM has the Wave function as the one containing the charge. Since wave function is quantized and doesn't accelerate.. then the electrons don't lose energy. In Copenhagen, we don't know how the wave functions become the chairs and tables. In Bohmian, they just use localized particles as the Chair and Tables. So outwardly they look differently, but inwardly they seem to be just the same. For example. In Bell Aspect Correlations. We don't know how both the wave functions in Copenhagen and BM talk at a distance of billions of light years. It is not the localized particles in BM that talk at all!

I've thought a long time for this thread so hope it won't be deleted without some comments. Thank you.