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I was reading a forum regarding the reality of the wave function, and one user (who apparently works in quantum foundations) stated that

"the wavefunction carries no energy or momenta and this does not sound like anything real."

https://www.researchgate.net/post/What_is_the_physical_meaning_of_the_wave_property_of_the_fundamental_particles

Is this true? The wave function doesn't carry any energy or momenta? If it doesn't carry them does that mean it cannot be real?

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It's a problem of perspective, really. I dont mean that in some strange quantum voodoo sense, but in philosophy of physics there are 2 main camps when it comes to the wavefunction: The realists and anti-realists. Now none of the physics is different in these views but the nature of reality is.

Without access to the forum I cannot say for sure what this particular user meant, and I am not in the business of telling you what to believe, so I'll give you what we know:

The wavefunction of a system tells us everything about the state that system is in. It can tell us (up to usually small uncertainties) the momentum of the state, the energy of the state, the physical position, as well as the expectation value of all these things. It can be the case that each particle in a system has it's own wavefunction, or that the whole system of many particles is described by a single wave function.

Many people such as Carlo Rovelli argue that the wavefunction is purely a mathematical tool, a convenient way to describe the system but having no actual reality. People like Sean Carrol on the other hand take the wave function literally, and argue that since it is the non-relativistic, spinless limit of the Dirac bi-spinor, its simply an approximate way of talking about excitations in a quantum field.

This all stems from the fact that the wave function itself is not an observable of the theory. For further reading, the SEP is a good place to start.

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Is this true? The wave function doesn't carry any energy or momenta?

Energy and momentum are real numbers , the wavefunction is a function of complex variables. Only its complex conjugate square connects with real numbers, and that is a probability distribution which can only be measured by observing interactons wit the exact same boundary conditions.

If it doesn't carry them does that mean it cannot be real?

For physics, real means measurable; so no, the wave function is not measurable by itself, it is part of the mathematical model that describes the quantum mechanical framework, just that, mathematics. The model fits measurements of probability distributions predictive in new situation, but its individual mathematical components are just that, mathematics.

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That quote is certainly applicable to the Copenhagen Interp. of QM where the wave function is really a catalog of possible experimental outcomes. It is strictly information and has no material properties.

To implement that interpretation in the context of a particle position measurement, start with a superposition of position eigenstates weighted with the position space wave function evaluated at the value of x corresponding to its weighted eigenstate.

Now, if an observer then makes a position measurement at a time t, seeing the particle is at position x, then the superposition is simply reinitialized to that eigenstate.

This procedure is sometimes referred to as wave function collapse, but nothing material is actually collapsed-an algorithm is merely re-parameterized.

The w-fcn's squared in the original superposition only provide the probability that a measurement, a process that is uncontrolled by a deterministic sequence of events, will result in a particular x-value at time t.

They represent predictions, not materialities.

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