Is there a 5th fundamental force which may be responsible for the behavior of matter to be wave or a particle?

Question

We already know about the 4 fundamental forces in nature which are gravitational,electromagnetic,weak nuclear and strong nuclear forces.

There are several other questions on this website which are somewhat related to this question but I want to know if there is any other fundamental force which is responsible for wave particle duality and is internal for the matter as a system and decides when matter would chose between particle and wave behaviour?

If I had not addressed the problem properly then I ask it in a short version below(I take matter as a system):

Is there any other internal fundamental force which is responsible for the wave particle duality of matter?

Answer 1

Basically...

No, there might be fundamental forces other than we know (however none have been detected so far at the LHC) but they would neither "explain" nor are required for explaining the wave-particle duality.

The behavior that came to be known as the wave-particle duality in the early days of Quantum Mechanics comes directly from the framework of Quantum Mechanics and doesn't require any further explanation, especially not at all in terms of any fundamental forces.

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Details

In Quantum Mechanics, the state of a particle, in position-representation, is represented via a complex-valued function $\psi(x)$ which gives (is) the probability amplitude of finding the particle at position $x$.

Now, the momentum is represented via the operator $-i\hbar\frac{\partial}{\partial x}$. A state can have a definite momentum $p$ if and only if the state is an eigenstate of the operator $-i\hbar\frac{\partial}{\partial x}$ with the eigenvalue $p$, i.e., iff $-i\hbar\frac{\partial}{\partial x}\psi(x)=p\psi(x)$ where the real number $p$ would be the momentum of the state. Such eigenstates of the momentum operator with some momentum $p$ have the general form of $\psi_p(x)=e^{\frac{ipx}{\hbar}}=\cos\Big(\frac{px}{\hbar}\Big)+i\sin\Big(\frac{px}{\hbar}\Big)$. As you can see, this is a wave in $x$ with wavenumber $k=\frac{p}{\hbar}.$

Similarly, the position is represented via the operator $x$. A state can have a definite position $x_0$ if and only if it is an eigenstate of the position operator $x$, i.e., iff $x\psi(x)=x_0\psi(x)$. Such eigenstates of the position operator with some position $x_0$ have the general form of $\psi_{x_0}=\delta(x-x_0)$. As you can see, this is a particle localized at $x_0$.

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Conclusion

This is what the wave-particle duality intends to tell us. A quantum state can behave as a particle well-localized at $x_0$ when we measure its position but the same can behave as a wave with a wave-number $k=\frac{p}{\hbar}$ when it has a momentum $p$. We don't need any fundamental forces to explain this as elaborated.

Answer 2

Quantum mechanics is a physics theory , and physics theories impose extra axioms on mathematical solutions of equations in order to fit observations and predict future behaviors. These axioms are called: postulates, laws, principles and depend directly on experimental observations.

The postulates of quantum mechanics make it a probabilistic theory, not a deterministic one. The wave function is postulated as defining the probability distribution by evaluation of $Ψ^*Ψ$ , a real number between 0. and 1.

The wave particle duality is the observation that when interacting, quantum mechanically described particles act like a classical particle. An accumulation of measurements though is needed for the QM solutions to predict the probable location of a particle, and that distribution has a wave behavior, because in general the quantum mechanical equations are wave equations. This can be seen clearly in the accumulation of data in a single electron at a time double slit experiment.

The standard model, and any extensions of it are a meta level on the wave function solutions of the quantum mechanical boundary conditions problem. So within the present framework any new forces from GUT theories or supersymmetry etc will not change the axiomatic status of the probabilistic nature of quantum mechanics.

There does exist serious research which tries to make the quantum mechanical level a meta-level of a deterministic system, which will reproduce all the successes of quantum mechanics in describing the data as emergent from an underlying theory. For example the Bohmian mechanics., or the research of G. 't Hooft, who has honored us by discussing it a few years ago, but these are not main stream research directions.

In deterministic theories, the probabilistic nature used in the postulates of quantum mechanics will be seen as emergent, but not by any particular forces at the standard model level and extensions. These will be emergent meta levels out of the hypothetical deterministic forces.