In de Broglie's double solution theory there are two waves. There is the wave-function wave which is statistical, non-physical and is used to determine the probabilistic results of experiments. It is a mathematical construct only. It doesn't physically exist. There is also a physical wave in a “subquantic medium” which guides the particle.

NON LINEAR WAVE MECHANICS by LOUIS DE BROGLIE

Since 1954, when this passage was written, I have come to support wholeheartedly an hypothesis proposed by Bohm and Vigier.

According to this hypothesis, the random perturbations to which the particle would be constantly subjected, and which would have the probability of presence in terms of [the wave-function wave], arise from the interaction of the particle with a “subquantic medium” which escapes our observation and is entirely chaotic, and which is everywhere present in what we call “empty space”. — Louis de Broglie

De Broglie’s “subquantic medium” could be the superfluid dark matter.

Interpretation of quantum mechanics by the double solution theory - Louis de BROGLIE

When in 1923-1924 I had my first ideas about Wave Mechanics I was looking for a truly concrete physical image, valid for all particles, of the wave and particle coexistence discovered by Albert Einstein in his "Theory of light quanta". I had no doubt whatsoever about the physical reality of waves and particles.

any particle, even isolated, has to be imagined as in continuous “energetic contact” with a hidden medium

For me, the particle, precisely located in space at every instant, forms on the v wave a small region of high energy concentration, which may be likened in a first approximation, to a moving singularity.

the particle is defined as a very small region of the wave — Louis De Broglie

If the notion of clumpy dark matter is mistaken for the state of displacement of the dark matter, then particles of ordinary matter move through and displace the strongly interacting dark matter, causing it to wave.

In a double slit experiment it would be the strongly interacting dark matter that waves.

In the following video the silicon bath represents the chaotic strongly interacting dark matter. In the video, in the double slit experiment example, the particle travels through a single slit and the associated wave passes through both.

https://youtu.be/WIyTZDHuarQ

In a double slit experiment the particle always travels through a single slit and the associated wave in the strongly interacting dark matter passes through both. As the wave exits the slits it creates wave interference which alters the direction the particle travels as it exits a single slit. Over time the particles form an interference pattern. Strongly detecting the particle exiting a single slit destroys the cohesion between the particle and its associated wave, the particle continues on the trajectory it was traveling and does not form an interference pattern.

It is the chaotic nature of the strongly interacting dark matter which causes the Casimir effect.

https://youtu.be/Dv8IRx43vy0

It is the chaotic nature of the dark matter which leads to the probabilistic results of experiments.

In the following articles the fluid is the strongly interacting dark matter.

Fluid mechanics suggests alternative to quantum orthodoxy

The fluidic pilot-wave system is also chaotic. It’s impossible to measure a bouncing droplet’s position accurately enough to predict its trajectory very far into the future. But in a recent series of papers, Bush, MIT professor of applied mathematics Ruben Rosales, and graduate students Anand Oza and Dan Harris applied their pilot-wave theory to show how chaotic pilot-wave dynamics leads to the quantumlike statistics observed in their experiments. — Larry Hardesty

When Fluid Dynamics Mimic Quantum Mechanics

If you have a system that is deterministic and is what we call in the business ‘chaotic,’ or sensitive to initial conditions, sensitive to perturbations, then it can behave probabilistically,” Milewski continues. “Experiments like this weren’t available to the giants of quantum mechanics. They also didn’t know anything about chaos. Suppose these guys — who were puzzled by why the world behaves in this strange probabilistic way — actually had access to experiments like this and had the knowledge of chaos, would they have come up with an equivalent, deterministic theory of quantum mechanics, which is not the current one? That’s what I find exciting from the quantum perspective. — John W. M. Bush