As far as I know there is currently no evidence for the existence of hidden variables, and several classes of hidden variables are ruled out by experimental evidence. I think the verdict on Bohm theory, which proposes  non-local hidden variables, is still under debate, but has not that many followers. I don't know of any proposed methods of only manipulating the "guiding wave" but am not up to date with literature in this field. So you may want to check that out.

If I understand your question/remarks correctly, you are not only proposing that hidden variables exist, but that they also have a hidden dynamics, and can somehow be changed by normal external fields. Do you have any evidence for that, or literature which discusses this suggestion?

This is reminiscent of the way I always thought Einstein got the idea for his hidden variables proposals (I don't have any historical evidence for it though). Einstein of course explained Brownian motion (even though he did not set out to explain something, he only suggests that what he calculates could explain Brown's observations a century earlier*) by invoking the collisions of a larger particle with the atoms or molecules of the fluid. At the time the "real" existence of these was also still debated, although the anti-atomists were dying out by that time, and loosing ground.  In fact Einstein's derivation contributed to the reality of the existence of atoms and molecules. In this case it is conceivable that manipulating the molecules changes the statistical motion of the larger particle. Some of my PhD work (a long, long time ago) points to that, although I never thought about it in that way: the statistical properties of the motion of the Brownian particle depend on the motion of the colliding molecules. And indeed the time scales of these motions play a role as well.

So if there are hidden variables in the Einstein Brownian motion sense, it could possibly allow experiments along the lines you propose. However, I also think it is just this type of hidden variables that is ruled out by the Bell inequalities, and Aspect's experiments in that matter. Here is a somewhat popular link to more recent developments: https://quantumfrontiers.com/2012/11/08/its-been-a-tough-week-for-hidden-variable-theories/

* Es  ist moglich  dass  die hier zu behandelnden Bewegungen mit der sogenannten  "Brownschen Molekularbewegung" identisch sind; die mir  erreichbaren Angaben uber letztere sind jedoch so ungenau,  dass ich mir hieriiber kein Urteil bilden konnte. 

Gert, about your link: To name something "a tough week for hidden variable theories" where the leading (and essentially the only ones considered by professional physicists) hidden variable theories are not even claimed to have a problem with this is misleading.  

Then, fortunately physics is not a democracy, so it does not matter how many proponent of dBB theory exist.  What matters are the arguments they have.  And the opponents of hidden variables are in this sense in a much more tough situation:  They have to reject basic principles of science, realism as well as causality, to get rid of the Mother of all hidden variables - the hidden preferred frame of the Lorentz ether - which would allow realistic and causal explanations of the violations of the Bell inequalities.  

So, essentially to get rid of hidden variables, one has to fall back to the level of astrology, where we have also no hidden variables to explain the influence of the planet positions on our fate.  

Ilja, I suggest you take up your gripe with the author of the website I linked to. I was clearly speaking about local hidden variables which are the type I understand from Gabriel's question he was taking about.  I offered the option at the beginning of my answer that he look into Bohm theory, and rather than ranting about your perceived opponents you could help him by explaining if it is possible to manipulate the pilot wave directly, and indeed if his question makes any sense if there are non-local hidden variables of the Bohm type. I am just telling him that I don't believe his ideas can work for the local hidden variables given what we currently know about those.

I am not enough of an expert in this field to have an expert opinion. Which, by the way, is not at all in agreement on anything. Here is another link (and, as you can see, if it were a democracy, Bohm would not stand a chance): http://www.preposterousuniverse.com/blog/2013/01/17/the-most-embarrassing-graph-in-modern-physics/ Although I have to admit the sample size is rather small for statistical inferences. And I'm sure that "Other" has at least as many theories as the number that are listed.

Thank you for your responses. I am not an expert either.  I am personally working on a view of quantum mechanics with no hidden variables and I realized that some of the hidden variables theories have not really been discarded by experiments. Only theories based in simultaneous causal and local realism have been fully “eliminated” and only a wide range of non-local theories (those that follow Leggett inequalities) as far as I know.

So I tried to think in ways to test them. I think that the proposed methods do may include some non-local hidden variables. In particular the statistical study of systems of many particles out of equilibrium may not need to be local. I think that the hidden variables theses only need to be contextual and somehow affected by the current technologies.

The proposed methods have also a practical application. Designing new ways to obtain the same quantum mechanical state, may lead to a wider and efficient technologies for quantum computing and technologies (as we have different type of transistor for different proposes).