# Does Antony Valentini's "sub-quantum measurement" really work?

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• Ali Lavasani
In summary, Antony Valentini proposes a new measurement method in Bohmian mechanics that allows for precise measurement of particle positions by utilizing a "non-equilibrium" particle with known position. However, this method relies on the wavefunction of the ensemble, which is 6-dimensional and inaccessible in our 3-dimensional world. Thus, the method is only useful in the limit of a.t -> 0, but becomes inaccurate as a.t increases. This leads to a trade-off between the accuracy of the wavefunction and the accuracy of the measured particle's position, making it impossible to precisely track the particle's trajectory. This is due to the nonlocality of Bohmian interactions, making the uncertainty in particle positions irreducible.
Ali Lavasani
In https://arxiv.org/pdf/quant-ph/0203049.pdf, which is in the realm of Bohmian mechanics, Antony Valentini claims that by having a "non-equilibrium" particle with arbitrarily accurate "known" position, we can measure another particle's position with arbitrary precision, violating Heisenberg's uncertainty principle.

In summary, the "sub-quantum measurement" method works as follows (see part 4 of the paper): In a simple case, we have y(t) = y(0) + a.x(0).t, where x and y are the positions of the measured and test (pointer) particles, respectively. We have kind of entanglement between the test particle's momentum and the measured particle's position (with Hamiltonian H^ = a.x^.p^y, where a is a coupling constant, py is the momentum canonically conjugate to y, and x is the measured particle's position). Here we have y(0) and y(t) with arbitrary precision, since the test particle is in quantum non-equilibrium.

The point is that, In order to predict the trajectory of the measured particle, x(t), we need BOTH x(0) and Ψ(x,y,t) (the wavefunction of the ensemble). This wavefunction would be 6-Dimensional in Bohmian mechanics and inaccessible to us in the 3-D world, so actually the theory would in general be useless. It's only in the limit a.t -> 0 that Ψ(x,y,t) ≈ ψ0(x)g0(y), and the total wavefunction would be approximately 3-D.

Now my question comes. Ψ(x,y,t) ≈ ψ0(x)g0(y) is only an approximation, being completely precise only when a.t = 0, in which case y(t) = y(0) and we lose connection to the measured particle's position (x(0)). In other words, the bigger the a.x(0).t, the more the error we have in our approximation of the ensemble's wavefunction as 3D. We can have a large a.t, in which case the wavefunction would be inaccurate and we would not be able to accurately calculate x(t) from x(0), OR we can have a very small a.t and a precise wavefunction, in which case the parameter a.x(0).t, our tool to determine x(0), would also be very small and maybe comparable to the uncertainty in y(0), which makes our measurement of x(0) inaccurate. So there doesn't seem to be any way to track the trajectory x(t) precisely, we need to make either x(0) or Ψ(x) inaccurate.

So is my discussion valid? Is the uncertainty in x(t) kind of irreducible, because of the uncertainty in any case we have, either in x(0) or in Ψ(x), which are in a kind of trade-off?

Demystifier
In the paper linked in my signature below I argue that the true reason for inability to measure Bohmian positions is the nonlocality of Bohmian interactions.

## 1. What is Antony Valentini's "sub-quantum measurement" theory?

Antony Valentini's "sub-quantum measurement" theory is a proposed explanation for the mysterious phenomenon of quantum measurement. It suggests that the collapse of the quantum wavefunction is not a random event, but rather a result of interactions between particles on a sub-quantum level.

## 2. How does Valentini's theory differ from traditional quantum mechanics?

Valentini's theory challenges the traditional interpretation of quantum mechanics, which states that the collapse of the wavefunction is a random process. Instead, it proposes that there are hidden variables at play that determine the outcome of a measurement.

## 3. What evidence supports Valentini's theory?

Valentini's theory is still a highly debated topic in the scientific community, and there is currently no conclusive evidence to support it. However, some experiments have shown results that are consistent with the predictions of the theory.

## 4. What are the potential implications of Valentini's theory?

If Valentini's theory is proven to be true, it could have significant implications for our understanding of the fundamental workings of the universe. It could also potentially lead to new technologies and applications in fields such as quantum computing.

## 5. Is Valentini's theory widely accepted in the scientific community?

Valentini's theory is still a highly debated topic, and there is no consensus among scientists about its validity. Some researchers have criticized the theory for its lack of testability, while others continue to explore its potential implications. Further research and experimentation are needed to determine the validity of Valentini's theory.

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