Sir Roger Penrose posits a new physics in the area between classical and quantum. The penrose diosi theorum suggests observer independent gravitationally induced collapse of the wave function. Might this have some experimental validity?
Then "beable" is an empty phrase, because we cannot know about any property of a system without measuring (or observing) it. Physics deals with what's observable and measuarable and not philosophical fictitions that cannot be observed and measured.No; this was never true. You were misreading the concept of a beable. Maybe this is the source of our continuing misunderstandings.
According to Bell, a beable of a system is a property of the system that exists and is predictable independently of whether one measures anything. A measurement is the reading of a measurement value from a measurement device interacting with the system that is guaranteed to approximate the value of a beable of that system within the claimed accuracy of the measurement device.
In classical mechanics, the exact positions and momenta of all particles in the Laplacian universe are the beables. and a measurement device for a particular prepared particle is a macroscopic body coupled to this particle, with a pointer such that the pointer reading approximates some position coordinate in a suitable coordinate system. Clearly, any given measurement never yields the exact position but only an approximation of it.
In a Stern-Gerlach experiment with a single particle, the beables are the three real-valued components of the q-expectation ##\bar S## of the spin vector ##S##, and the location of the spot produced on the screen is the pointer. Because of the semiclassical analysis of the experimental arrangement, the initial beam carrying the particle splits in the magnetic field into two beams, hence only two spots carry enough intensity to produce a response. Thus the pointer can measure only a single bit of ##\bar S##. This is very little information, whence the error is predictably large.
The thermal interpretation predicts everything: the spin vector, the two beams, the two spots, and the (very low) accuracy with which these spots measure the beable ##S_3##.
This contradicts the empirical outcome of the SGE. Even in the lab at university with its rather limited budget you can get very well separated beams of Ag atoms!If I find the result ##+1/2## or ##-1/2## with certainty, I can be sure that the measurement error according to the thermal interpretation is exactly ##1/2##, since this is the absolute value of the difference between the measured value and the true value (defined in the thermal interpretation to be the q-expectation ##0##). As a consequence, I can be sure that the standard deviation of the measurement results is also exactly ##1/2##.
Yes, but the spots are supposed to measure a very tiny spin of the order of ##\hbar##. On a scale where the positions of the two silver spots represent the numbers ##\pm \hbar/2##, these positions are approximations of any number of the order of ##\hbar## with an error of the order ##\hbar##, in particular, one of the q-expectation of the spin, as the thermal interpretations claims.Even in the lab at university with its rather limited budget you can get very well separated beams of Ag atoms!
There cannot be a contradiction in cases where no significant relative accuracy is claimed!This contradicts the empirical outcome of the SGE.