Recent content by Roberto Pavani

Following @Matterwave's suggestion, I have also contacted the corresponding author to share the numerical verification and the Fine's theorem argument. I'll report back if I receive a response.

You're right, my concern evolved during the discussion. Initially I was worried that the threshold shift might artificially inflate the correlations. But after thinking more carefully, I realized that Fine's theorem actually forbids any violation regardless of the offsets, the joint...

After further reflection and numerical verification, I can now state my concern precisely. The core argument (Fine's theorem): The CHSH bound ## |S| \leq 2## holds if and only if the four dichotomic observables admit a joint probability distribution (Fine, 1982). In the paper's setup...

I understand that Eq. (56) defines a different observable. My concern is that CHSH is ultimately computed from coincidence probabilities. Since the threshold shift changes the partition of events into ±1 outcomes, it also changes the coincidence statistics themselves. So I am trying to...

My concern is that Eq. (56) is not merely a linear re-expression of the same observable. The operation ## \phi \rightarrow \operatorname{sign}(\phi+\alpha) ## is nonlinear. Therefore it does not generally preserve inner products or correlations. In my simple example, ## \langle...

My concern is slightly different (perhaps due to my limited understanding of the subject). I fully accept that one may define a new observable by a unitary transformation. However, the quantities entering CHSH are ultimately probabilities (or correlations derived from probabilities). My...

My interpretation is that it is the sign (signum) function, not the sine function. The paper later treats the observable as dichotomic, taking values ±1, so the value at zero is probably irrelevant (measure zero for a continuous field). My question concerns the effect of shifting the threshold...

I'm reading these papers: https://arxiv.org/pdf/2412.03840 https://link.springer.com/article/10.1140/epjc/s10052-026-15445-1 and I'm struggling with Eq. (56). The Bell-CHSH enhancement appears only after replacing ## sign(φ(f)) ## with ## sign(φ(f)+α) ## whereas the undeformed observable...

Since the speed of light ## c ## follows directly from Maxwell’s wave equations and is invariant across reference frames, Einstein was among the first to recognize the apparent paradox and resolve it through Special Relativity (SR).

Maxwell wave equation

That's an interesting point I was just reading this: https://www.nature.com/articles/s41586-026-10859-z https://arxiv.org/abs/2509.19446 Where the "speed" is different on the axis causing birifrangence on the Vacuum

is probably a Pandora's box better left closed. Physics is very good at defining how energy is calculated and what role it plays in a theory, but much less so at answering the ontological question of what energy is.

Fair point. The standing-wave case may actually be an example of what you describe. One can have ## \mathbf{J}=0, ## while the field is naturally interpreted as a superposition of two counter-propagating components. Likewise, the time-averaged Poynting vector vanishes, ## \langle \mathbf{S}...

For the monochromatic case, ## \mathbf{J} \propto \frac{\mathbf{S}}{\hbar\omega}, ## so ## \mathbf{J} ## and ## \mathbf{S} ## are collinear. The factor ## 1/(\hbar\omega) ## only rescales the magnitude and does not affect the direction. It therefore seems plausible that the probability...