Abstract
How a proposed quantum nonlocal phenomenon could be incompatible with the requirements of special relativity is studied. To show this, the least set of assumptions about the formalism and the interpretation of non-relativistic quantum theory is considered. Then, without any reference to the collapse assumption or any other stochastic processes, an experiment is proposed, involving two quantum systems, that interacted at an arbitrary time, with results which seem to be in conflict with requirements of special relativity.
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According to Einstein, for a spatially distributed Schrödinger wave function (e.g., a diffracted wave function from a slit), as soon as the particle is localized (detected) on the screen, a peculiar action-at-a-distance must be assumed to take place which prevents the continuously distributed wave in the space from producing an effect at two places on the screen, or the value of the wave function must suddenly collapse to zero at all other regions where the wave function was spreading [1].
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In other words, with regard to the highest possible detector sensitivity and the prefect noiselessness of the systems, this extremely small amplitude, predicted by non-relativistic quantum theory, bears no physical meaning.
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We consider \(M c^2\gg\sqrt{\langle H^2\rangle}\) and then both the energy and its dispersion are much beyond the relativistic limit.
Acknowledgement
M Bahrami wants to thank Prof. G C Ghirardi of Trieste University, Italy for his valuable comments on this paper.
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BAHRAMI, M., SHAFIEE, A., SARAVANI, M. et al. Is quantum theory compatible with special relativity?. Pramana - J Phys 80, 429–437 (2013). https://doi.org/10.1007/s12043-012-0487-y
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DOI: https://doi.org/10.1007/s12043-012-0487-y