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Register a new userIs there a physical continuum?
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Added by
M\\'at\\'e Csan\\'ad
Publication date
2021
fields
Physics
and research's language is
English
Authors
Mate Csanad
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We are used to the fact that most if not all physical theories are based on the set of real numbers (or another associative division algebra). These all have a cardinality larger than that of the natural numbers, i.e. form a continuum. It is often asked, whether there really is a continuum in the physical world, or whether a future physical theory could work with just countable infinities. The latter could for example be compatible with a quantized space-time. In this paper we formulate a simple model of the brain and show that within the presented natural assumptions, the continuum has to exist for at least some physical quantities.
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Modern radio spectrometers make measurement of polarized intensity as a function of Faraday depth possible. I investigate the effect of depolarization along a model line of sight. I model sightlines with two components informed by observations: a diffuse interstellar medium with a lognormal electron density distribution and a narrow, denser component simulating a spiral arm or H~{sc ii} region, all with synchrotron-emitting gas mixed in. I then calculate the polarized intensity from 300-1800~MHz and calculate the resulting Faraday depth spectrum. The idealized synthetic observations show far more Faraday complexity than is observed in Global Magneto-Ionic Medium Survey observations. In a model with a very nearby H~{sc ii} region observed at low frequencies, most of the effects of a depolarization wall are evident: the H~{sc ii} region depolarizes background emission and less (but not zero) information from beyond the H~{sc ii} region reaches the observer. In other cases, the effects are not so clear, as significant amounts of information reach the observer even through significant depolarization, and it is not clear that low-frequency observations sample largely different volumes of the interstellar medium than high-frequency observations. The observed Faraday depth can be randomized such that it does not always have any correlation with the true Faraday depth.
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