Abstract
Most physics theories are deterministic, with the notable exception of quantum mechanics which, however, comes plagued by the so-called measurement problem. This state of affairs might well be due to the inability of standard mathematics to “speak” of indeterminism, its inability to present us a worldview in which new information is created as time passes. In such a case, scientific determinism would only be an illusion due to the timeless mathematical language scientists use. To investigate this possibility it is necessary to develop an alternative mathematical language that is both powerful enough to allow scientists to compute predictions and compatible with indeterminism and the passage of time. We suggest that intuitionistic mathematics provides such a language and we illustrate it in simple terms.
Highlights
Physicists are not used to thinking of the world as indeterminate and its evolution as indeterministic
Let us contrast the above assumption of the existence of a natural random process with the common assumption that real numbers faithfully describe our world, in particular that the positions of elementary particles in classical and in Bohmian mechanics are faithfully described by mathematical real numbers (Gisin, 2019)
Physical models should allow humans to tell stories about how nature does it, e.g. how the moon drives the tides, how white bears and kangaroos remain on Earth, how lasers operate and how time passes
Summary
Physicists are not used to thinking of the world as indeterminate and its evolution as indeterministic. Let us contrast the above assumption of the existence of a natural random process with the common assumption that real numbers faithfully describe our world, in particular that the positions of elementary particles (or their centers of mass) in classical and in Bohmian mechanics are faithfully described by mathematical real numbers (Gisin, 2019). Either all digits of the initial conditions are assumed to be determined from the first moment, leading to timeless physics, or these digits are initially truly indeterminate and physics includes events that truly happen as time passes (Gisin, 2020a) Notice that in both perspectives chaotic systems would exhibit randomness. This is the point of view of intuitionistic mathematics, as developed by L.E.J. Brouwer, where the dependence on time is essential (Standford 2021). Changing the mathematical language used by physics, from classical Platonistic to intuitionistic mathematics, could well make it easier to express some concepts and to rebut Dolev’s claim that passage cannot be part of physics (Dolev, 2018)
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