Infinite number of quantum particles gives clues to big-picture behavior at large scale

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In quantum mechanics, the Heisenberg uncertainty principle prevents an external observer from measuring both the position and speed (referred to as momentum) of a particle at the same time. They can only know with a high degree of certainty either one or the other—unlike what happens at large scales where both are known. To identify a given particle's characteristics, physicists introduced the notion of quasi-distribution of position and momentum. This approach was an attempt to reconcile quantum-scale interpretation of what is happening in particles with the standard approach used to understand motion at normal scale, a field dubbed classical mechanics.

In a new study published in EPJ ST, Dr. J.S. Ben-Benjamin and colleagues from Texas A&M University, USA, reverse this approach; starting with quantum mechanical rules, they explore how to derive an infinite number of quasi-distributions, to emulate the approach. This approach is also applicable to a number of other variables found in quantum-scale particles, including particle spin.

For example, such quasi-distributions of position and momentum can be used to calculate the quantum version of the characteristics of a gas, referred to as the second virial coefficient, and extend it to derive an infinite number of these quasi-distributions, so as to check whether it matches the traditional expression of this physical entity as a joint distribution of position and momentum in classical mechanics.

This approach is so robust that it can be used to replace quasi-distributions of position and with time and frequency distributions. This, the authors note, works for both well-determined scenarios where time and frequency quasi-distributions are known, and for random cases where the average of time and average of frequency are used instead.

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More information: J. S. Ben-Benjamin et al, From von Neumann to Wigner and beyond, The European Physical Journal Special Topics (2019). DOI: 10.1140/epjst/e2018-800063-2
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Citation: Infinite number of quantum particles gives clues to big-picture behavior at large scale (2019, April 11) retrieved 20 April 2019 from
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Apr 11, 2019
Part 1] Position and momentum are relative terms whereby they are observer-specific. Two observers can arrive at different values for position, for instance. We do not immediately realise this because we consider the measures against larger scale static frames but our relationship to those frames must also be established.

Instead of considering particles, why not go to the more fundamental level and consider the metrics of the inertial frame against which both the particle and the observer's position and momentum are measured?

Whilst an observer can always be at rest in his own inertial frame and therefore have an exact position within that frame, it is notable that frame is measured from the observer. We could say that no two inertial frames can have an exact position and momentum relative to each other.

Apr 11, 2019
Part 2] By considering this dynamic we are removing the particle from the equation and just considering the geometry of the inertial frame. The geometry should show that the relative position and speed of two inertial frames can never be correlated exactly, that inertial frames are intrinsically fuzzy at some scale relative to each other.

Does this fuzziness accumulate? Does General Relativity include a property reflecting this fuzziness? Are there any conditions whereby this fuzziness is amplified to larger scales, such as at extreme relative speed or extreme space-time curvature? If the fuzziness is not a property of the basic equations then we'll never know from modelling alone...

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