Physics and the IntegersAn essay response to the FQXi contest "Is Reality Digital or Analogue?" by Prof. David Tong, theoretical physicist at Cambridge University.
Leading on from the last post that discussed Informational Structural Realism as a way of looking at the world and doing away with both digital and continuous views of reality I thought I'd share this essay Physics and the Integers
that I really enjoyed as part of my recent readings on digital and continuous physics and reality. Not to fear: this essay is far more accessible than the article in my prior post.
This essay won second prize in the Foundational Questions Institute contest Is Reality Digital or Analogue?
The full list of essay entries for this contest answering this question can be found here: http://fqxi.org/community/forum/category/31417
. While the winning essays and those considered the best can be found here: http://fqxi.org/community/essay/winners/2011.1
; I really should get around to reading both the winning entry and the joint second place entry. Whatever your bias and preference you should be able to find a number of excellent entries to enjoy with novel arguments and insights into reality that you may not have considered before.
I first encountered Physics and the Integers
in popular (slimmed down, edited, equationless) format at Nature / Scientific American under the title The Unquantum Quantum
. However this is pay-walled unfortunately.The full essay Physics and the Integers is available here for free: http://fqxi.org/data/essay-contest-files/Tong_integers.pdf
Selected excerpts include:
➤ Quantum mechanics is not constructed from the integers. The fundamental object is a complex valued wavefunction ψ obeying the Schrodinger equation. Nor are there integers in the Schrodinger equation itself.
➤ God did not make the integers. He made the complex numbers and the rest is the work of the Schrodinger equation. The integers are not inputs of the theory. They are outputs. The integers are an example of an emergent quantity.
➤ The objects that we call fundamental particles are not fundamental. Instead they are ripples of continuous fields, moulded into apparently discrete lumps of energy by the framework of quantum mechanics which, in this context, is called quantum field theory. In this way, the discreteness of the particle emerges.
➤ To formulate the laws of physics in a discrete manner means to write them in such a way that they could be simulated on a computer. Can we simulate the known laws of physics on a computer? The answer to this question is, at least to me, extremely surprising: no one knows how to formulate a discrete version of the laws of physics.
➤ The current state of the art is that there is just a single class of quantum field theories which physicists do not know how to simulate on a computer. This is the class in which fermions that spin in an anticlockwise direction experience different forces from those that spin in a clockwise direction. Such theories are referred to as chiral [and they are special]. Perhaps the most special among them is the Standard Model. This is a chiral theory because only fermions that spin anti-clockwise experience the Weak force. Chirality is one of the most striking and important features of the Standard Model. Yet, when it comes to constructing a lattice version of the theory, it has consequence: no one knows how to write down a discrete version of the Standard Model.
➤ I find it striking that the discreteness we see in the world is not sewn into the equations of physics, but arises only when we solve them.
➤ But it may be worth considering the possibility that the difficulty in placing chiral fermions on the lattice is telling us something important: the laws of physics are not, at heart, discrete. We are not living inside a computer simulation.
The image / GIF below depicts a representation of a Spin-1/2 fermion that needs to be rotated through 720⁰ in order to return to its original state and was lifted from Wikipedia: https://en.wikipedia.org/wiki/Spin_(physics)
. It was mentioned in the essay a few times as an example of of a property - which the forces of nature treat differently depending if it spins one way or another - that suggests reality is continuous and analogue. #digital #continuous #physics