Discrete or Continuous
Contents
Full Title or Meme
The search for understanding about how the discrete events of an Eventful Universe can co-exist with the continuous models of space and time.
Context
Since the discovery, by Newton, of both the laws of motion and the calculus needed to describe it, the continuous model of reality has be the primary source of truth about physical reality. The arguments among physicists about the issue started in 1921 when Max Born tried to find a discretized version of calculus that would describe Quantum Mechanics..[1]
Arguments for Continuous
Remarks on Lubos Motl’s blog definately describe the reason why Physicists trained in calculus think discrete just won't work :
“There is strong scientific evidence today that the world isn’t discrete (and it isn’t simulated).
We do encounter integers and discrete mathematical structures in physics but in all the cases, we may see that they’re derived or emergent. They’re just limited discrete aspects of a more general and more fundamental underlying continuous structure, or they’re a rewriting of a continuous structure into discrete variables (eigenstates in a discrete spectrum) which makes it impossible to understand the value of certain parameters.
Quite generally, if the Universe were fundamentally discontinuous, it couldn’t have continuous symmetries such as the rotational symmetry, the Lorentz symmetry, and even descriptions in terms of gauge symmetries (which aren’t real full-fledged symmetries but redundancies) would be impossible. In a fundamentally discrete world, many (or infinitely many) continuous parameters would have to be precisely fine-tuned for the product to “look” invariant under the continuous transformations.”
Arguments for Discrete
- All of the particles of Physics, including light (energy) are discrete.
- We can only measure discrete events at the quantum level.
- Describing quantum objects with continuous calculus results in lots of infinities, particularly when electrons are considered to be point particles.
- Continuous functions eventually fail at the extremes, such as turbulence in fluid flow, where only discrete methods work.
- Zeno's paradox shows the utter absurdity of thinking that time and distance can be cut up into infinitesimal chunks.
- Crathorn (ca. 1330 AD) affirms that a continuum is divisible into a finite number of atoms that are not mathematical points but its real, physical parts. Atoms are thus real singular entities with discrete magnitude or quantity and a proper nature. For example, he says that there are atoms of gold and atoms of lead, and that these are different kinds of things.[2]
References
- ↑ David Lindley, Uncertainty Doubleday (2007) p. 107 ISBN 9780385515061
- ↑ William Crathorn Stanford Encyclopedia of Philosophy (2022) https://plato.stanford.edu/entries/crathorn/
Other Material
In computing a similar dichotomy is described as Digital versus Analog Computing(qv).
