Particles as sets?

For the discussion of the sciences. Physics problems, chemistry equations, biology weirdness, it all goes here.

Moderators: gmalivuk, Moderators General, Prelates

User avatar
Pfhorrest
Posts: 4462
Joined: Fri Oct 30, 2009 6:11 am UTC
Contact:

Particles as sets?

Postby Pfhorrest » Thu Apr 19, 2018 7:29 am UTC

Pardon that this is probably a dumb question but I'm half asleep right now.

As I understand it, basically all mathematical objects are reducible to sets, yes? E.g. a group is a special kind of set defined in relation to certain operations thereupon meeting certain rules?

And, as I understand it less clearly, the objects of modern physical theories are reducible to some kind of mathematical objects or another, yes? E.g. (and this is getting in over my head here) quantum fields are defined in terms of some kind of special unity group?

Is it consequently possible to e.g. describe an electron in terms of sets? Not that it would be useful for practical science purposes, but in principle?
Forrest Cameranesi, Geek of All Trades
"I am Sam. Sam I am. I do not like trolls, flames, or spam."
The Codex Quaerendae (my philosophy) - The Chronicles of Quelouva (my fiction)

User avatar
doogly
Dr. The Juggernaut of Touching Himself
Posts: 5379
Joined: Mon Oct 23, 2006 2:31 am UTC
Location: Somerville, MA
Contact:

Re: Particles as sets?

Postby doogly » Thu Apr 19, 2018 12:02 pm UTC

Sure, but sets don't have nice properties. Their only property is the number of things in them. It is a lossy reduction.
LE4dGOLEM: What's a Doug?
Noc: A larval Doogly. They grow the tail and stinger upon reaching adulthood.

Keep waggling your butt brows Brothers.
Or; Is that your eye butthairs?

Nicias
Posts: 161
Joined: Tue Aug 13, 2013 4:22 pm UTC

Re: Particles as sets?

Postby Nicias » Thu Apr 19, 2018 1:31 pm UTC

Also the sets involved would be absurdly complicated.

For instance, real numbers are usually defined as either equivalence classes of Cauchy sequences of rational number or of Dedekind (sp?) cuts or real numbers. If we go with the Dedekind cut definition, then every real number is actually a subset of the rational numbers.

The rational numbers are usually defined as equivalence classes of fractions of integers, with positive integers. So each rational number is really a subset of Z cross N.

The integers can be constructed as equivalence classes of ordered pairs of natural numbers. So each integer is really a subset of N cross N.

The natural numbers (inc zero) can be constructed as nested sets with 0 = {}, 1 = {0} = {{}}, 2 = {1}={{{}}}, etc. Or other similar constructions.

So a real number is a subset of a set consisting of subsets of the cartesian product of (subsets of N cross N) and N. Where N is a set consisting of nested sets terminating with the empty set.

That is just to get to a number like Sqrt(2).

To get complex numbers, add another layer, vector spaces, another layer, a manifold several more layers, function on a manifold, several more layers, by the time you get to gauge theory or some other mathematical description of an electron. The stack of sets is absurd.

User avatar
Eebster the Great
Posts: 2924
Joined: Mon Nov 10, 2008 12:58 am UTC

Re: Particles as sets?

Postby Eebster the Great » Fri Apr 20, 2018 12:38 am UTC

Nicias wrote:The natural numbers (inc zero) can be constructed as nested sets with 0 = {}, 1 = {0} = {{}}, 2 = {1}={{{}}}, etc. Or other similar constructions.

You want to construct the natural numbers in such a way that |n| = n, so a more typical construction would be 0={}, 1={0}, 2={0,1}, 3={0,1,2}, etc.


Return to “Science”

Who is online

Users browsing this forum: No registered users and 9 guests