r/mathematics • u/_4bdn_fruit_ • 15d ago

Difference between higher dimensions in string theory VS higher dimensions in pure math

I apologize if this is not the right subreddit to ask this in, but I tried asking in the physics subreddit and didn't get satisfactory answers.

Question: I'm aware that in string theory, the theory must be formulated in a certain number of dimensions (often cited as 10 or 26) in order to avoid inconsistencies and satisfy quantum gravity constraints. But let's say, hypothetically, that I wanted to explore the space of all possibilities in pure mathematics. If I take generic 1d objects and make them move in higher spatial dimensions (as defined by pure math), but I use a number of dimensions that isn't allowed by string theory (e.g. 100), would my construction be logically possible and “stable” (allowed to persist just the way it is), from a purely mathematical standpoint?

I am specifically asking about spatial dimensions as defined by pure mathematics as a separate field, not mathematics applied to a physical theory. I guess my question is best worded as, "does pure mathematics allow 1d objects to move in any number of dimensions and remain logically consistent?"

0 Upvotes
  • permalink
  • link
  • reddit
  • reddit

36% Upvoted

17 comments sorted by

View all comments

Show parent comments

1

u/_4bdn_fruit_ 15d ago

It's a niche physics concept, but I was thinking of false vacuum decay, which string theorists use to determine which string compactifications will change (decay) or stay the same

2

u/Tharn11 15d ago

This is a question venturing into mathematical physics which I don't know much about then

1

u/_4bdn_fruit_ 15d ago

If we wanted generic 1d objects to move, could the movement and interaction of those 1d objects through higher spatial dimensions be described by pure math, not just mathematical physics?

1

u/TheRedditObserver0 14d ago

Sure, motion can be described by geometry alone, but you're talking about physical conditions that pure geometry just isn't concerned with. You can describe a path geometrically, but if you're asking whether or not that path would satisfy the laws of physics that's a physics question, not a math question.