- #1

- 121

- 1

## Main Question or Discussion Point

Is there a strict connection between non-locality and non-linearity? Is it true that non-local systems must have non-linear equations? Are non-linear equations the consequence of non-locality?

- Thread starter cryptist
- Start date

- #1

- 121

- 1

Is there a strict connection between non-locality and non-linearity? Is it true that non-local systems must have non-linear equations? Are non-linear equations the consequence of non-locality?

- #2

- 121

- 1

Really? Isn't anyone can answer this?

- #3

- 32

- 1

The response of a material can be non-linear -this depends on the (external) field- while non-locality does not necessarily depend on the field. I don't know if this applies to all cases, this is simply my understanding.

You need to elaborate a bit here. What kind of "non-linear equations" do you have in mind ?Is it true that non-local systems must have non-linear equations?

The constitutive relations of a chiral medium can be linear and non-local.Are non-linear equations the consequence of non-locality?

- #4

- 121

- 1

Nevertheless, let's think the motion of a particle as an example. Let's assume we exposed particle to an instantaneous effect (for example that effect can change his position superluminally). Then this system is non-local, and it must have non-linear equations, right?

- #5

martinbn

Science Advisor

- 1,845

- 558

Isn't quantum mechanics linear and non-local?

- #6

- 121

- 1

- #7

- 32

- 1

A non-local eqn will pop out if the particle's position does not depend only on the applied field, sayNevertheless, let's think the motion of a particle as an example. Let's assume we exposed particle to an instantaneous effect (for example that effect can change his position superluminally). Then this system is non-local, and it must have non-linear equations, right?

* meaning that you don't always get quadratic or higher order terms of

- #8

martinbn

Science Advisor

- 1,845

- 558

You are asking about a strict connection between non-linear and non-local. If quantum mechanics is linear and non-local, then your question has a negative answer, no?

- #9

- 10,909

- 3,601

Yet, if QM were nonlinear (not merely by a collapse postulate, but at a more physical level), then, depending on the interpretation, it could be even more nonlocal than it is in the standard linear form.

See e.g.

http://xxx.lanl.gov/abs/0707.2319

and Refs. [1,2,3] therein.

- #10

- 121

- 1

So such field should affect particle's acceleration also, to have non-linear equations?A non-local eqn will pop out if the particle's position does not depend only on the applied field, sayF, but also on its derivatives, its curl for example. This does not necessarily* introduce nonlinearities in the eqns of motion.

* meaning that you don't always get quadratic or higher order terms ofF

Or quantum mechanics is wrong. Oops, I have to runYou are asking about a strict connection between non-linear and non-local. If quantum mechanics is linear and non-local, then your question has a negative answer, no?

So as far as I understand, although no strict connection between both, nonlocality increases from linear to nonlinear.

Yet, if QM were nonlinear (not merely by a collapse postulate, but at a more physical level), then, depending on the interpretation, it could be even more nonlocal than it is in the standard linear form.

See e.g.

http://xxx.lanl.gov/abs/0707.2319

and Refs. [1,2,3] therein.

- #11

- 32

- 1

No. Why do you say this ?So such field should affect particle's acceleration also, to have non-linear equations?

What do you mean by "So as far as I understand, although no strict connection between both, nonlocality increases from linear to nonlinear.

- #12

- 380

- 1

not settled yet.Isn't quantum mechanics linear ?

- #13

- 121

- 1

- Replies
- 2

- Views
- 1K

- Replies
- 80

- Views
- 4K

- Last Post

- Replies
- 4

- Views
- 1K

- Last Post

- Replies
- 194

- Views
- 27K

- Last Post

- Replies
- 17

- Views
- 810

- Last Post

- Replies
- 7

- Views
- 2K

- Replies
- 3

- Views
- 5K

- Replies
- 2

- Views
- 660

- Last Post

- Replies
- 10

- Views
- 2K

- Last Post

- Replies
- 2

- Views
- 1K