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What are local laws? I was reading this line in a book...

Newtons second law is a local law. This means that it applies to a particle at a particular instant without taking into consideration any history of the particle or it's motion.

What does this mean in simpler terms?

Are their non local laws as well? Please explain with an example.

I'm a high school student.

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  • $\begingroup$ Force is associated with its point of application. The object carries no memory of forces applied previously and accelerates according to the force applied at an instance of time. A simple restatement: if force is applied on body A for some time interval, then only body A will accelerate during that interval of time only $\endgroup$
    – khaxan
    Commented Oct 1, 2023 at 5:44
  • $\begingroup$ Which reference? Which page? $\endgroup$
    – Qmechanic ♦
    Commented Oct 1, 2023 at 6:25
  • $\begingroup$ @Qmechanic If you're asking about the book, it's Cengage Mechanics-1, page 6.3. Probably not a common book, you can look at the edit, i elaborated what was written. $\endgroup$
    – Aditi Bansal
    Commented Oct 1, 2023 at 6:30
  • $\begingroup$ Wikipedia says non locality refers to action from a distance so a simple example can be gravity $\endgroup$
    – khaxan
    Commented Oct 1, 2023 at 6:59
  • $\begingroup$ @khaxan here when the term local was used, it was used with reference to laws (N2) and not force, although, yes, gravity could be an example of " non local force " . i don't understand what non local law would be though. $\endgroup$
    – Aditi Bansal
    Commented Oct 1, 2023 at 7:21

1 Answer 1

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I will give you two examples. First a local law and then a non-local law, explaining each with examples to make it much simpler.

Ok Local laws, such as Newton's second law for a car, tell you how fast the car accelerates at a particular moment if you know its current mass and the applied force. In contrast for non-local laws such as the gravitational law for two planets in space, consider not only how they are positioned at a given moment but also how their masses and positions continuously affect their orbits over time. The past is also important for these calculations.

I hope my answer will help you.

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  • $\begingroup$ so you mean that since the gravitation law or say the coulombs law consider the relative distance between the planets or particles, which is governed by what forces were acting in the past, they are non local laws $\endgroup$
    – Aditi Bansal
    Commented Oct 1, 2023 at 7:43
  • $\begingroup$ I'm not sure what you mean. From my understanding non-local laws also consider how the object has evolved over time taking into account all the forces, influences that have acted upon it in the past and will affect it in the future. In contrast local laws describe how an object behaves right now, given its current conditions. $\endgroup$
    – mathema
    Commented Oct 1, 2023 at 7:52
  • $\begingroup$ well the formula of force of gravitation law tells us that it just depends upon the masses and distance between the two masses at any given point of time. so how does it care about what happened in the past? $\endgroup$
    – Aditi Bansal
    Commented Oct 1, 2023 at 7:57
  • $\begingroup$ if i understand it correctly, the system of 2 planets has "evolved" in the sense that the distance would be varying because of other forces/other gravitational forces acting by other planets/moons. $\endgroup$
    – Aditi Bansal
    Commented Oct 1, 2023 at 8:05

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