Locality is:

the principle of locality states that an object is only directly influenced by its immediate surroundings.

The first classical theory violated it:

In the 17th Century Newton's law of universal gravitation was formulated in terms of "action at a distance", thereby violating the principle of locality.

Newton of course was aware of this:

It is inconceivable that inanimate Matter should, without the Mediation of something else, which is not material, operate upon, and affect other matter without mutual Contact…That Gravity should be innate, inherent and essential to Matter, so that one body may act upon another at a distance thro' a Vacuum, without the Mediation of any thing else, by and through which their Action and Force may be conveyed from one to another, is to me so great an Absurdity that I believe no Man who has in philosophical Matters a competent Faculty of thinking can ever fall into it.


Gravity must be caused by an Agent acting constantly according to certain laws; but whether this Agent be material or immaterial, I have left to the Consideration of my readers.

Isaac Newton, Letters to Bentley, 1692/3

That is he 'gives' up on the problem; luckily so - as it took 350 years and the genius of Lorentz, Poincare and Einstein to return locality to Gravitation; they had already by then had the example of Coulombs force which also violated locality but which was resolved by Maxwell.

Is this a principle one that originates with Newton (despite his lack of success in incorporating it); or one that had already been thought through?

Its the same principle that makes violations of locality in QM problematic.

Leibniz has a principle of Continuity:

“Nothing takes place suddenly, and it is one of my great and best confirmed maxims that nature never makes leaps.”

But its not clear to me that this helps.

  • Quantum mechanics is local arxiv.org/abs/quant-ph/9906007 arxiv.org/abs/1109.6223.
    – alanf
    Sep 26, 2014 at 9:54
  • locality in QM is contentious; how has Deutsch shown this? Sep 28, 2014 at 2:56
  • The equations of motion of quantum mechanics such as the Heisenberg equation of motion for observables are local. They predict that the Hermitian operator values of the observables of one system will come to depend on those of another only if they interact directly or indirectly. Deutsch and Hayden explain how "non-local" phenomena such as the EPR experiment come about as a result of local information flows. The idea of non-locality comes from a crude equivocation between a measurement result and the corresponding observable.
    – alanf
    Sep 29, 2014 at 8:23
  • Locality is a complex topic; its incorporated in QM generally speaking in relativistic QFT; after all it is relativity that guides our understanding of space & time; its this idea of locality that I'm noting in my question; Deutsch & Hayden are talking about non-local states or entanglement - a different (but connected) idea. Sep 29, 2014 at 14:03

1 Answer 1


I would like to draw attention to writings of Rene Descartes. This is from Part II of his Principles of Philosophy (Kluwer, 1982)

33. How in all movement a complete circle of bodies moves simultaneously. It has been shown above that all places are full of bodies and that the size of each part of matter is always exactly equal to that of its place; {so that it is not possible for it to fill a bigger one or to fit into a smaller one, or for any other body to find room in its place while it is there}. From this it follows that no body can move except in a {complete} circle {of matter or ring of bodies which all move at the same time}; in such a way that it drives another body out of the place which it enters, and that other takes the place of still another, and so on until the last, which enters the place left by the first one at the moment at which the first one leaves it. We easily conceive of this in the case of a perfect circle, because we see that no vacuum and no rarefaction or condensation are required to permit part A of the circle to move toward B, provided that part B moves simultaneously toward C, C toward D, and D toward A. But the same thing can also be' understood even in the case of an imperfect circle... [where] we can suppose that speed of movement compensates for narrowness of space. Thus, in any given length of time, the same quantity of matter will pass through one section of this circle as through another. (pp.55-56)

I think it could be understood as if he applies the idea of locality to interactions of various parts of matter in the Universe. This idea he extends to the movement of celestial bodies. This quotation is from the Treatise on Light and other principal objects of the senses (The World and other writings, CUP, 2004)

Chapter 10 Of the planets in general, and in particular of the Earth and the Moon. ...Now two things follow from this which seem to me to be very significant. The first is that the matter of the heaven must make the planets turn not only around the Sun, but also around their own centre, except where there is something particular preventing them from doing so, and consequently that the matter must form around the planets small heavens that move in the same direction as the greater heaven. The second is that, if two planets meet that are unequal in size but disposed to take their course in the heavens at the same distance from the Sun, and if one of them is exactly as massive as the other is larger, then the smaller of the two, moving more quickly than the larger one, must become joined to the little heaven around that larger heaven and turn continually around it. (p.45)

Finally, he explains the gravity in the same way as sum of local interactions; the explanation is rather lengthy, this is just little piece of it:

Chapter 11 On weight. ...But now I want you to consider what the weight of this Earth is, that is, what the force is that unites all its parts and makes them all tend toward the centre, each more or less according to the extent of its size and solidity. This force is nothing but, and consists in nothing but, the parts of the small heaven which surround it turning much faster than its own parts about its centre, and tending to move away with greater force from its centre, and as a result pushing the parts of the Earth back toward its centre. (p.47)

I do not think that Descartes was the first who had been advancing the idea of locality in his time; probably, the concept was already in the air. However, he develops it quite systematically.

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