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Granted that physicists have always been concerned about causation, the laws of physics stated in terms of equations have nothing to say about causation. Are they correlational laws, causal relationships, or something else?

When we say force is the cause of motion, we are talking metaphysics. — Henri Poincaré

Spacetime tells matter how to move; matter tells spacetime how to curve. — John Wheeler

Fields tell charges how to move; charges tell fields how to vary. — Leonard Susskind

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    Do you know the context of Poincaré's statement?
    – Jo Wehler
    Commented Apr 21 at 6:22
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    The quote is from "Henri Poincarè: Science and Hypothesis" see gutenberg.org/files/37157/37157-pdf.pdf p.110
    – Jo Wehler
    Commented Apr 21 at 7:24
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    You will get better answers to this question on Physics SE.
    – g s
    Commented Apr 22 at 17:26
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    They are constraints, not causes. Causation is a phenomenon of (general) relativity, giving a natural partial order to events. The equations of physics constrain what phenomena they can explain in an acausal fashion: neither do equations cause physics to happen a certain way, nor do observations change a model by fitting it well/poorly.
    – Corbin
    Commented Apr 22 at 21:04
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    @Corbin please write an answer explaining causal sets
    – quanity
    Commented May 1 at 9:46

6 Answers 6

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  • Physicists observe correlations.
  • Physical laws explain observations by inventing physical concepts and clarifying their relation. These relations are often causal relations.
  • Physical laws do not deal with what-is questions like “What is gravity?”, “What is mass?”.
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    what do you mean by "what-is" questions, as it's the first i've heard of it. what is the gravitational constant? what is the cause of this man's lung cancer? what is keeping this boat from sinking? i would think scientists do ask what an atom is, and while i am not correcting you, i am a bit confused
    – andrós
    Commented Apr 21 at 6:36
  • @user66697 Some philosophers would call what-is questions also metaphysical questions, questions which ask for the essence of a phenomenon.
    – Jo Wehler
    Commented Apr 21 at 6:49
  • if you can expland your answer with the (non) history of 'essence' in science, that would be amazing
    – andrós
    Commented Apr 21 at 6:50
  • @JoWehler what about constraints ?
    – quanity
    Commented Apr 21 at 15:12
  • @quanity Please explain to me what you mean with your question about constraints; thanks.
    – Jo Wehler
    Commented Apr 21 at 15:34
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Equations by definition simply equate, so if you state the laws of physics as equations, without any of the associated narrative, then you are not stating the laws of physics!

Some equations express cause and effect relationships, some express correlations, some are definitions- you have to consider the context.

For example, there is an equation P1V1=P2V2 which expresses the principle that the product of the pressure and volume of a gas at constant temperature is fixed- it doesn't have a fixed cause and effect directionality. F=ma, on the other hand, is intended to express cause and effect, as you would know if you had read Newton's book (which is freely available on the internet).

Equations such as those that define entropy or temperature are just that- definitions.

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  • It sounds as if you had read Newton's Principia - in English, in Latin? ... But seriously: Do you know whether Newton explicitly speaks about causality, using the terms cause and effect?
    – Jo Wehler
    Commented Apr 21 at 7:00
  • @JoWehler Hi Jo, hope all's well with you. I'm afraid my Latin didn't get beyond grade B at O-level. There are English translations on line. It was a long time ago that I looked at one- might be interesting to take a quick look yourself and see what you make of it. I read it only out of curiosity to see how the great man expressed himself. Commented Apr 21 at 7:20
  • @MarcoOcram if F and a have causal relationship then there must be a time gap
    – quanity
    Commented Apr 21 at 16:09
  • @quanity: Why? We can't measure the acceleration change immediately, we would have to wait for the object's position to change by a noticeable amount and backsolve for acceleration. So in that sense, there empirically is a time gap. But it seems as if you're claiming that causation ontologically requires a gap between cause and effect, and I'm just not sure how you justify that claim.
    – Kevin
    Commented Apr 21 at 21:26
  • It might be worth mentioning Norton's dome and related objections to Newton's view of causality.
    – Corbin
    Commented May 2 at 18:33
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Granted that physicists have always been concerned about causation,

I'd take exception to that, most physicist are expressely uninterested in metaphysical questions, at best they try to answer ontological ones: which makes perfect sense as soon as physics and philosophy become disctinct.

On the other hand, there is a technical notion of "causal" that is specifically relevant since Einsteinian relativity, but, again, it has no metaphysical import, it is about the "causal structure" of the Universe, meaning constraints on the possible history of "events".

the laws of physics stated in terms of equations have nothing to say about causation. Are they correlational laws?

Not exactly: every equation in physics expresses a relationship between physical quantities.

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In classical physics every state evolved from the previous state. This is called determinism and it means that every state was caused by a sequence of previous states. By this principle you should be able to calculate from a precisely known state backwards and forward in time and therefore predict past and future. So in that sense every state has a cause and is a cause.

But quantum mechanics showed us that the universe is not deterministic but probabilistic. But even there we have equations describing change over time (Schrödinger equation), but they don't describe the change of the state of a system directly but the probability of measurement outcomes which can change over time. But even then the current quantum state is determined by previous quantum states.

So you could argue that every law of physics using time t as a variable implies a causation, but the causation only becomes apparent, when you look at different points in time. And you basically have to do consider this as causation, because if you don't, causation is non-existent anywhere.

As to what Poincaré might have meant, I would think it points to the actual idea of a force. Not only is there no such isolated thing, there were even forces that had to give way to better explanations, most impactful probably gravitation, which was replaced by the curvature of spacetime. So a force is merely a concept invoked to express a change to a system from the outside. An electron might change its direction in the presence of a magnetic field, but we don't even know what a magnetic field really is, since it has no other effect than affecting electric charges. We kind of standardized the unit Newton, but we get to it in many different ways with unrelated sets of units.

And as for causation we are unable to explain how any causation might even take place. On the quantum level it is often called the "collapse of the wave function" when something actually causes something else. Better is maybe the expression "update of the wave function". This happens when something like a measurement takes place, meaning any interference with a quantum system, including observation. The system seems to basically snap into another state and so far we have no useful model describing this.

Some additional ideas are on https://en.wikipedia.org/wiki/Causality_(physics)

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  • "If I had asked physicists what they wanted, they would have said, 'better explanations'."
    – Scott Rowe
    Commented Apr 23 at 10:58
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Granted that physicists have always been concerned about causation, the laws of physics stated in terms of equations have nothing to say about causation. Are they correlational laws?

The laws of physics stated in equations constrain causal relationships. For example, there are many theorems about how events can depend on one another in general relativity:

https://arxiv.org/abs/2009.07555

In quantum theory it is also possible to reach conclusions about how different systems interact to cause the results of experiments:

https://arxiv.org/abs/quant-ph/9906007

https://arxiv.org/abs/1109.6223

Those equations are part of the explanations physicists provide for how the world works, why specific events happen and so on. The laws of physics are not about correlations any more than the claim that dinosaurs existed is about dinosaur fossils.

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  • Thanks for the links! I'm enjoying the first paper. You might get more clicks if you give their titles or further explain why these specific papers are worth reading.
    – Corbin
    Commented May 2 at 18:34
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Causation is a phenomenon of (general) relativity, giving a natural partial order to events. The equations of physics constrain what phenomena they can explain in an acausal fashion: neither do equations cause physics to happen a certain way, nor do observations change a model by fitting it well/poorly. — my earlier comment

I agree with and have upvoted all prior answers. This is an invited answer focusing on causal sets (WP, nLab).

Quoting nLab, a causet "is a concept with an attitude: In itself it is just a partially ordered set (or poset, for short), but meant to be understood as a set of spacetime events subject to the relation of causality." Formally, a causet is a partial order where every interval is finite.

This condition is subtle enough to need explanation. The interval has finitely many smoothly-deformable paths, and its cardinality is related to the topology of spacetime. For example, consider a room with two entrances and the events "I am outside the room" and (later) "I am inside the room". I can walk through either entrance, but I can't smoothly deform my walking-path from one entrance to another, so the interval between those events has cardinality two.

An immediate consequence of this framing is that the laws of physics, particularly those which include time, are outside of causality. To be causal is to be embedded within some sort of smooth Lorentzian space.

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  • Is elements of cosets atoms of spacetime or just events
    – quanity
    Commented May 5 at 11:19
  • @quanity: The elements of causets are moments where particles are interacting with each other; we could imagine a Feynman diagram for each event. The individual atoms/quarks/etc. are not necessarily localized to any particular neighborhood, so it is not quite correct to say that a particular atom belongs to an event. Fundamentally, this is a point-free approach, and so atoms are not as important as the geometry of spacetime.
    – Corbin
    Commented May 5 at 18:33

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