A bit deeper analysis will lead you such a mathematical framework which is Greens function and propagators. They take care of cause-effect phenomena

A tremendously exciting discussion : Generally considered a relationship of great intimacy, mathematics has been described as "an essential tool for physics" and physics has been described as "a rich source of inspiration and insight in mathematics" Eugene Wigner the NL wrote the following article

decades ago:

https://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html

For an inclusion of cause and effect kindly take a look at :

https://cseweb.ucsd.edu/~goguen/courses/275f00/s3.html

Please take a look at the following useful links:

https://archipel.uqam.ca/443/1/gingras-mathematics.pdf

Yawar Hussain Khan

The application of Green's function starts with an assumption of cause-effect which is your point. But in the end it is just numbers equaling numbers. But which is real. I admit my thinking on this is a bit fuzzy - that is why the question. Consider a simple example of the use of Green's function - a charge is placed in a volume. Then calculate to field at some point. Is the field at the point real or just a math calculation which represents the primary cause (the charge) causing any effect that the math would calculate as the effect of the field. Indeed, are fields real? I suggest fields are not real, but I form a hypothesis that a plenum (ether) is real as one of the components of the universe.

Consider the Newton's law F=ma. The m is (1) the gravitational mass as determined by the reaction of another body, (2) the weight, or (3) the resistance to moving of a body. This brings in the need for some kind of equivalence principle which must be ASSUMED. That is a problem for physics although math handles it. But this leaves a great deal of physics lacking. We can measure the a. Is the F real, no - it is a mapping. This presents 2 types of physical quandary which modern physics in their math heavy approach missing some physical issues which could lead to subtle physics such as photon mass and behavior. Because the photon doesn't behave as a typical 3D body, much confusion results about the reality of the photon.

Ijaz Durrani

Thanks for your reply. I particularly like the second reference. I note in chemistry the arrow relationship denotes a direction of a reaction usually with some energy release. Usually the reaction is not reversible unless there is a double arrow.

A comment: "....physical laws cannot be proved:..." . They can be rejected. indeed, all current physical laws are rejected in some sphere of influence. So, Breadth of applicability is a goal.

see the comment to Yawar Hussain Khan above regarding F=ma. and

Scalar Theory of Everything STOE unites the big, the small, and the four forces (GUT) by extending Newton's model, IntellectualArchive, v. 9 (4),P. 14. http://intellectualarchive.com/?link=item&id=2414

Long ago, when I was an undergraduate in Mathematics and Physics, questions on issues like causality appeared from time to time. There were those who advocated from what you might refer to as "purist" positions. That is to say, there were Mathematicians who believed that Math could produce the equations of physics a priori, and there were Physicists would disagreed stating that the physical principal was a prerequisite. One such discussion occurred between myself and a powerful, highly talented Algebraist on the topic of deriving the Schrodinger Equation. He actually performed the derivation for me. Still, I tend to side, in part , with the Physicists. A physical law say, F = ma, (in a preceding post) or a physical principle say, causality should be grasped as a idea before introducing the math. The caution I would observe is that many ideas, when expressed in equation form, have a tendency to refer to a set of underlying coordinate systems. An example would be Euler's equations for inviscid fluid flow. One can obtain this system in coordinate free form, but usually it is usually not expressed in this way. Unfortunately, when one begins thinking of deeper topics in physics like "Strings" or "Inflation", the single idea concept may be harder to grasp. Mathematics tends to take over in those cases. Of course, there are limitations to what can be demonstrated by the math as regards Godel's theorems. This topic makes for a very good discussion. I offer my compliments to all participants.

Douglas Vinson Nance

A theory, math or physics, starts with propositions (assumptions) from which the theory is developed. I'm questioning if causality is one of the big criteria. Certainly, the equations in physics helps identify measurements and support theories with prediction. Beyond that, I'm unsure what comes next. On the one hand, I've seen several papers suggesting a math manipulation of symbols produce some relationship which suggests a new interpretation. Usually these involve wavelength and energy. If causality were imposed, these models would not indicate anything. On the other hand, imposing causality on all derivations should have some rules which may yield new insights. What constitutes a cause - a measurement? Then Force and energy are not effects - the effect must also be a measurement. But they could be a mapping- a kind of holding action. So, what is the Field equation of General Relativity or the Schrodinger equation?

Looks like you mention a few FQXi topics which I have followed with little enlightenment progress.

see

https://www.sciencedaily.com/releases/2012/10/121002145454.htm

Maged Gumaan Bin-Saad

Thanks for the link.

The last paragraph puts the question I think I'm asking for some insight "...causal order might not be mandatory property of nature." Is it?

I start with Liebniz discussion of the order of events in his relational physics. I tend to discount Quantum math requirements because they are statistical in approach (well except for de Broglie. But if the causal principle(that causal order IS mandatory for a model) is adopted, then Quantum is rejected. The difficulty of causal order for separated in space and time events become a relativity question which may yield totally different physics if the implications of entanglement and quantum eraser experiments are considered (a much faster than light force). The faster than light communication IS suggested in the STOE to explain the photon (particle) interference effect.

How important is causality? is important for the STOE.

Physicist Carlo Rubbia made the statement (and I paraphrase), “Physics is essentially an experimental science.” An interpretation of that idea is that observations drive the development of conjecture, laws, principles, models and so forth. I cannot disagree with that concept, but it also makes me uneasy in that humans are limited by their senses and a three-dimensional environment that is inescapable. Practically every experience in life is founded in causality, but causality has not been recognized as a physical law. Perhaps it is more of a principle or postulate that exists either outside or on the boundary of Physics. Analogies (not to be taken too seriously) might be the postulates of Special Relativity or the Wavefunction representation found in Quantum Mechanics.

A reasonably close tie-in to Causality is Time Asymmetry, or one may refer to it as the “Arrow of Time” described by Hawking among others. Your questions motivated me to do a little extra reading on these issues, so I chose two references:

(i) The Physics of Time Asymmetry, P.C.W. Davies, Univ. of California, Berkeley 1974 and (ii) The Time Asymmetry of Causation, H. Price and B. Weslake, The Oxford Handbook of Causation, 2009. In some sense, causation can be thought of as an asymmetry, i.e., CAUSE->EFFECT expressed with the cause preceding the effect. Or the configuration of a physical configuration prior to the cause is referred to as the antecedent of the effect. Hume’s idea of causation is very tightly bound in that the cause is immediately adjacent to the effect. A problem with Time Asymmetry and Causation from this view is that Thermodynamics is not time reversible casting uncertainty onto the antecedent. The uniqueness of an antecedent from two closely related effects seems to be important. From what I have read, there is no consensus on the symmetry of causation. Of course, consensus is no way to run a science, but it is what it is in the absence of proof. In my view, causation is more properly regarded as a principal with boundaries that are not well defined. It is probably valid for systems of macroscopic objects. But when one considers the quantum realm or the early moments in the formation of universe, the orientation of cause and effect are less certain. As I was taught, there is a lot space in a Hilbert Space. In an attempt to answer a question, a measurement is indeed a cause, but in many cases, we have to regard the measurement apparatus and the measurement subject as a unified system that is, in some cases, entangled or inseparable. As a result, the orientation of cause and effect become unclear. Moreover, the field equations of General Relativity and the Schrodinger Equation begin to look more like models with underlying principles that are somewhat uncertain and limited by observation. These thoughts are just that, and not to be taken too seriously.

Douglas Vinson Nance

You are correct. Causality and the arrow of time are being consistently ignored as both Quantum probabilities and General relativity seem to develop math models at the expense of little regard for causality. Then there are the many complex papers on how to determine causality after the models have made liberal use of probability and shifting parameters from one side to the other of equations with only the number relations of math as a justification. This is the reason for the question.

The FQXi site seems to be devoting more to causality, sometimes called correlation.

Thanks for your insight. Perhaps, the comment should extend to fundamental principles.

Douglas Vinson Nance

Thanks for the reference. I've ordered the Oxford handbook and 2others -by Bohm and by Bunge.

I am glad that you included the comment that causality is sometimes called correlation. It should have occurred to me earlier. After thinking about it, that "dual" relationship makes a lot of sense to me since so much of modern physics relies on correlation. It's an especially impactful idea when one thinks on the idea of a wavefunction, a largely unbounded entity in space that can carry information apparently without considering causation. Correlation can, however, apply. I've done a great deal of work on probability and statistics, so although the application is different, I am reminded of R.A. Fisher's assertion, i.e., "correlation does not imply causation". That statement seems appropriate here. Also, I should say that the article in the Oxford Handbook by Price and Weslake has a more philosophical rather than physics slant. My mention of that fact is not timely, so I do apologize.

Douglas Vinson Nance

Conceptually, if the Universe is one, then we might posit all events are correlated with all other events. Correlation can be due to a common cause or causal. At great distances such as between galaxies, correlation can be due to like processes. Thus, the Hubble Law suggests the redshift of light starts with emission at the same frequency as on Earth. Nearly all cosmological observations have like assumptions. The definition of causality is very important.

So, the postulate that the Universe is one backs away correlation to seek a better characterization and use of causality.

You mentioned Hume's idea that observations are only that one observation follows another. That is, there is no observation of the connectedness of observation. Hume seems to be following Liebniz's discomfort with philosophy following observation in his relative concerns. But a theory may be causal (100% observation of correlation. This places a quandary about modern physics - Quantum Mechanics (QM) being statistically driven. Then we add the nature of measurement of very fine parameters - measurement uncertainty. Born's suggested a Principle of Causality (actually a Principle of Determinism) be discarded (or changed?). John von Neumann suggested the QM model be discarded for a more causal model. I concur. But this may mean a different view of causality, which is this question's subject.

See how rapidly we are getting philosophical and far afield. But this subject has been ignored and physics is needing a paradigm shift.

I'm waiting for the books to arrive. But there are many philosophical views on causality. I hope these books will offer a different view than what the older (pre-QM) suggested.

The philosophical view of physical causality as exemplified by the Price and Weslake (P&W) article views causality from what I refer to as an altitude of 50,000 feet. I was anxious to get more detail say, from ground level or at least from the top of the weeds. You may already know of this work, but I selected a paper on Quantum Causality, e.g., M. Ringbauer et al., “Experimental test of nonlocal causality”, Science Advances 2, (8), 2016. It’s a fairly recent work that is decidedly more complicated. It does tie into the P&W article through the concept of intervention. The core of this work addresses relaxation of some of the assumptions behind Bell’s inequalities. The research is experimental and based upon the theory of causal modeling. In the first experiment, Bell’s local causality assumption is relaxed in that the causal influence of one measurement is allowed to influence the other measurement. This experiment centers around the Clauser-Horne-Shimony-Holt (CHSH) scenario for a dichotomy of observables. For the intervention, we force an input variable to take on a certain value of choice. The other measurement remains unperturbed. As a result the outcome variable associated with the altered input can influence the other output variable. The mathematics behind this process is based on conditional probability and allows the strength of the causal link to be quantified. The experiment utilizes polarization-entangled photons; two settings and two outcomes are tested by two different observers. The CHSH violation is sought and examined. The result for this test is that for CHSH violations above a certain level in the CHSH inequality CANNOT be fully explained by direct causal influence. Hence, a new view of causality is needed.

In the second experiment, the two observers can measure among 3 dichotomic observables. Unlike the first experiment, this experiment is device-independent because the associated inequality is symmetric under exchange of parties say, Alice to Bob, Bob to Alice, etc. in the parlance of Quantum Cryptography. The interventional elements are removed from the experimental set-up. The measurements are made by the two observers in 3 directions cast in the equatorial plane of the Bloch sphere. The results in this case show that for a maximal inequality violation, additional assumptions are required about the underlying causal mechanisms. Hence, a direct causal influence from one outcome to the other CANNOT explain the quantum correlations. I also used an additional reference on relaxing causal assumptions for Bell’s theorem, e.g., R. Chaves et al., “A unifying framework for relaxations of the causal assumptions in Bell’d theorem”, Phys. Rev. Lett., 114, 140403, 2015. As with the first experiment, we can say that a new view of causality is needed. As you have said, it’s very important and needs more attention. I am fascinated by the use of conditional probability and Bayesian networks in analyzing the experiments used here.

You may be interested in Vilasini Venkatesh "Approaches to causality and multi-agent paradoxes in non-classical theories" arxiv:2102.02393. I note that if causality is in the noted experiment, then some kind of faster than light speed cause is needed. That is against Special Relativity and why QM likes conditional probability.

I got the book by Bohm. He defines and studies what he calls Philosophy of Mechanism. Other than some interesting observation of current models, he doesn't get into the math failure to describe causality.

I've read most of the referenced books on causality. It seems to be a philosophical issue. That is, there are many definitions, some authors even change the definition within their text (a science no-no). So, we have the gut feel of how things work in our scale that we learned from infancy period. The need in science is to form a specific and actionable definition and procedure. This is a bit more than the original question. Is causality even a thing that needs definition?

I'm more mystified now than I was when I asked.

It is at this point where Physics becomes "fun", i.e., every "answer" begets more questions. I am reminded of the controversy between and Einstein and Bohr over the EPR (Einstein-Podolsky-Rosen) paradox. At the start, Bohr's response was somewhat "inflammatory", but he soon thought more and decided to "sleep on it". His ultimate response was more measured, and when the "why" of his more thoughtful tone was questioned, he replied, "because we are starting to understand it"; that is, understand the question. As you know, the foundations of Quantum Mechanics (as with causality) defy understanding in human terms, at least at this time. We certainly don't seem to have the "gut feeling" that you describe. Hopefully, in time (how long, who knows), we may understand more. If causality is, by itself, not suitable for a definition, then it is so widely applicable across macroscopic physics, that is likely to subordinate some other concept or principle that we don't know. That's my opinion, of course.

But yet something is missing in physics which results (causes?) in time symmetric equations, a model where entropy always increases, and high correlation of events.

"Causality" in Physics has nothing to do with the philosophical notions of "cause and effect". It is a technical term already incorporated in both the classical and quantum theories, implemented by the Green functions in the classical case and the causal propagators in the quantum one. By the way, the fact that the quantum propagator G, applied to the transition between two states |a> and |b>, has associated a certain transitions amplitude | |^2, which is called the correlation function valued on a,b, does not mean that causality is the same a correlation! This is a confusion discussed in basic courses on probability: two events may be correlated even if there is absolutely no causal relation between them (see, for instance, https://www.khanacademy.org/test-prep/praxis-math/praxis-math-lessons/gtp--praxis-math--lessons--statistics-and-probability/a/gtp--praxis-math--article--correlation-and-causation--lesson). In this particular case, causality means that if the spacetime separation between the events x and y is spacelike, then G(x,y)=0. This is one of the basic Wightman axioms for a Quantum Field Theory (very aptly called the "microscopic causality axiom"): https://en.wikipedia.org/wiki/Wightman_axioms.

José Antonio Vallejo

Yes. Yawar Hussain Khan made the same point earlier. Opinions differ on what Quantum "causation" has to teach us. In QM cause and effect are not always connected by a continuous process, quantum causes may act "instantaneously" at a distance, or quantum causes may act after their effects. How does Quantum deal with "non-locality". My understanding is that Green's functions are correlation functions. I agree correlation is not the same as causation. I think the causation has to be continuous because the time/distance between measurement has to be (much) less than our ability to measure (hbar).

I asked this question from the viewpoint of attempting to get a Theory of Everything. Quantum can make many predictions. However, it is still a probabilistic model and doesn't link with Cosmology. There are several interference experiments that reject the wave model of light. So, I've developed a photon model of light that follows Bohm in that the photon has a definite position and momentum at all times and is generally classical. I'm trying to fill in some holes in the model. Causality from the classical and cosmological worlds stand in the way. The quantum realm, then, should look more like a self-similar world to the classical and cosmological world.

Many thanks for your contribution.

Mathematical physics refers to the development of mathematical methods for application to problems in physics. Physics is often treated as an esoteric, challenging field, but much of physics is very basic, describing how things move in everyday life. You don't have to be a mathematical genius to study physics, but you do need to know the basics, and college physics classes often use calculus and algebra. Yes,physics can exist without mathematics. Even mathematics was made only due to physics. Math is only the tool of physics.. Because of the complex interdependence of physics and mathematics their relation is not free of tensions. The ability to identify cause–effect relations is an essential component of the scientific method. The identification of causal relations is generally accomplished through statistical trials where alternative hypotheses are tested against each other. Traditionally, such trials have been based on classical statistics. However, classical statistics becomes inadequate at the quantum scale, where a richer spectrum of causal relations is accessible. Here we show that quantum strategies can greatly speed up the identification of causal relations. We analyse the task of identifying the effect of a given variable, and we show that the optimal quantum strategy beats all classical strategies by running multiple equivalent tests in a quantum superposition. The same working principle leads to advantages in the detection of a causal link between two variables, and in the identification of the cause of a given variable.

"The unreasonable effectiveness of mathematics in the natural sciences"

---Eugene Wigner.

https://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html

Regards--

Ijaz Durrani

Thanks. You had mentioned this before. Part the issue is how to distinguish correlation from causation?

Dear Dr John Hodge--I apologize for being repetitive: The difference between correlation and causation is :" A correlation between variables, however, does not automatically mean that the change in one variable is the cause of the change in the values of the other variable. Causation indicates that one event is the result of the occurrence of the other event; i.e. there is a causal relationship between the two events." As far as Mathematical Physics is concerned it is the causality that matters not correlation-ship. as Physics in toto is purely a cause and effect study whereas Mathematics may entail correlations ---the latter part of Mathematics is ineligible to form a part of Mathematical Physics!!

Regards--