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Complex numbers are not, as you suggest, "...an integral part of physical reality". Neither, as you say, does the "quantum wave distribution function necessarily uses complex numbers". Not necessarily. Quantum mechanics can be mathematically formulated using the real numbers, the complex numbers, or the quaternions. See, e.g., https://arxiv.org/abs/1101.5690 ...
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I think you might be confusing determinism with what’s called ‘chaos.’ Chaotic systems are deterministic, nonlinear systems, which are characterized as ‘chaotic’ because of their extreme sensitivity to initial conditions. ‘Nonlinear,’ just means that they can be described by nonlinear differential equations. The so-called ‘butterfly effect’ is a colorful ...
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The short answer: Your premise is not correct. Quantum Mechanics is not necessarily complex-valued. Here is a primer from Physics.SE if you are solid on the math.
An explanation that is light on math: Complex numbers represent a particular collection of symmetries that behave in a particular way. They happen to be closely related to Real numbers because ...
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You have clarified that you understand some descriptions of physics are about hypothetical well-isolated systems with different initial states.
However, when it comes to the Butterfly Effect you reject the concept of taking a well-isolated system with initial states, and demand that it explain the entire universe.
The Butterfly Effect describes a thought ...
15
Your question is about metaphysical realism and skepticism. There are indeed radical sceptic arguments against realism such as Descartes's demon, brain in a vat or the idea that one is actually dreaming, but also reasons to resist these arguments.
First note that there can be no empirical evidence for or against such radical scepticism because these ...
15
The butterfly effect is formally captured mathematically. Consider a chaotic system (such as a mathematical equation of the weather) and an initial state. If we use those equations, we can calculate what the state will be at some future time (say, 1 month in the future). For this deterministic system, that is the only possible state we can be at in 1 ...
10
It is weirder than that: The wave function actually represents the square root of a probability, to the degree that makes any sense. (The simplest mathematical contrivance modeling this is that a particle's mass is re^it where t is time. So it 'rotates' in complex space, and its energy and mass are split into real and imaginary components.) When you ...
9
A universe having a finite volume can be unbounded in length and have unbounded cross-sectional area.
The example I have in mind is mathematical, not physical. It's called Gabriel's Horn. It's a standard example in first-year calculus.
It's also called Toricelli's Trumpet, after Evangelista Torricelli, a student of Galileo. His discovery of this strange ...
9
The view OP is alluding to is called mereological nihilism (mereology is a branch of metaphysics that studies relations between parts and wholes). It is the view that only "simples" (fundamental entities) exist, and composition of simples does not give rise to new objects. Applied consistently this means that, strictly speaking, not only time but chairs and ...
8
Most physicists don't accept infinities for a very obvious reason: such infinite physical objects are not quantifiable! That is, we can't measure them or even prove that they are infinite.
Through the history of physics, infinities were raised in formulas, and usually in these cases the formulas were thrown away, considered as incomplete, or they kept ...
8
The "butterfly effect" appears to be a modern variant of the ancient philosophical axiom "Parvus error in principiis, magnus in conclusionibus" or "Parvus error in principio, magnus est in fine":
A small error in the beginning (or in principles) leads to a big error in the end (or in conclusions).
See St. Thomas Aquinas De Ente et Essentia, proemium, ...
7
Are Why-questions "fundamentally metaphysical in nature"? No. Bas van Fraassen is a prominent example of a recent philosopher who understands scientific explanation as answering Why-questions, and who is also an fairly strict empiricist, meaning that he does not think science has access to nature beyond what is observable. See his The Scientific Image for ...
7
Strictly speaking there are no absolute necessities in physics. But strictly speaking there are no absolute necessities in mathematics and logic either. Mathematical theories have axioms, necessity of conclusions is relative to them, and to logic used. The law of excluded middle is rejected by intuitionists, the law of non-contradiction by dialetheists (see ...
7
There are several notions of intuitionistic continuum, the closest ones to Aristotle's are Brouwer's "fluid continuum", and especially late Weyl’s version of it since On the New Foundational Crisis of Mathematics (1921). We have to keep in mind, however, that Brouwer and Weyl received their view through a major intermediary, Kant. Although Aristotle’s and ...
7
In my opinion, the best response to ontological uncertainty is to strive to live in a way that is meaningful regardless of the true nature of reality. While it may seem implausible, it may be less so than it seems.
Consider the following --we don't know how our universe originated, we don't know what its fate is, we don't know with any certainty our own ...
7
At the present time, we do know not 2, but 4 kinds of physical interaction forces:
Gravity
Electromagnetism
Weak interaction (explaining phenomena from radioactivity)
Strong interaction (explaining phenomena from particle physics)
The latter three kinds of interaction have been successfully unified within the standard model by a common type of ...
7
In my opinion you are mixing up different points:
Physics does not use complex numbers to count entities. It is sufficient to count mangos by non-negative rational numbers, i.e. 1 mango, 1.5 mangos, 1/3 mango etc.
You are right that quantum mechanics is based on the psi-function which is a complex function. The squared modulus of this function, a real ...
6
This is a particularly sticky wicket because (a) we are delving into the philosophy of quantum mechanics (which is beset on all sides by those who wish to pervert it to their own ends) and (b) because we are confounding our understanding of the problem by confusing what we mean by "exists."
To make this question more meaningfully answerable I will address ...
6
Not sure this is a philosophy question.
Before relativity simultaneity was just when two things happen at the same time. The distance between events only depended on time (t). Then, with relativity the idea of proper time became introduced as a new way of measuring "how far apart" events are. This does not always coincide the original idea, as it contains ...
6
Bergson's thesis was not that time is space-like, but that time understood "in the common way" is space-like. Bergson argued that practical reasons cause us to regard time as space, but that strictly speaking, the thesis that time is space-like is not merely wrong, but self contradictory. Influences from Aristotle and Kant can be detected in Bergson. For ...
6
I suspect that Petitot is misremembering and interpolating. Husserl did generally consider (formal) metaphysics to be the doctrine of individuation. For example, in a 1918 letter to Weyl, thanking him for a copy of Das Kontinuum, he writes:
"Finally a mathematician shows appreciation for the necessity of phenomenological modes of treatment in all ...
6
Even if you assume determinism without quantum complications, I think a better interpretation (more consistent with Lorenz's original math) is this: Given a complete description of the state of the Universe at one point in time, calculating all the causes and effects forward may come to a point with, say, a hurricane in Florida. Suppose that we rewound back ...
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All you need is a system that is not in thermal equilibrium (which is practically any macroscopic system), or equivalently a system into which you can inject a reasonable amount of entropy. This process is termed quantum decoherence. The mathematics is nontrivial, but the bottom line is that it's essentially a statistical property, and as such a single ...
5
Randomness and causation are in different categories. Something can be both random and caused, or random and uncaused (if you believe in such things). Randomness is not a property of origin (cause) but of comprehension (understanding the origin).
Random can mean simply "unpredictable", or "of or characterizing a process of selection in which each item of a ...
5
If I interpret this correctly you seem to be asking whether some kind of rudimentary form of awareness may be a property of all matter?
One person who I think would answer in the affirmative is Graham Harman in his metaphysics of 'polyspychism'. The most clear and complete exposition of his system is called The Quadruple Object, a great introduction can ...
5
We have a good number of fragments that are attributed to Parmenides himself. Specifically regarding the void, Parmenides asserts that you cannot separate what is from what is, because doing so implies a something that is not. Since what is not is not, it can't be used as a property of difference. Thus, there can't be any difference in the world, which ...
5
Imagine an exotic "universe", which does not have deterministic laws, but does have a notion of discrete time. At each step in time, the state of the universe — its "material" content — is given by a set of objects. It has no conservation laws as such.
What happens is at each step, the set of material elements is replaced by either the power-set of its ...
5
Forget about the "natural" thing for a second. Let's look at your sentences again:
All matter attracts all other matter;
¬(φ ∧ ¬φ).
The first is a physical principle and it does seem to be true of our universe, so we may go ahead and call it "natural". The second is a logical principle, which, having nothing to do with our universe is ...
5
I am not sure that saving phenomena can be used to argue that Plato and Aristotle admitted or did not admit that different suppositions might be consistent with them. At the time Plato posed the problem of reconciling apparent motions of planets with the Pythagorean ideal of uniform circular motions not only wasn't Ptolemy's system around, but no such theory ...
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A manifold is a space, not an object in space. The line you draw on paper is not a manifold, although it may be an attempt to visualise one.
The reason you should not think of manifolds as embedded is that it leads to wrong intuition about shortest paths, distances, curvature: if you visualise a 2D sphere embedded in 3D space, you might think the »real« ...
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