Hu2 on Tue, 3 Feb 2026, 08:50 replied to
Superposition: A classical coin spinning on a table is, for a moment, in an undetermined state. However, it actually has a definite orientation at all times (classical ignorance). A quantum coin (analogy for a particle's spin or polarization) truly exists in a state of "superposition," meaning it is both heads and tails simultaneously, or more accurately, it exists in a state that is a weighted sum of both.
- Phase: Unlike a classical spinning coin, a quantum particle has a phase. Feynman emphasized that the probability amplitude for a particle to go from one point to another is a complex number, not just a simple probability. The "twirling" or "spinning" state of a quantum particle represents this phase—the complex amplitude that allows for interference between different possible states before a measurement is made.
- The Act of Observation: Wave function collapse is the abrupt change of a quantum system from a superposition of multiple possibilities to a single, definite outcome upon measurement. In the coin analogy, when you stop the "quantum coin" by "slamming it down on the table" (measuring it), the superposition vanishes, and the coin takes on a definitive state of either heads or tails.
- Feynman's View on "Collapse": Feynman's path integral formulation offers a different perspective on "collapse." Rather than a mysterious, instantaneous physical event, Feynman’s approach treats it as a consequence of measuring only the "final" state.
- Environmental Interaction: In modern terms, the collapse is often seen as a result of interaction with the environment (decoherence).
- Before the measurement, the system is in a pure state; upon interaction with a "measuring apparatus," the system becomes entangled with the environment, causing the wave function to appear to collapse.
- 3. Key Distinctions in Feynman's Approach
- Sum Over Paths: In the two-slit experiment, Feynman explains that the particle does not take one path or the other; it takes all paths. The "collapsing" occurs when a detector is placed, forcing the system to "choose" a path, which effectively changes the experiment's results from a complex interference pattern to a simple, classical probability pattern.
- Probability Amplitudes: Instead of talking about the probability of heads/tails, Feynman would calculate the amplitude for the coin to be heads, and the amplitude for it to be tails, adding these complex numbers together before squaring them to find the total probability.
- No "Hidden" Script: Feynman’s approach emphasizes that there is no hidden script or predetermined state. The result is truly random at the moment of measurement, or more precisely, the outcome is determined only when the measurement takes place.
- In summary, the "twirling coin" is a metaphor for a quantum particle in a superposition of states with a specific phase, while the "collapsing" of that coin is the act of observation that reduces that complex, multi-state system into a single classical outcome.
says:
“So, a "fact check" amounts to checking how justified a belief held by an individual (or a group of individuals) is!”
I was uncomfortable about the statement implied by this sentence, so I thought about it before I went to sleep yesterday and after I woke up in the morning to find out what I was uncomfortable about. And after going through ways of checking whether something is a fact or not, in terms of the four definitions I had suggested, I came to the conclusion that I agree with hu3.
“We are constantly focusing on the notion of truth. What about its counterpart, i.e. falsehood?”
In two-valued logic, if a proposition is not true, it is false, and if it is not false, it is true. Hence, if we establish that the negation of a proposition P is false, then it follows that proposition P is true. In mathematics, the form of proof in which we establish that a proposition is true by showing that its negation is false is called Reductio ad Absurdum (also called Proof through Contradiction)Argumentum ad
Interestingly, a conjecture in mathematics is a proposition that has not been proved to be either true or false. So there are three values here, namely, Proved to be True, Proved to be False, and Not Yet Proved to True or False. But “Not yet proved to be true or false” is not the same as “Neither true nor false”. In three valued logic, there are three values, namely, True, False, and Neither, thereby rejecting Aristotle’s Law of Excluded Middle.
In Multivalued Logics, there can be more than three values. The opening para of the Wikipedia entry on many valued logic is:
“Many-valued logic (also multi- or multiple-valued logic) is a propositional calculus in which there are more than two truth values. Traditionally, in Aristotle's logical calculus, there were only two possible values (i.e., true and false) for any proposition. Classical two-valued logic may be extended to n-valued logic for n greater than 2. Those most popular in the literature are three-valued (e.g., Łukasiewicz's and Kleene's, which accept the values true, false, and unknown), four-valued, nine-valued, the finite-valued (finitely-many valued) with more than three values, and the infinite-valued (infinitely-many-valued), such as fuzzy logic and probability logic.” (https://en.wikipedia.org/
wiki/Many-valued_logic)
Of particular interest to me in this what is called tetralemma or catushkoti in Buddhist logic, which has four values: P, not-P, neither P nor not-P, and P and not-P. Modern logicians see this as a precursor to Quantum Logic where a proposition can be true in one context (or one history) and false in another.
One way of understanding this is to consider the proposition “The sum of angles is two right angles” This is true in Euclidean geometry and false in spherical geometry, Another example comes form the question “Is light a particle or a wave?”. The answer in Quantum Mechanics is “It is a particle under one experimental conditions and a wave under another”. (Wave-Particle duality.) I see this statement as say “It is true under one set of experimental conditions and not-true under another.”
What I have stated above is not a response to what hu3 says, but simply reflections triggered by what he says.
“By the logic of our argument, falsehood would also be attributed to beliefs.”
I agree.
“By the same account, can we say that for every falsehood, there is some degree of likelihood that it may turn out to be true?”
That follows from what Feynman articulates in his public lecture at the 1955 autumn meeting of the National Academy of Sciences:
“The scientist has a lot of experience with ignorance and doubt and uncertainty, and this experience is of very great importance, I think. When a scientist doesn’t know the answer to a problem, he is ignorant. When he has a hunch as to what the result is, he is uncertain. And when he is pretty darn sure of what the result is going to be, he is still in some doubt. We have found it of paramount importance that in order to progress we must recognise our ignorance and leave room for doubt. Scientific knowledge is a body of statements of varying degrees of certainty — some most unsure, some nearly sure, but none absolutely certain. [Emphases mine. Hu1]
A General remark:
The English words fact, true, and know share an attitude to total certainty , and hence are not open to doubting and questioning. In contrast, the following formulations avoid total certainty, and hence are open to doubting and questioning:
“I assume that P is a fact”
“I assume that P is true”
“As far as I know, P”
“I am convinced that P is true”
“I believe that P is true”
“P is rationally justified”
“It is reasonable to conclude that P is true”
In the climatic moment in the movie Agora, the heroine Hypatia says “You will not, and cannot, doubt what you believe – I must” [Watch the YouTube Video clip “Question your beliefs - Agora” (https://www.youtube.com/
watch?v=4N8EFH-qYJ4) ] For me, this axiom is at the heart of what I take to be academic knowledge.
