The electron is not in any state until it's measured, so there is no contradiction. — Sam26
Well, what Godel demonstrated is that consistency is unprovable within the system. Further, that there are true statements also unprovable within the system. The "within the system" making all the difference. The unprovable true statements being, when added, just the axioms of an augmented system.in its current form, is consistent...or not. — TheMadFool
Sure, in English/language/logic. But whoever said that those were in fact adequate to describe nature?To be up and down at the same time is a frank, outright contradiction. — TheMadFool
consistency is unprovable within the system — tim wood
to say that a system is unprovable is not to say that processes within the system are not provable, or in any way inconsistent. 2+2=4 being a simple example of a true and consistent expression from within mathematics. — tim wood
The electron is not in any state until it's measured, so there is no contradiction. One could think of it as the potentiality of states, or, there is the probability that it will be in this state or that state when measured. So, it's not that it's both up and down at the same time.
This reply is only meant to address some of your concerns. It doesn't address your comments or questions about Godel. — Sam26
It's a misinterpretation of Schrodinger's cat to think the cat is both dead and alive. You can never observe the cat in both states. And, once you do observe it, it's then in one state or the other, so no contradiction. — Sam26
Man, if you don't believe I'll just die. Just do a little more reading, and you too, will agree. lol — Sam26
1. How on earth does math state, as a mathematical equation probably, the contradiction referred to above (bolded/underlined) without itself being contradictory? This is diabolical sorcery: Here is a mathematical equation :point: Schrodinger's equation perhaps and it's not a contradiction BUT when translated into English, :point: both up AND down, it is a contradiction. — TheMadFool
2. Is it possible that quantum mechanics reveals that math is inconsistent? — TheMadFool
The issue is only that something was lost in the translation from math to English. Paraphrasing SMBC, "Quantum superposition... It doesn't mean spin-up and spin-down at the same time. At least, not the way you think.
...
It means a complex linear superposition of a spin-up state and a spin-down state. You should think of it as a new ontological category: a way of combining things that doesn't really map onto any classical concept." — Andrew M
No — Andrew M
Then why all the hullabaloo about Schrödinger's cat? There's something odd about quantum mechanics, that's for sure. — TheMadFool
Why? Using only the axioms of math, whatever they are, we've arrived at a contradiction. What's the next step? — TheMadFool
The hullabaloo is about how to interpret the math, not the math itself. Many Worlds is closest to treating a superposition as a conjunction with the caveat that the opposite spin states are indexed to different worlds: thus no contradiction. — Andrew M
No, the math doesn't imply a contradiction. Here's an example of a superposition in Dirac (Ket) notation:
|ψ>=0.6|up>+ 0.8|down>
The '+' in Dirac notation is not a logical 'and'. To link the formalism to observation, square the coefficient for a state to calculate the probability that that spin state will be observed (e.g., 0.6*0.6=36% probability of observing spin-up).
You would need additional assumptions to derive a contradiction. See, for example, Bell's Theorem. — Andrew M
Just an observation: electrons are not really 'particles' but rather localized excitations in the electron field. — Photios
That's what I was getting at. What about Schrödinger's cat thought experiment? I suppose it's a veiled criticism of the Copenhagen interpretation which is open to so-called quantum weirdness. — TheMadFool
It is typical of these cases that an indeterminacy originally restricted to the atomic domain becomes transformed into macroscopic indeterminacy, which can then be resolved by direct observation. That prevents us from so naively accepting as valid a "blurred model" for representing reality. In itself it would not embody anything unclear or contradictory. There is a difference between a shaky or out-of-focus photograph and a snapshot of clouds and fog banks. — The Present Situation in Quantum Mechanics, 5. Are the Variables Really Blurred? - Erwin Schrodinger
Yes, despite my math illiteracy, I can tell, it's safe to assume, that there's no mathematical contradiction. The question then is, why do people, scientists, Schrödinger himself for example, resort to analogies that are frank contradictions (the cat is both dead and alive)? — TheMadFool
↪SolarWind
The measuring can happen in a variety of ways. It seems to be a kind of disturbance, conscious or otherwise. It's a disturbance of the wavefunction. The main point, though, is that there aren't contradictions happening, as far as I can see. — Sam26
The funny thing is that there is never a contradiction if you only look at what arrives in the consciousness. Every consciousness carries out its own private collapse of the wave function (->Wigner's friend).
If every observer has his own wave function according to his state of knowledge, then the contradictions are cancelled. — SolarWind
Contradictions are about statements or propositions, reality itself is not contradictory. Contradictions only occur in language, i.e., when using concepts. — Sam26
The traditional source of the law of non-contradiction is Aristotle's Metaphysics where he gives three different versions.[14]
1. ontological: "It is impossible that the same thing belong and not belong to the same thing at the same time and in the same respect." (1005b19-20)
2. psychological: "No one can believe that the same thing can (at the same time) be and not be." (1005b23-24)[15]
3. logical (aka the medieval Lex Contradictoriarum):[16] "The most certain of all basic principles is that contradictory propositions are not true simultaneously." (1011b13-14) — Law of non-contradiction - Wikipedia
Suppose this :point: E is the equation for the superposition of spin states of a particle. — TheMadFool
Suppose this :point: E is the equation for the superposition of spin states of a particle.
Your task: Translate E into English. — TheMadFool
You appear to be operating with two related agendas: 1) to find a solid bridge between language and reality, and I am pretty sure that, as language is ever descriptive, it can not ever be real, or, 2) to be satisfied that at some level of smallness, reality itself ceases to be real.
And this reflective of a dissatisfaction with your own understanding - some variety of which in some or another application we all feel. But what I think you have got, and all that you have got, is that language takes in the fringes of reality clumsily and with difficulty, and at the extremes not at all, until someone invents new language to cover it. That is, I am very sure that the reality you question has itself no problem with being real. — tim wood
Get involved in philosophical discussions about knowledge, truth, language, consciousness, science, politics, religion, logic and mathematics, art, history, and lots more. No ads, no clutter, and very little agreement — just fascinating conversations.