It's not that it's complicated, but that scientific analysis generally takes place on a different level - that of the scientific analysis of objects, forces and energy. The question of the role of the observer is not complicated in that sense, but it's also not an objective question. That's why it evades scientific analysis - not that it's complicated or remote, but that it's 'too near for us to grasp'. — Wayfarer
When you interact with others on the forum, you are not interacting with physical objects, but with subjects and their ideas. It is vastly different to how you interact with physical objects. — Wayfarer
That sounds mostly reasonable, but the branching part based on something making observations still bothers me a bit. What is the branching mechanism? Perhaps I should have started with that question instead. — Marchesk
To see an interference pattern, you'd have to perform a joint measurement on the two qubits together. But what if the second qubit was a stray photon, which happened to pass through your experiment on its way to the Andromeda galaxy? Indeed, when you consider all the junk that might be entangling itself with your delicate experiment -- air molecules, cosmic rays, geothermal radiation ... well, whatever, I'm not an experimentalist -- it's as if the entire rest of the universe is constantly trying to "measure" your quantum state, and thereby force it to become classical! Sure, even if your quantum state does collapse (i.e. become entangled with the rest of the world), in principle you can still get the state back -- by gathering together all the particles in the universe that your state has become entangled with, and then reversing everything that's happened since the moment of collapse. That would be sort of like Pamela Anderson trying to regain her privacy, by tracking down every computer on Earth that might contain photos of her! — Decoherence and Hidden Variables - Scott Aaronson
"The computable numbers are countable since they be put in a one-to-one correspondence with the natural numbers."
— Andrew M
Not to disagree, but an assertion like that requires a demonstration that they’re countable. — noAxioms
The computable numbers are an infinite set. We have provided an injective function g that maps every computable number to a single natural number: a Godel number. Any set with such a function is countable, and therefore computable numbers are countable. — Alan Turing and the Countability of Computable Numbers - Adam A. Smith
"However the real numbers are not countable per Cantor's diagonalization proof. Thus there are some real numbers that are not computable."
— Andrew M
Interestingly, the real number generated by Cantor's diagonalization proof is a computable number, so I’m not sure if this counts as evidence that there are some real numbers not computable. Once again, not disagreeing with the conclusion, only with how it was reached. — noAxioms
OK, they managed to test something whose outcome (the CHSH inequality violation) was already predicted by quantum theory. It’s a new test, but not one that changed the theory or any of its interpretations in any way. — noAxioms
Thanks for the larger context Bell statement. I agree with it fully. What is ‘jumping’ in that quote? “Do we not have jumping then all the time?”. — noAxioms
Meanwhile, I still don’t see what the AI in the box will do. Bell’s statement is pretty clear that a real human in there wouldn’t serve any special role or purpose, so why would an AI be any different? — noAxioms
"Let’s begin with a thought-experiment: Imagine that all life has vanished from the universe, but everything else is undisturbed. Matter is scattered about in space in the same way as it is now, there is sunlight, there are stars, planets and galaxies—but all of it is unseen. There is no human or animal eye to cast a glance at objects, hence nothing is discerned, recognized or even noticed."
— Charles Pinter, Mind and the Cosmic Order — Wayfarer
"Objects in the unobserved universe have no shape, color or individual appearance, because shape and appearance are created by minds. Nor do they have features, because features correspond to categories of animal sensation. This is the way the early universe was before the emergence of life—and the way the present universe is outside the view of any observer."
— Charles Pinter, Mind and the Cosmic Order — Wayfarer
Pinter's asserted view of "the way the present universe is outside the view of any observer" is a performative contradiction. — Andrew M
. So the moon is round, orbits the Earth and pre-existed life on Earth from a human point-of-view. — Andrew M
Pinter's asserted view of "the way the present universe is outside the view of any observer" is a performative contradiction. That's the problem with the so-called view from nowhere in a nutshell. — Andrew M
I pondered over this for several days trying to understand the arguments. I still hold to what I said. The section you mention nicely shows that the x generated from the list of computable numbers is not itself a computable number, but I was speaking of the x generated from Cantor’s original proof of some real not being a rational number. That x is computable, but not rational, and thus cannot be used as evidence that there are some real numbers not computable.Interestingly, the real number generated by Cantor's diagonalization proof is a computable number, so I’m not sure if this counts as evidence that there are some real numbers not computable. Once again, not disagreeing with the conclusion, only with how it was reached.
— noAxioms
It isn't a computable number (though it is a real number) - see the section entitled "A counter proof?" at the above link. — Andrew M
Collapse seems to be a choice of classical description of a quantum state, in other words, an interpretation-dependent thing. In interpretations with ‘jumping’, yes, it happens all the time, everywhere. In interpretations without it (such as Everett’s relative state formulation, pre DeWitt’s MWI), it’s just a classical effect, not anything physical that happens.What is ‘jumping’ in that quote? “Do we not have jumping then all the time?”.
— noAxioms
He's referring to the collapse of the wave function (i.e., a discontinuous change in the otherwise continuous time evolution of the Schrodinger equation).
I have serious doubts about that. It is a suggestion that there is an empirical difference between the interpretations, and yet I see not explicit prediction from any pair of interpretations that differ.Presumably [the AI in the box] wouldn't. But an AI (unlike a human) could be run on a quantum computer as part of a carefully controlled experiment, thus testing physical collapse theories that differ from standard quantum theory.
You had to reach to Tel Aviv university to find a page closer to your definition?Try this:[ tau.ac.il/education/muse/museum/galileo/principle_relativity.html ] — Metaphysician Undercover
This is blatantly wrong. For one, the appearance of the sun revolving around the Earth once a day is not explained by the Earth revolving around the sun once a day any more than we’re revolving around all those other objects (moon, stars, etc) once a day. Secondly, the sun revolving around the Earth (once a year) violates basic Newtonian physics (lacking a reaction for the action of the sun). Newton’s laws were not in place back then so Galileo wouldn’t have known that.Galileo formulated the principle of relativity in order to show that one cannot determine whether the earth revolves about the sun or the sun revolves about the earth. — tau
This statement is especially ambiguous. Which of them is moving/immobile relative to what exactly? Humans tend to imply the ground since that’s their lifelong reference, but the implication is begging in this context.It is of course possible to determine that one body is moving relative to the other, but it is impossible to determine which of them is moving and which is immobile. — tau
Maybe you should try to actually understand what I’m talking about instead. I’m referencing far more reputable sources than are you. I’m pointing out explicitly what’s wrong with the pages you choose to quote. I don’t see you doing that with my references.I spend all my time just having to show you that you don't know what you're talking about.
You had to reach to Tel Aviv university to find a page closer to your definition? — noAxioms
This is blatantly wrong. For one, the appearance of the sun revolving around the Earth once a day is not explained by the Earth revolving around the sun once a day any more than we’re revolving around all those other objects (moon, stars, etc) once a day. Secondly, the sun revolving around the Earth (once a year) violates basic Newtonian physics (lacking a reaction for the action of the sun). Newton’s laws were not in place back then so Galileo wouldn’t have known that.
Anyway, his pitch of principle of relativity used a boat’s relation to the water as the example, not celestial mechanics. The idea was that one could not tell from inside the boat whether the boat was moving relative to the water or not. — noAxioms
This statement is especially ambiguous. Which of them is moving/immobile relative to what exactly? — noAxioms
Humans tend to imply the ground since that’s their lifelong reference, but the implication is begging in this context. — noAxioms
I’m referencing far more reputable sources than are you. — noAxioms
I pondered over this for several days trying to understand the arguments. I still hold to what I said. The section you mention nicely shows that the x generated from the list of computable numbers is not itself a computable number, but I was speaking of the x generated from Cantor’s original proof of some real not being a rational number. That x is computable, but not rational, and thus cannot be used as evidence that there are some real numbers not computable.
The page you linked does show other ways to demonstrate exactly this, but the diagonalization method is not one of them. — noAxioms
Collapse seems to be a choice of classical description of a quantum state, in other words, an interpretation-dependent thing. In interpretations with ‘jumping’, yes, it happens all the time, everywhere. In interpretations without it (such as Everett’s relative state formulation, pre DeWitt’s MWI), it’s just a classical effect, not anything physical that happens. — noAxioms
"Presumably [the AI in the box] wouldn't. But an AI (unlike a human) could be run on a quantum computer as part of a carefully controlled experiment, thus testing physical collapse theories that differ from standard quantum theory."
I have serious doubts about that. It is a suggestion that there is an empirical difference between the interpretations, and yet I see not explicit prediction from any pair of interpretations that differ. — noAxioms
The fundamental idea is that the unitary evolution of the wave function describing the state of a quantum system is approximate. It works well for microscopic systems, but progressively loses its validity when the mass / complexity of the system increases.
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Such deviations can potentially be detected in dedicated experiments, and efforts are increasing worldwide towards testing them. — Objective-collapse theory - Wikipedia
This Article is intriguing. At first I thought they had found a way to reverse time in the quantum world, but rather they rejuvenated a photon, taking it back to a previous state.
The mathematics involved is probably linear (much is in the quantum world), since most non-linear systems are not reversible. — jgill
Cantor's proof (by contradiction) shows that the set of real numbers is uncountable and thus can't be enumerated. Since the set of real numbers can't be enumerated, the diagonalized number therefore can't be computed. A similar point is made by Carl Mummert (a professor of computing and mathematics) on Mathematics Stack Exchange. — Andrew M
Yes, that's right. Here's the paper for anyone else interested. — Andrew M
Since axioms are produced by mathematicians who practise pure mathematics, and those people who apply mathematics have a choice as to which axioms are used, it would appear like we ought not use axioms like these, which necessitate that aspects of reality will be unintelligible to us. Instead, we ought to look for axioms which would render all of reality as intelligible. — Metaphysician Undercover
There was a member here, active a couple years ago, I can't remember the name, but a self-proclaimed physicist who was big on this time reversal stuff. — Metaphysician Undercover
What do you think this means, to assume numbers which cannot be counted nor computed? — Metaphysician Undercover
Since axioms are produced by mathematicians who practise pure mathematics, and those people who apply mathematics have a choice as to which axioms are used, it would appear like we ought not use axioms like these, which necessitate that aspects of reality will be unintelligible to us. Instead, we ought to look for axioms which would render all of reality as intelligible. — Metaphysician Undercover
The computable numbers include the specific real numbers which appear in practice, including all real algebraic numbers, as well as e, π, and many other transcendental numbers. Though the computable reals exhaust those reals we can calculate or approximate, the assumption that all reals are computable leads to substantially different conclusions about the real numbers. The question naturally arises of whether it is possible to dispose of the full set of reals and use computable numbers for all of mathematics. This idea is appealing from a constructivist point of view, and has been pursued by what Errett Bishop and Fred Richman call the Russian school of constructive mathematics. — Computable numbers - Use in place of the reals - Wikipedia
I was seduced by infinity at an early age. Georg Cantor’s diagonality proof that some infinities are bigger than others mesmerized me, and his infinite hierarchy of infinities blew my mind. The assumption that something truly infinite exists in nature underlies every physics course I’ve ever taught at MIT — and, indeed, all of modern physics. But it’s an untested assumption, which begs the question: Is it actually true?
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Yet real numbers, with their infinitely many decimals, have infested almost every nook and cranny of physics, from the strengths of electromagnetic fields to the wave functions of quantum mechanics. We describe even a single bit of quantum information (qubit) using two real numbers involving infinitely many decimals.
Not only do we lack evidence for the infinite but we don’t need the infinite to do physics. Our best computer simulations, accurately describing everything from the formation of galaxies to tomorrow’s weather to the masses of elementary particles, use only finite computer resources by treating everything as finite. So if we can do without infinity to figure out what happens next, surely nature can, too — in a way that’s more deep and elegant than the hacks we use for our computer simulations.
Our challenge as physicists is to discover this elegant way and the infinity-free equations describing it—the true laws of physics. To start this search in earnest, we need to question infinity. I’m betting that we also need to let go of it. — Infinity Is a Beautiful Concept – And It’s Ruining Physics - Max Tegmark
The assumption that something truly infinite exists in nature underlies every physics course I’ve ever taught at MIT — Infinity Is a Beautiful Concept – And It’s Ruining Physics - Max Tegmark
He was a Q-physicist who left the profession to play his guitar, as he explained to me. — jgill
Our challenge as physicists is to discover this elegant way and the infinity-free equations describing it — Infinity Is a Beautiful Concept – And It’s Ruining Physics - Max Tegmark
I only mean that as n increases so does the function, with no upper bound. I don't mean it ultimately ends up at a magical point at infinity. — jgill
Intuitively, Smooth infinitesimal analysis can be interpreted as describing a world in which lines are made out of infinitesimally small segments, not out of points. These segments can be thought of as being long enough to have a definite direction, but not long enough to be curved.
Until we take notice of the reality of how space and time are actually quantized in real discrete units, these attempts, such as limits and infinitesimals, will remain ideals of theory which do not adequately represent the quanta of reality. — Metaphysician Undercover
There was a member here, active a couple years ago, I can't remember the name, but a self-proclaimed physicist who was big on this time reversal stuff. — Metaphysician Undercover
Maybe he’ll come back in the past. ;-) — Wayfarer
Perhaps space and time are not "actually quantized in real discrete units". — jgill
The mathematical axioms assume a continuity which is infinitely divisible. However, it can be demonstrated in theory (Pythagoras and Zeno), that these axioms will inevitably lead to problems in application. The conclusion we can draw, or which I would say we ought to draw, is that this idea, of infinite divisibility, is just an ideal which does not truly represent the nature of reality. — Metaphysician Undercover
In mathematical physics, the concept of quantum spacetime is a generalization of the usual concept of spacetime in which some variables that ordinarily commute are assumed not to commute and form a different Lie algebra. The choice of that algebra still varies from theory to theory. As a result of this change some variables that are usually continuous may become discrete. Often only such discrete variables are called "quantized"; usage varies.
Physical spacetime is a quantum spacetime when in quantum mechanics position and momentum variables x , p x,p are already noncommutative, obey the Heisenberg uncertainty principle, and are continuous. Because of the Heisenberg uncertainty relations, greater energy is needed to probe smaller distances. Ultimately, according to gravity theory, the probing particles form black holes that destroy what was to be measured. The process cannot be repeated, so it cannot be counted as a measurement. This limited measurability led many to expect that our usual picture of continuous commutative spacetime breaks down at Planck scale distances, if not sooner.
But that number (from Cantor’s proof) is generated from a countable list of rationals, not an uncountable list of reals. So it can be computed. It doesn’t require the ordering of the reals. That was my point,.Cantor's proof (by contradiction) shows that the set of real numbers is uncountable and thus can't be enumerated. Since the set of real numbers can't be enumerated, the diagonalized number therefore can't be computed. — Andrew M
I am not really clear on what a formal statement of metaphysical Copenhagen interpretation would say. I’m more familiar of its roots as an epistemological interpretation where collapse (of what is known) very much does occur, but it is just a change in what is known about a system, not a physical change. They’ve since created a not-particularly well defined metaphysical interpretation under the same name, and if it doesn’t suggest physical collapse, I’d accept that statement.Copenhagen-style interpretations also generally deny a physical collapse. So, in that sense, Copenhagen and Everett/MWI agree (and disagree with physical collapse theories such as GRW).
The empirical difference is between physical collapse theories such as GRW, and non-physical collapse interpretations (such as MWI and Copenhagen). From Wikipedia:
Cool. Interesting to watch then. Thanks.Such deviations can potentially be detected in dedicated experiments, and efforts are increasing worldwide towards testing them. — wiki
Totally agree with this, but it renders meaningless a statement about a single body in the absence of something relative to which motion can be defined.One body relative to the other body, is what is being discussed. Obviously, each is moving and neither is immobile. — Metaphysician Undercover
If there are two bodies with relative motion, then per the definition of motion, both are moving relative to the other, and the differentiation can easily be made by measurement. If there is but the one body, then motion isn’t defined at all.The principle of relativity states that there is no physical way to differentiate between a body moving at a constant speed and an immobile body.
I don’t. I said in my prior post that I could accept it, despite the non-relative wording of it.Why do you incessantly resist and deny the point of the principle of relativity?
If what is being discussed is one body relative to the other body, your choice of wording leaves the second entity unspecified, merely implied, like there’s some embarrassment about it. So say it. Relative to what is nothing immobile?The basic principle is that nothing is immobile (nothing is at rest).
And here I thought it was the definition of motion that did that. The principle of relativity seems to still hold even if you discard the relative definition of motion, and Einstein’s theories along with it.The principle of relativity renders the concept of "at rest" as obsolete.
If the PoR makes the concept of ‘at rest’ invalid, why does it (or at least the version of PoR that you prefer) reference it?… because by the principle of relativity "at rest" is not a valid concept.
Anyway, I will accept this as well. You don’t seem to be pushing the alternate definitions. In Minkowskian spacetime, a rest frame can be any arbitrarily selected frame and the is the implied second object relative to which motion is defined. The selected frame is an inertial one if Newton’s laws of motion hold in it, but other frames (with different laws) are also allowed.Then through extension of Newton's first law, a rest frame, or inertial frame, can be derived from any body displaying uniform motion because "uniform motion" is the concept which has take the place of "at rest".
I don’t find it unintelligible, but I do find fascinating the complete inaccessibility of such numbers to us. The vast majority of real values are these inexpressible values. I gave a few examples of them, especially ones that don’t require units which themselves are only approximately defined.What do you think this means, to assume numbers which cannot be counted nor computed? To me it's a form of unintelligibility, to say that there are numbers which cannot be accessed by us, or used in any way. — Metaphysician Undercover
Totally agree with this, but it renders meaningless a statement about a single body in the absence of something relative to which motion can be defined. — noAxioms
If what is being discussed is one body relative to the other body, your choice of wording leaves the second entity unspecified, merely implied, like there’s some embarrassment about it. So say it. Relative to what is nothing immobile? — noAxioms
And here I thought it was the definition of motion that did that. The principle of relativity seems to still hold even if you discard the relative definition of motion, and Einstein’s theories along with it. — noAxioms
If the PoR makes the concept of ‘at rest’ invalid, why does it (or at least the version of PoR that you prefer) reference it? — noAxioms
My apologies for hanging on this point so much, but you seem to contradict yourself regularly, saying that the concept is invalid, but regularly referencing the invalid concept nonetheless. I personally don’t find the concept invalid at all. It’s just a totally different set of definitions with totally different physics than what Einstein proposes. I don’t prefer these alternate definitions, but I cannot prove them wrong. — noAxioms
Cantor's proof (by contradiction) shows that the set of real numbers is uncountable and thus can't be enumerated. Since the set of real numbers can't be enumerated, the diagonalized number therefore can't be computed.
— Andrew M
But that number (from Cantor’s proof) is generated from a countable list of rationals, not an uncountable list of reals. So it can be computed. It doesn’t require the ordering of the reals. That was my point,. — noAxioms
Copenhagen-style interpretations also generally deny a physical collapse. So, in that sense, Copenhagen and Everett/MWI agree (and disagree with physical collapse theories such as GRW).
— Andrew M
I am not really clear on what a formal statement of metaphysical Copenhagen interpretation would say. I’m more familiar of its roots as an epistemological interpretation where collapse (of what is known) very much does occur, but it is just a change in what is known about a system, not a physical change. They’ve since created a not-particularly well defined metaphysical interpretation under the same name, and if it doesn’t suggest physical collapse, I’d accept that statement. — noAxioms
I was trying to argue that the probability wave is outside of space and time... — Wayfarer
So whether they're discharged one electron at a time, or at a faster (or is that 'higher'?) rate, then you still get the same pattern.
The fact that the effect can't be replicated by a physical (water) wave is, I think, due to the interference pattern not actually being 'waves' as such, but something for which the interference patterns of waves is just an analogy.
The argument that started this was about whether this means that time (being 'rate') is not a factor; which also that means that space (i.e. proximity of particles) is not a factor (as proximity is an aspect of space-time.) So, what is causing the interference pattern is outside, or not a function of, space-time.
This new ontological picture requires that we expand our concept of ‘what is real’ to include an extraspatiotemporal domain of quantum possibility,” write Ruth Kastner, Stuart Kauffman and Michael Epperson.
Considering potential things to be real is not exactly a new idea, as it was a central aspect of the philosophy of Aristotle, 24 centuries ago. An acorn has the potential to become a tree; a tree has the potential to become a wooden table. Even applying this idea to quantum physics isn’t new. Werner Heisenberg, the quantum pioneer famous for his uncertainty principle, considered his quantum math to describe potential outcomes of measurements of which one would become the actual result. The quantum concept of a “probability wave,” describing the likelihood of different possible outcomes of a measurement, was a quantitative version of Aristotle’s potential, Heisenberg wrote in his well-known 1958 book Physics and Philosophy. “It introduced something standing in the middle between the idea of an event and the actual event, a strange kind of physical reality just in the middle between possibility and reality.”
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