Quantum Theory From Five Reasonable Axioms · HackerPapers discussions

Quantum Theory From Five Reasonable Axioms — mentioned by magicalhippo

Mon, 03 Mar 2025 11:27:51 GMT

> Quantum Mechanics is essentially just probability with complex numbers For some more on that topic: https://arxiv.org/abs/quant-ph/0101012 https://www.scottaaronson.com/democritus/lec9.html

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Quantum Theory From Five Reasonable Axioms — mentioned by magicalhippo

Fri, 22 Dec 2023 19:36:09 GMT

Reminds me of a paper by by Hardy[1] where he introduces five reasonable axioms (his words). Classical and quantum probability theory obeys the first four. However the fifth, which states that there exists continuous transformations between pure states, is only obeyed by the quantum theory. In that sense he argues that quantum theory is in a sense more reasonable than classical theory. There's also an interesting link between this and entanglement[2] which seems to rule out other probability theories, leaving only quantum theory able to exhibit entanglement. Not my field at all though, just…

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Quantum Theory From Five Reasonable Axioms — mentioned by magicalhippo

Wed, 22 Dec 2021 12:29:56 GMT

Lucien Hardy wrote a paper[1] showing how one "naturally" ends up with a quantum theory by demanding a few reasonable axioms. The paper also goes into how this implies complex numbers (and rules out quaternions). Scott Aaronson has a more accessible (and humorous) article on it here[2]. Entanglement has been shown to be intimately linked to this[3] result, which is interesting given the experimental evidence[4] for entanglement. Not my field, but I found this interesting at least. [1]: https://arxiv.org/abs/quant-ph/0101012 [2]: https://www.scottaaronson.com/democritus/lec9.html [3]…

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Quantum Theory From Five Reasonable Axioms — mentioned by cevi

Sun, 17 Oct 2021 14:49:17 GMT

Unlike perpetual motion or free energy, the math and physics behind quantum computing is rock solid - the possibility is baked into the framework of quantum mechanics at an absolutely fundamental level. Even if it turned out that all of quantum field theory was completely bogus, I would still expect the basic framework of quantum mechanics (i.e. unitary evolution, the Born rule for converting amplitudes to probabilities, density matrices describing mixed states) to be correct. If quantum computing was not possible, that would mean that everything we thought we knew about physics was…

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Quantum Theory From Five Reasonable Axioms — mentioned by boris_m

Tue, 28 Sep 2021 15:22:32 GMT

There is some: https://arxiv.org/abs/quant-ph/0101012 And according to the first sentence of the summary the current formulation is axiomatic as well...

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Quantum Theory From Five Reasonable Axioms — mentioned by chriswarbo

Wed, 14 Apr 2021 18:46:19 GMT

Keep in mind that 'information propagation' is pretty fundamental: we can use it to define light cones (if A can propagate information to B, then A/B are in each others past/future light cones). We can use light cones to define time (past/future) and space (neither). That's a pretty standard approach to relativity (I can't remember whether I covered it as an undergraduate, but I certainly encoutered it around that time). (Shannon) information theory is also closely related to probability, and quantum theory is a form of probability theory (e.g. https://arxiv.org/abs/quant-ph/0101012 ). Hence…

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Quantum Theory From Five Reasonable Axioms — HN submission

Mon, 28 Oct 2019 19:16:54 GMT

Quantum Theory from Five Reasonable Axioms

17 points; 1 discussion reply on HN. Paper and source history. A submission is not an endorsement.

Quantum Theory From Five Reasonable Axioms — mentioned by mikhailfranco

Mon, 05 Feb 2018 14:03:13 GMT

I find Lucien Hardy's discussion enlightening: Quantum Theory From Five Reasonable Axioms https://arxiv.org/abs/quant-ph/0101012

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Quantum Theory From Five Reasonable Axioms — mentioned by mikhailfranco

Wed, 23 Aug 2017 11:50:00 GMT

My random stream-of-consciousness reference reactions ... Tegmark & Lin's discussion of how deep learning maps onto the physical world: Why does deep and cheap learning work so well? [1][2] The work of Aerts et al. more than 10 years ago, including how vector space models of human categorization show QM structure [3]. Lucien Hardy's exquisite teasing out of the difference between classical and quantum probability: Quantum Theory From Five Reasonable Axioms [4] It turns out that the innovation, power and strangeness of QM is related to separating physical processes into: 1. Linear continuous…

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Quantum Theory From Five Reasonable Axioms — mentioned by Xcelerate

Thu, 30 Mar 2017 11:43:52 GMT

> and it is amusing how many professed non-many-worlders say such things. I'm not saying I do or don't believe any of this (if anything, I'm interpretation-agnostic at the moment). I'm just pointing out that there is a contradiction in having one postulate demand unitary state evolution (the Schrödinger equation) for some ill-defined "system" while another postulate says that unitarity is broken at the system/environment boundary. While there's been plenty of attempts to work around this (e.g. https://arxiv.org/abs/quant-ph/0101012), I wouldn't say that anyone has formulated a consistent set…

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Quantum Theory From Five Reasonable Axioms — HN submission

Mon, 14 Sep 2015 22:31:43 GMT

Quantum Theory from Five Reasonable Axioms (2001)

37 points; 6 discussion replies on HN. Paper and source history. A submission is not an endorsement.

Quantum Theory From Five Reasonable Axioms — mentioned by Totient

Sat, 27 Sep 2014 19:18:08 GMT

I love this description of quantum. The paper Aaronson links to, "Quantum Theory from Five Reasonable Axioms" (http://arxiv.org/abs/quant-ph/0101012), is also a great read. The "probability in L^2" cleared up a lot of confusion for me, although I still have a very poor intuition for what the Born probabilities are probabilities of. If you believe the MWI story, it seems like it's the probability you will "find yourself in the universe where this outcome happened" but even that sounds odd to me.

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Quantum Theory From Five Reasonable Axioms — mentioned by bentoner

Fri, 20 Jun 2014 14:24:25 GMT

It's not surprising to me that no physics journals would accept it. Physics journals are, sadly, extremely wary of accepting anything that seems philosophical. For example, serious people writing serious papers on the foundations of quantum mechanics used to have a hell of a time getting them published. To give a particular example (and I hope I'm not mis-remembering), I don't think Lucien Hardy was able to get this paper [1] accepted. (It now has 215 citations.) [1] Lucien Hardy, Quantum Theory From Five Reasonable Axioms [quant-ph/0101012], https://scirate.com/arxiv/quant-ph/0101012

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Quantum Theory From Five Reasonable Axioms — mentioned by mikhailfranco

Sun, 03 Mar 2013 20:01:48 GMT

Truly one of the most remarkable and important things I have seen in a very long time. Two page summary: http://www.tcm.phy.cam.ac.uk/~mdt26/tti_talks/deBB_10/bush_t... Longer presentation with lots of pictures (10MB): http://www.iap.fr/activites/seminaires/GReCO/2013/presentati... When combined with Quantum Information Theory that shows QM as 'just' a probability theory, and simple axiomatic approaches like Lucien Hardy's "Quantum Theory From Five Reasonable Postulates": http://arxiv.org/abs/quant-ph/0101012 Some of the mystery of spooky QM, long perpetuated by the Copenhagen Interpretation…

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Quantum Theory From Five Reasonable Axioms — HN submission

Thu, 19 Aug 2010 19:18:23 GMT

Quantum Theory From Five Reasonable Axioms

1 point; 0 discussion replies on HN. Paper and source history. A submission is not an endorsement.