Foundations Definition and 116 Threads

Can mathematics rest on new foundations? See the attachment. a little explanation about the form of addition adding or joining , as performed R a+b=c same as now, combined numbers 222+33=2253, when they are the same along (gap) they are joined, here 2 and 3, we get 5 R2 here there is an...

As this has been a key point, in several threads in particular the last close one https://www.physicsforums.com/threads/local-mechanism-for-nonlocal-anticorrelations-inside-spin-theory.1066463/ I though I would clarify what this means becuase it is a pity to confuse it with classical (newtons)...

I feel silly for asking, since I have accepted this always as true, but I don't have a reference for what ##0^p## equals when ##p## is a positive real number. This dawned on me when trying to show the positive definiteness of the ##p##-norm for ##x\in\mathbb R^n##, that is, $$x=0\iff...

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I have a hard time to grok QM. I wonder if it is my fault. Probably QM and all the interpretations are incapable to explain the world as we observe it (either in Newtonian mechanics, or in Special Relativity), not counting gravitation, also not allowing "objective collapse" (which would be a...

Interested in foundations of physics, Quantum Mechanics.

See, Derivation of the Schrödinger Equation from Newtonian Mechanics Edward Nelson Phys. Rev. 150, 1079 – Published 28 October 1966 Abstract, "We examine the hypothesis that every particle of mass m is subject to a Brownian motion with diffusion coefficient ℏ2m and no friction. The influence...

The book wanna show how to find potential of a dielectric. The problem arises when it uses a vector identity. Still there is no problem. My problem is that I cannot understand why ##\rho_P= -div P##? I think it should be ##-div' P##. The book is wrong? In next page it uses ##-div'## In...

In a different thread, hungrybear asks, Are the implications of MWI really this horrifying? The argument being that every conceivable world must happen to some extent, so that includes worlds so horrific that the mere possibility of their existing makes life intolerable here. Of course there...

Loophole-free test of local realism via Hardy's violation (2024) Si-Ran Zhao, Shuai Zhao, Hai-Hao Dong, Wen-Zhao Liu, Jing-Ling Chen, Kai Chen, Qiang Zhang, Jian-Wei Pan "Bell's theorem states that quantum mechanical description on physical quantity cannot be fully explained by local realistic...

I've been researching the MWI, and just when I thought I was starting to get it, I got confused again. There aren't many worlds; there's one in superposition? What's the difference? When do worlds(?) split? Will someone please explain the theory in a simple way, but not so simplistically I might...

I hate to bring up an old saw again, but I've been listening to Carroll and some others wax poetically about Many Worlds. And Jurek's work on decoherence and pointer states seem to address some of the problems with the MWI. However, I haven't seen any compelling explanation as to why an...

I once conjectured that Bohmian mechanics arrived at an unfortunate point in time, when interest in QFT overshadowed potential opportunities offered by Bohmian mechanics: One of those opportunities was the analysis of non-locality, later done by Bell, and the reason why I brought up Bohmian...

The editors of high impact journal Nature Physics explain why the field of quantum foundations is important for physics. https://www.nature.com/articles/s41567-022-01766-x

I'd like someone to check that this solution is right, and if not, give me the point of failure and not the answer. Thanks!

I was on you-tube and saw a video from Oxford on QM foundations. I didn't agree with it, but that is not an issue - I disagree with a lot of interpretational stuff. The video mentioned a paper they thought essential reading...

Steven Weinberg wrote a book again. Did anyone read it? https://www.amazon.com/dp/1108841767/?tag=pfamazon01-20

Does anyone have any thoughts on this book? https://www.amazon.com/dp/9813234121/?tag=pfamazon01-20

Recently, it has come to my attention a field called Quantum Foundations. This is exactly what brought me into Physics, even though back then I didn't know it was a research area. In my Physics classes, I got disappointed and unmotivated at the "Shut up and calculate!" attitude of my Physics...

Has anyone come across Quine's New Foundations? https://plato.stanford.edu/entries/quine-nf/ https://en.wikipedia.org/wiki/New_Foundations I'm not very knowledgeable about set theory, mathematical logic, or the foundations of mathematics, but I found what I read interesting. The basic idea (as...

Back in the day, there were a few Quantum Interpretation polls on here, as of late I have not seen any. I love that we now have a sub-forum for Foundations discussions. I figured it would be interesting to see how the participants of PhysicsForums feel about the different interpretations these...

I'm looking for a book on foundation of quantum mechanics. I started reading the book "do we really understand quantum mechanics" of franck laloë , and it seems to be very chatty and long. Do you have any recommendations? Thank you

I want to do my Phd on foundations of quantum mechanics, but I don't find researchers in the U.S.A that work on that. Is there a good way to search other than to go to each university and go over the PI's? Thanks

Is it possible for new forces or fields of nature to be connected to quantum foundations? For example, new forces or fields that choose the decoherent histories or branches. Or generally actualize one of the decoherence branches? Or should new forces or fields of nature be reserved for...

Hey, applied maths and physics student here. I started wondering recently what the meaning of measurement was in quantum mechanics, and I remembered that I had once heard of the bohmian interpretation which challenged the impression I had so far (which was that hidden variables had been...

Physicists often discuss interpretations of quantum mechanics (QM), but they rarely discuss interpretations of relativity. Which is strange, because the interpretations of quantum non-locality are closely related to interpretations of relativity. The field of interpretations of relativity is...

Cliff Notes Version Quantum Interpretations and Foundations guidelines All PF guidelines applicable to any forum apply here, plus the following. Questions in initial posts of threads may cite unpublished textbooks or pre-publication papers such as ArXiv, subject as always to review of sources...

What are the best books on QT Foundations out there? This seems to be a difficult question which has very different answers depending on who you happen to ask. There seem to be at least two different levels, e.g. intermediate texts and advanced texts, with a very wide gap in between, which is...

I'd like to draw attention to a very recent paper by Jürg Fröhlich, a well-known mathematical physicist from the ETH Zürich. It starts out as follows: Section 2 is titled ''Standard formulation of Quantum Mechanics and its shortcomings''. Surely @vanhees71 has very convincing reasons why this...

Hi I am currently trying to learn about smooth manifolds (Whitneys embedding theorem and Stokes theorem are core in the course I am taking). However, progress for me is slow. I remember that integration theory and probability became a lot easier for me after I learned some measure theory. This...

This thread is a shootoff from this post in the thread Summary of Frauchiger-Renner. The topics are related, but this thread offers a new perspective that diverges from the main subject of that thread. In QM foundations, the sheer amount of interpretations, disagreement among experts about what...

Hi all, I have been trying to read up on quantum foundations after being first introduced to it on this Perimeter Institute page: https://www.perimeterinstitute.ca/research/research-areas/quantum-foundations/more-quantum-foundations However, I have had difficulty finding notes and papers on...

Hey there! While considering going into foundational issues in QM (reading abou entanglement and Bell's theorems now), I realized I may need a better grasp of QM. I have studied both Griffiths' and Cohen-Tannoudji's (both volumes, excluding the appendices) books. I am not very confident in my...

Some years ago now, I was a regular reader and poster here and had a lot of fun arguing about the meaning of Bell's theorem, the relative merits of different "interpretations" of QM, etc. I just popped in for the first time in a long time, and it is nice to see some familiar faces (and many new...

I'm going to start my first year as a Physics major in University, so I'll be taking first year Physics with one variable Calculus with Linear Algebra. I have taken math up to Calculus but I found that I have some gaps in Algebra, Geometry, and Trigonometry. Not any serious gaps, I know most of...

Hello, all. I am looking for some good books to start becoming invested in mathematical logic, the foundations of the field of mathematics, and also basically in general the philosophical heart of this wide subject which has interested me greatly. Now I have already read Shoenfield and Halmos...

Hey guys, so I stumbled across this, and I'm kinda confused on how do they get the sign convention of the value. I've attached the figure and also the soil pressure for better reference. Take for example at C, how do they get the minus and positive sign convention? Thanks a bunch. P/S : Please...

I am looking into self studying astrophysics, but not to an academic professional level. I am at the moment going through the Khan Academy material in maths, physics and astronomy. I am in no hurry to grasp all the material, as my reason for self study is more interest than professional...

Restricting to finite dimensional QP, suppose a system is in a state S1, an experiment is done, and state S2 is one of the eigenstates (assume all eigenvalues are distinct). The probability that the system transitions from S1 to S2 is p = Trace( S1*S2), using state operator notation. On the...

Ah. It was skepticism about publishing, not about giving a comprehensive account! Yes, I am preparing a book on quantum mechanics, which will contain an account of the thermal interpretation - but primarily to macroscopic, nonrelativistic reality, where it is obvious that it gives the correct...

For properly normalized extensive macroscopic properties (and this includes the center of mass operator), there is such a proof in many treatises of statistical mechanics. It is the quantum analogue of the system size expansion for classical stochastic processes. For example, see Theorem 9.3.3...

What are the prerequisites to read this book? In the book he stated that there are no GR and QFT knowledge assumed but some people said that it is not true. Can anyone comment on this book? Thanks.

Hello everyone, I've never used PF before, so I'm not exactly sure I'm posting in the right place. Anyway, here's what's going on : I'm currently preparing a Master's in neurobiology. I stopped studying sciences (i.e., physics, chemistry, maths) in high school, but somehow managed to catch up...

I'm hoping to do a foundation year for mechanical engineering next year, can anyone recommend to get this book in preparation for it?: https://www.waterstones.com/book/foundations-of-mechanical-engineering/anthony-johnson/keith-sherwin/9780412616006 Thanks

That doesn't follow. Selecting a system to study is necessary for most of physics. But it is always a subjective act - since Nature isn't divided into system and the rest of the universe. Most of the time we don't want to consider the universe as a whole but only the particles in a particular...

So far in Landau, we've covered the following: Axiom 0: The "equals sign" is an equivalence relation (reflexive, commutative, and transitive). Axiom 1: $1$ is a natural number. Axiom 2: For each $x$ there exists exactly one natural number, called the successor of $x$, which will be denoted by...

I wans't sure on where I should post this question. So, if this place is inappropriate, please move it to a proper section. The question is as its posed in the title of this topic. What we mean by foundations of physics? when someone talks of the foundations of physics, what is he/she talking...

Hi. I hope this is not too far into philosophy. Set Theory is commonly accepted as the foundations of Mathematics. Is it possible to develop a different type of Mathematics by using Fuzzy sets or Rough sets instead?

My question is about foundations of the special relativity theory. In Minkowski's way of presenting special relativity, with a signature "+ - - -", one associates to every couple of events, a spatio-temporal distance which is null on the light cone, positive if the two events are causally...

Hello PhysicsForums! I am a Physics/Math double major undergraduate junior. I've always loved math, and to study the universe; so I decided to combine both and become a physicist! I did my Gen Phys 1-2 (with Calc) and most of my math at a state college and then I transferred to a university...