Theory Definition and 1000 Threads

In first part,since every block of 4 consecutive symbol contain at least 2 a's The answer in notes is given (aa(a+b)(a+b)+a(a+b)a(a+b)+a(a+b)(a+b)a+(a+b)aa(a+b)+(a+b)a(a+b)a+(a+b)(a+b)aa)+ But this wont be true since if we choose aabbbbaa which is possible according to the above regular...

Nikola Tesla, the prominent 20th century inventor, stated in his book "My Inventions" that all human movements appear to come from the will but are are actually generated from the outside. He goes on to say that this phenomenon is of incalculable vale to the human race and he urged further study...

The Threat Of A.I. Is Already Here: “…Bill: So what is it? Can you give an example? How will it be different from these rudimentary forms of A.I.? Gideon: “The public is now getting a glimpse of it. You would want to reference the project known as OpenAI and ChatGPT. Also, Midjourney is very...

In page 67 of book "The mathematical theory of black holes" by S. Chandrasekhar in chapter 2 "Space-Time of sufficient generality" there is a theorem that metric of a 2-dimensional space $$ds^2 = g_{11} (dx^1)^2 + 2g_{12} dx^1 dx^2 + g_{22} (dx^2)^2$$ can be brought to a diagonal form. I would...

Hi Pfs i am interested in spin networks (a pecular lattices) and i found two ways to define them. they both take G = SU(2) as the Lie group. in the both ways the L oriented edges are colored with G representations (elements of G^L the difference is about the N nodes. 1) in the first way the...

Quantum Bayesianism takes the view that the there are no quantum states in the objective sense and that the probabilities should only be interpreted as what information an agent has about the system. Isn't this the same as claiming that there are hidden variables, and that probabilities arises...

I am interested in stomach acid and heat expansion, for instance the stomach will become heated due to an athelete competing. The heat causes atheletes to live shorter than people who don't have their body heated so often. I do a lot of differential equations and number theory, but I was...

I created a YouTube channel (here's the link) a few months ago in which I post detailed lectures in higher mathematics. I just finished my Group Theory Course. Here is a sample video. Apart from that, so far I have uploaded A first course on Linear Algebra (which I am currently renovating). A...

Hello! I am reading this paper and in deriving equations 6/7 and 11/12 they claim to use second oder time dependent perturbation theory (TDPT) in order to get the correction to the energy levels. Can someone point me towards some reading about that? In the QM textbooks I used, for TDPT they just...

Let ##Q_{n}(x)## be the inverse of an nth-degree polynomial. Precisely, $$Q_{n}(x)=\displaystyle\frac{1}{P_{n}(x)}$$, It is of my interest to use the set notation to formally define a number, ##J_{n}## that provides the maximum number of solutions of ##Q_{n}(x)^{-1}=0##. Despite not knowing...

Question is indeed very short and clear, but answer will eliminate many doubts and misleading conclusions. Theory predict downwash that will cause reduction in airflow angle,this we call effective airflow(airflow with lower angle compare at geometric AoA). Does wing of aircraft during flight...

I have read in some books and articles that the Dirac-Bergmann procedure to deal with constraints in phase space does not care about holonomic and Non-holonomic constraints, but I've been unable to find a single example. So, I wanted to test that assertion by solving a simple non-holonomic...

Then please explain how the transition in conceptual language from a single quantum field (extending all over spacetime, or at least over the lab during a day) to an ensemble of particles can be justified from the QFT formalism.

This is usual induced drag diagram. I have 2 questions: From Kutta–Joukowski theorem Fr is always perpendicular to effective airflow. 1. Does it mean for case without effective airflow(zero induced downward velocity), Fr is perpendicular to freestream airflow,so drag is zero? When effective...

I know that linear control theory, in the form ##\dot{x}=Ax+Bu##, ##\dot{u}=Cx+Du##, can be put in the form of a matrix Riccati equation. But is there really an advantage to doing so?

I am reading about symmetries in crystals, and my knowledge in the field of group theory is almost nill. I am reading that, in the worst case, the electrical and thermal conductivity tensors can possess, at maximum, 6 different entries rather than 9, thanks to Neumann's principle which states...

I recently viewed some online free lecture series on Special theory of Relativity. I think I have an understanding of the basics so far, but would like some books for problems on special relativity. (Preferably solutions or at least answer keys included). It would be a great help if they...

a) The solution says that there are 2 bonding electrons and that the 2px and 2py electrons have no effect on the bond order. I don't understand why this is case. b) Why is it that, to form OH+, specifically a nonbonding electron is removed from OH, not a bonding electron? Thank you.

Is there any use for this concept in classical branches of physics? Can it be of any help for a physicist in resolving problems (or, at least, in resolving them more efficiently when compared with traditional methods)? The word «classical» means exactly that, i. e. mechanics, hydrodynamics...

Am going through this notes...kindly let me know if there is a mistake on highlighted part. I think it ought to be; ##α^2=5+2\sqrt{6}##

edit: Hello everyone! When I posted the question, latex equations that were visible in "preview" do not seem here. So, I upload a pdf version of the question. We consider zero free charges and currents: ρ=J=0 $$ \mathbf{\nabla} \times \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t}...

From what I understand only the past and future timelike separated events ever matter for me as an observer. Does that mean there could be a theory where a thing like spacelike separated events does not exist? I mean they never matter for any prediction anyway?

Note that I'm not interested in using it for physics, but instead for deep learning.

My understanding of quantum theory and information theory is that, given complete information on the state of the universe at present, it is possible to predict its state at all times in the future and past. 3 questions: 1: is this true? 2: how are quantum-probabilistic outcomes accounted for...

(2,0) theory is a six-dimensional field theory that has achieved a mild degree of notoriety. "(2,0)" is a notation for degree of supersymmetry, in dimensions where supersymmetries can have a "chirality" (left-handedness vs right-handedness); in this case, it means that this is a field theory...

Hi, In my situation, I am dealing with two ideal gases traveling down a pipe at the same bulk velocities. I am only considering a 1-D treatment at the moment and I would like to find out at which point the two gases should be considered a well mixed, homogeneous mixture. Would anyone know...

In a paper by Bain (2011), particles are left with little ontological value because of the Reeh-Schlieder theorem, the Unruh effect and Haag's theorem. The author claims (and here I am copying his conclusion): First, the existence of local number operators requires the absolute temporal metric...

The given question from Electromagnetic Theory (which is based on Dielectric Boundary Conditions) is as follows: Interface b/w two dielectric medium has a surface charge density (suppose xyz C / (m ^ 2) ). Using boundary condition find field in 1 (relative permittivity =xyz) if field in 2...

I was just wondering what all of your guys favorite theory! For me it is a tie between special relativity and general relativity. I mainly want to know so I can look up any theories posted and learn about them. So what’s your favorite theory?

Hi, For an engineer who graduated and finished typical Cal A,B,C + Linear Algebra + ODE, what book do you recommend to start reading to be a transition to advanced pure math subjects like abstract algebra and number theory? I did deep google search & concluded that that book supposed to include...

In the BCS theory the Cooper pair density depends on temperature, meaning that pairs can be created/annihilated by temperature variations. Obviously, momenta of annihilated pairs dissipate on the atom lattice, so an initial supercurrent dissipates. On the other hand, in some experiments a...

Galois died in a duel at the age of twenty. Yet, he gave us what we now call Galois theory. It decides all three ancient classical problems, squaring the circle, doubling the cube, and partitioning angles into three equal parts, all with compass and ruler alone. Galois theory also tells us that...

Physicists search for explanations and a theory of everything, but how do we know that the 'everything' is any particular way? What if there is no ONE theory of everything. What if there is an infinite number of TOE's that can be shown to exist? How would we choose among them? For example what...

Hi As high school teacher, I sometimes have those extremely talanted and self driven pupils. In their final year, they are required to make a science or math project, roughly one month full-time studies, approx 15-20 pages report. This academic year, one of my students have learned some group...

I am proposing a new theorem of computability theory: THEOREM 1: There are numbers k and s and a program A(n,m) satisfying the following conditions. 1. If A(n,m)↓, then C_n(m)↑. 2. For all n, C_k(n) = A(n,n) and C_s(n) = C_k(s). 3. A(k,s)↓ and for all n, A(s,n)↑. Here C_n(∙) is a program with...

Does nature err slightly beyond order into chaos in the context of chaos theory? And I'd like to proffer the idea that the point at which order tips into chaos actually fluctuates. Nothing in nature is absolutely perfect therefore do natural errors at the point in which order tips into chaos...

Lawrence Krauss, "The greatest story ever told ... so far", pp. 108-109. "Gauge symmetry in electromagnetism says that I can actually change my definition of what a positive charge is locally at each point of space without changing the fundamental laws associated with electric charge, as long...

It is usual, in plasma physics, to combine the kinetic description for electron fluid and the hydrodynamic description for ion fluid, when studying the plasma properties or the dynamics of the electrostatic waves. I am wondering what are the physical meaning and limits of such an approach. Thanks.

Christoph Schiller, "From maximum force to physics in 9 lines -- and implications for quantum gravity" arXiv:2208.01038 (July 31, 2022). This paper asserts that nine propositions can be used to derive the Standard Model and GR and can point the way to quantum gravity, although he cheats a bit...

This statement got me thinking, would it be possible for 1 universe (out of the infinite collection of universes) to be stationary infinitely alternating between state A & B, or using the dice analogy throwing a 1 and a 2 over and over effectively making this universe appear looped in time...

Heisenberg is regarded as a major figure of the Copenhagen interpretation. In a certain degree, he is influenced by Logical positivism. Despite of that, has he any ontological commitments regarding the Quantum theory? Or, he considers the Quantum theory merely as calculation procedure for...

"M. Shupe [Phys. Lett. 86B, 87 (1979)] has proposed that all quarks and leptons are composed of two even more elementary constituents:" (Griffiths) I am redoing the book of elementary particles from Griffths, and this exercise has showed really interesting to me. How is the currently status of...

Hello, I have the opportunity of choosing an elective course on control theory before embarking for my master's program in computational neurosciences and I am weighing the pros and cons. I am looking for advice from PF members who specialized in this field. Since I have chosen enough courses...

From experience how would you balance time on learning theory and problem solving? Maybe learn the theory enough that if you got stuck on a difficult problem you would be able to understand the solution without scratching your head too much? Im using University physics by young and freedman...

## y-x \gt 1 \implies y \gt 1+x## Consider the set ##S## which is bounded by an integer ##m##, ## S= \{x+n : n\in N and x+n \lt m\}##. Let's say ##Max {S} = x+n_0##, then we have $$ x+n_0 \leq m \leq x+(n_0 +1)$$ We have, $$ x +n_0 \leq m \leq (x+1) +n_0 \lt y+ n_0 $$ Thus, ##x+n_0 \leq m \lt...

https://arxiv.org/abs/1803.08928. This is a simple and elegant theory, but there are some things I don’t understand. Why would the anti-universe exist before the Big Bang? From the viewpoint of the anti-universe, isn’t our universe time-reversed? Also, unless the total charge of...

Is there any approach in any books out there, where we consider that in universe exists only one field, let it be called the Unified Field (UF), in which all of the known fields (gravitational, EM field, quark field, gluon field, lepton field, Higgs Field, e.t.c.) are just components (pretty...

Why do scientists refer to evolution as a theory which leads to the argument that evolution is "just a theory"? Why don't they use a less confusing word?

Proof: Let ## n\geq 1 ## be a natural number. Note that ## 5^{2}\equiv 4\pmod 7\implies (5^{2})^{n}\equiv 4^{n}\pmod {7} ##. Now observe that \begin{align*} (3\cdot 2^{5n-2})&\equiv (3\cdot 2^{3}\cdot 2^{5n-5})\pmod {7}\\ &\equiv [3\cdot 2^{3}\cdot (2^{5})^{n-1}]\pmod {7}\\ &\equiv [24\cdot...

Proof: Let ## n\geq 1 ## be a natural number. Then \begin{align*} 6^{n+2}+7^{2n+1}&\equiv (6^{n}\cdot 6^{2}+(7^{2})^{n}\cdot 7)\pmod {43}\\ &\equiv (6^{n}\cdot 36+49^{n}\cdot 7)\pmod {43}\\ &\equiv (6^{n}\cdot 36+6^{n}\cdot 7)\pmod {43}\\ &\equiv (6^{n}\cdot 43)\pmod {43}\\ &\equiv 0\pmod {43}...