Theory Definition and 1000 Threads

Homework Statement Problem: We want a closed loop control loop for the given process (see bode plot), the control loop requirements are: Steady state error needs to be zero. The gain margin needs to be infinite. The phase margin needs to be 40 degrees. Questions: Which controller will be...

I am reading Tom Leinster's book: "Basic Category Theory" and am focused on Chapter 1: Introduction where Leinster explains the basic idea of universal properties ... I need help in order to fully understand the proof of Lemma 0.7 ... Lemma 0.7 and its proof read as follows:In the above proof...

Hello, i would like to ask You a question about difference in results between Euler-Bernoulli method of analysis of stress in short slender beam and 3D FEA method mentioned in ansys aim tutorial here: https://confluence.cornell.edu/pages/viewpage.action?pageId=33636829 The problem looks like...

This is related to string theory

Suppose that ##n,j \in \mathbb{N}##, ##j \in [0, n-1]##, and ##n~|~2j##. Why is it the case that ##j = 0## or ##2j = n##? This is used in a proof of something else, but I am getting tripped up on this part. I know it has to do with the fact that ##j \in [0, n-1]##. Is it because ##n## can't ever...

Physics could be fundamentally discrete. Are their any notable theories that have discrete mathematics at its core and have QM, GR and differential equations in general as emergent features?

This is a thought experiment, and I am making it as simple as possible. It all takes place out in space. It is necessary to create something that is like a common nail with a large head. It is made of the most ridge material possible, something that is held together by the most potent force...

<Moderator's note: Moved from homework.> Hi all, I have an issue understanding a statement I read in my text. It first states the following Proposition (Let's call it Proposition A): The number of unordered samples of ##r## objects selected from ##n## objects without replacement is ##n...

There are several interpretations of QM which differ from being deterministic or non deterministic, with or without hidden variables and local or non-local. As I understand it ST poses the existence of vibrating strings, that is, physical objects with definite properties, moving along a world...

Have thought about this for sometime but couldn't get deeper. I have speculated that wave-particle duality is a direct result of the relativity theory. Especially it could arise from the factor of length contraction (dimensionality reduction). So far, the particle reality is based on various...

I'm a speculative fiction writer and playwright, a retired archirect with a master of architecture degree in theory, and a theater producer, director, and acting improvisor. I'm currently working on a TV series of 169 episodes exploring life in a contemporary parallel universe very much like...

I found an article written by physicist George Ellis that confused me a little. http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.498.4569&rep=rep1&type=pdf At some part, he says: 3.2 Non-uniqueness: Possibilities There is non-uniqueness at both steps. Stating “all that is possible...

Jacob Bekenstein asserts that the entropy of a black hole is proportional to its area rather than its volume. Wow. After watching Leonard Susskind's video 'The World as a Hologram', it seems to me that he's implying that we are all black hole stuff. Perhaps we (our galaxies and their black...

Lately AdS/CFT seems to have been a very promising tool to simplify calculations in HEP (ex. quark-gluon plasma) and offer some insights into quantum gravity. I was considering doing a Master or PhD thesis in this field, but I'm wondering if the prospects are more reasonable than just string...

are open strings like world lines? and closed strings like loops?

What can 'game theory' tell us about life? The prisoner's dilemma is an issue of Pareto optimality, wherein the best possible outcome is one where both parties cooperate with each other to derive the highest Pareto optimality. But, the issue is that the highest Pareto optimality for the...

Hi all, Only one is true at a time "general theory of relativity or Planetary orbits are elliptical...please clarify me I will thank full to you..

What is the basic idea and purpose of the thermal field theory? I don't need a full in depth description of it, not at the moment at least. I am just trying to understand how it is relevant in the calculation of angular distribution of temperature of CMB(Comic Microwave Background) over the sky.

Homework Statement $$ L = -\frac{1}{2} (\partial_{\mu} A_v) (\partial^{\mu} A^v) + \frac{1}{2} (\partial_{\mu} A^v)^2$$ calculate $$\frac{\partial L}{\partial(\partial_{\mu} A_v)}$$ Homework Equations $$ A^{\mu} = \eta^{\mu v} A_v, \ and \ \partial^{\mu} = \eta^{\mu v} \partial_{v}$$ The...

I am 2nd year physics undergrad. Just want to study a bit about materials in my free time. I have no idea about engineering books. Please suggest some good books. Thanks.

So I have been reading '2D Topological Quantum Field Theory and Frobenius Algebras' by Joachim Kock recently and I couldn't help but wonder, how is this related to physics? I'm currently in the first chapter and he defined a TQFT as a monoidal functor. Now this seems somewhat abstract (which I...

Who am I kidding? Of course it is. But, everywhere I look, the series of increasing levels of orbitals is till σ*2pz only That's all. So if I need to find bond order of , say, some molecule with greater number of e- like BF3 with 24 electrons, how do I proceed?

One of the constants in chaos theory is symbolically labeled as beta, however I haven't found an official definition. The other constants Prandtl and Rayleigh deal with viscosity and diffusivity so they must be appropriate for the specific situation. Is beta simply a constant that can be changed...

In asking a question about analysis textbooks there was a bit of a chat about things like S = 1 - 1 + 1 - 1 ... = 1 - (1 + -1 +1 -1 ...) or 2S = 1 or S=1/2. I will say straight away the answer to what's going on - what infinite sums are, are simply definitions and believe it or not there are a...

What was the problem between Maxwell's EM theory and the principle of relativity? Why went the theory against the principle? I understand that the EM theory says that Light was a wave and ether is it's medium. On the other hand the principle of relativity says that there is no state of...

Allegedly, string theory (in it's simplest form) predicts that cosmological constant must be negative (or zero). Can someone explain where does this result come from? A reference would also be welcome.

Homework Statement A particle moves on the ##xy## plane having it's trajectory described by the Hamiltonian $$ H = p_{x}p_{y}cos(\omega t) + \frac{1}{2}(p_{x}^{2}+p_{y}^{2})sin(\omega t) $$ a) Find a complete integral for the Hamilton-Jacobi Equation b) Solve for ##x(t)## and ##y(t)## with...

How work AC/DC current in Quantum Field Theory

Art Hobson said that quanta propagate in space to infinity. (sorry can not give a link)

How work triboelectricity in QFT? Materialists exchange electrons as well as in classical theory?

It is very difficult for me to understand that a theory based only in "very logical" and "common sense" assumptions (S-Matrix theory, prestring era) makes (some) valid predictions in non-p QCD, while lattice QCD does not. Could the experts comment on this subjet? P.S.: Not interested in string...

Hello guys, I'm wondering if there are some important restrctions on the 'applicability' of first order perturbation theory. I know there's a way to deduce Schwarzschild's solution to Einstein's field equations that assummes one can decompose the 4D metric ##g_{\mu\nu}## as Minkowski...

The Klein-Gordon equation has the Schrodinger equation as a nonrelativistic limit, in the following sense: Start with the Klein-Gordon equation (for a complex function ##\phi##) ## \partial_\mu \partial^\mu \phi + m^2 \phi = 0## Now, define a new function ##\psi## via: ##\psi = e^{i m t}...

What is exactly Weizsäcker's ur-alternatives theory? How is it related to digital physics theories? Is it related to pancomputationalism? Does it defend that a universe can be described as being fundamentally made of qubits? Would this mean that that universe would be fundamentally made by...

Homework Statement Hi, I am looking at the attached question, parts a) and b).Homework Equations The Attempt at a Solution so for part a) it vanishes because in the ##lim \epsilon \to 0 ## we have a complete derivative: ## \int d\phi \frac{d}{d\phi} (Z[J]) ## for part b) we attain part a)...

I would be grateful for opinions on the following book as a good advanced undergraduate/ beginning graduate book for self study ... "Graduate Algebra: Commutative View" by Louis Rowen ... (American Mathematical Society, 2006)Conveniently Louis Rowen has published a book for a "first course" in...

Hello all, Can you tell me what is the best book to study QFT when you are thinking to follow a PhD in cosmology (Dark energy, scalar fields, extension to GR, string theory).

I find the de Broglie-Bohm pilot wave theory interesting but what I still feel missing in the descriptions I could find so far is that it reformulates what we already know but nobody speaks of new testable predictions that could eventually distinguish it from other interpretations (such as a new...

Hello guys, i`m currently making simulation of 2 dimension rolling disk on elastic sin/cosine plane. I`m just wondering if the theory applicable.

So during my PhD I've done one analytic based theory paper with one advisor and will now do an experiment paper with another advisor. I'm curious as to how this will look applying for postdocs. Would this allow me to apply for either theory or experiment? Or would it just make me look not...

Hello! I am reading Griffiths and I reached the Degenerate Time Independent Perturbation Theory. When calculating the first correction to the energy, he talks about "good" states, which are the orthogonal degenerate states to which the system returns, once the perturbation is gone. I understand...

Hello, I am currently taking a circuits class and I was looking for the solutions manual for the book Basic Circuit Theory by Charles Desoer. I haven't been able to find it anywhere but I really want it to practice more of the problems. I am able to do some but I never know if they are right or...

I am trying to read about and understand string theory. But in trying to understand how it reconciles with the world of quantum field theory and quantum mechanics, I am getting a little confused. How does the string move through and propagate through the quantum field? Does string theory...

Hello Everyone. I Was Wondering how excatly the Gauge invariance of the trace of the Energy-momentum tensor in Yang-Mills theory connects with the trace of an Holonomy. To be precise in what I'm asking: The Yang-Mills Tensor is defined as: $$F_{\mu \nu} (x) = \partial_{\mu} B_{\nu}(x)-...

Besides the Feynman lectures on gravitation, I'm looking for modern and complete treatments of the topic of classical gravitation as a field theory in flat space time. Any suggestion?

Homework Statement Approximately 4% of the intensity of light is reflected at a glass-air boundary. Classically one expects roughly 8% of light to be reflected from a thin glass plate (4% at the front and back boundary). Outline briefly what quantum theory predicts for a single photon instead of...

I'm self-studying field theory and trying to solidify my understanding of index manipulations. So I've been told that there is a general rule: " If the index is lowered on the 'denominator' then it's a raised index". My question is whether this is just a rule or something that can make sense...

Homework Statement Homework EquationsThe Attempt at a Solution How to do part biii? I tried to find change of U and W, then use ΔU-W=Q=0. I can find the change in U by using the fact the rms of the x-component of the velocity is doubled. Therefore, originally, if isotropic <c2> =...

In Stanley Kubrick's Dr. Strangelove or : How I Learned to Stop Worrying and Love the Bomb, is depicted, rather comically, a mad scientist who understands that the doomsday weapon is actually an absolute deterrent against nuclear war. The only misfortune is that nobody knew about it in time as...

I'm wondering if one can arrive at E=mc^2 using only the physics of the late 19th century, in the following way: As light waves pass over an electrically charged particle, they push it in the direction of the wave motion, transferring both (kinetic) energy and momentum to the particle. Let's...