A theory is a rational type of abstract thinking about a phenomenon, or the results of such thinking. The process of contemplative and rational thinking is often associated with such processes as observational study or research. Theories may either be scientific or other than scientific (or scientific to less extent). Depending on the context, the results might, for example, include generalized explanations of how nature works. The word has its roots in ancient Greek, but in modern use it has taken on several related meanings.
In modern science, the term "theory" refers to scientific theories, a well-confirmed type of explanation of nature, made in a way consistent with scientific method, and fulfilling the criteria required by modern science. Such theories are described in such a way that scientific tests should be able to provide empirical support for it, or empirical contradiction ("falsify") of it. Scientific theories are the most reliable, rigorous, and comprehensive form of scientific knowledge, in contrast to more common uses of the word "theory" that imply that something is unproven or speculative (which in formal terms is better characterized by the word hypothesis). Scientific theories are distinguished from hypotheses, which are individual empirically testable conjectures, and from scientific laws, which are descriptive accounts of the way nature behaves under certain conditions.
Theories guide the enterprise of finding facts rather than of reaching goals, and are neutral concerning alternatives among values. A theory can be a body of knowledge, which may or may not be associated with particular explanatory models. To theorize is to develop this body of knowledge.The word theory or "in theory" is sometimes used erroneously by people to explain something which they individually did not experience or test before. In those instances, semantically, it is being substituted for another concept, a hypothesis. Instead of using the word "hypothetically", it is replaced by a phrase: "in theory". In some instances the theory's credibility could be contested by calling it "just a theory" (implying that the idea has not even been tested). Hence, that word "theory" is very often contrasted to "practice" (from Greek praxis, πρᾶξις) a Greek term for doing, which is opposed to theory. A "classical example" of the distinction between "theoretical" and "practical" uses the discipline of medicine: medical theory involves trying to understand the causes and nature of health and sickness, while the practical side of medicine is trying to make people healthy. These two things are related but can be independent, because it is possible to research health and sickness without curing specific patients, and it is possible to cure a patient without knowing how the cure worked.
Hi,
I have undergraduate level knowledge about mathematics, quantum physics, and general theory of relativity. Now I am curious about chaos theory, and I would be grateful for suggestions of good introductory books to chaos theory. They may be both introductory and a bit more advanced.Sten Edebäck
I am not sure this is the right section to ask this question, but here it goes. So, I was studying Stat. Physics and I came across this paper, A Mathematical Theory of Communication. What it's so important about this paper?
For those who forgot the previous chapters:
https://www.physicsforums.com/threads/ultra-hyperbolic-pde-and-f-theory.766711/#post-4827614
So I now found in Google the following book which I ran to buy:
https://www.amazon.com/dp/3838130510/?tag=pfamazon01-20
unfortunately it's only 200 pages...
Hi,
I was working on the following problem:
Two classes ## C_1 ## and ## C_2 ## have equal priors. The likelihoods of ## x## belonging to each class are given by 2D normal distributions with different means, but the same covariance: p(x|C _1) = N(\mu_x, \Sigma) \text{and} p(x|C_2) =...
I'm currently a fresh grad student in theoretical physics, and I'm still deciding to choose which research group to join. My current understanding (maybe I'm wrong) is the PhD theme pretty much determines the topic for future post-doc research so I kinda need to choose very carefully.
I'm...
In algebraic geometry, the central notion is that of a scheme. This is the replacement for the classical notion of a variety. A scheme is a topological space X equipped with a sheaf of rings. I just assume that this notion of a scheme replaces the idea of a variety? or is that notion still...
I've been assigned to do a problem from Landau which you can read below:
I have no problem with finding the energy. Then I write down the equations:
\begin{equation*}
\begin{cases}
(V_{11}-E^{(1)})|c_1|e^{i\alpha_1} + V_{21}e^{i\alpha_2}|c_2| = 0\\
V_{12}e^{i\alpha_1}|c_1| +...
In a inertial frame of reference ##S## body accelerate with constant acceleration ##a##. Can then exist inertial frame of reference ##S'## which moves with speed ##u## relative to ##S## in which body does not accelerate? And why?
Trying to get my head around some basic points of measure theory
So rational numbers are dense in the reals. I.e., if with , then there exists an such that . It follows that there are then infinitely many such.
The Lebesgue measure of any single irrational (or rational number) is zero in...
This is not my homework. I took it upon myself to answer a textbook question for mental stimulation. I wanted to know if someone can verify if these were the correct values that needed to be solved for, process, and final answer, and if not, what needed to be considered.
For the initial...
Hi, I saw this video by numberphile, and near the end they mention how at the point of a right angle the equation shows infinite velocity for fluids. I'm wondering if this isn't perhaps related to Cantor's solution to Zeno's Paradox of distance (there's always a midpoint). Because I feel like at...
I'm in not too urgent (but a little pressing, i.e. I have an assignment on this due Friday... 😣 ) need of some reference that treats the theory of dislocations in crystal with a mathematical emphasis (i.e. tensors); specifically, pertaining to Burgers' vectors and the strain response to applied...
hello :)
i would very much like study some quantum field theorie, but have not previously study any regular quantum mechanic (i am not so interest in regular quantum mechanic, but more the relativistic theories).
so i ask, this is possible or not? to what extent knowledge of regular quantum...
Ok, first I want to say that I am an electrical engineer. I want to be very clear that I am trying to understand a specific situation that I came across. I am searching for an answer of why and how this situation could happen. I don't want a solution for the problem, just a theoretical, physical...
From a retiree’s stack of left behind books, I picked up a copy of Two-Person Game Theory (1966) by Rapoport. Is this an acceptable first (and possibly only) reading on the topic?
Assume that I have the Lagrangian
$$\mathcal{L}_{UV}
=\frac{1}{2}\left[\left(\partial_{\mu} \phi\right)^{2}-m_{L}^{2} \phi^{2}+\left(\partial_{\mu} H\right)^{2}-M^{2} H^{2}\right]
-\frac{\lambda_{0}}{4 !} \phi^{4}-\frac{\lambda_{2}}{4} \phi^{2} H^{2},$$
where ##\phi## is a light scalar field...
In this case, the lagrangian density would be
$$\mathcal{L}=\frac{1}{2}((\partial_{\mu}\Phi)^2-m^2\Phi^2)-\frac{\lambda}{4!}\Phi^4$$
whe $$\Phi$$ is the scalar field in the Heisenburg picture and $$\ket{\Omega}$$ is the interacting ground state. Was just curious if there were ways to do Feynman...
I know in the Heisenburg picture,
$$\Phi(\vec{x},t)=U^{\dagger}(t,t_0)\Phi_{0}(\vec{x},t)U(t,t_0)$$
where $$\Phi_{0}$$ is the free field solution, and
$$U(t,t_0)=T(e^{i\int d^4x \mathcal{L_{int}}})$$. Is there a way I could solve this using contractions or Feynman diagrams?
Because otherwise, it...
Hello everybody,
I hope it is the right section to post.
For an exam, I should delve into a topic concerning graph theory. My work should include theoretical explanation, pseudo code, correctness analysis, complexity analysis and code implementation (C ++, python or other).
Could someone...
Hi,
I was recently being taught a control theory course and was going through a 'derivation' of the controllable canonical form. I have a question about a certain step in the process.
Question: Why does the coefficient ## b_0 ## in front of the ## u(t) ## mean that the output ## y(t) = b_0 y_1...
We know about the Higg's field and boson, so what if gravity is the same.
There has long been a dispute as to weather gravity is a field or a particle.
Why can't it be like the Higg's boson.
I am studying the 'toy' Lagrangian (Quantum Field Theory In a Nutshell by A.Zee).
$$\mathcal{L} = - \frac{1}{4} F_{\mu \nu}F^{\mu \nu} + \frac{m^2}{2}A_{\mu}A^{\mu}$$
Which assumes a massive photon (which is of course not what it is experimentally observed; photons are massless).
The...
Hello,
I am spending time learning more about the theory of special relativity and string theory. One of the things that I have read about string theory is that it includes other dimensions in relation to space (space has 9 dimensions in string theory, supposedly). However, from what I...
Hi, I have a course on calculus of variations and Sturm Liouville theory and was wondering if anyone had any good textbook suggestions? If they had questions and solutions it would be a bonus! I have put all the subtopics of the course below.
Calculus of variations
Variation subject to...
Relevant Equations:: ##\ket{\vec{p}}=\hat{a}^{\dagger}(\vec{p})\ket{0}## for a free field with ##[\hat{a}({\vec{k})},\hat{a}^{\dagger}({\vec{k'})}]=2(2\pi)^3\omega_k\delta^3({\vec{k}-\vec{k'}})##
$$ \bra{ \vec{ p'}} T_{\mu,\nu} \ket{ \vec...
There are several models of brane cosmology (https://en.wikipedia.org/wiki/Brane_cosmology) and several physicists working in this field (e.g Lisa Randall and Raman Sundrum), but as you will notice, apparently they are all directly related to string theory. This has several consequences, for...
A neutral uranium atom has 92 electrons and 92 protons. in a violent nuuclear event a uranium nucleus is stripped of all 92 electrons. The resulting bare nucleus captures a single free electron from the surroundings. Given that the ionization energy for hydrogen is ##13.6eV##, derive the...
. I should preface by saying I'm a geologist not a physicist... Gotta say I usually avoid people who talk about the simulation stuff but I just saw a Tedx by George Smoot and it wound me up...
Anyway, the simulation hypothesis seems to me, and most other scientists to basically be a bit of a...
Hello. What are the problems specifically or mathematically or physically that physicists find difficulty in solving to make a theory of quantum gravity? Thank you.
Others are telling me the Einstein Field Equations can work in other dimensions other than 4D (3D space + 1D time). How true is it? So I'd like to ask for clarifications. I googled about it and found one reference for example:
Kaluza–Klein theory - Wikipedia
I assume the Einstein equations is...
String Theory and related theories like M Theory have strong constraints in the number of dimensions where they can be formulated (for example, in the case of M theory, it is only allowed in 11D or in the case of bosonic string theory is only allowed in 26D.
Since string theory and related...
Lattices are studied in mathematics. What physicists call a "lattice theory" uses the mathematical object that is a lattice, but it involves other things, such as associating elements of a group with the links between nodes of a lattice. Is there a mathematical term for lattices with this...
If (u,v) = 1, prove that (u+v,u-v) is either 1 or 2.
Where (,) means:
$$ux_1 + vx_2 = 1$$
$$u + v(x_2/x_1) = 1/x_1, u(x_1/x_2) + v = 1/x_2$$
$$u + v = 1/x_1 + 1/x_2 - v x_2/x_1 - u x_1/x_2$$
$$u - v = 1/x_1 - 1/x_2 + u x_1/x_2 - v x_2/x_1$$
Now we can express (u+v,u-v). But i am not sure if...
why the general wave vector q (in the proof of Bloch theorem in Ashcroft Mermin) is represented by k-K, where k is in the 1st BZ ? why not q=k+K ( usual vector form) what is special about k-K?
Is it possible to have some kind of General Relativistic Quantum Theory without passing through the stage of Quantum Field Theory (where Quantum Theory is married to Special Relativity)?
Einstein attached primary significance to the concept of general covariance as shown in this letter in 1954...
As I've been studying statistical mechanics as well as some other things, I keep hearing about "information theory". For instance, I've heard about information theory as it relates to entropy, regarding some theorems of statistical mechanics, and I even heard about it in a Carl Bender lecture...
In the book: SET THEORY AND LOGIC By ROBERT S.STOLL in page 19 the following theorem ,No 5.2 in the book ,is given:
If,for all A, AUB=A ,then B=0
IS that true or false
If false give a counter example
If true give a proof
I am self-studying Ivan Niven's An Introduction to the Theory of Numbers. Unfortunately, I find myself stuck while doing the problems. With this in mind, I would like to ask whether anyone here has the solution manual for Niven's textbook. Hopefully a softcopy version is available? Thank you in...
Hello there. What will physicists do after a theory of quantum gravity is found?Will they ask, if it is found ,more questions about it and try to develop it?What other questions will they make probably?Thank you.
Some good introductory string theory books that I know are
GSW
Polchinski
McMahon
Becker
What are the good books at a more advanced level? Are there any such books, or do I have to dig it out of the research papers? There is a set of books called "mirror symmetry" and "dirichlet branes and...
Consider the following scenario. A material has the E-k band scheme as shown in the figure (extended scheme of zones). Could anyone give me a suggestion regarding the following :
Electrical character of the material with the temperature.
Sign of the Hall coefficient.
Sign of the effective mass...
So I know Dalton's law as stated above which I think is applicable in this question. Then I know the effusion rate is ##\frac{1}{4} n \bar{v}##, and from this we can make a differential for the time evolution of the number density of the gas in the container which is:
##\frac{dn}{dt} =...
Every second the universe branches into 5000 universes and each of those 5000 universes branches into 5000 more after one more second.
Now, consider an 80 year old person, he has lived close to 80*365*24*60*60 seconds, which is 2.5 Billion seconds. So, in his life time, universe has branched...
Hi,
I'm reading the following paper (L. Chua) about the state-of-art of dynamic non linear circuit analysis -- Chua_Dynamic_Circuits
I've a doubt about Theorem 2 on section 3.2 On the Existence of the Resistor Function that establishes sufficient conditions for the existence of network...
From the german Version of Carlo Rovellis book "La realtà non è come ci appare. La struttura elementare delle cose" I have learned about the theory of Loop Quantum Gravity that
space and time arise through the interactions of gravitational quanta,
the space quanta have discrete volume spectra...