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.
Cosmological inflationary models are general models in the sense that they could be applied to a variety of fundamental theories. Most physicists working in inflation assume that there is only one (but yet unknown) fundamental theory which through inflation would produce multiple regions or...
I only see it brought up in creationist attacks on evolution, definitely NOT trying to bring that up - curious if and how real biological science uses it. There are a couple of (expensive) older books and paywalled papers that seem legit, but cannot find much else
for example...
Let us first take the S-matrix expansion (i.e. Dyson's formula)
\begin{align*}
S_{fi}&=\langle f | T \left\{ \exp\left( i\frac{\lambda_3}{3!}\int d^4 x :\phi \phi \phi (x) : + i\frac{\lambda_4}{4!}\int d^4 x :\phi \phi \phi \phi (x) : \right) \right\}| i \rangle \\
&= \langle f | i...
The weakly coupled theory is given by the Lagrange density$$\mathcal{L}=\mathcal{L}_0 + \mathcal{L}_I=\frac 1 2 \partial_{\mu} \phi \partial^{\mu} \phi - \frac{m^2}{2} \phi^2 - \frac{\lambda_3}{3!} \phi^3 - \frac{\lambda_4}{4!} \phi^4 \tag{1}$$
Where
\begin{equation*}
\mathcal{L}_0 = \frac...
YouTube has been suggesting videos about category theory of late, and I have spent some time skimming through them, without really understanding where it's all going.
A question came to mind, namely:
It seems reasonably conceivable that group theory could perhaps supply a vital key to the...
The claim states the following:
Let ##(X,\mathcal{A},\mu)## be a measurable space, ##E## is a measurable subset of ##X## and ##f## is a measurable bounded function which has a bounded support in ##E##.
Prove that: if ##f\ge 0## almost everywhere in ##E##, then for each measurable subset...
I was reading the book "A Fortunate Universe" by Geraint Lewis and Luke Barnes and something caught my attention:
At page 195 the authors say that universes with different symmetries could be modeled and they would have dramatic results like having different conservation laws.
I asked Mr...
Hey guys, I decide I need to learn the mathematics of molecular-orbital theory, to build on the qualitative approach of my chemistry coursee. To do this I also first need to study single-electron systems and then many-electron systems, the Born-Oppenheimer approximation, and relevant topics...
I've completed my PhD and am leaving the field to take up a career elsewhere, however I'm interested in developing my knowledge of string theory as a (potentially lifelong) side project. I have a solid understanding of GR and some extensions (my PhD was in relativistic effects in cosmology, and...
I know $$ i\mathcal{M}(\vec {k_1}\vec{k_2}\rightarrow \vec{p_1}\vec{p_2})(2\pi)^4\delta^{(4)}(p_1 +p_2-k_1-k_2) $$ =sum of all (all connected and amputated Feynman diagrams), but what is meant by 1 loop order? In other words, when I take the scattering matix element...
Hello. I do not understand how to solve systems of three or two congruences of one unknown of first order, a congruence of one unknown of second order and a system of diophantine equations of two or three unknowns. Could someone help me by providing examples in these cases? Thank you.
I’m reading Lancaster & Blundell, Quantum field theory for the gifted amateur (even tho I”m only an amateur...) and have a problem with their explanation of symmetry breaking from page 242. They start with this Lagrangian:
##
\mathcal{L} =
(\partial_{\mu} \psi^{\dagger} - iq...
Hi
all, I was reading this article
https://asiatimes.com/2020/11/the-big-bang-never-happened-but-fusion-will/
And I got somewhat confused. As most I've been taught that BB has succeeded in giving most of the cosmological predictions that we observe [nucleosynthesis, formation of galaxies, cmb...
For the first question, i believe that mechanical energy is conserved hence we can derive the total energy i think. In regards to the second question, I'm assuming its at room temperature, so helium is monotonic therefore it has 3 degrees of freedom, therefore its internal energy is 3/2KT. I am...
Hello there.Questions I have: what is the value of group theory?I am not trying to say that it is not important I want to know what made mathematicians study these objects and we still study them today.I know there are very interesting for me at least examples of groups like the Lie group but...
I was wondering that if there was a theory that didn't have a mathematical formula yet but had experimental data how would a scientist go about publishing it?
This isn't what I'm doing I'm just trying to see a possible process. Additional circumstances would be that the person publishing is a...
Summary:: Control Theory root equation pole
Hi, I ran into a simple question but somehow I can't get it right.
My work this far:
## G_0(s) = G(s) \cdot K \cdot \frac{1}{T_I s} = \frac{k}{\tau s +1} \cdot \frac{2\beta \tau -1}{k} \cdot \frac{2\beta^2 \tau}{Kks} = \frac{2\beta^2\tau}{s(\tau s...
Hi!
So I have just been studying Yang-Mills theory advanced quantum field theory.
In chapter 72 of Srednicki's book Quantum Field Theory they list the Feynman rules for non-abelian gauge theory.
I was asked if I could show some sample allowed diagrams but I could not.. In standard particle...
Cumrun Vafa and colleagues have recently posted a new theory of the early universe in the paper:
https://arxiv.org/abs/2009.10077
If anyone could explain the main themes of the paper in laymen friendly manner that would be really appreciated. In particular
what is topological gravity ? how is...
For any physical theory to be accepted, the consensus is that there must be a radical categorical separation between the formalism in which the theory is described (using exact mathematical language) and the empirical situation in which it is validated (using real world tools, materials and...
Before I attempt to delve into the math of tensors and curved spacetime, I'm hoping to get a more general intuitive grasp of things. As such, I'm parsing through a lot of lower level articles on these topics, and several that I've come across have argued that Newtonian gravity can be thought of...
Hopefully, I am in the right forum.
I am trying to get an intuitive understanding of how fiber bundles can describe gauge theories. Gauge fields transform in the adjoint representation and can be decomposed as:
Wμ = Wμata
Gauge field = Gauge group x generators in the adjoint...
Given that Penrose now got the Nobel prize for a theory that is almost impossible to verify experimentally in a near future (that is, for theorems that predict singularities inside black holes), does it mean that now string theory can also get a Nobel prize? (If so, Witten and Schwarz would be...
Summary:: Need lecture notes for many body
I want a lecture notes of a many body introduction course according to the book of "many body theory of solids" by John C.Inkson,
Could anyone help me?
It is a wonderful book for learning QFT. Interesting problems with detailed solutions. I have tried the problems from chapter 1 to chapter 7. In most chapters, I could at least solve some part of the problems. But I got stuck in chapter 4, the Dirac equation. I could not solve any of the...
"The dual space is the space of all linear maps from the original vector space to the real numbers." Spacetime and Geometry by Carroll.
Dual space can be anything that maps a vector space (including matrix and all other vector spaces) to real numbers.
So why do we picked only a vector as a...
Quantum mechanics has argued for years that space is not a vacuum.
Arguments attempting to brush aside quantum mechanics vacuum theory claiming, it's 'just a quantum mathematical theory' can now put to rest.
In this article, laboratory experimentation demonstrates that the Casimir Effect can...
hi guys
i saw this problem : if G is a group and a,b belongs to G and O(a) = e , b.a =a.b^2 then find O(b) , but i want to tackle this problem using Cayley diagrams , so my attempt is as following :
$$ba =ab^{2}$$
then i might assume b as flipping , a as rotation :
$$ fr = rf^{2}$$
then...
Hi,
I just had a quick question about conventions in potential flow theory:
Question: What is the convention for ## \Gamma ## for the streamline ## \Psi = \frac{\Gamma}{2\pi} ln(\frac{r}{a} ) ## and how can we interpret the Kutta-Jukowski Theorem ## Lift = - \rho U \Gamma ##?
Approach:
For the...
Homework Statement:: What is the convention for ## \Gamma ## for the streamline ## \Psi = \frac{\Gamma}{2\pi} ln(\frac{r}{a} ) ## and how can we interpret the Kutta-Jukowski Theorem?
Relevant Equations:: ## v_{\theta} = - \frac{\partial \Psi}{\partial \theta} ##
[Mentor Note -- moved from the...
Hi everyone,
I'm working through some group theory questions online. But unfortunately they don't have answers to go with them. So, I'm hoping you can say if I'm on the right track.
If this is a binary operation on ℝ, am I right in thinking it satisfies the closure and associativity axioms...
I'm trying to dig up anything that supports or discounts Schommers' theory as it relates to Projection Theory. Tried some Googling and came up with naught.
I have failed a course on group theory for physicists in my university, and i need a good book to learn group theory from because anthony zee's book is simply too hard to read. His book is verbose, glosses over many concepts, and is not very rigorous. Then the exercises in the book are very...
Prof Wetterich has proposed that atoms are shrinking rather than the Universe is expanding.
Here is a 2013 Nature News article describing his theory:
https://www.nature.com/news/cosmologist-claims-universe-may-not-be-expanding-1.13379
Here is his 2013 paper "A Universe without expansion"...
Hi,
I needed some help with robotics but, strangely, found only a small number of threads about robotics topics. I don't know the reason for this but I think it'd nice if PhysicsForums had a separate sub-forum for robotics. Anyway, which sub-forum should be used to post questions about robotics...
Hello,
The sigma $(\sigma)$ molecular orbitals are symmetrical around the bond-axis while pi $(\pi)$ molecular orbitals are not symmetrical. For example, the linear combination of 1s orbitals centered on two nuclei produces two molecular orbitals which are symmetrical around the bond-axis. Such...
Usually, I saw that string theory (perturbative, or matrix models) are made in a fixed background. Even if you consider that the metric is quantized and etc. there is an apparent physically motivated need for making a sum over topologies (manifolds, conifolds, orbifolds, and etc), for example...
I was reading about the renormalization of ##\phi^4## theory and it was mentioned that in order to renormalize the 2-point function ##\Gamma^{(2)}(p)## we add the counterterm :
\delta \mathcal{L}_1 = -\dfrac{gm^2}{32\pi \epsilon^2}\phi^2
to the Lagrangian, which should give rise to a...
Hi,
I've a doubt about the applicability of the substitution theorem in circuit theory.
Consider the following picture (sorry for the Italian inside it :frown: )
As far I can understand the substitution theorem can be applied to a given one-port element attached to a port (a port consists of...
At least according to Tim Anderson Ph.D who wrote the paper in Physics Review.
https://news.knowledia.com/US/en/articles/a-5th-dimension-may-explain-quantum-theory-the-infinite-universe-medium-6f1d6fd371e068a07f357b9babe9ab2eec06d034
What do you make of this?
"The paper simply presents...
I usually don't read papers on philosophy of quantum field theory, but this one is really good: http://philsci-archive.pitt.edu/8890/
In particular, the prelude which I quote here is a true gem:
"Once upon a time there was a community of physicists. This community be-
lieved, and had good...
In Dynamical Systems Theory, a point in phase space is interpreted as the state of some system and the system does not exist in two states simultaneously. Can some phase spaces be given an additional interpretation as describing a field of values at different locations that exist...
I read this paper where if you take the alcubierre metric calaculations while including torsion in GR you get positive energy spin requirements instead of exotic matter. Here is the link: https://arxiv.org/abs/1807.09745
Could it be because a spinning quantum vacuum will be less stiff like a...
Hello! Let's say we have 2 states of fixed parity ##| + \rangle## and ##| - \rangle## with energies ##E_+## and ##E_-## and we have a P-odd perturbing hamiltonian (on top of the original hamiltonian, ##H_0## whose eigenfunctions are the 2 above), ##V_P##. According to 1st order perturbation...
https://arxiv.org/abs/0805.3819
Approximating the Standard Model and gravity with dust on \mathbb{R}^{0|18}
Robert N. C. Pfeifer
[Submitted on 25 May 2008 (v1), last revised 11 Jul 2020 (this version, v14)]
This article describes a single species of non-interacting massless dust on...