Fundamental Definition and 907 Threads

Are the four fundamental interactions (or "forces") e.g. gravity, weak, color, electromagnetic believed to be the result of "phase changes" as the universe expanded from the quark-gluon plasma?

Hello everyone, I'm a Belgium based writer, currently working on my debut novel that mixes scientific fact with Biblical mythology. My main characters are the physical manifestations of concepts. Now, Amber, the lead, is Koved, the Malach ("angel"/manifestation) of gravity. Her predecessor...

I am a condensed matter grad. student, but do not work on Graphene. I am interested in learning about the fundamental physics in graphene (e.g. the need to use Dirac equation to represent the motion of electrons). I know that many books are there, but not all are geared towards fundamental...

OK, I need some help understanding some stuff. The way I see it: you've got 4 fundamental forces in physics right? I believe these are gravity, electromagnetic, strong interaction and weak interaction. The electromagnetic spectrum is basically waves with photons (photons in all of the...

Homework Statement Homework EquationsThe Attempt at a Solution if the material are the same in both strings, then the density should be the same. v = sqrt (tension/μ) tension in the first string should be 30 kg x 9.8 m/s^2 = 294 N next, v = λƒ and string#2 needs to have twice the...

In quantum field theory, a fundamental particle is an excitation in the underlying field, but what does that mean? Do fundamental particles have any physical existence according to QFT?

Hi, I was wondering if there is any need in the theory of relativity for Newton's Gravitational Constant 'G' to remain a fundamental constant. Constant in Coulomb's Law can be expressed in 'c' and 'pi', then why Constant in Newton's Law needs to be a fundamental constant??

Physics deals with finding out the basic rules by which the universe works. For me, physics is the most fundamental understanding of the universe. So theoretically, everything could be explained by the laws of physics. Is there any field that deals with the idea? Similarly, chemistry is...

After having some quite philosophical debates about the nature of truth and the limits of what we can truly understand, I've been trying to find out what is 100% scientifically provable to be an absolute truth. I know that this is quite wishy-washy question but I'm hoping to find answers on here...

Homework Statement I'm having trouble wrapping my head around this concept. I understand integration and differentiation individually. I even understand the algebraic manipulations that reveals their close relationship. However, the typical geometric interpretation of a 1-D curve being the...

Is the fundamental theorem of algebra (for polynomials on the complex plane) equivalent to the statement that any polynomial p of degree n>0 can be written p(z) = c(z - a_1 ) (z- a_2) \cdot \cdot \cdot (z - a_n ) or am I missing some subtle distinction? And if not equivalent, does the theorem...

When proofing the poisson brackets algebraically, what is the tool of choice. Can one use the muti dimensionale chain rule or how is it usally done?

Is it possible that fundamental point like particles (ie electrons) are actually particles with shape size and structure that are too small for any of our current technology to detect?

I know that according to the first fundamental theorem of calculus: $$\frac{d}{dx} \int_a^x f(t) dt = f(x)$$ I also know that if ##F## is an antiderivative of ##f##, then the most general antiderivative is obtained by adding a constant. My question is, can every single antiderivative of ##f## be...

"If ##f## is continuous on ##[a,b]## and: $$g(x) = \int_a^x f(t) dt$$ Then ##g## is continuous on ##[a,b]##, differentiable on ##(a,b)##, and ##g'(x) = f(x)##." This is the first fundamental theorem of calculus. I'm curious as to why ##g## is only differentiable on ##(a,b)##, but not ##[a,b]##.

I was reading about double integral when a doubt came to my mind: how to find the antiderivative of the function f(x,y), like bellow, and compute the fundamental theorem of calculus for double integral? \int_{2}^{8} \int_{2}^{6} f(x,y) dx \wedge dy = ? OBS: It's not an exercise. I know how...

Hi folks.I'm 3rd grade mechanical engineering student.I want to make cpu cooler.I will make pid controlled fan with an arduino. PID path is easy but I could not find anything about fan dynamics. I want to design my own fan.I need something like "fundamentals of fans" that should answer my...

1. If g(x) = ∫ f(t) dt = xln x, find f(1) The ∫ has x^2 on top and 0 on bottom. 2. g'(x) = f(x) <--FTC1 The Attempt at a Solution g'(x) = f(x) u=x^2 g'(x) = u*lnu * 2x(derivative of inner function) g'(x) = 2x(x^2)ln(x^2) f(1) = 2(1)(1^2)ln(1^2) f(1) = 0, since ln(1) = 0 I...

kreil submitted a new PF Insights post Retrocausality: How Fundamental is the Arrow of Time? Continue reading the Original PF Insights Post.

Homework Statement In Herbert Callen's text 'Thermodynamics and an introduction to thermostatistics', 2nd edition, Problem 1.10-1 on page 32 presents ten potential fundamental equations of thermo systems, labelled (a) - (j), and asks the reader to identify the five that are invalid because they...

In my lecture we were discussing the Lagrangian construction of Electromagnetism. We built it from the vector potential ##A^\mu##. We introduced the field tensor ##F^{\mu \nu}##. We could write the Langrangian in a very short fashion as ##-\frac{1}{4}F_{\mu \nu}F^{\mu \nu}## In the end we...

I want to ask that what should be considered the most fundamental in physics I.e. whether the Standard Model or Dimensional units or the fundamental forces?

Hi, What is the basic idea about particle interaction in QM? Say you have first one single charged particle in an "empty universe". Here I think the first issue is given: That's impossible, you'll need masses (or better: energy) from a GRT view. Okay, say we watch this single charged...

Let r:R2 →R3 be given by the formula Compute the second fundamental form with respect to this basis (Hint: There’s a shortcut to computing the unit normal n). I can't find thi shortcut, does anyone help me? I'm solving it with normal vector and first and second derivate, but I obtained...

Suppose F is a field and that ## f(x) ## is a non-constant polynomial in ##F[x]##. Since ##F[x] ## is a unique factorization domain, ## f(x) ## has an irreducible factor, ## p(x) ##. Then the fundamental theorem of field theory says that the field ## E = F[x]/<p(x)> ## contains a zero of ## f(x)...

Are quarks really considered fundamental particles that cannot be divided further? If an up quark can transmute to a down quark and release a W+ boson which decays to a positron and a neutrino (for example) - doesn't this mean that there is substructure to a quark? What exactly is it that makes...

Homework Statement 1) How do I know when to use Green's Theorem, the Fundamental Theorem for Line Integrals or the regular method of using parametrization? 2) Assuming that the three methods above are all used to solve line integrals, why do the Fundamental Theorem and Green give different...

Homework Statement Hi, I've been working through a practice problem for which I used the fundamental theorem of calculus, or one of its corollaries. The setup is a population changing over time. The population, P(t) at t = 0 is 6 billion. The limiting population as t goes to infinity is given...

I have been getting ready for my Intro to Modern Physics final. The professor likes to ask a lot of questions like Which of the following neutron reactions proceeds via the electromagnetic force? Or something like this... I have been looking all over the internet and my textbook. All I can...

Hello I'm a 15year old boy living in Korea, and lived in the U.S. for a couple of years. I want to learn physics in a very fundamental(?) way, for example, knowing the reason why from Newton's law of gravitation F = GmM/r^2, F is proportion to the SQUARE of r (not cube or power of 4??)...

In Chapter 7 of John M. Lee's book on topological manifolds, we find the following text on composable paths and the multiplication of path classes, [f] ... ... Lee, writes the following:In the above text, Lee defines composable paths and then defines path multiplication of path classes (not...

I would just like to ask a basic question as to whether there is any sign of there being a minimum energy block size which may hint at a fundamental particle building unit, or whether there is just a continuum of energies as far as we know so far.

Say I have the statement ##\int \frac{\mathrm{d} y}{\mathrm{d} x}\mathrm{d}x = y##. How does the fundamental theorem of calculus make this necessarily true? When I see the formal statement of the theorem, it is usually in terms of a definite integral such as ##F(x) = \int_{a}^{x}f(t)dt##. How...

This is not a homework question per se, but rather something I have come across during a homework project. Using Audacity, I recorded a few different instruments playing the same notes (investigating timbre). I noticed that (using a steel string acoustic guitar) the first harmonic at 131 Hz...

If electrons are fundamental particles and leptons then what happens when they emit or absorb photons or Z particles? What is known about the mechanism of these aborptions or emissions for any particles? Do the absorbed electrons gain mass as particles are described to do as they move nearer to...

Curious if anyone has insight into why a new long baseline neutrino experiment, DUNE, is being funded when the MINOS infrastructure has been in place for a few years. The experiments seem approximately the same, traveling similar distances to detectors in the Soudan Mine and to the underground...

I have impression that physicists consider QM laws as fundamental, meaning that there should be a way how QM mathematical form is realized in reality. On the other hand QM laws could be effective laws resulting from some process of evolution. In that case it should be possible to characterize...

Prove that the limit as n approaches infinity of ((2^n * n!)/n^n) equals to zero. The hint is to use Stirling's approximation. What is this?

Many physical laws involve relationships between time derivatives to space derivatives of one or more quantities. For example, thermal conduction relates the thermal energy time rate of change [dQ/dt] to temperature space rate of change [dT/dx]. In fluid flow, the Navier-Stokes Theorem relates...

Fundamental assumtption: "a closed system is equally likely to be in any of its g accessible micro- states, and all accessible micro- states are assumed to be equally probable." There's just a few things I don't understand about this, 1. Isn't saying that a closed system is equally likely to...

I understand that the fundamental theorem of calculus is essentially the statement that the derivative of the anti-derivative F evaluated at x\in (a,b) is equal to the value of the primitive function (integrand) f evaluated at x\in (a,b), i.e. F'(x)=f(x). However, can one imply directly from...

In the fundamental theorem of calculus, why does f(x) have to be continuous in [a,b] for F(x) = \int_a^x f(x) dx ?

Would it be a legitimate (valid) proof to use an \epsilon-\delta limit approach to prove the fundamental theorem of calculus? i.e. as the FTC states that if f is a continuous function on [a,b], then we can define a function F: [a,b]\rightarrow\mathbb{R} such that F(x)=\int_{a}^{x}f(t)dt Then F...

I am reading Manfred Stoll's book: Introduction to Real Analysis. I need help with Stoll's definition of the natural logarithm function (page 234 -235) The relevant section of Stoll reads as follows: In this section we read: " ... ... To prove (a), consider the function $$L(ax), x \gt 0$$...

Homework Statement Assume that y1 and y2 are solutions of y'' + p(t)y' + q(t)y = 0 on an open interval I on which p,q are continuous. Assume also that y1 and y2 have a common point of inflection t0 in I. Prove that y1,y2 cannot be a fundamental set of solutions unless p(t0) = q(t0) = 0.The...

The invariant of SL(2,C) is proven to be invariant under the action of the group by the following \epsilon'_{\alpha\beta} = N_{\alpha}^{\rho}N_{\beta}^{\sigma}\epsilon_{\rho\sigma}=\epsilon_{\alpha\beta}detN=\epsilon_{\alpha\beta} The existence of an invariant of this form (with two indices...

I am reading Manfred Stoll's book: Introduction to Real Analysis. I need help with Stoll's proof of The Fundamental Theorem of the Calculus - Stoll: Theorem 6.3.2 Stoll's statement of Theorem 6.3.2 and its proof reads as follows: In the above proof we read: Since $$\mathscr{L}( \mathscr{P}...

Homework Statement What are the fundamental frequencies for a 50 kHz square waveform of 50% duty cycle and a 25 kHz sinusoidal waveform, respectively? (The duty cycle of a square waveform is the ratio between the pulse duration and the pulse period.) Homework Equations My teacher then gave...

Homework Statement Evaluate the definite integral of the algebraic function. Use a graphing utility to verify your result. Integral from [1 to 2] of (3/x^2 - 1) Homework Equations The answer is 1/2 f(x)dx= F(b) - F(a) The Attempt at a Solution I tried taking it to make it -x^-3 - 1x as the...

Homework Statement Solve the integral equation for y(x): y(x) = 1 + ∫ { [y(t)]^2 / (1 + t^2) } dt (integral from 0 to x) See attached image for the equation in a nicer format. Homework Equations Fundamental Theorem of Calculus The Attempt at a Solution dy/dx = y(x)^2 / (1 + x^2) ∫ dy/y^2 = ∫...