Relation Definition and 1000 Threads

As far as I understand it, the non-zero vacuum energy attributed to a quantum field (at each point in space-time) is precisely due to the Heisenberg uncertainty principle (and the fact that the energy of the quantum field at each space-time point is quantised). Accordingly (in order to satisfy...

Hi! Well, I'm programming a vehicle's physics, and I have trouble finding a way to calculate Rolling resistance, though i searched a lot. I already have the Traction Force and the Drag Force, but now I need Rolling Resistance. The best thing i found is that Froll = Croll * P, where Croll is the...

The magnetic moment ##\vec{M}## of a charged particle is defined as ##\vec{M}=\frac{1}{2}q\,(\,\vec{r}\times\vec{v})##. Starting with torque ##\vec{N}=\vec{M}\times\vec{B}##, I arrive at a contradiction. Consider a charge particle moving at a constant speed ##v## anticlockwise in a circle of...

I am wondering if it's possible for a relation to intercept with both it's derivative and indefinite integral at the same location (not including e^x as it shares the same rule as both it's integral and derivative). This is also assuming the constant of the indefinite integral is equal to zero...

Homework Statement What is the electric field strength at the position of the proton in the figure?(Figure 1) Assume that B = 0.10 T and F = 3.4×10−13N . Figure 1: https://session.masteringphysics.com/problemAsset/1385081/6/35.P29.jpg Homework Equations Honestly I don't know. Since we have a...

As I understand it one is forced to use 4-vectors since we require objects that transform as vectors under application of Lorentz transformations and 3-vectors do not (technically they do under rotations, but not under boosts). Equivalenty, if one starts off with Minkowski spacetime from the...

This is something I've been curious for some time. I've heard that there is a relation between gravitational waves and black holes. Moreover, this year the quite important paper "Observation of Gravitational Waves from a Binary Black Hole Merger" was published. Now, I'm starting to study...

Homework Statement Find a tight upper bound for the recurrence relation using a recursion tree argument Homework Equations T(n)=T(n/2)+T(n/3)+c The Attempt at a Solution I don't know how to do this problem because the tree doesn't have symmetry. One side of the tree can keep going because of...

I have a hypothetical question. If there was a relatively Earth-like planet out there that somehow experienced a rather catastrophic meteor impact large enough to alter its axial tilt close to 0 degrees, would such an event render the planet essentially a desert world? I.e. there are no more...

Homework Statement Let ##u## and ##v## be differentiable functions of ##x,~y## and ##z##. Show that a necessary and sufficient condition that ##u## and ##v## are functionally related by the equation ##F(u,v)=0## is that ##\vec \nabla u \times \vec \nabla v= \vec 0## Homework Equations (Not...

Hi, I have transmission line with dispersion relation ω=sin(kx), so then means that for one value of ω I have two values of k. I apply voltage with some frequency with is allowed to move in the line. First question is, how can I influence what k will be generated inside the line. The another...

Homework Statement Prove the following relation for ##\zeta:=r e^{i \theta}##: S(\zeta)^\dagger a S(\zeta)= a \cosh r - a^\dagger e^{i \theta} \sinh r with ##S(\zeta)=e^{1/2[\zeta^\ast a^2-\zeta(a^\dagger)^2]}## and ##a## being the annihilation operator with eigenvalue ##\alpha##...

hi every one can you tell me how to calculate the absorption coefficient of a thin film using the absorption and the transmittance spectrum plotted as a function of the wavelength (knowing that i don't know the thickness of the film )

Let A= {1,2,3}. Let R= {<1,1>,<2,2>}. I(A) (Identity Realtion) on A >(def)> {<x,x>|x $$\in$$ A} So that mean : $$\forall$$ <x,x> x $$\in$$ A (That how I understood it) My question: Is R is identity relation on A ? Thank you !

Why is ##a_{ji}dG_j'=dG_i'## ? from the third last line below. ##G_i=a_{ji}G_j'## because a vector labelled by the space axes is related to the same vector labelled by the body axes via a rotation transformation. If ##a_{ji}dG_j'=dG_i'##, then we are saying a vector ##dG'## labelled by the...

The function ei(p.r – Et) is the central player in non-relativistic QM. Yet the expression (p.r – Et) is the Minkowski inner product of the space-time four-vector, (t,r), and the four-momentum (E,p) and as such is Lorentz invariant. According to Feynman, De Broglie realized the relativistic...

Homework Statement Consider a particle with mass m oscillates in a simple harmonic potential with frequency ω. The position, x, and momentum operator, p, of the particle can be expressed in terms of the annihilation and creation operator (a and a† respectively): x = (ħ/2mω)^0.5 * (a† + a) p =...

The equation following (3.80) seems to suggest that the velocity vector ##\vec{\dot{r}}## must always be parallel to the position vector ##\vec{r}##. But clearly this is not true as a particle's velocity can be in any direction. What's wrong?

Homework Statement Show that the scatter angles of the photon (θ) and electron (Φ) in the Compton effect are related by the relation: ##cot (θ/2 )=(1+\frac{hf}{mοC^2}) tan(Φ) ## Where f is the frequency of incident photon 2. The attempt at a solution I wrote down the equations of conservation...

Homework Statement Prove that isomorphism is an equivalence relation on groups. Homework Equations Need to prove reflexivity, symmetry, and transitivity for equivalence relationship to be upheld. **We will use ≅ to define isomorphic to** The Attempt at a Solution Let G, H, and K be groups...

Homework Statement I posted this in anther forum but I think it might be better to post it here. I was wondering if anyone could help me understand the conversion between lux and W/m2 with relation to luminous efficacy (lm/W). Thanks :) Homework EquationsThe Attempt at a Solution

<< Moderator note: Split from https://www.physicsforums.com/threads/why-do-we-need-quantum-mechanics-so-much.859210/ >> What about particle physics? It bases on QFT therefore on QM.Is that right?

Homework Statement Homework Equations a/b=c/d The Attempt at a Solution I started out with transitivity and I figure it's transitive because a/b=e/f = af=be=(a,b)R(e,f). It can't be symmetric because ad does not equal bc, 1*4 does not equal 2*3 I'm I correct or completely wrong?

Why are ##<j_1j_2m_1m_2|jm>## and ##<j_2j_1m_2m_1|jm>## negative of each other when ##j_1+j_2-j## is odd as given below? I would expect ##<j_1j_2m_1m_2|jm>## and ##<j_2j_1m_2m_1|jm>## to always have the same sign since nature doesn't care which particle we label as particle 1 and which as...

So, after time-independent 1D Schrodinger equation is solved, this is obtained E = n2π2ħ2/(2mL2) This means that the mass of the 'particle' is inversely related to the energy eigenvalue. Does this mean that the actual energy of the particle is inversely related to its mass? Isn't this counter...

If we have Poisson bracket for two dynamical variables u and v, we can write as it is known ... This is for classical mechanics. If we write commutation relation, for instance, for location and momentum, we obtain Heisenberg uncertainty relation. But, what is a pedagogical transfer from...

I am not a mathematician but, as such, I think I have a pretty good background in mathematics. I have a good understanding and experience with calculus, differential equations, linear algebra, and probability theory. I also have interest in abstract algebra concepts, though I wouldn't say I am...

Whats the relation between compression and strength? When we build a structure, the ground or the land underneath the structure gets compressed and becomes rock solid. So how does compression make a substance strong? Is a compressed substance having more tensile strength?

Whats the relation between the centre of gravity of a structure and the middle third rule?

Homework Statement I have the following matrix: 0 0 0 1 1 0 0 0 = A 0 1 0 0 0 0 1 0 and the vector v = (1,0,0,0) If I perform Av, this gives: Av=(0,1,0,0) And If I keep multiplying the result by A like A*A*(Av), the outcome will be something like j= (0,0,1,0) k=(0,0,0,1) l=(1,0,0,0) The...

Homework Statement The problem is in the context of convection in the troposphere Show that when an ideal gas expands adiabatically, the temperature and pressure are related by the differential equation \frac{dT}{dP} = \frac{2}{f+2} \frac{T}{P} Homework Equations Ideal gas law PV = nRT...

look to post 3. original question had a lot of misconceptions.

Hello. I'm not sure if this is an A level thread however I'll just post it here. I have a question that regards dark energy in relation to space time. I've learned that dark energy only affects space and not time. However I've also learned that space and time are intrinsically intertwined as...

Below I have uploaded the page I am having trouble with. Here it says that it is using induction on n but I don't understand how it uses the formula for when n=j to derive the formula for when n=j+1

Is there a formalism that relates the properties of energy (electromagnetism) to the properties of spacetime (relativity)?

I am having a lot of difficulty understanding this concept. Suppose you have two objects [FONT=Courier New]A,B[FONT=Courier New] [FONT=Courier New]of mass A',B' [FONT=Arial]connected by a massless rope. Let K Newtons be the force applied on object A .What is now the tension along the rope ...

If the gene is smaller, is the protein that it codes for smaller too? Vice versa?

In the weak field limit, we have dt = (1 + 2\phi)^{-\frac{1}{2}}d\tau where the usual meaning of the symbols applies. This means that in GR dτ < dt analogous to SR. Let suppose we measure the period dtS of a photon emitted at the surface of the Sun as well as the same photon, i.e. same atomic...

I know that 1. To show the relation is reflexive, we need to show that for any x, using the definition of R, we have xRx. The definition of R means that we must have |x - x| is even.2. To show that R is symmetric, we would have to show that if xRy then yRx. In the context of the definition...

I state that I am a beginner in QFT, but it seems to me that the methods to regularize the integrals of the perturbation series before renormalize serve to cut off the high-energy modes that are responsable for the UV divergences. This ( the cut off of high-energy modes ) nevertheless is not so...

For an electron can I not do the following to determine both the position and momentum? I take a screen with a small hole and I eventually make the hole smaller and smaller. Cathode rays emitted will hence get diffracted after passing through the hole making momentum more and more uncertain...

Let us define a relation a on the set of nonnegative real triples as follows: (a1, a2, a3) α (b1, b2, b3) if two out of the three following inequalities a1 > b1, a2 > b2, a3 > b3 are satisfied. a) (3) Test a for Transitivity and Antisymmetry We call a triple (x, y, z) special if x, y, z...

Hi, Two questions. 1) I'm having trouble understanding the stability of the stable Lagrangian points (L_4 and L_5); Wikipedia explains that if an object in the L_4 or L_5 of a planet is pushed closer towards the common center of gravity of the Sun and the planet, the increased speed that comes...

I'm trying to figure our the relation between cross section, scattering angle and KE? I'm doing a few exercises where I've been given kientic energy and scattering angle and have to calculate the cross section. Cross section is in units of Barns (m2), and KE is 1/2 kg*m2*s-2, but I can't seem...

For someone who's familiar with the de Broglie relation it's easy to say that for k=0 we have p=0 but how would we know that before deriving the result? In this image the author derives de Broglie relation by considering a wave packet in motion. As you can see where I have star-marked the author...

Homework Statement What is the Lorentz-transformation that one would use to go from the lab frame to the Breit Frame? [/B]

I have a question about what I would call a relation inside a relation. Like: A={1,2,3) and B={a,b,c} R1={(a,1) ,(a,3), (b,2), (c,1,), (c,3) } R2={(a,a), (b,a), (b,c), (c,a) } R3=R1R2 Like this. I have 2 regular relations. Then I form another relation using these 2. How do I do that? Like...

Hi All, My apologies, I think I may have asked this question already, but I could not find it. Here it goes: I have seen the usage of the word 'relation', specifically a relation between tables but I have not seen a formal definition. From what I understand, tables X,Y are related to each other...

Is there a relation between the fact that the derivative of x^2 is 2x and that the difference between 1,4,9,16, ... is 3, 5, 7, 9, ...? And why is the difference always 2?

I need to get a few things straight about the integration operation (as an intro calc student). I understand that integration is a process that takes a function and returns its antiderivative. We can think of it as an operator, where ##\displaystyle \int...dx## is kind of like an opening and a...