Constant Definition and 1000 Threads

Hello, for my PhD, I've been studying an influence of a gain medium on spectral linewidth of light inside a fiber cavity. I've encountered a formula in one paper to which I don't how to get to (see screenshot), it's the formula (A3). On the left hand side there is electric flux density, the...

It is "easy" to produce experimental setups that could and should for all practical purposes be described as having a constant background magnetic field everywhere, especially in the "asymptotic region" where the detectors are located. You can do this both in vacuum, and inside a solid sample...

Proof: Let ## x\geq 2 ##. Observe that \begin{align*} &\sum_{n\leq x}\frac{d(n)}{n^2}=\sum_{d\leq x}\frac{1}{d^2}\sum_{q\leq \frac{x}{d}}\frac{1}{q^2}\\ &=\sum_{d\leq x}\frac{1}{d^2}(\frac{(x/d)^{1-2}}{1-2}+\zeta {2}+O(\frac{1}{(x/d)^{2}}))\\ &=\frac{x^{1-2}}{1-2}\sum_{d\leq x}\frac{1}{d}+\zeta...

I think the question is wrong. My answer : But it should be wrong because : I think the question is wrong … But I'm not sure …

Impossible?!? By my estimation the equation that describes this motion is given by: $$Pt = \frac{1}{2}m{ \dot x}^2$$ or $$\dot{x} = \sqrt{\frac{2P}{m}} \sqrt{t}$$ but this implies: $$\ddot{x} = \sqrt{\frac{2P}{m}} \frac{1}{\sqrt{t}}$$ So, no matter how small we make the power, we appear...

This is a multiple choice question. I assumed that this is an escape velocity question. I have been going round and round... Here's what I have done:

I understand that the uncertainty is low when you're dealing with a "macro" scale area that is much bigger than Planck's constant. But what's confusing to me is when you know with extreme precision the location, but there's so many particles involved that there is little uncertainty since the...

C = sqrt(E/M)...this would suppose the ratio of the amount of energy vs. the amount of mass in the universe. If not, why not. If there is no mass, just energy, or much less mass at the moment of the hypothetical Big Bang, then, there C would be significantly higher, thus explaining cosmic...

How is the real understanding, when an external constant E potential (voltage) is imposed/applied on a LR circuit, that is being charged as the characteristic L/R inductor time constant: the greater R the shorter time inductor get (full) charged This absolutely independent to the E; it could...

A standard textbook problem features a constant B field and a conducting loop that increases in area at constant rate. It is easy to work out the induced EMF and the associated electric field magnitude and direction (CW or CCW). The magnitude of the E field is E = B v where v is a velocity...

A University of Oxford and Cambridge Collaboration in 2014 produced a series of lectures "Cosmology and the constants of nature". John K Webb spoke on the topic of variations in the values of fundamental constants. Latest developments here. Who else is doing similar research?

I'm wondering if there is a way to find the proper volume of the warped region of the Alcubierre spacetime for a constant ##t## hypersurface. I can do a coordinate transformation ##t=τ+G(x)##, where ##G(x)=\int \frac{-vf}{1-v^2f^2}dx##. This eliminates the diagonal and makes it so that the...

I am having some hard time to finding out where i should start. I remember see the strucutre constant arrising when we evaluate vertices on feynman diagrams for QED interactions... But i am too ignorant to know how to proceed..

I was reading about thermodynamics in my textbook wheni came across the following thermodynamics constants: However, i don't understand why did we define 1/V inthe constants. What is the point in doing this?

The wikipedia article on Lunar distance contains a confusing graph. The graph seems to suggest that the eccentricity of the lunar orbit is maximal in january and ~july, and minimal in april and ~october. I think the eccentricity should be constant. Is wikipedia right or wrong, or is there some...

Hello! Just now I began to question myself about something I learned many years ago. When we are outside of a pool and see a coin in the floor of the pool (underwater) we think that the coin has an apparent depth that is smaller than the real depth. To calculate this we extrapolate the light...

Var (Y) = a2 . Var (X) (6.96)2 = a2 . (8.7)2 a = ± 0.8 But the answer key states that the value of a is only 0.8 Why a = -0.8 is rejected? Thanks

My references are: https://en.wikipedia.org/wiki/Friedmann_equations#Detailed_derivation https://en.m.wikipedia.org/wiki/Cosmological_constant Ω_Λ is a term in the Friedmann equation along with terms for radiation, mass, and curvature. Λ is the coefficient of the term g_μν in the Einstein field...

I'm studying oceanography and the author of the book that I'm currently reading stated that sea surface water is relatively constant during the day, changing very slowly during the year. He says "this is because almost all the energy received from the sun is used in the evaporation of water"...

Hello everyone! I was doing some dimensional analysis to find an equation that gives a acceleration as a function of time, using constant power. I came up with the equation $$a = k\sqrt {\frac P {mt}}$$ I differentiated velocity with respect to time in order to check my work and also checked out...

In natural units, it’s known that the unit of the cosmological constant is ##eV^2##. I don‘t get why in this paper : https://arxiv.org/pdf/2201.09016.pdf page (1), it says the value of ##\Lambda \sim meV^4##, this means ##\Lambda \sim (10^6 ~ eV)^4 \sim 10^{24} eV^4 ##, shoud not the unit ##eV...

In question 1, the spring constant from the two formulas was not the same. When we used the first formula, we got that the spring constant was 7.83 N / m. The second formula we got that the spring constant was 8,03 N / m. In questions 2 and 3 I do not know and am unsure about how to answer...

If the question had been asking about the flux through the whole surface of the cylinder I would have said that the flux is 0, but since it is asking only about the lateral surfaces I am wondering how one could calculate such a flux not knowing how the cylinder is oriented in space. One could...

Why, in a nutshell, are there two coupling constants for the EM field, the fundamental electric charge, e, and the Fine Structure Constant? If a brief answer is not possible, can you recommend good literature on this subject? Thanks in advance.

The question constantly arises how the speed of light is measured and what does it mean that the speed is constant, including at remote points for the observer, including at points beyond the local frame of reference, as you understand it in general relativity (GR). First of all, it should be...

@PeroK sent me here based on a discussion starting at https://www.physicsforums.com/threads/some-ideas-on-interstellar-space-travel.1006562/post-6550265. Summary: Someone claimed that an accelerated observer's clock (observer at 1g from Earth to halfway to Alpha Centauri, then -1g the rest of...

Does relativity imply that everything that goes at a constant velocity must not emit radiation of any kind?

( This question came up in the context of flat earth. Sorry for that, but hopefully the question itself is not dumbtarded. ) Basically one "model" for gravity that some FErs subscribe to, is that the Earth disc is accelerating upwards at 9.8 ms-2. And one debunk of this proposition was that the...

So basically we can have a constant current but i don't understand this circuit. for example: i can have the Ia what ever I want with current divider rule: Ia = Iq * R2/R3. So Ia is proportional to the ratio of R2/R3. And if i give a resistor at the collector terminal, if i change it between...

That may seem like a silly question, but suppose the crew of an interstellar vessel wanted to measure the mass of their ship, perhaps to estimate remaining resources. Unless they have very well calibrated thrust and a very well calibrated accelerometer, the only option is to do so...

I understand the relativistic effects at high speeds, what accounts for the constant speed of light at low speeds? Example... If I travel towards a beam of light at 25 MPH, I will still measure the light as traveling towards me at the speed of light and not the speed of light plus 25 MPH.

How to prove that \[ \sum_{i=1}^{\infty}\frac{1}{2^{3i}}\left(\csc^{2}\left(\frac{\pi x}{2^{i}}\right)+1\right)\sec^{2}\left(\frac{\pi x}{2^{i}}\right)\sin^{2}\left(\pi x\right)=1 \] for all \( x\in\mathbb{R} \). Using graph, we can see that the value of this series is 1 for all values of x...

If there were humans on Earth 2.5 billion years ago (universe 20% younger) and they had today's equipment , would they measure the Hubble constant smaller, larger or the same?

A gas with a volume of 8m^3 with a temperature of 400K gets warmed up to 550K with a constant pressure of 200Kpa. How much work has the gas done to the environment? I think i might need to use the ideal gas law for this which is: ( P * V / T = N * K ) Where V is volume, T is temperature and N...

My guess is that I could compare it to the time interval of the free fall motion(stage2). Would that be enough to let it make ‘sense’? As we know that stage 1 has an acceleration of 16m/s^2 and free fall one of 9.81m/s^2. Then.. is it sufficient to reason that the time needed to complete stage...

Suppose I have 2 variables q and t (time), where q is some reparameterization of x (position) : ##x \to q = x f(t)##. Suppose I have a partial differential equation : $$\frac{\partial u(q,t)}{\partial t} = k \frac{\partial u(q,t)}{\partial q}$$ where k = constant Then I do a separation of...

I need help with this question how in the world is it A and C. In A everything is cancelling out so nothing is movingfand nothing moving to the right. In C its not moving to the right. Isnt it suppose to be D since sits going right constant to 20N.

One recent example of a thread discussing flat or not is: https://www.physicsforums.com/threads/could-the-universe-be-infinite.1011228/ . I found an interesting 2021 article regarding the Hubble constant tension...

The question is of what does it depend on? We take it for a constant still how do we know that its the exactly the same as in a vacuum in a center or closer to the center of our galaxy for example. Why is the number what it is?

For background, consider this paper, which describes circular orbits for the two-body problem in the presence of a cosmological constant: https://arxiv.org/abs/1906.05861 What they describe is a system with three regimes of behavior: stable circular orbits below a certain radius, unstable...

When analysing the time-complexity of an algorithm I was told to assume that a hash map is ##0(1)##. A cursory google search afterward revealed that this is true because the time complexity of the hash function is independent of the size of the hash table. That seems alright but if you have a...

I averaged the masses and times (which i took the time given and divided by 10 because in the problem it says you measure the time it takes to complete 10 oscillations) then plugged them directly into the T=(2(pi)((m/k)^1/2) and got the wrong answer. This is really confusing me because I don't...

What other experiments, besides the M&M experiments confirmed the constant velocity of light? Thank you in advance for the response.

Here's where I got the questions: These are from a worksheet I downloaded online: Answer Key The answer key says that the answer to the first question is 500J and for the next question it's 433J. It says constant speed though, so I don't understand why the answers aren't zero. I get how they...

I am just learning about e-field simulations and I came across two different types of dielectric constants: optical and static. I'm unsure which to use and in which cases. I would like to simulate e-field intensity to help ensure I'm always below the dielectrics breakdown strength.

##f(z)## is holomorphic on ##\Omega## so f(z) satisfies the C.R. equations, i.e., for ##f(z)=u+iv## ##u_x=v_y## ##u_y=-v_x## and for ##-f(z)=-u-iv## ##u_x=v_y \Rightarrow -u_x=-v_y## ##u_y=-v_x\Rightarrow -u_y=v_x## so -f(z) satisfies the C.R. equations and hence ##-f(z)## is holomorphic...

Using Gauss's Law By using a symmetry argument, we expect the magnitude of the electric field to be constant on planes parallel to the non-conducting plane. We need to choose a Gaussian surface. A straightforward one is a cylinder, ie a "Gaussian pillbox". The charge enclosed is...

(P.S! this is an open question, feel free to answer)

I have attempted but I don’t get anywhere.

Hello, there. Looking at the Einstein-Hilbert action $$S=\frac 1 {16\pi G}\int R \sqrt{-g}d^4 x,$$ I am wondering why the normalization constant is ##1/16\pi G##. In the textbook by Carroll, he mentions that the action is so normalized to get the right answer. I think this is related to...