Density Definition and 1000 Threads

The vacuum density, or the zero point energy, of a field, doesn't change as space expands, it remains constant. But, aren't particles and virtual particles just fluctuations of these fields? Meaning as space expands, more and more particles are being created, violating conservation of energy?

suppose the universe started shrinking. because the density vs mass is a 1/M^2 factor, density can be made arbitrarily small given high enough mass. so it's not hard for all the mass in the universe to quickly reach black hole density. when critical density of the universal is reached, what...

Hi all, Just had a look at the 2016 paper by Wang, Zhu, and Unruh, "How the huge energy of quantum vacuum gravitates to drive the slow accelerating expansion of the Universe," Qingdi Wang, Zhen Zhu, and William G. Unruh, Phys. Rev. D 95, 103504 – Published 11 May 2017 The paper states...

suppose we are working on a step potential problem, and two transmitted wave functions,corresponding to one particle, are obtained. Let's name them ##|1>## and ##|2>##. How can we interpret physically the case where ##<1|2>##=##-<2|1>##? or in position...

Summary: What are the basic assumptions of QM about the density matrix? The subject of density matrix in quantum mechanics is very unclear to me. In the books I read (for example Sakurai),they don't tell what are the basic assumptions and how you derive from them the results of the density...

We want to calculate the ao/a(teq) of the equilibrium point between ρm and ρr (ρm= ρr ) My book solves it this way; ρm(t) / ρr(t)= a(t) ⇒ ⇒ (ρm/ ρr)teq =1 = = (ρm/ ρr)o * a(teq)/ ao I don't understand the a(teq)/ ao part. If ρm(t)= ρο/αo3 and ρr(t)= ρο/αo4 then it should be ρm(t)/ ρr(t) =...

Hi, I could you explain me what is the density of a constant (particurarly the spring constant, or should I say "stiffness" constant)? I guess it's a probabilty function but would like more details. I would like an answer that at first describe the concept and later refine the mathematical...

Probability density function plays fundamental role in qunatum mechanics. I wanted to ask if there is any analogous density function in classical mechanics. Obviously if we solve Hamilton equations we get fully deterministic trajectory. But it should be possible to find function which shows...

I am new to data science and I am trying to create an algorithm for the DBSCAN. I can label each point as core-border-noise. But after this step I am stuck. How can I separate the density reachable cores and create clusters from these points ?

Summary: If SCRAM completely removed all moderator from the reactor, would decay heat still be an issue? My understanding of how decay heat occurs after shutdown in large scale Nuclear Power Reactors. Is that Beta Decay causes residual Neutron activity at a small fraction of the operating...

Densities of Normal Air is 1.225 kg/m3 at STP, whereas the density of Liquid Air is 870 kg/m3. That means liquid air is 710x denser that normal air. Then suppose, we compress normal air to more than 710 atmospheric pressure, then it could have a density more than that of liquid air. Is this...

count(ℝ) > count(ℚ) ; count(ℚ) == count(ℕ) But still in-between any members of ℝ, we are quarantine to find element of ℚ Can someone help me understand: were are these members of ℝ we cannot account for? For reference: https://en.wikipedia.org/wiki/Rational_number "The rationals are a dense...

I have the solution to the problem but I think I found either a typo or steps that were not included. I think I have made sense of the problem but I would like to double check that I'm doing this right. Thanks. ρn = mn/Vn mn ≈ ma Rn = 10-5Ra This is were I am having issue. The solution says...

(Just as clarification on what I am doing, I am attempting to use MATLAB to create PSD plots of time series from pressure and accelerometer sensors. Wave gauge sensors might still be helpful for me. I did not discuss accelerometer sensors in the post but maybe I could figure it out if I get the...

Since sphere is made of l.i.h material, $$\vec{J_f}= \sigma \vec{E}$$ We compute electric field E using $$\vec{E} = -\nabla V$$ $$= -\nabla \left(V_0cos\theta\right)$$ $$= -\frac{\hat\theta}{r}\frac{{\partial}}{{\partial\theta}}\left(V_0cos\theta\right)$$ $$\vec{E}=...

I was looking for a derivation for the density of states and I came across this page: https://ecee.colorado.edu/~bart/book/book/chapter2/ch2_4.htm I followed the derivation and came up with: g(E) = (1/L3)dN/dE = (1/L3)L3/∏2*k2 * dk/dE =K2/∏2 * dk/dE =K2/∏2 * g(E) =...

I first took out the variation of conductivity along the radius of cylinder.Also we know that J=sigmaE.Therefore i have to find variation of E also.But how will i find that as potential is also not given.Help.

Does ##w## = -1 by itself imply that spacetime is flat, or is it only due to ##\Omega##Matter + ##\Omega##Λ = 1 ?

I am reading a text which talks about the WIMP speed distribution in the galactic halo in the frame of the Sun and Earth. The point where I am stuck it is trying to explain the concept of Gravitational Focusing of WIMPs at the location of the Earth due to the gravitational well of the Sun...

1] Let X,Y,Z be independent, identically distributed random variables, each with density $f(x)=6x^5$ for $0\leq x\leq 1,$ and 0 elsewhere. How to find the distributon and density functions of the maximum of X,Y,Z.2]Let X and Y be independent random variables, each with density $e^{-x},x\geq...

If you have two different liquids (water and oil for example) mixed together and free floating without gravity, will they separate as they do here on Earth? If so, what property would determine the layering structure? I suspect they would separate, and if left undisturbed probably form a...

I am wondering if can the colour of a liquid be related to its density?

I was trying a problem from Griffith's Introduction to QM. The problem was: The needle on a broken car speedometer is free to swing, and bounces perfectly off the pins at either end, so that if you give it a flick it is equally likely to come to rest at any angle between 0 to ##\pi##. a)Find...

I assumed to find it I would need to find the area under the graph. I also assumed that the part under x would cancel out so I would be left with 2b*10=1 if it was, in fact, true that it had to equal to one. So my final answer was (1/10)/2 nm^-1 but the actual answer was 0.0845 nm^-1/2 and I'm...

I understand that the energy of an electric field arises from the work put into gathering the electrons together to create the field. Bringing electrons close together requires energy because they naturally want to repel. This potential energy is stored in the field itself and the field has an...

This article about an "Armageddon" scenario says that astronomers don't have a very good idea about the density of asteroids. https://slate.com/technology/2019/05/international-planetary-defense-conference-asteroid-impact.html I had thought that they had a much better idea about it. Can't the...

I recently measured the specific gravity of salt water (NaCl) with a hand refractometer of solution to be 1.028 d 20/20 and 36-37 0/00 at 20 deg C. the d 20/20 and 0/00 are the units on the refractometer view screen. I am not sure if the 0/00 means percentage or g/kg. I am trying to convert...

Firstly i worked out the scale factor of the universe R(t)/R(t0) = 1/1+z = 1/1+11.1 = 1/12.1 = 12.1^3 = 1/1772 The distance between the galaxies were 12.1 times less than today and the volume was 1772 times smaller than today. Then I think the average density in the universe at that time is...

Recent observations report w < -1.3 for z > 1.5. What was the dark energy density compared to matter density during that time? Was the universe briefly accelerating?

Hello, I am using a code on EUCLID future mission. The original author of this code has set a value for the density of galaxy equal to : ng = 354543085.80106884 I think this is expressed in inverse steradian. I think that EUCLID mission has a 30 arcmin^-2 value for density of galaxies...

E0=V/d = 100/0.1 =1000v/m In slab 1, E1=E0/k1=500v/m In slab 2, E2=E0/k2=250v/m Applying Gauss' Law to a box surface surrounding the interface with area equal to the plates we have (-E1+E2)*A = Q/epsilon_naught So charge density sigma = -250 epsilon_naught But answer given is...

ρο/a4 ρο/a3 k Λ Βig Bang Big Crunch Polynomial Expansion Exponential Expansion x 0 x 0 >0 x +1 x +1 x 0 <0 x -1 x -1 >0...

I am new to the site I apologize If I am posting incorrectly or doing something wrong. I need help figuring out how to increase magnetic field density (gauss/tesla's) extending from a magnetic object's surface, most magnets magnetic density is all in the center. I need this in order to induce a...

Hello everybody, In this Wikipedia article we find an equation for a photon gas which contradicts an equation given by Stefan Weinberg in his book "The first three minutes": https://en.wikipedia.org/wiki/Photon_gas The equation given here has 16 π k^3 ζ(3) T^3 in the numerator and c^3 h^3...

So I am a bit stuck on this question as my result using the above equations dose not give an numerical value which I assume from the question is needed. So here my method for solving My first thought was that if on the planet the person can throw a rock 10 time further then that it implies in...

In ##t = 0##, we have ##\rho (0) = | + \rangle \langle + |##. The time evolution of the density matrix is given by ##\rho(t) = e^{-i\hat{H}t} \rho (0) e^{i\hat{H}t}## (I am considering ##\hbar = 1##). I can write the state ##| + \rangle ## as a linear combination of the eigenstates of the...

Number of states in that volume of k-space, ##n(k)dk## is: $$n(k)dk = (\frac{L^3}{4 \pi^3}) \cdot 4 \pi k^2 dk = \frac{L^3}{\pi^2}dk$$. Then the notes state that by defintion, ##n(k)dk = n(E)dE##, and hence $$n(E)d(E) = \frac{L^3}{\pi^2}dk$$. I don't quite see why this is true - isn't it the...

Let ##(x_1,y_1)## and ##(x_2,y_2)## be the point where the rods intersect the ##x,y## plane. I know that on any given point there will be the superpositions of ##E_1=\frac{2\lambda}{4\pi \epsilon_0}\frac{1}{(x-x_1)^2+(y-y_1)^2}\hat{r}_1## and ##E_2=\frac{2\lambda}{4\pi...

From what I have read gravitational waves are caused by the acceleration of massive object causing ripples in space time. What specifically causes this, and how does general relativity predict these. Does it have to be a high density of matter, or a large amount of it. How do these waves affect...

Homework Statement The charge of uniform density 50 nC/m3 is distributed throughout the inside of a long nonconducting cylindrical rod (radius = 5.0 cm). Determine the magnitude of the potential difference of point A (2.0 cm from the axis of the rod) and point B (4.0 cm from the axis). a . 2.7...

Homework Statement A charge Q is uniformly distributed along the x-axis from x = a to x = b. If Q = 45 nC, a = –3.0 m, and b = 2.0 m, what is the electric potential (relative to zero at infinity) at the point, x = 8.0 m, on the x axis? a . 71 V b. 60 V c. 49 V <-- correct answer d. 82 V...

Hi, my teacher showed us how we can derive de relation between spectral radiance and density of cavity (of a black hole), but I have a doubt. This is the equation of the energy that are coming from definited directions by the intervals of angles θ and Φ with frequency in a determined interval...

Ok, we all know that density is mass/volume. So if air is 1.22kg/m3,If we increase pressure, volume will change, therefore density can change. So how does one calculate density of air at higher elevations. Where i currently live, at 4700ft above sea lvl, I am guessing air density is not...

Homework Statement Find the Center of Mass locations of a thin stick of mass M and length L, whose left ends are at x=0. The stick has uniform mass density λ1 = 2M/3L along the left half, and has uniform mass density λ2 = 4M/3L along the right half. Homework Equations I know that this is...

The energy density of an electromagnetic field with a linear dielectric is often expressed as . It is also known that energy can be found by . Using the latter, the energy density is found to be , as is well known. If you integrate the latter only over free charge and ignore bound charge, you...

Pressure initial: 95 kPa Final pressure: 190 kPa Change in enthalpy: -2.96 kJ Initial volume: 0.045 cu.meter Density: 1.11 kg/cu.meter pV=c

Admitted I know very little about QM, but I've been thinking about black holes and I wondered if there would be an upper limit to density of an object of the smallest size allowable if the particles are not being observed by anyone (since black holes are black)? I ignorantly wondered that...

Homework Statement The density of a rod in function of space is given as ##\rho (x)=\frac{c}{x^2}## 1. What kind of density is this? 2. What is the dimension of ##c##? 3. What is the mass of the rod in the intervals - [1 m, 2 m], - (1 m, 2 m), - (0 m, 1 m), - [0 m, 1 m]? 4. Can a plate with...

Saha-Boltzmann equation describes the ratio of number densities between any two consecutive ionization states and its product with the number electron density i.e. $$n_e\frac{n_{i+1}}{n_{i}}$$ Here, ##n_e## is the electron number density, ##n_{i+1}## is the number density in ##i+1## ionization...

Homework Statement For a constant power signal x(t) = c, determine the auto correlation function and the spectral density function. Homework Equations The auto correlation function is: $$R_x (\tau) = \int_{-\infty}^{\infty} E(x(t) \cdot x(t+\tau)) d\tau$$ To my understanding, here to find...