Expansion Definition and 1000 Threads

Why should you prefer the view that cosmological expansion is due to distant galaxies moving apart according to the Hubble Law instead of cosmic space stretching, like stretching of space(-time) in the vicinity of black holes?

Is dark energy the reason for the expansion of the universe?

Homework Statement A generic state represented by the wave function ##\psi (\vec(x)## can be expanded in the eigenstates with defined angular momentum. Write such an expansion for a plane wave traveling along the z direction with momentum ##p = \hbar k## in terms of unknown coefficients ##c ( k...

I've seen the derivation for the adiabatic expansion of an ideal gas which gives the result ## TV^{\gamma - 1} = constant ## which I understand. I have also seen the a similar result, ## pV^{\gamma} = constant ##. But I can't see how to get from the first expression to the second. Any ideas?

I have a function cx(x-l) where c is constant I want to expansion this function cx(x-l) to \sum_{n=-\infty}^{\infty}a_{n}e^{-\alpha x} how can i do it? you have a idea

Sometimes I go back and think about this stuff, and I always find something I don't understand very well. Consider an irreversible isothermal expansion of an ideal gas from state ##A## to state ##B## and suppose I know the amount of heat given to the system to perform the expansion - I'll...

If a gas is suddenly allowed to expand freely and adibatically inside a container then from the first law of thermodynamics dQ=0, My question is whether the change of internal energy would be 0 and if it then how would the work done be 0 (since accessible volume of the gas changes inside the...

A question regarding the redshift of star light being proportional to the star's distance from us. I suppose there were other, competing explanations for this when it was first observed (e.g. that light somehow loses energy/frequency extremely slowly over large distances), in addition to the...

Why do we live in such a privileged time? arXiv:1810.10547 [pdf, ps, other] The End of Cosmic Growth Eric V. Linder, David Polarski Comments: 5 pages, 6 figures Subjects: Cosmology and Nongalactic Astrophysics (astro-ph.CO) The growth of large scale structure is a battle between gravitational...

I apologize if this has been asked before, but I have never seen a satisfactory or straightforward answer. When we say the universe is expanding, do we mean it is "growing" or "stretching"? In other words, if you considered a sheet of graph paper expanding, are we adding more squares or...

Homework Statement Find a Laurent series of ##f(z)=ze^{1/z}## in powers of ##z-1##. Is there an easier way to go about this as this is not a typical expansion I see on textbooks. It seems that my incomplete solution is too complicated. Please help, exam is in two days and I am working on past...

Hi, I would like to expand the following expression: 1/[((a+s)*(1+b/s)^m)], where a, b, and s are real nonnegative values and m is an arbitrary positive integer. Particularly, according to partial fraction expansion, it becomes: Sum[A_j/[(1+b/s)^j],{j,1,m}]+B/(a+s). I look for a closed-form...

Homework Statement Using log taylor expansion to express cumulants in terms of moments I have worked through the expansion- ##log(1+\epsilon)= ...## see thumbnail- and that's ok; my question is why does the expansion hold, i.e. all i can see is it must be that ##k## is small- how is this...

Does anyone know if the accelerating expansion of the universe was measured in more than one direction? Unlike the expansion having no obvious center, it seems like the accelerating expansion would have to point to a “center”. Our galaxy, for example, cannot be accelerating away from a...

Why is the accelerating expansion of the universe not explained simply by the perspective of acceleration caused by a constant (non accelerating) universal expansion? Let's take two particles (X,Y) in a 1d expanding universe where it expands universally by 1 unit per per unit time. O represents...

Homework Statement Suppose we are given the power series expansion ##f(x) = -\sum_{n=1}^{\infty} \frac{x^{n}}{n} ## which converges for |z|<1. What is the radius of convergence? Sum this serie and derive a power series expansion for the resulting function around -1/2, 1/2, 3/4 and 2. The...

Homework Statement Find Partial Fraction Expansion 10/[s (s+2)(s+3)^2] Homework EquationsThe Attempt at a Solution 10/[s (s+2)(s+3)^2] = A/s + B/(s+2) + C/(s+3)^2 + D/(s+3) A = 10/[(s+2)(s+3)^2], s approaches 0 = 10/(2*3^2) = 5/9 B = 10/[s (s+3)^2], s approaches -2 = 10/(-2) = -5 C =...

Homework Statement Coefficient of xy(z^-2) in (x-2y+3(z^-1))^4 Homework EquationsThe Attempt at a Solution [/B] I was wondering if anyone could give me an explanation for my answer? The coeffecient of xy(z^-2) does not = 4 where I would be able to use the multinomial theorem. So since I...

I've been trying to wrap my head around the geometry of the expansion of space, from Science Channel shows I vaguely understand the "every point in space is moving away from every other point in space" and iirc this was uniformly so. Is that correct? If not ignore the rest of this post I suppose...

SR says that there is length contraction in the direction of movement. This works nicely for light going from the back of the ship to the front. From my perspective, the ship is moving away but that is offset by the ship's contraction. But things get tricky for light going from the front of the...

I pulled this quote from an article on the Hubble Constant: "...for example, if the Hubble Constant was determined to be 50 km/s/Mpc, a galaxy at 10 Mpc, would have a redshift corresponding to a radial velocity of 500 km/s." In this illustration provided from the article, if this was the...

Hello guys I struggle since yesterday with the following problem I am reading the book "Elements of applied bifurcation theory" by Kuznetsov . At one point he has the following Taylor expansion of a nonlinear system with respect to x=0 where ##x\in \mathbb(R)^n## $$\dot{x} = f(x) = \Lambda x +...

I read in a so called sci-fi website from my country that as the universe is expanding we may not be able to get to certain galaxies in a possible interstellar travel. That information seems ok for me. But then there was a comment by a reader concluding from the website post that there is coming...

Just a thought I had today. I read an article that mentioned how the universe is expanding faster and faster and how dark energy may be the cause for this, but I wondered, what if the accelerating expansion of the universe is not caused by dark energy but simply by the gravitational attraction...

I came across the following working in my notes and would like some help understanding how the step was done. Many thanks in advance! The following is the working, and we assume that ##\beta## is small $$\frac{1}{1+ \beta \hbar \omega /2 + (7/12)(\beta \hbar \omega)^2 +...} \approx 1 - (\beta...

I seek a little help in understanding why we can see so far into the past to be able to view events where the light from these events should have long ago overtaken wherever the masses ended up. I get it that there was a considerable time during which the limits of the space expansion exceeded...

1) space is expanding at an increasing rate, therefore things are getting farther from each other and therefore increasing in velocity. 2) the faster an object moves relative to another, the more mass it has 3) supermassive objects can turn into neutron stars, black holes, etc. Therefore, will...

I'm having trouble with trying to find the expansion coefficients of a superposition of a Gaussian wave packet. First I'm decomposing a Gaussian wave packet $$\psi(\textbf{r},0) = \frac{1}{(2\pi)^{3/4}\sigma^{3/2}}\text{exp}\left[ -\frac{(\textbf{r} - \textbf{r}_0)^2}{4\sigma^2} + i\textbf{k}_0...

Homework Statement Consider the isentropic expansion of air from a fixed given reservoir (i.e. total pressure and temperature). Investigate the behaviour of the value of the Reynolds number of the flow, as a function of the Mach Number M of the expanded flow. For small values of M, the...

Bessel function using g(x,t)=g(u+v,t)=g(u,t)g(v,t) to show that J_{0}(u+v)=J_{0}(u)J_{0}(v)+2\sum_{s=1}^{\infty}J_{s}(u)J_{-s}(v) ___________________________________________________________________________________________ my solution g(u+v,t)=e^{\frac{u+v}{2}(t-\frac{1}{t})}...

I am looking at a couple of very interesting papers, published in MNRAS, that deduce, that the accelerated expansion of the Universe we observe can be attributed to gravitational waves, produced by a very distant merger of two or more universe-mass-scale black holes. The last one is on the...

How does the expansion of space cause light to lose energy?

This idea has always bugged me: If we are looking at the past when observing the redshift of far away galaxies (ex: 10 billions light years).. then how can we tell that the universe at the present time is still expanding at same rate, deaccelerated, or stopped expanding?

My discussion of the Friedmann metric comes from the derivation presented in section 4.2.1 of the reference: https://www1.maths.leeds.ac.uk/~serguei/teaching/cosmology.pdf I have a couple of simple questions on the derivation. The are placed at points during the derivation.I note the...

Homework Statement An iron ring of radius 2.1 m is to be fitted on the rim of a wheel of radius 2.121 m. The coefficient of volume expansion for iron is 3.6 x 10-5 K-1. By how much should the temperature of the ring be increased? (a) 532 °C (b) 833 °C (c) 278 °C (d) 378 °C Homework Equations...

Homework Statement Expand ##(1+3x-4x^2)^{0.5}/(1-2x)^2## find its convergence valueHomework EquationsThe Attempt at a Solution on expansion ##(1+3/2x-3.125x^2+4.6875x^3+...)(1+4x+12x^2+32x^3+...)## ##1+5.5x+14.875x^2+42.1875x^3+... ## how do i prove for convergence here?

The definition of the angular diameter distance is the ratio of an object's physical transverse size to its angular size. However when I was reading my textbook, *Astrophysics in a Nutshell by Dan Maoz pp.220-221*, I am having some trouble trying to understand the notion of **angular diameter...

Homework Statement Consider a perfect monoatomic gas at pressure $p_i$ 1.2 atm and temperature $T_i$ 300K, that is in equilibrium inside a cylinder having a volume $V_i=1L$ and which piston has a mass of 1kg and is at an height of 50 cm. Admit that a mass M=3.13kg is over the piston. When that...

In case of isobaric expansion, the system expands at constant pressure(the external pressure i.e. the resistance is constant.).In case of flow work, the fluid trying to exit the control volume, pushes against the pressure at the exit of the control volume or when entering the control volume, the...

In an isothermal expansion of an ideal gas, can the piston be made to expand isothermally if the initial system pressure is equal to the initial surrounding pressure?(In most of the books and video lectures whenever they explain isothermal expansion, they assume initial system pressure to be...

Initially, the pressure of the gas inside the cylinder is higher than the atmospheric pressure and the piston is held in the contracted position by some means.When the piston is released, it expands and the pressure and temperature of the system decreases but the volume increases.In order to...

Hi, Joule's original gas expansion experiment is often presented like in the following link: http://demonstrations.wolfram.com/JouleExperimentOnFreeExpansion/ The apparent lack of temperature change in this experiment is often used in textbooks to demonstrate that the energy of an ideal gas is...

Hey everyone 1. Homework Statement I want to compute the Taylor expansion (the first four terms) of $$f(x) =x/sin(ax)$$ around $$x_0 = 0$$. I am working in the space of complex numbers here. Homework Equations function: $$f(x) = \frac{x}{\sin (ax)}$$ Taylor expansion: $$ f(x) = \sum...

Homework Statement Homework EquationsThe Attempt at a Solution Coefficient of volume expansion γ = ∆V/V∆T VT2 = constant Differentiating we get , T2∆V + 2VT∆T = 0 ∆V/V∆T = -2/T So , option 2) looks right . Is that correct ? How do I interpret the answer ? Does that mean the...

I was just curious because if space can expand faster than light, doesn't that mean there will be a lot of space that we just can't see? Do objects just vanish because we can't see them? For instance, if a hypothetical alien lived in MACS0647-JD galaxy which is 13.3 billion light years away...

Homework Statement A rod of length ##L_o## is kept on a friction-less surface. The coefficient of linear expansion for the material of the rod is ##\alpha##. The the temperature of the rod is increased by ##\Delta T## the strain developed in the rod will be? Homework Equations $$ \Delta L=...

I am extremely confused by the use of the term coefficient of increase of something. For example , if it is stated that the index of refraction varies linearly with a coefficient of 2.5×10^-5, how is this coefficient defined? Is it simply the slope of the line plotted with index of refraction on...

Question about accelerating expansion Why do I see everything backwards? Here is a paragraph from Bernard Schutz’s excellent book on General Relativity, p. 352: (referring to the famous plot from the High-Z Supernova Search Team: Riess, et al, 1998) The top diagram shows the flux (magnitude)...

Homework Statement Adiabatic expansion of an ideal gas is carried out in a steady flow process. The initial pressure of the gas is 2.5 bar. The volume is expanded from 1.2m3 to 3.8m3. Heat capacity ratio (γ) = 1.42. Calculate enthalpy change of the process. Homework Equations PV = nRT W = ∫...

Hello everyone. I am trying to generate the KL expansion of a stochastic process. I use a Monte Carlo sampling method to generate the process, which involves two random variables and I compare it with it's theoretical mean for 50 values of time and they look quite similar. Then, I calculate the...