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Why is all the information contained only in the sidebands in AM? (And what is this supposed to mean? I read it off a textbook.)
Also, why does an increase in bandwidth lead to an increase in quality of the signal?
|
I am having a bit of trouble understanding what an ideal wire is.
Let's assume there is a positive charge on the positive terminal of the battery and a negative on the other side which will give us the same results. Now electric potential is given as integral of E.dr. Therefore the potential will decrease with the dist... |
When calculating the entropy of an classical gas we consider the Gibbs correction factor, when dealing with quantum gases we consider the appropriate Fermi/Bose statistics.
But in my introductory notes to statistical mechanics one calculates the canonical partition sum of $N$ harmonic oscillators without such correctio... |
What is the relation between tensor calculus and Einstein's field equations? or What is the contribution of tensor calculus to Einstein’s field equations?
|
If we consider two hadronic processes with the same final state, example :
should one also include an interference term in cross-section despite the different propagators?
What would be in cases like Vector Meson Dominance, when we have additional channel mediated by photon?
Or should we only include interference ter... |
This was how the orbital angular velocity/ angular velocity of precession was shown to be calculated in my textbook ($\phi$ is angle made by top with vertical)
$$dL=L_\text {spin}\sin\phi d\theta$$
But , $$\omega_ \text{precs} =\frac{d\theta}{dt}$$
$$\omega_ \text {precs}= \left|\frac{d\vec L}{dt}\right| \left[ \frac{1... |
How does the amount of liquid in a cylindrical can affect its motion when rolling down an inclined plane?
|
The height of the cylinder is $3 \text { m }$ and the diameter is $45 \text { cm }$. The cylinder is filled with water. The block is of weight $30\ \text { kg }$ with dimensions $30\text { cm} \times \ 30 \text { cm} \times 30\text { cm} $. The block is put on the water's surface but it automatically sinks.
Please sug... |
I am trying to self study QFT and i am very confused about the covariant derivative.
When we require our theory to be invariant under local gauge transformations we kind of "guess" that we need to change our differential operator so that the term and find e.g
$$
\displaystyle D_{\mu }:=\partial _{\mu }-iqA_{\mu } \qua... |
Suppose we add to the Yukawa sector of the SM a complex scalar $T^\alpha(3,1)^{-1/3}$, where $\alpha=1,2,3$ is a $SU(3)_C$ index and the charges assignment means that it transforms as a triplet under $SU(3)_C$, a singlet under $SU(2)_L$ and has $Y=Q=-1/3$. Assume $T$ much heavier than the proton.
If we restrict to the... |
I'm a newbie in QFT and I have some doubts with this simple exercise:
Using the Wick Theorem evaluate
$$\langle0|T(\phi^4(x)\phi^4(y)|0\rangle$$
Use a diagrammatic approach to represent the possible contractions
(how many $\phi$-lines are attached to each vertex).
Determing numerical factor in front of each diagrams.... |
I am currently trying to understand a really old paper of Jackiw and Coleman: "Why dilatation generators do not generate dilatations".
There, at some point they arrive at the following integral from a Feynman propagator (wth loops) and regulator masses:
\begin{equation}
\lim_{M_f \rightarrow \infty} g^2 M_f Tr \int \fr... |
And what element does visible green glow indicate in our own atmosphere?
https://youtu.be/HDlsdVuv6qQ
|
Could a solid, isolated body have arbitrarily low entropy but arbitrarily high temperature?
I'm trying to build an intuition: if according to statistical mechanics, entropy is a measure of disorder and temperature is a measure of energy, could all particles (at least in theory) have high kinetic energy and be moving in... |
I do not understand why people say that electrons move from high to low potential, the potential of an electron due to a proton is given by $\frac{-Kq}{r}$ where $r$ is the distance from the proton. Now, naturally the electron will get attracted to the proton and lets suppose it gets to a distance $r_1$ where $r_1$ is ... |
I have heard countless times (and not just when discussing the Heisenberg's Uncertainty Principle) that making a short pulse using sine waves requires more and more sine waves to localize the pulse closer and closer, and for a pulse to be localized perfectly you would need infinite sine waves. Unfortunately, this expla... |
At first glance, one might think that the two body problem with inverse square force is a symmetric problem. The force (in the reduced mass frame of reference) depends only on the distance $r$, without an angle dependence.
However, most orbits are elliptical, hence something had to break the perfect symmetry. It cannot... |
There's something I don't understand: I've learned that quantum wave functions can be described as a "ket vector" in an abstract vector space called Hilbert space. The position wave function, for example, used to express the probability of finding the particle at a point, can be described as a vector in an infinite dim... |
A block of mass $M$ is attached to one end of a light string which is wrapped on a disc of mass $2M$ and radius $R$. The total length of the slack portion of the slack portion of the string is.
The block is released from rest. The angular velocity of the disc just after the string becomes taut is?
I understand this q... |
I am currently working through some problems in thermodynamics. I am given the following relationship:
$$TdS = C_vdT + l_v dV = C_pdT + l_p dP$$
where $l_p$ and $l_v$ are some functions of state variables and the number of particles is constant. I want to show two relations:
$$\begin{align} C_p-C_v =& \ l_v\frac{\parti... |
According to Manohar:"argument applies almost without change to a practical example,the derivation of the HQET Lagrangian to one-loop."
on page 37 of the following paper on effective field theories:
https://arxiv.org/abs/1804.05863
Question: I want to know what is the IR scale we expand the full theory in terms of it t... |
One would have expected there to be lower pressure on the outside of the truck because of the faster airflow - implying the sidewalls would be sucked outwards. Of course, there is some flapping and instability as well. It does not seem to be dependent on the shape of the front of the truck.
|
I am still trying to understand the meaning of an ideal current source. To this end, I drew this abstract circuit above. Let's say the current source is ideal, and the voltage symbols you see represent ideal voltmeters, reading the voltage over their respective terminals. Va reads the voltage drop over I, the ideal cu... |
I am trying to derive $$pV^\gamma - p_0V_0^\gamma = 0$$ from the first law of thermodynamics and the ideal gas law. I thought of two seemingly identical ways, which yield different results. Maybe someone can tell me where I went wrong.
For an adiabatic process, there is no heat transfer. $$\delta Q = 0$$
This is substi... |
I wanna to understand, why when one gonna to construct interacting theory of spin 3, one need also include infinite tower of spins 4, 5, 6 , ...
As I know, this statement correct even in classical theory.
Why there are not such obstructions for spin 2 and spin 1?
What is fundamental distinction between such theories (s... |
I have a network of states, each linked with neighboring states by unique forward and reverse transition rates ($k_{f}$ and $k_{r}$) - let's just say these are chemical species with multiple intermediate reactants and reversible intermediate reactions. At long timescales, this system will reach a stationary distributio... |
I need this information to check whether I can use gravitation as a metaphor in a talk. How does gravitational forces differ when two objects are moving in parallel versus they are moving towards each other? What is happening in the former scenario? Are they staying in parallel for as long as no other force applies?
I... |
Let us define
$$\tag{1}
Q=i\nabla_\mathbf{k}\delta(\mathbf{k-k'})\left[\rho_{nm}(\mathbf{k'})-\rho_{nm}(\mathbf{k})\right],
$$
where $\delta(\mathbf{k})$ is a Dirac delta, and $\rho_{nm}(\mathbf{k})$ is a reduced density matrix. I wish to show that
$$\tag{2}
Q =i\delta(\mathbf{k-k'})\nabla_\mathbf{k}\rho_{nm}(\math... |
I am studying this book: Quantum Information Meets Quantum Matter -- From Quantum Entanglement to Topological Phase in Many-Body Systems (https://arxiv.org/abs/1508.02595).
In chapter 7, it introduces the ideas of generalized local unitary (gLU) and generalized stochastic local (gSL) transformations to define different... |
In a simple pendulum, $\alpha$ is angle between string and vertical, $T$ is tension in string and $mg$ be pull on the bob.
$T$ has 2 component $T\cos\alpha$ and $T\sin\alpha$
$mg$ has 2 components $mg\sin\alpha$ and $mg\cos\alpha$.
I get that $mg\cos\alpha=T$ and $mg=T\cos\alpha$. So I got 2 values of tension at a sam... |
From the official GPS website:
How accurate is GPS for timing?
GPS time transfer is a common method for synchronizing clocks and networks to Coordinated Universal Time (UTC). The government distributes UTC as maintained by the U.S. Naval Observatory (USNO) via the GPS signal in space with a time transfer accuracy rela... |
Its a broad question, so I'll tell you the situation where I stumbled across this.
In corona discharge, or when any electron beam travel through air, it hits the air molecules (consitituent molecules in mixture) and they get excited and lose energy afterwards in form of photons.
how kinetic energy of electron transfer... |
I ran across this problem on an exam a couple days ago:
Consider the transformation to the new coordinates $(r,u,z,\bar{z})$
$$r=\sqrt{(x^1)^2+(x^2)^2+(x^3)^2} \qquad u = x^0-r \qquad z=\frac{x^1+ix^2}{x^3+r} \qquad \bar{z}=\frac{x^1-ix^2}{x^3+r}$$
Find the metric tensor $g_{\mu \nu}$
At first glance, it seamed easie... |
There is one thing that always troubled me in quantum mechanics, how do you justify the expression of the energy and momentum operators, namely $\hat{E} = i\hbar\frac{\partial}{\partial t}$ and $\mathbf{\hat{p}} = -i \hbar \mathbf{\nabla}$?
The only justifications I've seen were always the same: take a plane wave funct... |
In classical theory, particles are similar to little, hard balls, that can scatter off each other in elastic collision. Waves, on the other hand, can pass through each other unaltered, although they will interfere. Is there any situation in which waves, eg sound waves, can interfere in such a way that the outcome if as... |
I'm a newbie in physics, so I went reading on wiki to learn about heat of fusion but then it said how $1 \:\rm kg$ of ice at $0^{\circ} \rm C$ under wide range of pressure needs $333.55 \rm kJ$ energy to fully melt it. See:
https://en.m.wikipedia.org/wiki/Enthalpy_of_fusion (first paragraph)
So if the ice absorbed ener... |
In many cases when there is friction acting on a body which is rolling without slipping ( for eg : a body rolling down a inclined plane ),
We say, that the work done by the friction is zero as the velocity of point in contact is zero adn it works out.
But the question,I am having is how does friction still comes into p... |
When we talk about electricity through a circuit because of a battery it is said that the electrons from negative terminal travel to positive terminal of the battery.
I can't help but imagine about the free electrons in that wire, does the electrons of negative terminal repel them and in that way we say the electron mo... |
I am looking for a reference that discusses the thermodynamic properties of Abrikosov lattices in d-wave superconductors, especially the discussion to calculate the specific heat of vortex lattice in the limit where they are rigid enough to maintain the lattice structure.
|
This paper published in 1969 indicates that a majority of the mass-energy of the universe may be contained in gravitational waves:
"Turning next to phenomena on a galactic scale, we find it conceivable that over the past ~10^10 years the Galaxy may have radiated away as much as 10 times its present mass."
Has the rea... |
I've noticed that several references take for a fact that by studying Kähler gravity on a Calabi-Yau threefold one can demostrate that any lagrangian submanifold embedded in the threefold posees three dimensional $SL(2,\mathbb{C})$ Chern Simons theory as its worldvolume theory.
For an example of a paper were this is ex... |
Suppose there are 2 scientists who have decided to measure the location of an electron at a same fixed time. Is possible that while one observes the wavepacket localized at (position=x) while the other observes the wavepacket localized at (position=y). The condition however is position x is not equal to y.Please dont c... |
I've seen the reaction:
$$
^{9}_{4}\mbox{Be} + ^{4}_{2}\mbox{He}\, \rightarrow\, ^{12}_{\,\,6}\mbox{C} + \mbox{n}\,.
$$
But what I don't understand is why Carbon 13 is not made, or if there is actually some carbon 13 made?
|
The cohesive energy of a solid is the (average) energy required to isolate the atoms of a solid, which means it's given by the difference between by the energy of solid and the energy of the isolated atoms.
I assume in this context by "energy of the atoms" we mean the total binding energy of the electrons to the nuclei... |
I’d hope to keep this simple.
If we decide to measure electron spins along the vertical axis using a Stern-Gerlach device we get an overall even split between up and down.
Therefore it is said electrons are in an equal superposition before they are measured. Does this have any relation to reality though?
Why is it not ... |
What inspired me to ask this question was from my curiosity and hobby to understand the Science/Physics behind comics, anime, and mangas. I've seen tables of the ultimate tensile strength or yield strength of various objects before they break but it's still not what I'm looking for. To be more specific, I'm not asking ... |
In Hamiltonian Mechanics, a version of Hamilton's principle is shown to evolve a system according to the same equations of motion as the Lagrangian, and therefore Newtonian formalism. In particular, letting $\delta$ indicate a variation of the path through phase space,
$$ \delta \int_{t_1}^{t_2} \big(p_i \dot{q}_i - H(... |
What is the physical principle behind the following behavior:
When left with the remainder of a bag of chips, or cookie crumbs, etc., when shaking this container, the smaller particles will settle to the bottom and the larger particles will rise to the top
|
If this isn't the right place for this question, please tell me.
My question is how does a person's voice affect how a soundwave looks? For example, if I say the letter "a" it would sound different than if you said the letter "a", but my question is if there is a pattern to this, or maybe if we are able to derive a wav... |
In Morris-Thorne Wormhole there is a quantity called proper radial distance given by:
$$\ell(r) = \pm \int^{r}_{r_{0}} \Biggr(\frac{r-b(r)}{r} \Biggr)^{-\frac{1}{2}}dr \tag{1}$$
This function must to be finite for every value of $r$.
The fact is, it seems that this is a strong condition for the mathematical viability o... |
Suppose a system of particles is subject to internal forces, some of which are conservative and some of which are non-conservative. Let $\Delta E$ be the change in mechanical energy of the system as it undergoes a change in configuration and $W_{nc} $ be the work done by the non-conservative forces in that change in co... |
Consider some stationary charge in an inertial frame of reference.
Consider an observer accelerating with respect to that charge. Does the accelerating observer see radiation? It would be reasonable to assume so.
From what I've read, though I'm not too sure, this is called "Unruh Radiation," and apparently there is no ... |
So, the equation for pressure is $p=F/A$.
I saw in a video that the pressure exerted in an area is the same as that exerted on the walls of a container.
So to find out the pressure exerted on the cylinder walls I need to know the area of the base of the top of the cylinder.
The radius of the base of the top is $1.85$ c... |
In Volume II Chapter 42 (on General Relativity), Feynman uses the equivalence principle to show that clocks etc. higher in a gravitational field run faster, and as a result emit photons with higher frequency .
Then he says that this can be demonstrated in two other ways:
a) via conservation of energy: an atom in excite... |
Ferro-electricity is the property of some dielectric materials to keep a net residual polarization even after the electric field is removed. They tipically present a hysteresis cycle doing this.
It is said that all ferro-electrics are also pyro-electrics, but why is this?
I know that Pyro-electricity is due to an asy... |
Phys.org IBM researchers create world's smallest magnet
The above article talks about using single, individual holmium atoms in one of two states (spin-up or spin-down? Or just north-pole-up vs. down?)
in future computers...
Is this an example of so-called 'spintronics'?
|
How would one go about drawing the Feynman diagram for the following reaction?
$$\Xi^{-} \rightarrow n\space+\pi^{-}$$
In terms of quarks:
$$dss\rightarrow udd\space + d\overline{u} $$
Could the reaction be mediated by two $W^{\pm}$ bosons similar to the $K^{0}\rightarrow \overline{K^{0}}$ reaction? In the $\Xi^{-}$ c... |
The abstract of the new arXiv preprint Observation of Excess Electronic Recoil Events in XENON1T contains the following sentence:
The excess can also be explained by $\beta$ decays of tritium, which was initially not considered, at $3.2\sigma$ significance with a corresponding tritium concentration in xenon of $(6.2 \... |
I am not sure if I am understanding this right, but I was wondering what is actually what happen when you measure in quantum mechanics. When you have a system, you can describe it has a wave function in position space $ \psi(x) $ and it could be a superposition of different states of the system, with some probabilities... |
My question is very general and it isn't limited to the system that I calculated the fields. I need a general answer or a particular answer for my problem. I found two fields $\mathbf E,\mathbf B$ solutions for a specific system, and I know that these field plus electromagnetic waves are solutions too. So which has to ... |
In a youtube video, a German physicist Wolfgang Ketterle showed that two halves of the condensate creates interference pattern as though they are waves. I paused the video but still unable to understand how the laser cut through the ultra cold atoms that vibrates in lock-step? Do you mean the laser is acting on individ... |
I am interested in understanding the consequences of squaring the Einstein Hilbert action:
$$
S=\int \sqrt{\left( \left(R\sqrt{|\det g_{\mu\nu}|} \right)^2 + L_m \right)}d^4x
$$
The field equations resulting from the variational approach leads to
$$
R\sqrt{|\det g_{\mu\nu}|} \left( R_{\mu\nu} -\frac{1}{2}g_{\mu\nu} R \... |
In Matthew D. Schwartz's QFT book, Chapter 28, the author claims when $\hbar \rightarrow 0$, the following equality (eq 28.4) holds:
So how can I see the second "$=$" holds? It seems the method of stationary phase is inapplicable?
UPDATE:
Below are my calculations:
By definition,
\begin{equation}
\langle \Omega|\phi(x... |
Does anyone have experience in looking at Drude theory from the perspective of plasma physics instead of the standard, condensed-matter, "electrons in a metal" sort of thing and can point the way? I'm a grad student working on this topic for my masters thesis and I've spent the last hour or so reading the "Plasma Fluid... |
On Wikipedia it was stated that a wave's speed $v$, wavelength $\lambda$ and frequency $f$ are related by the identity
$$v(\lambda)=\lambda f(\lambda).$$
The function $f(\lambda)$ tells us that the frequency of a wave depend solely on its wavelength. Why is that so?
|
Will the coin spin forever or will it be de-accelerated by the gravitational force?
|
We have learned creation operator $\hat{a}^\dagger_i$ adds a particle in $i^{th}$ state, and annihilation operator $\hat{a}_j$ remove a particle from $j^{th}$ state. They can be interpretated in such ways, and when we act them on number state we can get some very elegant results.
But how do we actually express them ind... |
We have learnt that when an force displaces object along its direction then it is work done. so there is dot product in its formula (I guess). So is it also right to say that work done is cross product of displacement and force if we consider the perpendicular component of force regardless the typical definition of wo... |
There's a pretty common physics chestnut about what would happen if the sun just up and disappeared. "How long would it take for us to notice?" The answer is of course roughly eight minutes-- that's how long it would take for the last emitted photon to reach us, at which point the sky would suddenly go dark. That's als... |
When I was studying current electricity I found out that the amount of heat dissipating across a resistor is equal to the potential energy lost by an electron. Now I thought that a resistor provides an obstruction and electrons collide to lose energy. When an electron moves near a proton potential energy is lost even t... |
Is it possible to do anything to a coin in space, so it begins to spin, using sunlight as the energy source?
|
Deuteron is p-n, so naively should have zero electric quadrupole moment. However, experimentally it turns out quite large: $0.2859\ e\cdot fm^2$ from https://en.wikipedia.org/wiki/Deuterium#Magnetic_and_electric_multipoles
This Wikipedia article explains it by adding $l=2$ angular momentum states - should we imagine i... |
Let's suppose we have hyper entanglement of two photons such as
$$|ψ\rangle = \frac{1}{\sqrt{2}}(|HH\rangle_{ab}+|VV\rangle_{ab})\otimes\frac{1}{\sqrt{2}}(|SS\rangle_{ab}+|FF\rangle_{ab})$$
where $|H\rangle, |V\rangle$ is polarization bases, while $|S\rangle, |F\rangle$ is time-bin bases. (a,b are each party, Alice and... |
Verlinde ( https://arxiv.org/abs/1611.02269 ) tries to deduce MOND from emergent gravity. Can you help?
Emergent or entropic gravity goes back to Jacobson. He starts with
the entropy-area connection $S= A\,{kc^3}/{4G\hbar }$ (Bekenstein-Hawking)
the temperature-acceleration connection $T= a \, {\hbar}/{2\pi kc}$ (U... |
I can understand the difference between the definition of rotational and irrotational flow if the flow is in a straight pipe. But in case of circular flow, that confuses me.
Let's consider a flow that is rotating about the origin point $O$.
In both figures, the fluid particle is shown by green color with some axes att... |
In $2d$ systems, the relation between the conductance $G$ and conductivity $\sigma$ is given by $$G = \sigma W/L$$ (page 1, Electronic Transport in Mesoscopic systems, Supriyo Datta) where $W$ is the width and $L$ is the length of the sample.
In usual $3d$ systems, the relation between them is $G = \sigma A/L$, where $... |
Classical $1/r$ gravity arises from general relativity when curvature is neglected and speeds are small compared to the speed of light.
In de Sitter space with a positive cosmological constant $\Lambda$, curvature cannot be neglected, but is small. What happens if one tries to deduce "classical" gravity form general re... |
I'm assuming since trains move so fast, there are Bernoulli effect-induced winds happening around it, with the direction perpendicular to the body (is this true?).
If I were to put wind turbines on a train whose axes are perpendicular to the body of the train to utilize the Bernoulli-induced winds, would I be doing som... |
Assume we have a system with N particles, each particle in one of $\gamma$ different single particle states $|k^\gamma\rangle$. The state space of the multi-particle system is spanned by the basis
$$\mathcal{B}=\{|k^{p_1},k^{p_2}...k^{p_\gamma}\rangle\}_{\textrm{All permutations } p_i\in\{1..\gamma\}}$$
where the follo... |
Some interpretations, like the many-worlds interpretation, treat the wavefunction (modulo an overall phase factor) as objective and fundamental.
But consider the following example for a qubit: a classical probability distribution over wavefunctions with a 1/2 probability of $|0\rangle$ and a 1/2 probability for $|1\ran... |
The Bohr radius ($a_0$ or $r_{\text{Bohr}}$) is a physical constant, equal to the most probable distance between the nucleus and the electron in a hydrogen atom in its ground state. It is named after Niels Bohr, due to its role in the Bohr model of an atom. Its value is $5.29177210903(80)×10^{−11}\ \mathrm m$.
Source: ... |
How does a satellite planetary path depend on its speed and other factors.
I want to know more about parabolic, elliptic and hyperbolic paths of satellite.
|
I have stumbled across this question and cannot seem to find an answer to it.
Consider an operator $\textbf{A}$ with eigenkets $|{a_{i}\rangle}$ and distinct eigenvalues $a_{i}$ . One can check that the following operator is null:
\begin{equation}
\prod_{i} (\textbf{A} - a_{i}).
\end{equation}
Now, given this, what is ... |
I want to find the work done by the force of gravity to move an object of mass $m$ from infinity to a point $P$ at distance $r_p$ from a body of mass $M$ (that I assume fixed). The formula should be
\begin{equation*}
W = \int_{\infty}^{P} \vec{F}(r) \cdot d\vec{r}
\end{equation*}
The force is conservative, so I can ass... |
Can the timbre variable have such influence on a specific "sheet music" for two or more instruments someone would execute, that its actual interpretation could transform it on a another music? I mean, if you synthesize the timbre of the sound wave of each instrument section on a computer, changing it fast enough, can t... |
I am reading Negele & Orland's "Quantum many-particle systems". In problem 1.9 you show that the (Bethe ansatz) wave function
$$ \psi(\{x \}) = \exp \left( - \alpha \sum_{i < j}^N |x_i - x_j| \right) $$
solves the Schrödinger equation for $H= - \sum_{k=1}^N \frac{\partial^2}{\partial x_k^2}$ (free Hamiltonian, in units... |
I was going through the chapter of "Newton's Laws of Motion", where I was introduced to the concept of inertia in Newton's First Law. I saw that all objects that have mass will have inertia. But I do not really get it.
What is the reason behind objects having inertia? And why is it that only those objects that have m... |
In the physics of waves, I often see expressions like
$$A\exp(i\omega t) + f(t)$$
where $A$ is a constant, $w$ is the angular frequency and $f(t)$ is an arbitrary function that depends on time.
It also often said that when such expressions are averaged over a long time, terms like $A\exp(i\omega t)$ makes 'no contribut... |
I know that the Translation operator shifts particles/fields in a direction and can be written as $$\hat{T}(x) = e^{-\frac{i}{\hbar}\hat{p}x}.$$
What confuses me is that when we rewrite $\hat{p} = \frac{h}{i}\nabla$ we obtain:
$$\hat{T}(x) = e^{-\nabla x} = e^{-1} ~??$$
Which doesn't make sense.
|
Is it possible to calculate the amount of water (mol, mass...) in a gas, in a heat exchanger (open system) if I know the partial pressure of the water? The stream through the tubes is mainly benzene and hydrocarbons.
I first tried to use the ideal gas law with the compressibility factor, but that equation is meant for ... |
According to Peskin and Schroeder (P&S)'s book, on pp. 156-157, the two processes $e^+ e^- \rightarrow \mu^+ \mu^-$ and $e^- \mu^- \rightarrow e^- \mu^-$ are connected via $s \leftrightarrow t$ crossing symmetry.
I tried to see it but I only found $s, t, u$ (Mandelstam variables) changes as
\begin{align*}
s \rightarrow... |
The Joule-Kelvin (or Joule-Thomson) expansion is an isenthalpic expansion in which the reduction of a gas' pressure from $ P_{i} $ to $ P_{f} $ results in a change in Temperature. It results in cooling only if the gas is already below a so-called "Inversion Temperature". Now, it makes sense to me that this inversion te... |
According to the wikipedia page on Strong Gravity, the theory is considered "non-mainstream", but from what I can gather there have been some very interesting progress and results since it was first proposed by Salam and Sivaram in the late 70s.
One of these seem to be the BCJ Double copy and the so-called Color-Kinema... |
Spin lies in $\rm SU(2)$ space, i.e. $S^3$ space, but when we write the spin coherent state:
$$|\Omega(\theta, \phi)\rangle=e^{i S \chi} \sqrt{(2 S) !} \sum_{m} \frac{e^{i m \phi}\left(\cos \frac{\theta}{2}\right)^{S+m}\left(\sin \frac{\theta}{2}\right)^{S-m}}{\sqrt{(S+m) !} \sqrt{(S-m) !}}|S, m\rangle$$
where $\Omega$... |
I am studying the renormalization procedure from the Ramond book. I understand the computation but I miss some physical insight. I will present my understanding here and the question that I have in mind.
So we start from a Lagrangian density (scalar $\lambda \phi^4$ theory)
$$ L_i(\phi, m, \lambda^*)$$
which Green func... |
I was doing the following problem:
A solid cube of wood of side $2a$ and mass $M$ is resting on a horizontal surface. The cube is constrained to rotate about an axis $AB$. A bullet of mass $m$ and speed $v$ is shot at the face opposite $ABCD$ at a height of $4a/3$. The bullet becomes embedded in the cube. Find the mini... |
This is from lecture 8 of MIT OpenCourseWare's 2.003SC Engineering Dynamics (https://www.youtube.com/watch?v=zNCBDrnT05E&t=3120s) from minute 52:00 to 56:48.
The situation is there is a cart accelerating down a slope. As the cart accelerates down, the water level in the cart adjusts to be parallel to the slope. The pro... |
I have been unable to find a short statement of Noether's second theorem. It would be helpful to have the following:
A short mathematical statement of the theorem. Does it imply a conservation law and strong identities?
A short derivation of it, so that it is clear what assumptions are made. (Here I have in mind that... |
Imagine two blocks of masses M1 and M2 attached by a massless string. If a force F is applied in the horizontal direction to one of the blocks, then what is the direction of the tension acting on the string?
|
I hear this sentence sometimes: "quantum theory is inconsistent with relativity theory".
Is it possible to interpret this really in a formal system logically? I tried to understand the term "to be consistent with" to be implying that all the first order theory extension of these two in mathematical proofs gives a contr... |
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