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Prove $\exp (-i \phi(\hat{n} \cdot \vec{\sigma}))=\cos \phi-i(\hat{n} \cdot \vec{\sigma}) \sin \phi$ using certain property

I'd like to prove $$e^{-i \phi(\hat{n} \cdot \vec{\sigma})}=\cos \phi-i(\hat{n} \cdot \vec{\sigma}) \sin \phi$$ using $$\sigma_{i} \sigma_{j}=\delta_{i j} I+i \varepsilon_{i j k} \sigma_{k},$$ where $\...
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0answers
5 views

Kinetic Energy of an Electron

I am being asked the question below, and I don't quite understand it. I have tried derriving the equation for hours, and I still can't get it. After reading online, I don't think it's possible in the ...
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0answers
10 views

Carlo Rovelli's analogy of gravity as running down the beach into the sea where the resistance of water makes us fall down into the waves

In "The Order of Time" (page 12), Carlo Rovelli explains how things fall due to the slowing down of time and uses the following metaphor: "Where time passes uniformly, in ...
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0answers
9 views

Einstein's light speed postulate

I have seen two statements of Einstein's 1905 light speed postulate; for instance, in Andrew Steane's Relativity Made Relatively Easy: There is a finite maximum speed for signals. There is an ...
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1answer
16 views

With reference to orthonormal bases, can someone explain this please

$e_i$ and $e_j$ are orthonormal bases. $a$ is a vector; $$a = \sum_{i=1}^N a_i e_i $$ Question is, how the operation below equals $a_j$ \begin{align}\langle e_j|a\rangle&= \sum_{i=1}^N\langle e_j|...
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0answers
10 views

Understanding how soap works in water

Can mycelles be formed in water even without grease in the middle? Can soap molecules be dispersed individually inside water, with hydrophilic and hydrophobic parts both immersed in water? Is this ...
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0answers
10 views

Incompressible flow / The number of fluid elements per unit volume

If we have a steady isothermal incompressible flow (with non-zero velocity field), the density must be constant and uniform, right? Can we conclude that the number of fluid elements(fluid parcels/very ...
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0answers
15 views

Time spent by a comet inside the Earth's orbital (Kepler problem re-visit)

I come across this interesting problem comet-x-earth. It was an exam problem asking the time that a comet will be spent inside the Earth's orbital. I make an illustration for the problem: The comet ...
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0answers
8 views

What is the difference between irreversible and reversible isochoric processes done on an ideal monatomic gas in a frictionless system?

Suppose we had two thermal reservoirs at $T_{c}$ and $T_{h}$ with $T_{c} < T_{h}$ and an infinite series of thermal reservoirs with a continuous range of temperatures between $T_{c}$ and $T_{h}$. ...
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2answers
23 views

Why is Griffiths ignoring the bounded surface current caused by the magnetization of the cylinder?

My problem arises in Griffiths's book chapter 6, when he discusses the auxiliary field $\mathbf{H}$. At first he claims that Ampere's law inside a magnetized material is as follows: $$\nabla \times \...
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1answer
22 views

In elastic collision, should gravitational potential energy not be considered?

In elastic collision of two bodies, kinetic energy is conserved, i.e. $$ \frac{1}{2}m_1u_1^2 + \frac{1}{2}m_2u_2^2 = \frac{1}{2}m_1v_1^2 + \frac{1}{2}m_2v_2^2 $$ If the two bodies are under the ...
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0answers
12 views

Steps behind meson decay amplitudes

I am a graduate student with a somewhat basic level of exposure to qft. As part of my degree I have been tasked with calculating meson decay amplitudes in a paper provided to me by my supervisor but ...
1
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1answer
11 views

Query regarding instantaneous velocity and instantaneous acceleration

Suppose an objects velocity is 5m/s at t=1 sec and 8m/sec at t=2 sec then the acceleration here is 3m/sec^2.i.e at t=1 sec the acceleration is 3m/sec^2.this isnt instantaneous acceleration.right?it is ...
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1answer
39 views

Shouldn’t the magnetic field of a solenoid be affected by length?

I’m in an electricity and magnetism course right now and I literally can’t find an answer to this question, so I was wondering if someone could help. In order to find the magnetic field inside a ...
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0answers
27 views

Order of divergences in the $\phi^4$ theory

On page 324 of his book on qft, Peskin analyzes the superficial degree of divergence of the 1-loop self-energy correction of the $\phi^4$ scalar theory. Realizing that $D=2$, he concludes that the ...
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0answers
12 views

Cauchy's theorem of existence of stress: prove action/reaction principle directly on a particular example

I'm trying to solve an exercise that I found on Gurtin's book (Exercise. 7 pg 107) An introduction to continuum mechanics Let $\mathbf{s}(n,x)$ be the traction from Cauchy's hypothesis, where $n$ is ...
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1answer
20 views

What exactly are the 2 points where a magnetic needle becomes horizontal?

Textbooks and websites say: A magnetic needle rests making different angles with horizontal when suspended at different places of the earth In the explanation, they say that the magnetic needle ...
-1
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0answers
27 views

Which physics book has the maximum application of calculus? [closed]

I have read so many books on physics. I have solved a lot of problems but I am looking for some book where I can find a lot of applications of calculus? Problems are also calculus based?
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0answers
39 views

Why do we treat the action as dimensionless in QFT?

When determining whether the couplings in a QFT Lagrangian are relevant/irrelevant/marginal, we set $\hbar = c = 1$ and use the fact that the action is dimensionless to find the dimensions of the ...
3
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0answers
33 views

Would birds be able to fly if the air had no viscosity? [duplicate]

There are already many answers to the general question of why birds or planes can fly. But my question is more specific: I would like to understand the relative importance of the viscosity. The air ...
1
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1answer
35 views

What does “entropy” really mean?

I'm currently taking a course of introduction to biophysics in college and we currently covered a subject called entropy (S). We did some maths based on the Carnot cycle and came up with the following ...
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0answers
15 views

Average secret key rate calculation

I am working on a problem related to average secret key rate calculation in satellite quantum key distribution (QKD). The problem is similar to a paper on arXiv:1712.09722 (P. No. 21). In a single ...
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0answers
31 views

Does the Schwarzschild metric prove that around the earth, 99.9999% of the warping of spacetime is temporal?

In several posts on Quora, here Howard Landman writes that the Schwarzschild metric shows/proves that around a smaller body, like the Earth or the Sun, 99.9999% of the warping of spacetime is time, ...
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0answers
17 views

Calculate pressure increase due to heating of water in closed chamber

I would like to be able to calculate the increase in pressure generated by heating a liquid in a closed chamber (no air gap, completely filled). For example, I want to make sure that I don't exceed ...
0
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0answers
16 views

Probabilities in the Bell experiment

I have some doubts on the calculations behind Bell's experiment, which goes as follows: a pair of entangled photons is shared between two scientists, Alice and Bob, who possess a bunch of polarizers ...
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0answers
8 views

What is diffractive dissociation in collisions?

Correct me if I am wrong: If we collide protons with protons then we can have elastic scattering, inelastic scattering (large momentum transfer between partons), and diffractive dissociation. I am ...
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1answer
20 views

Why $C_p=C_v$ for incompressible substances?

I'm learning entropy change for incompressible substances and on the way I saw this equality of $C_p=C_v$. I can't seem to understand this equality and I'm not able to visualize any such example. My ...
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0answers
17 views

Preparing Mixed States

Let's say we want to obtain a spin-$\frac{1}{2}$ 50% in the $|0 \rangle$ and 50% in the $|1 \rangle$ state with density matrix $\rho=\frac{1}{2} \mathbb{1}$. I am well aware that by creating the $0^{...
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2answers
25 views

Simplifying Wave Algebra - Possible binomial theorem?

In my physics class today, we were looking at the expression $(1-(u/v))^{-1}$. In a single step, the professor showed that this expression equals $1+u/v$. How is that? Is it the binomial theorem? So ...
-1
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1answer
14 views

Should the directional parts of vectors be treated as a value or a line?

Should the directional parts of vectors be treated as a value or a line? Say $\newcommand{\veca}{\mathbf{a}}\newcommand{\vecb}{\mathbf{b}}\veca$ is some vector. We can write $$\veca=|\veca|\hat{\veca}...
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0answers
9 views

Find the space and body centrodes for the motion of the second disk [closed]

A circular disk, of radius $a$ and centre $O$ , turns in its own plane about its centre with angular speed $\omega$. A second circular disk, of radius $b$ and centre $C$ , coplanar with the first, ...
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1answer
14 views

Is there any way to focus the mechanical vibration or stress of an object?

I am looking for a way to focus the vibration of a metal sheet at a specific point on that sheet so that other points vibrate less. Just like light and lens. Is there any way to focus the mechanical ...
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3answers
67 views

If videogames do not conserve momentum, must that mean that they do not have translational symmetry? [closed]

I've heard said many times that symmetries in our universe imply the existence of conserved quantities. One example often given is that translational symmetry implies that momentum is conserved. This ...
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0answers
14 views

How to calculate the overall entropy when continuous 2D positions are known?

If I have the positions of particles in continuous 2D space, how do I calculate the entropy of the system? The particles are invariant, I just need some measure of how organised they are, but I'm not ...
1
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0answers
43 views

How is the ladder paradox resolved when the doors are locked?

I understand the ladder paradox but am confused by a variation of it where an action is taken to trap an object that is lorentz-contracted. The same question was asked here, but to the best of my ...
0
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1answer
38 views

What are the major difficulties to the production of elements?

Searching online about this topic only gives results about nucleosynthesis (making elements by nature) and the 24 radioactive artificial elements. Why isn't there any information about methods to make ...
1
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1answer
29 views

Does relative work done affect temperature of a body?

Imagine a bus travelling at a speed of 20m/s towards the positive x-axis with respect to ground frame. That bus is quite long(just for a safer Side) and two persons 'A'and 'B' located inside that bus ...
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0answers
9 views

Properly accounting for indistinguishability of (homonuclear) diatomic molecules in “internal” partition function

I have always liked Schroeder's take on the partition function being a product of translational and internal degrees of freedom: $$ Z_1 = Z_{trans} Z_{int} $$ where $Z_{int}$ can be rotational, ...
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0answers
20 views

Why a glass tube doesn't break due to pressure difference when all the air is removed with a pump (like in Thompson's experiment-cathode ray tube)

My question has to do with the electron discovery experiments made by Thomson. But also it could be a general question on how glass reacts to high pressure difference. So, if all the air was removed ...
0
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1answer
19 views

Boundary conditions in method of images for an infinite grounded plane

We have a charge $q$ situated above a grounded infinite plane at some distance. This $q$ will induce some charge on the plane. But I've read that one of the boundary conditions for potential is that ...
-1
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2answers
42 views

Time Slows Down or Speeds Up for the Traveler According to Special Relativity? [duplicate]

Einstein's 1905 postulates entail that, if two clocks are in relative motion, either clock is slow as judged from the other clock's system (SYMMETRIC time dilation). An obvious implication is: Time ...
2
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2answers
31 views

Doubt regarding derivation of relativistic Bernoulli function

The relativistic form of the radial momentum equation for spherical fluid flow is $$\gamma_v^2v\frac{dv}{dr}+\frac{1}{\rho}\frac{dp}{dr}+\frac{d\Phi}{dr}=0$$ where $\gamma_v=\dfrac{1}{\sqrt{1-v^2}}$ ...
0
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0answers
41 views

Why we move forward in time? [closed]

I am a high school student and these topics are not taught at this level. I read A Brief History of Time by Stephen Hawking and it aroused my curiosity. I have a question or a bunch of questions that ...
0
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1answer
23 views

Calculus and trigonometry course

Can anyone please tell me any book or refer any kind of short term course on calculus and trigonometry required for physics.
1
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2answers
58 views

Transition amplitude, $\langle f|i\rangle$ or $\langle f|S|i\rangle$?

I have seen the transition amplitude was written in different ways, but I don't understand. For example, in Mark Srednicki's textbook section $10,11$, it is written as $\langle f|i\rangle$. But in ...
2
votes
1answer
59 views

Does kinetic energy affect temperature of an object? [duplicate]

Imagine a fundamental particle at rest with respect to ground frame and has temperature $x$ degrees celsius and imagine a 'similar' particle moving at a very high speed (take any value which would ...
0
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0answers
26 views

Energy Level Splitting in Ammonia

I was learning basic quantum mechanics using Feynman Lectures on Physics. In Chapter 8 Feynman has described ammonia inversion due to tunnelling. Feynman has first used the base states as the two ...
1
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0answers
18 views

How do I derive a particular form of the Langevin equation from Mori's generalized master equation?

Preliminary: I have a generalized Langevin equation for a set of relevant operators, written in Liouiville space as $\{|A_{v}\rangle \}$, and obtained via Mori's projection operator technique: \begin{...
0
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1answer
23 views

Physical Interpretation of Normal Modes

For a simple case of frictionless coupled oscillators shown in the figure below: (Image: two pendula of equal length and equal masses suspended from a level ceiling and connected by a spring) (and ...
3
votes
2answers
54 views

Are all atoms spherically symmetric? If so, why are atoms with half-filled/filled sub-shells often quoted as 'especially' spherically symmetric?

In my atomic physics notes they say In general, filled sub-shells are spherically symmetric and set up, to a good approximation, a central field. However sources such as here say that, even for the ...

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