Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Can work hardening of a metal be avoided? My left earbud recently broke mid-wire: the bit that I like to fiddle with and bend. I fixed it, but I was wondering whether there are metals that don't work harden, or resistant to it?
Is there a way that you can treat normal metal to prevent it from, or at least reduce the e... | Work hardening does not cause things to break, but in fact will cause them to resist further plastic deformation increasing their strength. Wires bent back and forth may eventually break due to fatigue. The material at the edge is compressed and stretched resulting in fatigue. How much cyclic stress there is determines... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/160146",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 4,
"answer_id": 0
} |
How does QFT interpret the Negative probability problem of the real scalar fields' Klein-Gordon equation? I am totally a beginner in QFT, here's the problem that I got: for the real scalar fields, are there any elementary particles descriped by them. If so, how to understand the negative probability problem?
| Quantum field theory solves the problem by giving a different interpretation to the "probability". In the case of complex fields, quantum field theory also introduces antiparticles.
In the first-quantized Klein-Gordon equation, the time component $j^0$ of the probability current vector $j^\mu$ may indeed be both posit... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/160230",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
"answer_count": 1,
"answer_id": 0
} |
Evidence that stationary masses in space actually attract each other I'm finding it rather difficult to find experimental evidence that two stationary masses in space (unaffected by external massive bodies or gravities) actually attract one another. For moving masses, this is abundantly clear (planets, asteroids, etc.)... | The first measurement of the gravitational constant was done by Henry Cavendish in a lab, in which the gravitational force between two lead balls was measured. They weren't moving. http://en.wikipedia.org/wiki/Cavendish_experiment
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/160362",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
"answer_count": 5,
"answer_id": 2
} |
Is the moment-curvature relation for an elastic beam general? The relationship between the moment and the curvature for an elastic beam is
$$M = -EI\kappa$$
Previously, I have only used this with small deflections in static calculations. I am currently working on a dynamic cable model with bending stiffness for a physi... | Not sure you care anymore, but - for large deflections, this does not hold. As the pretty pictures at wikipedia show, an elemental does not remain perpendicular to the neutral axis when bending deep beams, so that goes out the window. The second is the neutral axis in general shifts towards the compression side, beca... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/160497",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
Finding turbulent velocity Fourier mode amplitudes from kinetic energy spectrum A random vector field, such as a turbulent flow, can be decomposed into Fourier modes. Taking a snapshot in time (say an initial condition) we have that the randomly fluctuating component of the flow can be described by the sum of fourier m... | Under the definition you use for a Fourier transform, which is the discrete Fourier transform, then we have:
$$
\mathbf{u}(\mathbf{x}) = \sum_{i} \hat{\mathbf{u}}(\mathbf{k}_{i}) e^{i \ \mathbf{k}_{i} \cdot \mathbf{x}}
$$
which has the inverse given by:
$$
\hat{\mathbf{u}}(\mathbf{k}) = \sum_{j} \mathbf{u}(\mathbf{x}_{... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/160663",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 1,
"answer_id": 0
} |
How much weight would I need to put on the end of a tube to break it? Say I have a tube with a circular cross-section made from some material (for an example, I'd like to use acrylic). I support it horizontally from one end and hang a weight from the other end. How heavy does the weight have to be to break the tube?
Wh... | The equation you would apply is:
$\sigma = \frac{M*Y}{I}$
Where M is the bending moment or torque, $Y$ is the distance from the center of the cross section to the top or bottom most fiber, and $I$ is the moment of inertia of the cross section about its x-axis. $\sigma$ is the stress.
So,
Maximum moment = $M= F * 60$ i... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/160728",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
Showing $\frac{\delta V_{out}}{V_{out}}=\frac{\delta R_2}{R_2} \frac{R_1}{R_1+R_2}$ Consider a voltage divider with $V_{out}=V_{in} \frac{R_2}{R_1+R_2}$. Show that for a small change in $R_2$, the voltage divider equation is:
$\frac{\delta V_{out}}{V_{out}}=\frac{\delta R_2}{R_2} \frac{R_1}{R_1+R_2}$. I've been trying ... | First, let put $V_{in}$ in this way:
$$
V_{in}= \frac{R_1+R_2}{R_2}V_{out}
$$
Now, diferentiate the equation $V_{out}=V_{in} \frac{R_2}{R_1+R_2}$ :
$$
\delta V_{out}=V_{in}\delta \frac{R_2}{R_1+R_2}=V_{in}\left ( \frac{1}{R_1+R_2}- \frac{R_2}{(R_1+R_2)^2} \right )\delta R_2= V_{in}\left ( \frac{R_1}{(R_1+R_2)^2} \righ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/161074",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
How do we prove that two conjugate operators $X$ and $Y$ induce $\sigma_x$ and $\sigma_y$ driving terms when restricted to a two level subspace? Suppose I have a Hamiltonian for a particle moving in a one dimensional potential
$$H = H(X,Y) \qquad [X,Y] = i$$
where $X$ is the dimensionless position, $Y$ is the dimension... | Consider a Hermitian operator $X$, and denote by $x$ its projection to the two-dimensional subspace. Then, $x$ is Hermitian as well. If you assume that the diagonal is zero (e.g. because you shift the energy + choose a rotating frame accordingly), then $x$ is of the form $x=\alpha_x\sigma_x+\beta_x\sigma_y$ with real ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/161158",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
} |
If the solar system is a non-inertial frame, why can Newton's Laws predict motion? Since there is no object in the universe that doesn't move, and the solar system likely accelerates through space, how did Newton's Laws work so well? Didn't he assume that the sun is the acceleration-less center of the universe? Shouldn... | When 1686 Newton writes "Principia...", the inertial frame concept does not exist yet. However, we can find in it Corollary IV (introducing the center of mass CM concept for any interacting body set), Corollary V (Galileo's Principle of Relativity, applied to any limited body set with CM at any uniform velocity), and t... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/161203",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "13",
"answer_count": 6,
"answer_id": 5
} |
Textbook recommendation for computational physics Can anyone recommend some good textbooks for undergraduate level computational physics course? I am using numerical recipe but find it not a very good textbook.
| I am using this.(freely available)
http://farside.ph.utexas.edu/teaching/329/329.html
A complete set of lecture notes for an upper-division undergraduate computational physics course. Topics covered include scientific programming in C, the numerical solution of ordinary and partial differential equations, particle-in-c... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/161368",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 3,
"answer_id": 1
} |
Geodesic deviation In S. Carroll Lecture Notes on General Relativity, chapter 6, pages 152-153 we have equation
(6.62)
$$\tag{6.62} \frac{\partial^2}{\partial t^2} S^\mu=\frac{1}{2} S^\sigma \frac{\partial^2}{\partial t^2} h^\mu_{\; \sigma}.$$
While trying to deduce that equation from the previous one
$$\tag{6.58} \fr... | No, the ∗ term is incomplete. The two total $D$-derivatives on the lhs. of eq. (6.58) in Ref. 1 is what is causing the curvature on the rhs. in the first place, see e.g. Ref. 2 p. 146.
Carroll is on the lhs. eq. (6.62) changing notation for the two total $D$-derivatives to two $\partial$-derivatives, but they are stil... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/161429",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Solving inhomogeneous differential equation with Green function I'm not sure if this question is for physics forum, but my book's title is "Green's Functions in Quantum Physics", so I ask here.
The book says that the Green's function defined as
$$
(z-L( \mathbf{r}))G(\mathbf{r},\mathbf{r'};z)=\delta(\mathbf{r-r'})
$$
... | Suppose for simplicity that $u(\boldsymbol{r})$ satisfies the boundary condition $u(\boldsymbol{r}_0)=0$ for $\boldsymbol{r}_0$ in the boundary then the integral on the right hand side of your last equation should satisfy
\begin{equation}
\int{d\boldsymbol{r}'G(\boldsymbol{r}_0,\boldsymbol{r}';z)f(\boldsymbol{r}')}=0
... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/161519",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
Problem on bending plates in Newtonian Mechanics? I am reading a book on interesting physics problems and demonstrations. One of the problems in the section on buildings, structures and equilibrium talks about a plate with one side attached to the wall. The plate will hang, and the question deals with the amount of wor... | Yes - if the plate is stiffer, then the deflection will be smaller and so the amount of work done (which is force times distance) will be less. For a typical linear elastic situation, the work done will be $\frac12 F x$ where $F$ is the final force and $x$ is the displacement. The factor $\frac12$ comes about from the ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/161626",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Would the blue glow of Cherenkov radiation be visible when diffused across ice, such as in the IceCube neutrino experiment? The blue glow characteristic of Cherenkov radiation is visible emanating from underwater reactors.
Is it also visible through ice, at the IceCube neutrino experiment (not that anyone is physicall... | The flash of Cerenkov light from a single neutrino interaction is probably not sufficient for the human eye to detect; this is why an array of PMTs is used to pick up the signal. It's not a question of light being transmitted, but whether the intensity is sufficient to be "visible". In a reactor there are very large nu... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/161703",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 1,
"answer_id": 0
} |
What exactly is an image? When we say several rays meet to form an image, what is that which is formed? Is it an arrangement of unknown entities? What exactly am I looking at when I see my image in a plane mirror?
| Short way, image is simple information. The act of seeing things is simple a correlation made by some physical system into human brains. When we talk about optics, we talk about this correlations uses purely light ray (a lot of photons). The image in the mirror follows this logic. But human eyes can only resolve (make ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/161803",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Is $∣1 \rangle$ an abuse of notation? In introductory quantum mechanics it is always said that $∣ \rangle$ is nothing but a notation. For example, we can denote the state $\vec \psi$ as $∣\psi \rangle$. In other words, the little arrow has transformed into a ket.
But when you look up material online, it seems that the ... |
What is the meaning of 3 in this case?
In this case, the character "3" is a convenient, descriptive label for the state with three quanta present.
It is often the case that an eigenstate is labelled with its associated eigenvalue.
In the harmonic oscillator case, the number operator commutes with the energy operato... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/161862",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 6,
"answer_id": 2
} |
Proof that all primitive cells have the same size A primitive cell of a crystal lattice is a set $A$ such that two copies of $A$ which are translated by a lattice vector do not overlap and such that $A$ tiles the entire crystal.
I have read (for example in the german “Festkörperphysik” by Gross, Marx), that all primit... | The quotient forming map $\Bbb R^n\to\Bbb R^n/\Lambda$ is a local isometry (as translations by elements of the lattice $\Lambda$ are isometries without fixed points) onto a torus, whose volume is equal to the (absolute value of the) determinant of the basis of $\Lambda$.
The preimage of each point of the torus has exa... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/161981",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 2,
"answer_id": 1
} |
What is negative energy? From what I've read negative energy is based on the Dirac sea concept of virtual particles. Negative energy is referenced by Casimir effects of virtual particle concentration differences between the space outside the experiment and inside the experiment i.e. the two uncharged metal plates. So i... | In terms of the Casimir Effect the vacuum state between the plates is at a lower energy state than that outside them. Taking the normal vacuum as baseline, the area between the plates is negative energy.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/162078",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 1,
"answer_id": 0
} |
What is the speed of sound in space? Given that space is not a perfect vacuum, what is the speed of sound therein? Google was not very helpful in this regard, as the only answer I found was $300\,{\rm km}\,{\rm s}^{-1}$, from Astronomy Cafe, which is not a source I'd be willing to cite.
| From the ideal gas law, we know:
$$
v_\textrm{sound} = \sqrt{\frac{\gamma k_\textrm{B} T}{m}}
$$
Assuming that interstellar space is heated uniformly by the CMB, it will have a temperature of $2.73\ \mathrm{K}$. We know that most of this medium comprises protons and neutral hydrogen atoms at a density of about 1 atom... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/162184",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "101",
"answer_count": 6,
"answer_id": 3
} |
Different kinds of trace for statistical ensembles In the chapter 7 of the book "A Modern Course in Statiscal Physics" by L. Reichl, we found $Tr[\hat{\rho}]=1$ for microcanonical ensembles and $Tr_N[\hat{\rho}]=1$ for canonical and grandcanonical ones. I looked for the meaning of $Tr_N$ in the book but I didn't find i... | Using the comment of @MarkMitchison, since $e^\hat{C}=\sum_{k=0}^\infty\frac{\hat{C}^k}{k!}$ and $e^x=\sum_{k=0}^\infty\frac{x^k}{k!}$ (as can be seen here), so $e^{\alpha\hat{I}}=e^\alpha\hat{I}$, and I "can take the first term outside the trace in Eq. (2). You don't need to assume any special properties of the trace"... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/162276",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
What does the statement "the laws of physics are invariant" mean? In the first paragraph of Wikipedia's article on special relativity, it states one of the assumptions of special relativity is
the laws of physics are invariant (i.e., identical) in all inertial systems (non-accelerating frames of reference)
What does ... | In layman's terms, it just means that the laws of physics are the same everywhere. This means that we are talking about one common set of laws. The fun part is figuring out how one common set of laws can behave the same, while they are taking place within different frames of reference. Thus we have a one, that is share... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/162335",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "16",
"answer_count": 10,
"answer_id": 8
} |
Is $ds^2$ just a number or is it actually a quantity squared? I originally thought $ds^2$ was the square of some number we call the spacetime interval. I thought this because Taylor and Wheeler treat it like the square of a quantity in their book Spacetime Physics. But I have also heard $ds^2$ its just a notational dev... | It is a square of a proper time interval or a square of proper distance (modulo an inessential sign).
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/162491",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "9",
"answer_count": 5,
"answer_id": 3
} |
selection of p substrate as wafer in typical cmos process flow why is p-substrate typically used as wafer in the typical cmos process flow? why not n substrate?with respect to memories, Has it got anything to do with the aplha-paritcle radiation induced errors (soft errors) ? please explain.
| Up until the mid-1990's, your could get silicon wafers grown by float-zone (FZ) or Czochralski (CZ), in (100), (110), and (111) orientations, doped with B, P, and the occasional exotic (As, Sb). By the introduction of 200mm (8") wafers, you became limited to (100) CZ B-doped wafers.
Why?
The float-zone process could n... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/162564",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
What is the criterion for a change to be adiabatic? I'm trying to understand whether the change of a parameter $\lambda$ of a Hamiltonian $H$ is adiabatic. Reading Landau and Lifshitz "Mechanics", I see
... let us suppose that $\lambda$ varies slowly (adiabatically) with time as the result of some external action; by ... | Look to the more fundamental, classical definition. Adiabatic just means 'without heat transfer'. But more specifically it requires defining a system or control volume where the heat is not transferred.
Your model or equations of motion must exist over some defined space and time interval. If heat is not transferred in... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/162632",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 2,
"answer_id": 1
} |
What physical evidence is there that subatomic particles pop in and out of existence? What physical evidence shows that subatomic particles pop in and out of existence?
| This answer is basically an argument about why you should treat the terms of a perturbation series as interesting objects under the right circumstances. It doesn't really change the fact that these are just mathematical terms, but it shows that they have explanatory value in addition to simply being part of the sum bec... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/162845",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "34",
"answer_count": 5,
"answer_id": 3
} |
Relation between area elements in finite deformation theory (continuum mechanics) There are relations for the line and volume elements in continuum mechanics. For example:
\begin{align}
\ \ \ \ \ \ \ \ \ \ \ \ \frac{V}{V_0}&={\rm det}(F)\tag{1}\\
\lambda^2&=(F^TFe_1\cdot e_1)\tag{2}
\end{align}
with $F$ being the defo... | Your first two equations can be written in other forms, so how about this? In 1-D:
$$\lambda=\frac{L}{^0L}$$
(I use a pre-superscript for initial values and post-subscripts for spatial directions). In 2-D:
$$\lambda_1\lambda_2=\frac{L_1}{^0L_1}\frac{L_2}{^0L_2}=\frac{A}{^0A}$$
In 3-D:
$$\lambda_1\lambda_2\lambda_3=... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/162984",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
} |
Could dark energy just be particles with negative mass? The title speaks for itself.
Dark matter: We see extra attractive force, and we posit that there are particles which create such a force, and use the measure of that force to guess their locations.
Dark Energy: We see extra repulsive force.
Only thing is, dark ene... | If dark energy would consist of particles, it would dilute with the growing radius of the universe to the third power, since the total number of particles would stay the same while the volume increases. What observations found was that dark energy rather behaves like a constant which does not thin out, that's why it is... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/163074",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
"answer_count": 8,
"answer_id": 2
} |
Why do you not get burned when you move your finger (quickly) over a candle flame? When we move a finger quickly over/through a candle flame, why doesn't it get burned?
http://en.wikipedia.org/wiki/Fire
| What happens when you place your finger in a flame is that energy is transferred from a hot gas to the mass of your finger. This transfer of energy takes time.
I guess this transfer is primarily through thermal conduction but the arguments probably apply for radiated energy too.
The time it takes to transfer a given a... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/163139",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 1,
"answer_id": 0
} |
Silicone tube with three holes, flow rate, pressure I have a silicone tube -- a saline solution flows in from one end, and then flows out of three holes of equal diameter and equal distance from each other that are along the side of the tube. What can I do to make the pressure at the three holes equal?
| If injected from a single end, and assuming a constant diameter pipe, the pressure decreases linearly along the length of the pipe due to friction. Therefore equal diameter holes will not yield equal flow rates or pressures.
For equal flow rates:
To control the flow rates, you must control the injection pressure (ex. ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/163339",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 3,
"answer_id": 0
} |
Why does a metal boat float? I was in class learning about density and stuff. Our teacher told us that things that are denser than water sink in water, and less dense things float.
Then, our teacher asked us why metal boats float in water, even though they are denser than water. Is it because of the surface tension of... | This is because the whole boat, along with the air in the boat, is lighter than the water it displaces.
For example, if a small boat will take up 1 cubic meter of water, then it has to be heavier than the weight of 1 cubic meter of water. This is explained in this post by What If here.
For the same reason that bowling... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/163408",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 5,
"answer_id": 0
} |
Dependence of streamlined flow on viscosity My teacher told true class the following statement:-
Streamlined flow is more likely for liquid with more viscosity as sturdy flow can only be achieved with slow speed.
It's true that viscosity causes slow speed of liquid but viscosity is due to relative motion of layers o... | What your teacher told the class is true, though it's more complicated than that.
For any flowing fluid there are two types of force. The viscous force is due to the viscosity of the fluid, and that's the obvious force that everyone thinks about. However a fluid has a mass, and therefore when it's moving it has a momen... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/163514",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 1,
"answer_id": 0
} |
Why is this way of calculating the diffraction pattern valid? I've seen that in some books (Fowles) the intensity of the diffraction pattern is calculated in the following way.
We place the source $S$ and the point at the screen $P$ in the line perpendicular to the aperture (second diagram). We calculate the intensity... | In Fresnel diffraction, you are evaluating the contribution of every possible ray from source to screen by computing the relative phase shift for each ray. The method you show is only valid if the distance from source S to aperture Q is much larger than the distance from Q to P: that is the only condition in which smal... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/163617",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
"answer_count": 2,
"answer_id": 0
} |
Can we measure the electron spin independently of its magnetic moment? What experimental evidence do we have for the intrinsic angular momentum of the electron (its spin)?
I am specifically interested in whether we have a value for this that is independent of the intrinsic magnetic moment, and hopefully a value for th... | In quantum mechanics, the magnetic moment operator is related to the spin operator by:
$\vec\mu = -\left(\frac{e}{mc}\right)\vec{S}$
In other words, they are directly proportional up to some known physical constants. This means that measuring the spin of an electron is exactly equivalent to measuring its magnetic momen... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/163722",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
"Find the Lagrangian of the theory" I've heard a few of my professors throw around the term "finding the Lagrangian of a theory". What exactly is this referring to. From what I understand it seems that you determine invariances (symmetries) and they give you a hint for what your Lagrangian is. Furthermore there is more... | Usually the terms "Lagrangian" and "theory" can be considered the same. For a new theory, you have a new Lagrangian. For example, when we say "QED is different from QCD", we mean their Lagrangians are different. Each theory has its own Lagrangian.
Although, observable quantities (and especially the equation of motion) ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/163847",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 2,
"answer_id": 1
} |
How to raise indices on the electromagnetic tensor How do you transform between the electromagnetic tensors $F_{\mu\nu}$ and $F^{\mu\nu}$?
$$
F_{\mu \nu}=
\begin{pmatrix}
0 & E_x & E_y & E_z \\
-E_x & 0 & -B_z & B_y \\
-E_y & B_z & 0 & -B_x \\
-E_z & -B_y & B_x & 0
\end{pmatrix},\\ \ F^{\mu \nu} =
\begin{pmatrix}
0 & ... | Index raising and lowering is defined through the metric, in this case the flat space metric (Minkowski)
$$
g^{\mu\nu} = \begin{pmatrix}
1 & 0 & 0 & 0 \\
0 & -1 & 0 & 0 \\
0 & 0 & -1 & 0 \\
0 & 0 & 0 & -1
\end{pmatrix}$$
We raise an index by aplying the metric to a tensor, like this $A^\mu=g^{\mu\nu}A_\nu$. Now, if you... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/163981",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
} |
Why doesn't the speed of the wind have an effect on the apparent frequency? A boy is standing in front of stationary train. The train blows a horn of $400Hz$ frequency . If the wind is blowing from train to boy at speed at $30m/s$, the apparent frequency of sound heard by the boy will be?
The answer: The frequency rema... | The formula for apparent frequency as heard by observer when velocity of sound and wind are in same direction is given by
$$n^\prime=\frac{v+v_w-v_o}{v+v_w-v_s}n$$
Where
$n$=original frequency
$n^\prime$=apparent frequency
$v$=velocity of sound
$v_w$=velocity of wind
$v_s$=velocity of source of sound
$v_o$=velocity ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/164486",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "10",
"answer_count": 4,
"answer_id": 3
} |
Why is work done on the system considered when calculating the work output? The thermodynamic efficiency $\eta$ is calculated by $\eta= \frac{W_{out}}{Q_{in}}$
Using the first law of thermodynamics we usually say that $W_{out}$ is $Q_c+Q_h$, where $Q_c$ is the heat dissipated into a cold reservoir, and $Q_h$ is the he... | The Carnot cycle is ... well ... a cycle. In each turn of the cycle, the system returns to exactly the same state over and over again. Pick a point, call it the beginning of the cycle. After one turn of the cycle, the system is where it started, with exactly the same energy it had when it started. During the cycle... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/164583",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
Bounded operator - definition? As mentioned also in Bounded and Unbounded Operator, an operator $A$ is said to be bounded, if
$$\|Af\|\leq k \|f\|,$$ where the constant $k$ does not depend on the choice of $f$ (let us consider a map to the same Banach space).
However, in a mathematical physics text I came across a def... | When one says that an operator is bounded, you can think of it as being bounded from above. This is different from being bounded from below. An operator can be bounded (from above) and bounded from below, or perhaps just bounded, or just bounded from below.
Observe that $(Af,Af)$ and $(\psi,B\psi)$ are slightly differe... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/164690",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "8",
"answer_count": 3,
"answer_id": 2
} |
Derivation of group velocity? In the standard simplified derivation of group velocity (which can be found here) we use two waves
$$y_1=A\sin(K_1x-\omega_1 t)$$
$$y_2=A\sin(K_2x-\omega_2 t)$$
In the proof we then get $$V_g=\frac{\Delta \omega}{\Delta k}$$
But I do not understand the step where this is then turned into
$... | The basic answer to your question is that the derivation is only valid for small $\Delta k$ (corresponding to $\Delta \omega$) so that the beats have a much smaller wavenumber and frequency than the two waves that you are adding. The group velocity only makes sense if you have well defined envelope. In this: https://ww... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/164829",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 0
} |
Conservation and forces/energy Are there really non-conservative forces in actuality ?
Feynman states in his book that in fact, all forces are conservative ( originating from conservative vector-fields ), provide we look close enough ( microscopic level ). The reasoning is that we can't allow non-conservative for... | All the known forces conserve energy, but they don't necessarily conserve energy in macroscopic modes.
For instance friction takes some of the energy of macroscopic motion and coverts it into an increase in temperature (i.e. energy in microscopic modes). Total energy is conserved but energy that is useful at the human ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/164916",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 1
} |
How could a cord withstand a force greater than its breaking strength? How could a 100 N object be lowered from a roof using a cord with a breaking strength of 80 N without breaking the cord?
My attempt to answer this question is that we could use a counter weight. But I don't really understand the concept behind coun... | Breaking strength refers to the maximum tension in the cord. Now, from the sounds of this problem, you've probably been doing force diagrams involving cords. What happens when you attach two cords to a single 100N object (and keep it stationary)? Is the tension in both of those cords 100N? Or is the combined force ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/165212",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
"answer_count": 6,
"answer_id": 4
} |
Sound waves during day and night A man stands on the ground at a fixed distance from a siren which emits sound of fixed amplitude . The man hears the sound to be louder on a clear night than on a clear day. Why?
| The speed of sound depends on the square root of temperature, so the refractive index is proportional to $T^{-1/2}$.
Let's assume that the sound is emitted isotropically. During the day, the usual situation is that the temperature decreases with height. Thus the refractive index increases with height. This will tend to... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/165331",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 3,
"answer_id": 0
} |
Is there a maximum frames per second (FPS)? Take a video camera and crank up the frames per second rate.
Disregarding current technological advancements, could a camera's FPS go so fast that any two captured images be identical? Would accomplishing this defy "time"?
| I've worked on a camera that has as one of its core features the ability to increase the FPS until you are counting single photons. Here is one of the pdfs about it. You will see from the figures that there is an intrinsic tradeoff between the noise/image-quality and the FPS, which is simply due to the statistics of ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/165381",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "23",
"answer_count": 7,
"answer_id": 0
} |
Definition of a normal mode? What is the formal definition of a normal mode for a string? And how does this relate to the definition from e.g. wiki that seem to be applied to discrete systmes of particles only? Also on a string what makes:
$$y=A\cos(kx)\sin(\omega t)$$
a normal mode, and
$$y=A\sin(\omega t+kx)$$ not? ... | Normal modes are the separable solutions to the string's (linear) partial differential equation
$$y(t) = X(x)T(t)$$
that arise from applying the solution method of separation of variables.
These solutions form an orthogonal (normal) basis for any solution.
Due to the form, a function of space only multiplied by a funct... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/165587",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 3,
"answer_id": 0
} |
Fractional exponent in a scalar quantum field: Is energy and momentum conserved in this case? Assuming that I would have the following term in the Lagrangian for a scalar boson field $$L=\int d^4x g (\phi^{2-p} \phi^{\dagger 2+p}+\phi^{\dagger 2-p} \phi^{2+p}))$$
with a fractional number $p$. Now I am inserting the Fou... | The $e^{\vec{x}\cdot(\sum \vec{k})}$ which leads to momentum conservation at each vertex when we go to momentum space feynman diagrams is a perturbative result at heart. Your model as it stands is not cast in a way conducive of perturbation theory..
Let's try this instead, if we want to have something amenable to pertu... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/165632",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Symplectic structure and isomorphisms In his book Mathematical Methods of Classical Mechanics, V.I. Arnold writes
To each vector $\xi$, tangent to a symplectic manifold $(M^{2n},\omega^2)$ at the point $\mathbf{x}$, we associate a 1-form $\omega^1_\xi$ on $TM_\mathbf{x}$ by the formula
$$\omega^1_\xi(\boldsymbol{\et... | Same as with the symplectic form: $\omega(v) = (u_\omega,v)$ defines the isomorphism between 1-forms and vector fields. When the metric is Euclidean the dual basis to an orthonormal basis corresponds to the basis itself.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/165753",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 2,
"answer_id": 0
} |
Kinetic energy of a variable mass particle If a particle's mass is a continuous differentiable function of time, $m(t)$,
and its position is also a continuous differentiable function of time, $x(t)$, what is the expression of its kinetic energy? Does $\frac{1}{2}mv^2$ still hold?
| Yes; if you integrate the correct form of Newton's 2nd law (see for example http://en.wikipedia.org/wiki/Variable-mass_system) you find the final kinetic energy is $\frac{1}{2}mv^{2}$.
Just for fun I worked out what happens if you naively use the normal form of the 2nd law:
$$\vec{F}_{net\,ext}= \frac{d\vec{p}}{dt}= \f... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/166000",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 2,
"answer_id": 0
} |
Mutually Commutative Operators What is the definition of a mutually commutative set of operators? I've found articles describing a complete set of mutually commutative operators, but I can't actually find what mutually commutative means. I ask because I'm asked to prove that a particular set of operators is mutually co... | Mutually commutative means that every operator in the set commutes with every other one. This implies that, if the operators in question are observables, they can all be measured simultaneously.
A complete set of mutually commuting observables is a set of observable, hermitian operators that commute - therefore their e... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/166060",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
Do transferring energy and applying force to a body imply same? Do transferring energy and applying force to a body imply same meaning? When we say, "I throw a ball using my pushing force so on the other hand, can I say that I transferred my kinetic energy to the ball therefore it became moving.
| Yes. When you apply a net force to a mass (please note the word "net"), the object become accelerated . This acceleration means the body changes velocity, and a change in velocity means there is a change in the energy, because of the energy formula:
$E=\frac{1}{2}mV^2$
The case of the circle is particularly interesti... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/166143",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 1
} |
Can mass be uncertain? If you can have uncertainty in momentum, then wouldn't you have uncertainty in mass and velocity?
Why can't mass be uncertain?
| Based on the simple definition of the Heisenberg uncertainty principal, uncertainty is an inverse ratio between location and velocity, so if you're willing to know very little about location, then you can measure velocity with accuracy.
Now, on the quantum level, particles can do strange things like borrow energy from ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/166226",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 2,
"answer_id": 1
} |
Does the speed of electrons depend on energy? I would like to know whether the speed of an electron depends on energy.
If yes then in a circuit when electrons flow out of a resistor the energy decreases by a considerable amount, leading to the charge per electron decrease and eventually to the decrease in current in a ... | If you have current flowing one way through a resistor, then the electrons flow through the other way. Since current flows from the high voltage end of a resistor to the low voltage end, then the electrons come in at the low voltage end and come out at the high voltage end.
When electrons (which are negatively charged... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/166312",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
} |
Why does the thought experiment of a photon bouncing of a mirror imply anything for other objects? Okay, so I am reading a book, "The Elegant Universe" by Brian Greene, which talks about motion and its effect on time.
Greene makes the point that time changes with motion by saying that if you have two mirrors and bounc... | This is an effect known as time dilation. In this post, I will be taking material from the excellent book, Einstein Gravity in a Nutshell, by A. Zee.
Figure 1 will be the basis for the argument.
We bounce a photon around to create a clock. It is postulated that the speed of light is the same in all frames. In the re... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/166448",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
} |
Can an object appropriately isolated from its surroundings become colder than its surroundings? Consider a sealed box, well-insulated on all sides, except for the lid which is transparent to infrared. An object is placed inside the box and the box is evacuated (purpose being to thermally isolate the contents of the box... | There is a well known sinkhole in Utah that displays similar characteristics to what is described in the [nice] accepted answer. There is relatively little standing between that location and the upper atmosphere Peter Sinks Utah
During calm cloudless nights, this high elevation basin dissipates daytime heat rapidly i... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/166526",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 4,
"answer_id": 2
} |
Predicting Polarity of capacitor in the given diagram I have to determine the polarity of the Capacitor in the given diagram.
I Approached the problem as follows:
When Magnet 1 moves with its North pole towards the coil, emf is induced in the coil as the magnetic flux through the coil changes. So, when seeing from the ... | The two magnets are mirrored, so from different sides the same current can appear either clockwise or anticlockwise.
Think if the coil was flat in the page and the north magnet was dropping from above. This creates an increasing $\vec{B}$ field into the page, so the emf must induce a current out of the page, and the c... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/166651",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 5,
"answer_id": 1
} |
Why does light travel as waves? Why does light travel as waves instead of say just a straight line? What are the forces that make a light photon travel in a wavelike pattern?
| Your wording suggests a few misconceptions:
*
*It seems you are thinking of light as having a corpuscolar nature (nothing wrong with that, you are in good company).
Well it turns out that things just do not work that way.
Phenomena like diffraction (to name one) tell us that we cannot describe the behaviour of light... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/166740",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 2,
"answer_id": 0
} |
Why is most probable speed not equal to rms speed for an ideal gas? The rms speed of ideal gas is $$\mathit{v_{rms}} = \sqrt{\dfrac{3RT}{M}}.$$
The most probable speed is the speed where $\dfrac{dP(\mathit
{v})}{dv} =0$ where $P(\mathit{v})$ is the probability distibution. Solving for $\mathit{v}$, we get $$ \mathit{v_... | In any probability distribution, there are many ways to find some kind of "average" value, that is, ways to define the "centrality" of the distribution. In discreet distributions you have almost certainly come across mean, median and mode, and perhaps also the different "flavours" of means - arithmetic, geometric, harm... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/167013",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
Understanding incompressibility (of rubber or viscoelastic material) Literature gives a lot of explanation why rubber is incompressible. However, I still need some thinking to understand physical behavior of rubber or any such material.
Often, incompressibility is tied to Poison's ratio ($\nu$) -> 0.5. At Poisson's ra... | Nothing is incompressible, but most liquids and solids have a very low compressibility i.e. a very high bulk modulus.
The reason for this is that in liquids and solids the atoms/molecules are in contact with each other. To squeeze them closer together you need to deform the bonds in molecules and/or the electron distri... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/167107",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 3,
"answer_id": 0
} |
Why are solar panels blue, rather than black, when black absorbs more light? This is an image of a solar panel array, courtesy of Wikipedia.
Some of these look rather black, but most of them are blue.
As far as I know, solar panels work by absorbing "light energy", and then converting this to "electrical energy". Some... | You're looking at solar cells for terrestrial operation. The main efficiency number is not Power_electric/Power_solar, but Power_electric/investment. Capturing the last few bits of blue light just isn't worth it.
In space applications, the investment is dominated by the launch costs. Using a more exotic material to ca... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/167190",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 3,
"answer_id": 1
} |
Why aren't all black holes the same "size"? The center of a black hole is a singularity. By definition, a singularity has infinite density. So how can a black hole with a different mass or density be described?
| What matters is the mass of the black hole. All black holes have a singularity that has no size, no space or time. These break down and become meaningless at the singularity. Since space is meaningless, so is density. It only has mass. The amount of matter that has fallen into the black hole determines its mass. The mo... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/167282",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "14",
"answer_count": 6,
"answer_id": 5
} |
On the definition of elastic restoring force in a spring How is the elastic restoring force defined exactly for a spring? We know by Hooke's law that
$$F_\text{restoring} = -kx$$
but what does $F_\text{restoring}$ really mean? I thought up till now that it was the force the spring pulled with at both ends if you stretc... | The word 'restoring' is synonymous with 'opposing' in that it matches the applied force, but in the opposite direction. But more so 'restoring' implies that energy is being stored - potential energy - which can subsequently be retrieved. The potential energy is the integral of force over the path of deflection:
$$E_p=(... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/167458",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 3,
"answer_id": 0
} |
Is it possible to use hot cloudy water as a cloud chamber? This morning I got some warm water from the shower head to a dark plastic basin to wash some sensitive clothes.
During the process lots of tiny bubbles got into the water so it had a cloudy appearance.
Since the water was quite warm the air in bathroom was hu... | Have you heard of the "bubble chamber"? It is like a cloud chamber, but uses liquid hydrogen (usually). When you take a liquid to a temperature/pressure where bubbles could form if there is a nucleation site, you can indeed observe traces.
Now whether you observed something like this in your bathroom is hard to estima... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/167504",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 1,
"answer_id": 0
} |
How does one experience single gravitons and/or Planck-force? Moving sufficiently far away from a light source one would not be able to measure a steady stream of light, but only single photons every now an then. The experience would be a very faint blinking.
Can this behavior be translated to gravity? From what I unde... |
From what I understand gravity is similarly quantized and transmitted via gravitons.
Well, we don't know that. There is no accepted quantum theory of gravity, only approximations like semiclassical approaches. We cannot give you a "mental picture" at the moment because we don't have one. We can speculate all day, and... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/167621",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 3,
"answer_id": 0
} |
Finding the appropriate coordinate transformation given two metrics Given the two-dimensional metric
$$ds^2=-r^2dt^2+dr^2$$
How can I find a coordinate transformation such that this metric reduces to the two-dimensional Minkowski metric?
I know that $g_{\mu\nu}=\begin{pmatrix}-r^2&0\\0&1\end{pmatrix}$ (this metric) and... | If you were to Wick rotate $t \rightarrow i \theta$, the metric would be $ds^2 = dr^2 + r^2 d\theta^2$, which is just flat space in polar coordinates. The standard cartesian coordinates can be obtained by $x=r\cos\theta$, $y=r\sin\theta$. The same procedure works in the original Lorentzian signature metric, but with hy... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/167822",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 3,
"answer_id": 1
} |
White, is it a colour or absence of colours? Our chemistry sir and we had an argument today at the lab, he says that white actually is not a colour, it is the abscence of colour, but we say that it is a colour and we gave the following point to substanciate our point that white is a colour:
When we see an object in red... | Colors have been defined by the International Commission on Illumination. They have defined the CIE XYZ color space where white is a color defined by the point x = y = z = 1/3.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/167935",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 5,
"answer_id": 4
} |
What happens to photons that get trapped in a black holes event horizon? So, I know that photons do not travel fast enough to escape a black hole once it passes the event horizon. Also, I know that the photons themselves aren't affected by the gravity, but rather their path instead. My question is, if the photons are s... | In a classical Schwarzschild black hole, inside the event horizon all things, whether they be massless photons or bodies with mass, will travel towards smaller radial coordinate. This applies even to light that is emitted outwards from inside the event horizon.
That is, both light and mass are inevitably compelled to m... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/168065",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
"answer_count": 3,
"answer_id": 1
} |
Frequency dependence of the speed of light in air According to this link, the speed of light of different colors in a medium should be different. But if the refractive index of light in air is 1 then this means that the speed of light in air and vacuum should be the same. Could anyone help me out here?
Thanks
| It is true in general that the speed of light in a medium will depend to some extent on the wavelength/frequency of the light itself, but in most (not all) everyday situations this is not apparent or important, and makes the theory of optics much easier mathematically.
As for the refractive index of air, it is not qui... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/168141",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 3,
"answer_id": 1
} |
Tensor product in quantum mechanics In Cohen-Tannoudji's Quantum Mechanics book the tensor product of two two Hilbert spaces $(\mathcal H = \mathcal H_1 \otimes \mathcal H_2)$ was introduced in (2.312) by saying that to every pair of vectors $$|\phi(1)\rangle \in \mathcal H_1, |\chi(2)\rangle \in \mathcal H_2$$ there b... | $|\phi(1)\rangle \otimes |\chi(2)\rangle $ is a cumbersome notation to write ket corresponding to $\psi$ function $\phi(\mathbf r_1)\chi(\mathbf r_2)$, where $\mathbf r_i$ refers to coordinates of the $i$-th subsystem. That's why the order of factors in $\otimes$ product does not matter; the resulting ket corresponds t... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/168231",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 3,
"answer_id": 0
} |
If we can see a galaxy can that galaxy see us? This is a question about the properties of the expansion of the universe. I can't say it any better than: If we observe a primordial galaxy that existed soon after the Big Bang, does it follow that the same galaxy, at roughly the same number of years after the big as we ar... | Yes.
The Milky Way is a very old galaxy, having formed roughly half a billion years after the Big Bang. So if we observe a galaxy that has a redshift of ~10, we are looking back in time to approximately this epoch, so an alien astronomer in that galaxy observing the Milky Way today would see it redshifted by the same ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/168381",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 3,
"answer_id": 0
} |
Mass, energy, and entropy. I have a seemingly simple question about the relation between these three that for some reason doesn't make sense to me. If entropy is the disorder of a system, then a low entropy state is one of higher energy. As we know, mass is energy. From here we must say that the more mass something has... | Calling entropy "disorder" is somewhat misleading, it can also be described as the amount of area containing an amount of energy or even information. A black hole will contain a significant amount of quantum data in an incredibly small space, making them objects with high entropy. However this is a fixed amount of entr... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/168468",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 4,
"answer_id": 3
} |
Distinguishing density operators with the same diagonal elements If I have two sources of qubits and one source produces the density matrix:
$$\rho_1 = \begin{pmatrix} 1 & 0 \\ 0 & 1\end{pmatrix}$$
and the other source produces:
$$\rho_2 = \begin{pmatrix} 1 & 1 \\ 1 & 1\end{pmatrix}$$
Is it possible to perform a measur... | The second density matrix is actually a rank-1 projection (if normalised) hence a dyadic product and therefore a pure state. It is enough then to measure against a state which is perpendicular to this vector (i.e. $(1/\sqrt 2,1/\sqrt 2)$) to say whether the qubit is not coming from the second source.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/168559",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Faraday's Law and Lenz's Law: Is there any theoretical explanations on why changing magnetic field induces an electric field? This is a more specific extension to this question I came across today
One certain aspect of Faraday's Law always stumped me (other than it is an experimental observation back in the 19th centur... | Indeed, this observation remains mysterious from a 19th century viewpoint.
Since we know special relativity, though, it is natural in the covariant formulation of electromagnetism that spatial and temporal changes of fields are interrelated. More specifically, we need to express the three-vectors $\vec E$ and $\vec B$ ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/168725",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "9",
"answer_count": 1,
"answer_id": 0
} |
Does the Earth revolve around the Sun? I am aware of this Phys.SE question: Why do we say that the earth moves around the sun? but I don't think this is a duplicate.
In a binary star system, where the masses of the 2 stars are not so different from each other, can we say that each star revolves around the other?
If yes... | There are at least 8 more planets in the solar system, besides the Earth (and some more were discovered). When Copernicus decided to place the Sun in the center of the solar system, instead of the Earth, that was mainly because this arrangement simplified drastically the form of the orbits of the other planets. With th... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/168824",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 3,
"answer_id": 2
} |
Charged black hole It is known that Einstein's equations admit solutions for charged black holes. The Reissner–Nordström metric in case of a non-rotating charged black hole and for rotating charged black holes there is the Kerr–Newman metric.
In Reissner–Nordström metric I can calculate electric field, it has the follo... | The issue is with your picture of the electromagnetic (and generally any) interaction as arising because of the exchange of real particles. However, the electrostatic interactions $\sim 1/r$ arise thanks to the "exchange of virtual particles". Virtual particles are not particles, they are called "particles" because the... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/168890",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
What happens to the photon if the frequency is lower than the threshold frequency? An electron is ejected only if the frequency of light is greater than the threshold frequency. What happens to the photon if the frequency is lower than the threshold frequency?
|
What happens to the photon if the frequency is lower than the
threshold frequency?
The idea is that there is a certain threshold energy required to remove an electron from an atom to far away from the atom (the work function). The absorption of the photon supplies this energy. This is an electronic process that dep... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/168988",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
Why does Li+ ion move to cathode in Li-ion battery? When Li-ion battery is discharged or being used, the positive lithium (Li+) ions move from anode to cathode through the electrolyte. Meanwhile the electrons move in the same direction through the external circuit. Why does this happen? I mean, why does a Li+ ion get a... | In electrolytic cells the negative electrode are called cathode while positive electrode are called anode , in which +ve ions move towards cathode as cathode is negative electrode, and -ve ions move towards anode , while in electrochemical cells cathode is positive electrode while anode is considered to be negative... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/169050",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 1
} |
Approximations of the kind $x \ll y$ I have an expression for a force due to charged particle given as
$$F=\frac{kQq}{2L}\left(\frac{1}{\sqrt{R^2+(H+L)^2}}-\frac{1}{\sqrt{R^2+(H-L)^2}}\right) \tag{1}$$ where $R$, $L$ and $H$ are distance quantities.
Now I want to check what happens when:
*
*$H\gg R,L$
*$R,H\ll L$
... | When considering these things, at least as a warm up to a more rigorous answer, it is worth thinking about what it means to say that $H>>R$. I take this to mean that, roughly, if I add $H$ to $R$ I'm going to get something close to $H$, as it is much larger. For example $1000000>>1$ so $1000000+1\simeq1000000$. When th... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/169371",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 4,
"answer_id": 3
} |
Free fall of mass-spring-mass system I am a little bit confused about the implication from my computation. Must have done something wrong in the computation.
Assume we hold the top end of the mass-spring-mass system in the air, and the system is at equilibrium. Now release the top end mass to let the system have a fre... | Of course, the solution is correct. Letting the system fall, the gravitation doesn't act on it anymore, and you have a mass-spring-mass system oscillating in absence of external forces.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/169470",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Can gravitational waves resonate? Can gravitational waves resonate? - Perhaps by creating standing wave interference in a cavity?
Could that feasibly happen either in nature or by engineering?
| It is theoretically predicted that superconducting layers might be able to act as reflectors through the so called Heisenberg-Coulomb effect. Out of these, you could of course form a cavity able to contain a gravitational wave in principle.
This effect has, to my knowledge, not yet been experimentally tested, although ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/169550",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "9",
"answer_count": 1,
"answer_id": 0
} |
Why are $SU(N)$ gauge theories easier to handle for $N\rightarrow \infty$? I was wondering if there was a intuitive/heuristic argument to understand why generalizing the QCD gauge group $SU(3)$ to $SU(N)$ and taking $N\rightarrow \infty$ simplifies the analysis of the theory. Since in this limit only planar diagrams su... | The intuitive idea is based on the Central Limit Theorem. Because suppose (as is usually the case) that your matter fields are in the fundamental representation of $SU(N)$, then the multiplet contains $N$ independent fields. Now the central limit tells us that the arithmetic average of $N$ independent random variables ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/169727",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 1,
"answer_id": 0
} |
Parameterization of an arbitrary element of $U(2)_L \times U(2)_R$ (Chiral symmetry with two quarks) When you write down the Lagrangian for two quarks :
\begin{equation}
\mathcal{L}_\text{QCD}^0 = -\frac{1}{4} G_{\mu\nu}^a G^{a\mu\nu}+ \bar\Psi i \gamma^\mu D_\mu \Psi
\end{equation}
you find an $U(2)_L \times U(2)_R$ g... | Let's see what relation can we find between $\alpha, \beta, \alpha^i, \beta^i$ and $\gamma, \delta, \gamma^i, \delta^i$
First using Baker Campbell Hausdorff lemma we deduce two things:
$$\alpha + \beta = \gamma \text{ and } \alpha - \beta = \delta$$
because $\mathbb{1}$ commutes with $\sigma$. And
$$e^{i\vec{\alpha}\c... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/169914",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
Electric field of a full disk - when $R \to 0$ - it's not equal to coulomb law An MIT document states that the electric field of a full disk, when $R \to 0$, is similar to Coulomb's law
$$\mathbf E_{disk}=2\pi k_e\sigma\left[1-\frac{x}{\left(x^2+R^2\right)^{1/2}}\right]\hat{i}=\frac{\sigma}{2\varepsilon_0}\left[1-\fra... | Remember that we keep leading order terms. So for the second part of the expression in parentheses, as $R \rightarrow 0$, we don't just get 1. Using the taylor expansion, we get
$$ \frac{1}{\sqrt{1+\frac{R^2}{x^2}}}\Rightarrow 1 - \frac{1}{2}\frac{R^2}{x^2}+....$$
Plug this into the original equation while remembering ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/169976",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Why the CMB has not been dispersed so far? Imagine you have a box of black body radiation. What happens if you open the box for a long time? It becomes dispersed and no radiation remains in the box.
Now, apply this example to the Cosmic Microwave Background radiation. The CMB has been produced about 380,000 years afte... | The CMB was emitted from everywhere, in all directions. The CMB emitted at the point where you are standing right now, has now been dispersed to a distance $d_\mathrm{CMB}$ equal to the distance that light can travel in the almost 13.8 billion years that have passed since it was emitted*.
(note that $d_\mathrm{CMB}$ is... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/170103",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 2,
"answer_id": 0
} |
How to approximate the force on a magnet below a coil o x
o x Coil with 4 turns
o x
o x
_
| |
| | Neodymium magnet
|_|
I need to know the force acting on a neodymium magnet which is placed below a coil. This simple looking problem is actually ve... | The field from a bar magnet is approximately a dipole. The field from a coil is approximately a dipole. The force between two dipoles will contain both a torque term, and a attraction / repulsion term - both of which will be proportional to current.
Equations for this can be found at http://en.wikipedia.org/wiki/Magnet... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/170185",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Has anyone tried Michelson-Morley in an accelerated frame? After doing much more digging than I thought I had to do, I found out that the speed of light is NOT invariant in an accelerated reference frame. Has anyone done any experiments to confirm this? In particular a Michelson-Morley experiment in an accelerated re... | even though John puts it down quite nicely, I don't think that was the answer you sought?
Yes, the Michelson-Morley experiment has, to my knowledge, only been done in accelerating reference frames, because of the rotation and gravity of the earth, some with precision high enough to measure both gravity or the rotation ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/170275",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
"answer_count": 3,
"answer_id": 2
} |
What would happen to a diamond if it was exposed to near vacuum at room temperature? I know that coal (graphite) turns into diamond when a high enough pressure is applied, but I guessed it would stay as a diamond unless it was incinerated by a high enough temperature.
However, I recently took a closer look at the phase... | Nothing happens. We have put many diamonds into vacuum chambers to do ion implantation. They remain diamond.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/170435",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
Why doesn't $x$ reach a constant for a block experiencing $v^n$ resistive force? I am stuck on the Exercise 3.5 of Newtonian Dynamics by R. Fitzpatrick:
A block of mass $m$ slides along a horizontal surface which is lubricated with heavy oil such that the block suffers a viscous retarding force of the form
$$F = - c\,... | From
$$\dfrac{dx}{dt}=\left(v_0^{1/2}-\dfrac{c}{2m}{t}\right)^2$$
and
$$v(t_f)=\left.\dfrac{dx}{dt}\right|_{t=t_f}=0$$
you should be able to get a finite bound on your last integral.
EDIT: one possible reason for which your final integral doesn't properly converge comes from an earlier step. Indeed, you moved from:
$$... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/170552",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
} |
Can only one electron or photon produce interference pattern? If we shoot one electron or photon at a time to a double slit for a long time, interference pattern will build up on the other side. If the gap between each electron or photon is long enough that they don't interfere it appears that a single electron or phot... | You can't predict where the electron will hit, but you can measure that it will hit at some discrete point. The probability distribution of final positions on the detector corresponds to the interference pattern.
You will see the pattern only after shooting many electrons:
https://physicsforme.files.wordpress.com/2012... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/170725",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 5,
"answer_id": 0
} |
Do photons with a frequency of less than 1 Hz exist? A photon with a frequency of less than 1 Hz would have an energy below
$$
E = h\nu < 6.626×10^{−34} \;\rm J
$$
which would be less than the value of Planck's constant. Do photons with such a low energy exist and how could they be detected? Or does Planck's constant ... | Yes. Essentially any frequency > 0 is theoretically possible. You may have confused this with the concept that it’s not possible for an electromagnetic wave with a given frequency f to have an energy less than E = h.f without eliminating the entire wave.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/170828",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 5,
"answer_id": 4
} |
Bending along an axis for strength? I read about this law / property a couple of months back, but I've forgotten what it's name was and I can't seem to find it by Googling. I was hoping someone could give me the name for this property. If I recall correctly, it was named after same famous mathematician like Gauss or so... | What you are looking for is the famous Theorema Egregium by Gauss, which asserts that the Gaussian curvature of a surface is invariant under local isometry. At the same time, the Gaussian curvature of a surface is the product of the principal curvatures.
Regarding a slight bend along the middle as a local isometry (of... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/171009",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 0
} |
How can one motivate the relativistic momentum? Motivating the non-relativistic momentum $$\mathbf{p} = m\mathbf{v}$$ is quite easy: it is meant to represent the quantity of motion of the particle, and since the mass is one measure of quantity of matter it should be proportional to mass (how much thing is moving) and s... | Special relativty is about Minkowski spacetime. A line element is given by
$$ ds^2 = c^2dt^2 - dx^2 - dy^2 - dz^2 $$
A free particle will move on a straight line, that is, it will minimize the path length
$$ L = \int ds = \int \sqrt{c^2 \left(\frac{dt}{d\lambda}\right)^2 - \left(\frac{dx}{d\lambda}\right)^2 - \left(\fr... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/171107",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 6,
"answer_id": 0
} |
The meaning of the temperature in the Shockley Equation In the Shockley equation, which is the model of the $I$-$V$ curve of a p-n junction, what does the Temperature refer to, carrier temperature or lattice temperature? When a p-n junction subjected on a forward current, is the carrier temperature higher than lattice ... | The Shockley diode equation doesn't distinguish between carrier ($T_{eh}$) and lattice temperature $T$; it assumes that they are in equilibrium, $T_{eh} = T$.
Just a word of caution. We can't really say we have a single hot-carrier because temperature is a property of a large number of particles. You can say that you h... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/171183",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Shadow of a ripple? Suppose a stone is thrown into a pool of crystal clear water and its a bright sunshiny morning. You can observe a shadow of the wave in the bottom of the pool. Why does this happen? Is it due to superposition of light or some other thing?
| The dark part of the shadow is the umbra, and the part that is a little lighter is the penumbra. They can be experienced on Earth, but more readily in space, such as during a solar eclipse, when the Moon moves in front of the Sun and leaves a shadow on Earth.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/171253",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "8",
"answer_count": 2,
"answer_id": 1
} |
Why does the human body feel loud music? I was sitting close to a speaker and I could feel the sound coming from it all over my body, especially in my heart, and it pounded with the loud beats of the music.
Was my heart pounding because of the excitement at listening to the music or was I really feeling the sound in my... |
was I really feeling the sound in my heart and all over my body?
It is definitely possible to feel sound. This occurs when the pressure is high enough and the frequency is low enough for the sense of touch. The heart can definitely produce a sensation of pain, perhaps also that of external pressure albeit with a rath... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/171342",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "9",
"answer_count": 4,
"answer_id": 2
} |
When a pn junction is formed, why is a positive region of charge formed on the n side of the junction? I understand that when electrons diffuse from n-side to p-side, negative charge is developed on the p-side. But the mere absence of electrons on the n-side doesn't make that positively charged. The n-side must be neu... | You can also see the fact that dopant atoms are themselves neutral, so an n-type semiconductor itself is neutral but has free electrons. If, for example, you apply an external voltage, "only" the free electrons will move away and you are left with a positively charged n-type semiconductor. As in p-type under an electri... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/171438",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 3,
"answer_id": 2
} |
How much mass is typically ejected from a supernova? How much mass is released from a supernova of a 15 solar-mass star? 20? 25? What is the relation between star mass and mass ejected?
| I like to explain this using a figure from a talk by Marco Limongi some years ago.
Based on a given set of models, the $x$-axis shows the initial mass of the models and the $y$-axis the final mass. The different coloured layers show the composition of the star at the moment of collapse. The mass ejected in the superno... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/171617",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
"answer_count": 1,
"answer_id": 0
} |
Is Magnus effect a corollary of Bernoulli principle? Magnus effect is commonly explained using Bernoulli principle. However, taking the lift on a rotating cylinder as an example, the velocity difference is caused by the extra work done by the rotating cylinder but not by the pressure difference, the Bernoulli principle... |
As shown in the figure, the rotating water in the bucket will become concave, and the faster the rotation, the more concave the water surface is. This shows that at a certain height H, the closer the water is to the center of rotation, the lower the pressure is. And the faster the water rotates, the lower the pressure... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/171863",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "14",
"answer_count": 4,
"answer_id": 1
} |
How does an Inductor "store" energy? It seems to me that an electromagnetic field is nothing more than a collection of photons, which as I've heard, extends through space infinitely. Why is it, then, that an inductor such as simple copper wire loop, can "store" energy in it as an electromagnetic field? Wouldn't the pho... | Your argument that the energy should radiate away would be true if your inductor were a good antenna, in which case it would be a bad inductor! The problem is an impedance mismatch: The inductor produces a magnetic field (which stores the energy you inquire about), but little electric field. That is the wrong ratio, or... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/171955",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 3,
"answer_id": 0
} |
Polyakov equation in the strings theory In the equation of Polyakov there wouldn't be in our universe 10 or 11 dimensions but more (26) because it is referred to the bosonic theory. Are there any connections between this equation and the invariance of Lorentz? Can you explain where, also in form of formula?
| There are a few different ways to see that the bosonic string lives in $D=26$. This, by the way, is known as the critical dimension of the theory. I'll give a brief sketch the answer, a more complete one can be found in any textbook, but in particular Polchinski's.
Classically, the Polyakov action has 3 main symmetries... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/172040",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
When to use $h = c_p\Delta T$ or $u = c_v\Delta T$ I'm getting myself confused on when to use $h = c_p \Delta T$ or $u=c_v \Delta T$, where $c_p$ is the specific heat at constant pressure and $c_v$ is the specific heat at constant volume.
It's in relation to thermodynamic processes such as expanding volumes with piston... | Fundamentally there's a simple difference: When you are working with a perfect gas at constant volume you can take the variation of inside energy equal to the heat absorbed in the transformation. In this case you must use $C_v$, obviously. In the other side, where the pressure is constant you can't consider the equalit... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/172146",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
} |
About Lorentz Group In definition of orthogonal matrices we say that the a matrix $A$ is orthogonal if $A^TA = I$, while for Lorentz Group it is written as $\Lambda^Tg\Lambda = g $. And we say that Lorentz transformation forms an orthogonal group
My Question is why do we insert the $g$ in the above definition?
| On a vector space $V$ with metric $g$ - be that euclidean, lorentzian or whatever - the Orthogonal group $O(V,g)\subset GL(V)$ is defined to be the group of (linear) isometries on $V$. More precisely, for an element $\Lambda\in O(V,g)$,
$$ g(\Lambda v,\Lambda u)=g(u,v)$$ holds for all $u,v\in V$. Orthorgonal trafos pr... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/172247",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.