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Newton's first law is part definition and part experimental. Isolated bodies move uniformly in inertial systems by virtue of the definition of an inertial system. In contrast, the assertion that inertial systems exist is a statement about the physical world. According to me, the assertion in the last lines follows from the following statement. It is always possible to find a coordinate system in …

I am reading about this apparatus at Wikipedia: https://en.wikipedia.org/wiki/Magneto-optical_trap And there is the following sentence which I don't understand: "As atoms travel away from the field zero at the center of the trap (halfway between the coils), the spatially-varying Zeeman shift brings an atomic transition into resonance which gives rise to a scattering force that pushes the atoms ba…

I have this diagram: And I have done these calculations: $$R_x=-20sin(30)+30cos(35)+80cos(45)=71.14 \; lb$$ $$R_y=20cos(30)+30sin(35)-80sin(45)=-22.04 \; lb$$ The magnitude of this resultant force is then: $$|R|=\sqrt{71.14^2+(-22.04)^2}=74.48 \; lb$$ Here's the part I need help with. I can get a theta angle for where the resultant force's angle is, but I want to figure out how one would get this…

I want to solve the diffusion equation in porous media with some external forcing at the origin. The regular diffusion equation- $$ \frac{\partial h}{\partial t}=D\nabla^2h $$ But I want to solve for pore pressure, so I am using $p=\rho g h$ where h is the pore pressure and h is the hydraulic head and D is a constant. Also, I am simplifying this for 1-D, so this equation becomes - $$ \frac{\parti…

I recently saw a video on gravitational waves that says that expansion of space can only be measured due to changes in speed of light as everything else that could have been used to measure the expansion has expanded too and hence the relative expansion has become zero. I feel that had space been the one to expand, we should have observed an increased speed of light. To illustrate further, say t…

The value of resistance is 3Ω and inductor impedance is j4Ω. As far as I have learned the wattmeter measures instantaneous power but shows reading for average power. As I solved for the given values the power comes out 12W in both cases even though they are connected at different points in the circuit and I want to know why? I can't seem to figure out the reason behind this. Can someone please po…

I used to live in France where there are coasts next to the Atlantic ocean an others next to the Mediterranean sea. One thing of common knowledge is that the first kind have water that is significantly colder than coasts next to the Mediterranean sea. My question is: is this a universal thing and if yes: is there some physical model or arguments that would explain this observation?

In theories with emergent low-energy degrees of freedom, one can sometimes construct effective variables whose equations resemble Maxwell’s equations. I am trying to understand what must actually be established before it is justified to say that the effective theory reproduces classical electromagnetism, rather than merely exhibiting Maxwell-like equations. Suppose effective fields can be identif…

I'd like to ask about an experiment on atmospheric pressure. To conduct the experiment, we need an empty PET bottle and make a small cut on the lower part of the bottle. A cut no greater than one-half the circumference is acceptable. Then, we press a table tennis ball against the cut to open the cut, being sure to make the ball stay put at the cut. Next, we soak the bottle into a bucket filled wi…

I'm going through Griffiths EM and I've come across an example on how to solve Laplace's equaton through separation of variables, trying to convert a partial differential equation into an ODE, which is much simpler to solve. Nonetheless, in one of the steps in his reasoning, there might be a division by zero which I'd like to have checked. Here is the textbook's example: Say you have 2 infinite p…

I am looking into the paper of Tersoff and Hamann - Theory of the scanning tunneling microscope. In this one there is the tunnel current written as $$I = \frac{2\pi e}{\hbar} \sum_{\mu ,\nu} f(E_\mu) [1- f(E_\nu +eV)] |M_{\mu\nu}|^2 \delta(E_\mu - E_\nu) $$ So in my lectures the tunneling current is written as $$I_T = \frac{4\pi e}{\hbar} \sum_{\mu ,\nu} |M_{\mu\nu}|^2\delta(E_\mu - E_\nu) [f(E_\…

Is it currently unknown what happened before the Big Bang? There are several theories about what may have existed or happened before the Big Bang, such as the Big Bounce and other models. Have any of these theories been experimentally confirmed or ruled out? Or do we currently have no conclusive experimental evidence to determine which, if any, is

I am sure this varies given the distance from moon to earth varies, but a range would be sufficient. I am trying to explain to a flat earther how there is not a lunar eclipse every full moon. My approach is to show that the 5 percent inclination of the moon's orbit to the ecliptic will result in a large enough gap for the umbra to miss the moon when projected at a great distance.

On p.2 in the first chapter of Thanu Padmanabhan's Sleeping Beauties in Theoretical Physics , theoretical physics is organized as a cube whose three axes correspond to the constants $c^{-1}$ , $ℏ$ , and $G$ . The interpretation of the c −1 and ℏ axes seems clear to me: c −1 introduces relativistic effects. ℏ introduces quantum effects. However, I am less clear about the status of the G axis. Elec…

Consider this situation given above. We have an arbitrarily shaped theoretical current loop made up of wire of zero radius in free space . Away from all electromagnetic, gravitational interactions. Meaning, THERE IS NO EXTERNAL FORCE ON THE CURRENT LOOP SYSTEM. Now consider an infinitesimal current element vector $idl$ at point A, like so. If we consider the magnetic field $B$ (A) at point A. To …

Twin Paradox dictates that moving observer ages slowly or simply that moving clocks ticks slowly. Theoretically, it can be argued that both (moving and stationary) clocks will see each other to be ticking slowly compared to itself, however, experimentally it is obvious that only one of the clocks should be ticking slowly compared to other. In this context, I assume that clocks represented by A a…

Given the fact that the velocity and acceleration four-vectors are always orthogonal to each other, I was trying to find the vectors that make an orthogonal basis in Minkowski space based off of these. For this I picked one axis in the direction of the velocity, and then I wanted to break up the acceleration into three component vectors orthogonal to each other and to the velocity vector. I am no…

In cosmological modeling, the Hubble expansion parameter $H(t) = \frac{\dot{r}(t)}{r(t)}$ can be analyzed geometrically by considering our 3D spatial section as an intersecting "slice" of a 4D hypersphere of radius $R$ moving at a constant transit velocity $v_w$ through a fourth spatial dimension. I am interested in the general conceptual formulation of this geometric setup and how the dimensionl…

I understand the concept of excess charge to be on the outside surface of the conductor. What happens if conductor is a 2 dimensional conducting Disk and 1 dimensional conducting needle? I am reading Griffiths and he seems to mention in a footnote that above cases will different without giving much details.

For simplicity, I will use the Nambu-Goto action, but the following question would probably be the same for the Polyakov action. According to David Tong's lecture notes on string theory, the Nambu-Goto action of a bosonic string is given by $$S[X] = - T \int_{D} \sqrt{- \det(X^\ast \eta)} \mathrm{d} x^1 \wedge \mathrm{d} x^2$$ where $X: D \to \mathbb{R}^{d-1,1}$ describes the path of the string a…