Path Definition and 1000 Threads

Why does light (or indeed any object) travel the shortest path between two points (whether for flat or curved space/space-time) ?

Hello All, I only have a vary basic understanding of physical concepts so please bear with me. I'm an object with mass greater than 0, a maximum speed, a maximum rate of acceleration and deceleration. Suppose I want to travel from point A to point B. The path is chosen for me and it leads...

Hello. I am doing some reading on QED and am getting a bit confused on the different conventions used. In Matthew Schwartz's book we have the Lagrangian given as: LQED = -¼ FμνFμν + iψ*γμ(∂μ + ieAμ)ψ - V(ψ*ψ) And the path integral factor is exp(iS). In another text, however, I see the QED...

Homework Statement A ripple tank is setup and a point selected on the second nodal line. determine the change in path length from two wave sources if they are in phase and separated by 2cm and the wave length is 5cm Homework Equations not really sure of what equations to use? The Attempt at a...

Hello, I'm FlashExplorer, and I'm a 22 year old guy. Ever since graduating from high school I haven't been able to pinpoint what I wanted to do as a career. First, I thought I wanted to get into IT because I've always been naturally technically inclined when it came to computers. I did OK with...

Hello, I am a senior high school student living in Western Europe. Although I haven't been really fond of mathematics in the past years, I have began to admire it as I advanced. This year I have been introduced to pre-calculus and I really liked it. Also my major interest since my childhood has...

Homework Statement I have these vectorfields defined on the specified set. All of them are conservative on their set. Also i have three unit circles C1, C2 and C3 centered respectively on (0,0) , (-2,0) and (-1,0) I need to find the line integrals over all of them on H (beregn = calculate...

if photons are traveling on the same path, and in only one direction, are they sometimes passing each other? Or are they staying in sequence? Assume the sources for these photons are variously moving in relation to each other. .

Hello,My name is guy I am currently in high school learning biology as my "major"(not sure how to call it ) subject as well as ecology, I've been always interested in biology but recently I got stuck thinking what do I want to do in biology.Biology is like a tree that has many branches and I am...

I am deciding what educational path to take. My end goal is to become an electrical/electronics engineer. I am good with my hands but need to work very hard on academics. I dropped out of high school my senior year(2012) for no good reason, I was not in the best state of mind then. (I earned my...

Why isn't (5.298) the following instead? ##K(x, t_1; x', t_0) = \delta(x-x')\,e^{-\frac{i}{\hbar}H(t_1-t_0)}## My reasoning: Since \Psi(x, t_1) = e^{-\frac{i}{\hbar}H(t_1-t_0)}\,\Psi(x, t_0)\\ = e^{-\frac{i}{\hbar}H(t_1-t_0)}\,\int\delta(x-x')\Psi(x', t_0)\,dx' The exponential operator with...

Source: http://web.mit.edu/dvp/www/Work/8.06/dvp-8.06-paper.pdf Regarding page 5 of 14, I don't understand the multiple integrals thing. Ain't we supposed to sum up all the paths like in this equation (4) but why do they instead multiply and integrate over integration and so on?Also for...

Homework Statement In a grid O(0,0) A(7,8) find the number of paths that 1. pass through (3,4) 2. don't pass through (3,4) 3. pass through M(2,3) AND N(4,6) 4. DON'T pass pass through M(2,3) and N(4,6) 5. pass through ONLY ONE of M(2,3) and N(4,6) 6. pass through AT LEAST ONE of M(2,3) and...

Homework Statement A bird flew along a helical path r(t)=<5cost,5sint,2t>, at time t=10 second, the bird died instantly. where did it hit the xy-plane ? g=32 ft/s/s. Homework Equations r(t)=(v_0 \cos\theta t) i+(v_0 \sin\theta t - 0.5gt^2 + h_0) j The Attempt at a Solution taking derivative...

I've written a java program to model the solar system. All my planets move in very well defined, stable orbits. The sun, on the other hand, is doing some very weird stuff. I've attached a plot of its path, a very zoomed in and a very zoomed out one. It isn't spiralling gradually inwards or...

Homework Statement If all the heat transport is by phonons, estimate the mean free path of phonons in Germanium at 300K using the following data. Thermal conductivity=80W/K m; Debye temperature=360K; atomic weight=72.6; sound velocity=4500m/s; density=5500kg m−3 Homework Equations K=CVvsl l...

Homework Statement A source injects an electron of speed ##v## into a uniform magnetic field of magnitude ##B##. The velocity of the electron makes an angle ##\theta## with the direction of the magnetic field. Find the distance ##d## from the point of injection at which the electron next...

Suppose I am on ISS and Earth is exactly below (at the right angle to the ISS's line of path). Now if I throw one ball below towards Earth from window at exactly 90 degrees to the line of path of ISS and one ball upwards at right angle to the line of path of ISS. **Assume normal human strength...

Hello, I have a simple question. Suppose a perfect point source in front of a mirror. The virtual image of the point source acts like a second point source. Now let's look at the interference of the direct point source light and the virtual point source, at some position. Since the path...

Homework Statement A beam of electrons travels east at speed, v = 6.10x 10^6 m/s . It passes through a magnetic field , B = 0.450T , directed from top to bottom. Describe exactly the path of the electrons motion? Homework EquationsThe Attempt at a Solution The path of a charged particle moving...

Assume a very large volume of a gas of a specific molecule. This molecule can absorb a photon and spontaneously quickly re-emit a photon of the same energy before the molecule can physically interact with another molecule. Therefore the energy of these photons never participate in the...

Hi everyone. I apologize, I’ve posted about the situation I’ve been going through before but I wanted to ask a different question. I've been feeling frustrated for a while with what I've been studying. Right after I graduated undergrad with a biology degree in 2013, I went into a PT program, but...

Hi physicists , I'm in high-school yet, and since I've started study physics for myself my aim is to understand more complex fields of physics, and one of these fields in QED(Quantum Eletrodynamics) and QCD(Quantum Chromodynamics), could anyone tell me what the path to go for a good basis for...

Its usually said that the propagator ## K(\mathbf x'',t;\mathbf x',t_0) ## that appears as an integral kernel in integrals in the path integral formulation of QM, is actually the Green's function for the Schrodinger equation and satisfies the equation below: ## \left[ -\frac{\hbar^2}{2m}...

It is common knowledge that the scattering of blue photons by the atmosphere is more significant than for other colors hence aerial images of Earth look bluesh. The graph below obtained from MODTRAN 'allegedly' supports this fact. While trying to quantify this effect, I've preformed several...

Homework Statement Homework EquationsThe Attempt at a Solution I formed a right angle triangle between the arrow downwards,d, and perpendicular line x from arrow. As such, sin θ = x/d. x= d sinθ path difference: d sinθ/λ My answer is C, but answer is B. Where did cos θ come from?

I am completely lost on how to solve this problem. Any hint would help There is a lost tourist in New York. The streets in New York run east to west and go from ..., S. 2nd St., S. 1st St., Broadway St., N. 1st St., N. 2nd St., ... The avenues run north to south and go from ..., E. 2nd Ave...

A satellite is in a circular orbit a distance $h$ above the surface of the Earth with speed $v_0$. It suffers a head-on collision with some debris which reduces its speed to $kv_0$, where $k$ is a constant in the range $0<k<1$, but does not change its direction. Calculate the eccentricity of the...

Hello, So I am working on a project that requires the movement of iron nanoparticles (let's assume 25nm in diameter, and let's assume the sphere is uniform and pure iron) through a (non-magnetic) gel using an externally applied magnetic field. Let's assume the total distance I want to move the...

Hi. I am just starting to study QFT using the path integral method and for which the main textbook is by Srednicki. Does anyone know of any good online videos which would be suitable Thanks

Given this magnetic circuit: With these dimensions: With this equivalent circuit: If I am using F = HL to calculate the mmf drops in RcoreAB(see equivalent circuit) and RcoreBCDA(see equivalent circuit) then how would I calculate L in the formula ?

Hello Forum, Electric current usually goes down the path of least resistance if it can. However, there are situations in which it prefers to go through a path of more resistance if the path of least resistance has no potential difference across. Are my statements correct? For example, see the...

I'm sure this is all something you hear a lot on this message board but I'd like to say it nonetheless. The space industry and astronomy at large are some of the only things I've ever felt passion for. I'd like nothing more than to work in that industry. My current plan is to major in physics...

Hello, I am having some trouble wrapping my mind around this concept. In the beginning of calculus I was taught that the derivative is relationship of change of one variable with respect to another variable, and that a good way to visualize this is the tangent of a curve at a point. My physics...

Homework Statement The problem puts forth and identity for me to prove: or . It says that I can use "straight-forward" calculation to solve this using the definition of nabla or I can use Gauss's and Stoke's Theorum on an example in which I have a solid 3D shape nearly cut in two by a curve...

Homework Statement Homework Equations The path integral equation, Stokes Theorem, the curl The Attempt at a Solution [/B] sorry to put it in like this but it seemed easier than typing it all out. I have a couple of questions regarding this problem that I hope can be answered. First...

How is a general path called instead of being a continuous function from an interval to some topological space, where we replace the domain from an interval to a compact set, is there a name for such a function? Perhaps I should add that the compact set is also convex.

In 2012, experimenters showed that when two entangled photons separate and when one goes through the double slit, we can tell which slit it went through and see that they still created an interference pattern because the photon that it was entangled to tells us which slit it went through. What...

Hi, I was wondering about a simple example.take a coil wound on a solenoid, one side of the solenoid core is permanently attached to a permanent magnet S pole, the other end of the solenoid core is not attached to any magnet. Now I take another magnet turn it with the N pole facing the solenoid...

Homework Statement A small purse manufacturer has a single machine that makes the metal parts of a purse. This takes 2 minutes. Another single machine makes the cloth parts in 3 minutes. Then it takes a worker 4 minutes to sew the cloth and metal parts together. How long will it take to make 6...

Homework Statement A wheelchair is pushed from the start to the finish from its resting phase and maintains a steady speed of 2m/s as the wheelchair travels to its destination, which is 25 m from the start. It takes 80.seconds to push the wheelchair from the start to the finish. What is the...

Hi, an exercise asks to show that $ \int_{0,0}^{1,1} {z}^{*}\,dz $ depends on the path, using the 2 obvious rectangular paths. So I did: $ \int_{c} {z}^{*}\,dz = \int_{c}(x-iy) \,(dx+idy) = \int_{c}(xdx + ydy) + i\int_{c}(xdy - ydx) = \frac{1}{2}({x}^{2} + {y}^{2}) |_{c} + i(xy - yx)|_{c}...

The full question is: "How can we take square root of both sides of an inequality or equation just by multiplying each side by numbers with negative rational exponents". I will include several examples to explain how I think about it. 1)a=b, a^(-0.5)*a=b*a^(-0.5) (but a^(-0.5)=b^(-0.5)) then...

thoughts on a major in computer hardware engineering and a minor in geology maybe geophysics something that would give me the oil and gas extraction qualification to be a petroleum engineer or a computer hardware engineer?

Why is it that, in the definition of the path integral, we have the product of neighboring integrals of the form : ∫Φdx1...dxn when the whole idea is based on adding the contribution of neighboring paths. I need some help understanding why it is of the form ∫Φdx1...dxn and not the form...

Homework Statement Hi, I am just trying to wrap my head around using path integrals and there are a few things that are confusing me. Specifically, I have seen examples in which you can use it to calculate the ground state shift in energy levels of a harmonic oscillator but I don't see how you...

Can anyone explain why a photon seems to travel in a perfectly straight 3D line over unimaginable distances? What exactly defines a straight-line? The concept appeals to Cartesian coordinate space. Is there any way to quantify the straightness of a photon path? Or, does the path taken by...

So if we have a non-simply-connected region, like this one to apply Green's Theorem we must orient the C curves so that the region D is always on the left of the curve as the curve is traversed. Why is this? I have seen some proofs of Green's Theorem for simply connected regions, and I...

Homework Statement using complete diode model explain which path will the current follow? given dynamic resistance is 240 ohm.compute current. 2. The attempt at a solution when we make complete diode model, ideal diode will be replaced by a switch and the given dynamic resistance. the silicon...

Just double checking this - I found this formula describing the radius of the path of an ion in a cyclotron: R = sqrt(2*E*m)/(e*B) .. where R is the radius in meters, E is the energy of the particle in joules, m is the mass in kilograms, c is the charge in coulombs, and B is the strength of...