Intuition Definition and 272 Threads

The proof for the above ubiquitous formula (as in the summary) in "Chain rule for one independent variable" at the beginning of...

I don't have an intuitive feel for Killing vectors. Wikipedia says, " . . . more simply, the flow generates a symmetry, in the sense that moving each point of an object the same distance in the direction of the Killing vector will not distort distances on the object." That just sounds like...

Hello everyone, I seem to be majorly lacking in regards to intuition with partial derivatives. I was studying the Euler-Lagrange equations and realized that my normal intuition with derivatives seems to lead me to contradictory or non sensical interpretations when reading partial derivatives...

I'm watching a nice video that tries to explain how linear algebra enters the picture in quantum physics. A quick summary: Classical physics requires that physical quantities are single-valued and vary smoothly as they evolve in time. So a natural way to model classical physical quantities is...

TL;DR Summary: Seeking good simulations to build my intuition Hi everyone, I am currently teaching myself classical mechanics, and am 3/4 of the way through "Vibrations and Waves," a textbook from 1971 which was used in the MIT course. It's going okay - I feel like I have a decent grasp of...

The figure illustrates the situation. The radii of the larger and smaller discs are 2R and R, respectively. Their masses are M and 2M, respectively (the largst disc has the smallest mass). Also, m=5/4 M, where m is the mass of the suspended object. The pulley is "massless" (negligible moment...

Principle of stationary action allows us to find equations of motion if we plug appropriate lagrangian into Euler - Lagrange equation. In classical mechanics, this is the difference in kinetic and potential energy of the system. However, how did Lagrange came to the idea that matter behaves...

My intuition about the Lie algebra is that it tries to capture how infinitestimal group generators fails to commute. This means ##[a, a] = 0## makes sense naturally. However the Jacobi identity ##[a,[b,c]]+[b,[c,a]]+[c,[a,b]] = 0## makes less sense. After some search, I found this article...

It is well known that [FONT=STIXGeneral-Italic]ϕ[FONT=STIXGeneral-Regular]3ϕ3 is d= 6 is asymptotically free, while [FONT=STIXGeneral-Italic]ϕ[FONT=STIXGeneral-Regular]4ϕ4 in d=4 is asymptotically slave (or "trivial" or marginally irrelevant, or has a QED style pole). The standard way is to...

Hi all, I'm a physics major and I'm taking a physical mechanics class and I have a really hard time even starting homework problems. Physics does not come easily to me and I have zero intuition when it comes to what formulas, rules, etc to use where/to start phys mech problems. How can I build...

I'm pretty sure the answer is overcharged by intuition. Can someone provide a reason?

As I understand it, when a body undergoes uniform circular motion its velocity does not change in magnitude but instead direction. This change in velocity, or acceleration, is directed inward towards the center of the circle. If a body was not experiencing a net centripetal acceleration, then...

Can someone give me a better intuition of bandwidth. The way I see it, is that the bandwidth is the range of frequencies which a signal/wave is allowed to have. This doesn't feel complete though. For example, how can I explain that TDMA, FDMA and CDMA are similar in this sense. As far as I know...

Pls Be Kind to answer. I have understood the derivation of the parabolic shape by equating the normal force, gravity and the centrifugal force. But this derivation begins with the fact that water is at equilibrium. I want an understanding (quantitative or qualitative) of why the water which was...

I am working on related rates problems involving figuring out how area of a square increases per second based on how much one side increases per second (or how the area of a circle increases based on increase of the radius, etc.). I was wondering about the practical significance of problems like...

Hi, I'm taking an introduction course to Special Relativity and encountered a fairly simple problem: Dirac travels to alfa centauri, which is 4.37 lightyears away. He stays there one Earth year and then travels back, and when he comes back he has aged 5 years. At what speed did he travel...

Here's a simple story. I'm running a pizza delivery store and hit upon a gimmick to increase sales, I call it "Schrodiners Slice". You call up and get paired up with the next caller and your orders are randomly shuffled. Maybe you get your order, but maybe you get the next persons order instead...

The equation: V(x) = 61*mV*(1/z)*(log[X(o)/X(i)]) Where: z = valence (charge of ion) [X(o)] = reference concentration (outside the cell) [X(i)] = concentration of species inside the cell I want to understand the intuition behind why the mV decrease as the charge increases. From what I...

My understanding of emf Let us consider 2 parallel plates with charges (opp. but equal in magnitude) stored on it. When we connect both the plates from the outer side, the electrons from the lower potential (i.e., negatively charged plate) moves to the higher potential (positively charged plate)...

How can traveling wave exist on transmission line if wires are perfect conductors (how voltages can be different at different positions on one perfect conductor)? I mean electric fiels should be zero on equipotential source. I know if length is too long compared to wavelength, we get phase...

Hi, I have been studying mathematics for quite some time now, and I have an understand of what each topic constituted up unti and including graduate level mathematics. However my computations in each topic are very instructive, as if each topic carries its own instructions for calculations...

Is Hamiltonian mechanics a mathematical generalization of Newtonian mechanics or is it explaining some fundamental relationship that has a meaning that extends into our nature ? I guess my question is what would led William Rowan Hamilton to come up with his type of mechanics or anything...

Consider a barometer kept in an elevator. When the elevator accelerates upwards, there is a pseudo force along with gravitational force acting on the liquid in the barometer. Due to which pressure on the liquid should increase, right? If pressure on the liquid increases then to balance this, the...

Hello, I am freshly retired and enjoy going back to the fundamentals. I followed the wonderful courses by Alain Aspect on Coursera on Quantum Optics 1 and 2 . The quantization of Electrodynamics is really easy stuff. Just follow the correspondence between Poisson brakets and Commutators ... and...

So I'm trying to get sort of an intuitive, geometrical grip on the covariant derivative, and am seeking any input that someone with more experience might have. When I see ##\frac {\partial v^{\alpha}}{\partial x^{\beta}} + v^{\gamma}\Gamma^{\alpha}{}_{\gamma \beta}##, I pretty easily see a...

This is just a conceptual question. I get that when a car is turning on an unbanked curve, the friction provides the centripetal force. I don't understand why this is though. I thought friction is supposed to oppose the direction of motion. But that would imply that the direction...

Assume that a resistor R charges a capacitor C, whose other terminal is connected to the ground. The charge at time t = 0 is assumed to be null and the supply voltage is equal to V. We have, as is well known, ##i = \frac{V}{R} e^{-\frac{t}{RC}}##. Integrating ##\frac{i^2}{R}## between t = 0 and...

What is the definition of consistency? I have seen a proof that shows a finite difference scheme is consistent, where they basically plug a true solution ##𝑢(𝑡)## into a finite difference scheme, and they get every term, for example ##𝑢^{𝑖+1}_𝑗## and ##𝑢^𝑖_{𝑗+1}##, using taylors polynomials...

So my basic understanding of an integral is that it finds the area underneath a graph. I understand the idea behind an integral being the summation of f(x) * delta x, where delta x approaches zero. If I look at the integral it's telling me that there's a change in mass that is being...

I know that a dot product of 2, 2 dimension vectors a, b = (ax * bx) + (ay * by) but it also is equal to a*bCos(θ) because of "projections". That we are multiplying a vector by the 'scalar' property of the other vector which confuses me because that projection is in the direction of the...

Homework Statement I am trying to figure out how an inductor works in depth. It should be something very simple to find, but I have yet to find an explanation that goes through the process step-by-step in a non-circular way. I can solve the inductor differential equations and do phasor...

I've understood the formal definition of limits and its various applications. However, I'm trying to dive more into the history of how the concept of limits were conceived (more than what Wikipedia tends to cover), and how to formally understand and visualise infinitesimals. For example, I know...

Please see the attached image. It's a part of a study guide for my final, but I didn't put it in the homework section because I already got the answer, I just don't know what it means. The question has to do with the differential of an arc length. I made some drawings to see if I could make some...

Is there any good physical or graphical intuition for why ##\frac{d \langle p \rangle}{dt} = -\frac{\partial V(\langle x \rangle)}{\partial x}##? Classically this is apparently true. Thanks.

If I say that something has triviality context, can I say that something is intuition? Is Triviality = intuition?!

So folks, I'm learning complex analysis right now and I've come across one thing that simply fails to enter my mind: the Cauchy Integral Theorem, or the Cauchy-Goursat Theorem. It says that, if a function is analytic in a certain (simply connected) domain, then the contour integral over a simple...

Homework Statement I was solving a problem and came to a part where I was dealing with the expression, 1 - e-t -------- 1 - et It turns out that this can be simplified to -e-t but I had no idea from simply looking at the first expression that it could be simplified, and I tried to continue...

Whilst I'm solving a maths problem I normally try and understand the problem visually. For example, in calculus I try to justify what I'm doing by seeing how certain expressions relate with the geometry of the problem. However, sometimes when the step are quite lengthy, it feels like I'm just...

I've been reading about self teaching physics (mainly because the college curriculum is too slow to get me to any meaningful level of understanding at the end of four years), and an issue was brought up about lack of intuition in quantum mechanics/GR, and depending too much on the math. I was...

I am trying to understand the geometric intuition of the above equation. ##\rho(\tau)## represents the rank of the linear transformation ##\tau## and likewise for ##\rho(\tau\sigma)##. ##Im(\sigma)## means the image of the linear transformation ##\sigma## and lastly, ##K(\tau)## is the kernel of...

I know that if a complex function is analytic , it means that i can reach the neighborhood of every complex point using a certain "stretch and rotation". In which way this fact conducts us to the "Cauchy Riemann equations" ? What's the intuition behind them ? Thanks

Homework Statement Homework EquationsThe Attempt at a Solution I assume that the particle is launched along the z- axis of the x-y-z frame which is fixed with the Earth and the Earth is rotating about the x – axis. Wrt an inertial frame, the particle will fall on A. The arc length...

One of the founding principles in GR is the principle of general relativity, which loosely states that all coordinate frames (inertial and non-inertial) are equivalent in the sense that the laws of physics are invariant. My question is, does the justification for this come from Einstein's...

I get the microstate-counting approach to finding the term symbols for a given configuration. But based on what I know about addition of angular momentum in quantum mechanics, I feel like there's a conceptual gap. When I do the microstate counting on the 2p##^{2}## configuration, I get singlet...

TL;DR Why does the Einstein equivalence principle imply that all forms of (non-gravitational) energy source curvature? Now, as understand it, the Einstein equivalence principle (EEP) implies (or at least suggests) that gravity is the manifestation of spacetime curvature, the reason being that...

The Einstein equivalence principle (EEP) states that “The outcome of any local non-gravitational experiment in a freely falling laboratory is independent of the velocity of the laboratory and its position in spacetime.” I’m trying to make sure I’ve understood this correctly. I’m I correct to...

Homework Statement solve for escape velocity from Earth's surface Homework Equations just either use the line integral, and the tangential term disappears, or just use the energy equations The Attempt at a Solution I've solved it, but I'm having some trouble just coming to grips with this...

Hi guys, I've been working through some notes on Transport Phenomena by Bird and I've basically been just developing velocity and shear stress profiles for various (simple) models by a differential momentum balance and I'm trying to understand why a certain result happens. When looking at...

Let ##p: X-->Y## be a cover map. Then the induced homomorphism will inject the fundamental group of X into the fundamental group of Y; furthermore, the image of the fundamental group of X under p will be a subgroup of the fundamental group of Y I read the proofs, but I'd like to have an...