A principle is a proposition or value that is a guide for behavior or evaluation. In law, it is a rule that has to be or usually is to be followed. It can be desirably followed, or it can be an inevitable consequence of something, such as the laws observed in nature or the way that a system is constructed. The principles of such a system are understood by its users as the essential characteristics of the system, or reflecting system's designed purpose, and the effective operation or use of which would be impossible if any one of the principles was to be ignored. A system may be explicitly based on and implemented from a document of principles as was done in IBM's 360/370 Principles of Operation.
Examples of principles are, entropy in a number of fields, least action in physics, those in descriptive comprehensive and fundamental law: doctrines or assumptions forming normative rules of conduct, separation of church and state in statecraft, the central dogma of molecular biology, fairness in ethics, etc.
In common English, it is a substantive and collective term referring to rule governance, the absence of which, being "unprincipled", is considered a character defect. It may also be used to declare that a reality has diverged from some ideal or norm as when something is said to be true only "in principle" but not in fact.
The definition is,
I rewrite it as $$(L[y_1] = L[y_2] = 0) \rightarrow (L[c_1y_1 + c_2y_2] = 0)$$.
However, I also wonder, whether it could also be rewritten as,
$$(L[c_1y_1 + c_2y_2] = 0) \rightarrow (L[y_1] = L[y_2] = 0) $$
And thus, combining, the two cases,
Principle of superposition...
Consider an object which is constituted of two different materials, which are inseparably mixed together, but which have different magnitude of masses. To calculate the gravitational force of the object upon another object, can the superposition principle be applied to the two constituent...
In a collapsing star, the expression for what goes on is "degeneracy pressure". The way it's put is that the Pauli Exclusion Principle just doesn't allow more than one fermion to exist in one place (state). So the star reaches a certain volume and, on the way, produces a lot of Energy.
I can...
First post on this forum, hopefully in the correct category and conforming to forum rules.
Will the object in below scenario move upwards, downwards or will it remain stationary?
An object is submersed in a container 'A' which contains a fluid 'B' (e.g. water)
The trapezium shaped object...
The virtual displacement should be given by
$$
\delta\vec{r} = \begin{pmatrix} \cos(\alpha) \\ \sin(\alpha) \\ \end{pmatrix} \delta s
$$
where ##\delta s## is a displacement parallel to the plane. The relevant force should be the gravitational force, as given above. Thus, the equations of...
I understand how to measure specific gravity of a rock. One weighs the rock then tares a beaker of water and then suspends the rock on a string to observe the “weight” gain of displaced water. My brain however could never get how, without adding a drop more water or adding the mass of the rock...
Check this one out about the number of hairs on a person's head, if not behind a paywall (I can't tell because I subscribe to Scientific American). Let me know if it is, and I will post a precis...
Wikipedia states the following in their article about the expansion of the universe:
If the cosmological principle was discovered to be false in our universe, i.e. our universe was discovered to be inhomogeneous or anisotropic or both on very large scales and the FLRW metric does not hold for...
I cannot explain that if I divide a magnet with a north and a south pole into 2 parts, the force in it rearranges itself into 2 poles. Where is the center of power? How can I explain the principle of magnetic force if I don't take it as a matter of fact.
How accurate of a measurement can we make on the position of a particle? I heard you need more and more energy to get a measurement more accurate. Would the energy needed to be infinitesimal accurate create a black hole upon. Measurement?
I have a question related to the uncertainty principle in QFT and if it is related to the early universe conditions.
Do we still have four-vector momentum and position uncertainty relation in relativistic quantum theory?
I have been following the argument related to the early universe and the...
How is the working principle of keyless drill chuck, the inventor confidently estimated that it'd have locking torque great enough as the same as to the keyed one just by turning around, fastening to motor spindle/connector?
Hello, I recently came across the following (apparent, I hope) paradox: suppose we have two H atoms. Now, a hydrogen atom is made up of one proton and one electron (fermions), so it is a boson. Then one could have two hydrogen atoms which are in the exact same state (including position). This...
Hi
the text is unfortunately a bit longer, but I have included it anyway to provide all the information.
I am not sure if I understood the task b correctly, but I understood it as follows: using the equation ##H(x,\dot{x},t)##, solve the differential equation for ##x(t)##.
Once you have...
hi everyone
"The principle of relativity: The laws of physics are the same in all inertial reference frames."
Is in classical physics The laws of physics aren't the same in all inertial reference frames!? Give an example in classical physics
Thanks
I am reading about symmetries in crystals, and my knowledge in the field of group theory is almost nill. I am reading that, in the worst case, the electrical and thermal conductivity tensors can possess, at maximum, 6 different entries rather than 9, thanks to Neumann's principle which states...
https://en.wikipedia.org/wiki/Handicap_principleThe handicap principle is a controversial hypothesis, possible confirmed by Alan Grafen. I would like to understand his reasoning.
A handicap is a harmful thing, like a peacock's tail, that attracts females precisely because it is harmful. Dawkins...
I'm solving problem number 5 from https://ocw.mit.edu/courses/8-05-quantum-physics-ii-fall-2013/resources/mit8_05f13_ps2/.
(a) Here I got:
$$
\beta = \frac{\hbar^{\frac{1}{3}}}{(\alpha m)^\frac{1}{6}}
$$
and:
$$
E = \left ( \frac{\alpha \hbar^4}{m^2} \right )^\frac{1}{3}e
$$
(b) Using Scilab I...
hello everyone
According to Einstein's second principle of relativity:
"The principle of the constancy of the speed of light: The speed of light in free space has the same value c in all inertial reference frames"
Does free space mean vacuum? Is this principle not valid in the air and the...
https://www.popularmechanics.com/science/a41106690/grandfather-paradox-time-travel/
I’ve been studying the self consistency principle, being the idea in time travel that history (the past) must be conserved. When I read about the grandfather paradox it sounded like the same thing. Are these two...
Summary: I am confused in when to use 1/2 e squared k
we studied in class that normally, the extension of the spring is directly proportional to the tension applied
and we did this question :
what is the work that has to be done for a spring to have an extension of length e
as the area of the...
https://arstechnica.com/science/2022/09/einstein-wins-again-space-satellite-confirms-weak-equivalence-principle/
See also http://dx.doi.org/10.1103/PhysRevLett.129.121102 (limited access)
In this 2D figure below, I can place:
a motor at O
a motor at J
gravity on each link
I can use Hamilton's principle, modified to the principle of virtual work and I can compute the motion of the linkage system.
I do not have to account for these force FOUR forces (in this planar problem)...
(expression given to be proven)
check for p(1)... 2=2
substitute (n+n) to
And here is the problem, I just can't find a way to continue solving this problem
As I understand it the principle states that the more accurately you measure one factor of an object, for example speed, the less you can tell of any other factors, for example position. To me this seems we will every only be able to measure an approximation of reality and thus determinism...
I understand the process of the calculus of variations.
I accept that a proper Lagrangian for Dynamics is "Kinetic minus potential" energy.
I understand it is a principle, the same way F=ma is a law (something one cannot prove, but which works)
Still... what do you say to students who say "I...
I have some questions on Franck Condon principle:
1. The principle states that if a molecule absorbs a photon of the appropriate energy, we could have both electronic and vibrational transitions and that is more likely to have a vibrational transition between states that have two "similar"...
Hello everyone!
I've been learning about hydrostatics and one thing that I've heard is that the pressure is the same throughout confined incompressible fluids, this is one of the reasons hydraulics work, because when you have the same pressure per square meter, you can change the mechanical...
Many tutorials that explain the weak principle of equivalence (Galileo, Newton) do not clearly state whether the body is affected by the force of inertia during free fall as a result of the gravitational acceleration of the body. In other words, the question is whether, during the free fall of a...
Summary: Request for an example of minimum energy principle usage
The minimum energy principle states that, for a system at constant entropy, volume and other extensive quantities, the internal energy is minimized at equilibrium. Can you give me an example in which, using this principle, is it...
Hamilton’s principle minimises kinetic energy minus potential energy, that is, with a fixed kinetic energy, Hamilton's principle maximises potential energy. What if we consider the limit that the kinetic energy or the mass/the inertia can be ignored then the lagrangian is solely the negative of...
The metric is $$ds^2 = \frac{dr^2 + r^2 d\theta ^2}{r^2-a^2} - \frac{r^2 dr^2}{(r^2-a^2)^2}$$
I need to prove the geodesic is: $$a^2 (\frac{dr}{d \theta})^2 + a^2 r^2 = K r^4$$
My method was to variate the action ##\int\frac{(\frac{dr}{d\theta})^2 + r^2 }{r^2-a^2} - \frac{r^2...
Below is my attempt at the problem. I used the distributive law and applied to what was given, (A∪B)∪Z which equates to (A∪Z)∩(B∪Z). I then applied the 2 set I/E formula to each union. Since there is an intersection between these two sets I added them.
But I end up with 2 P(Z) which doesn't...
In optics experiments, I often see the following optics configuration to rotate the polarization of an incident linearly-polarized laser beam. The final reflected beam has its polarization rotated by 90 degrees. My question is:
1) Between the quarter plate and the mirror( reflecting surface)...
If I have two identical particles of ##1/2## spin, for Pauli's exclusion principle all physical states must be antysimmetrical under the exchange of the two particles, so ##\hat{\Pi}|\alpha\rangle=-|\alpha\rangle##. Now, let's say for example this state ##\alpha## is an Hamiltonian eigenfunction...
In this video lecture (though I have linked the video at "current time", in case it doesn't; work please see the video at 19:16), the lecturer just works out (he is not explaining anything) the proof of Induction Principle starting from ##N##. Let me give out here what he did:
Statement: Let N...
I'd like to share the following competition problem:
My first reaction was that the thermometer will be able to measure heating due to the Unruh effect whilst his lab is accelerating.
(I do understand there are many ways to formulate the FE method, but I wish to understand this one.)
I understand that Hamilton's Principle is just that: a principle ( a law the recapitulates the equations of motion)
I also understand that the Principle of Virtual Work (PVW) is a reformulation...
Soo. I think this problem is too direct and easy so I think I got it in wrong way: p=h/r and then plug in the K and V and then we get E=E(r) and get derivative and we have minimum? What do you think? is there sth I am missing?
In the usual literature about analytical mechanics, I find very little about the Gauss principle of less constraints and the Gibbs-Apell equations. I think the only treatment I've seen on Gauss is given In Lanczos's The variational principle of mechanics".
So, I'm looking for introductory and...
When, if ever, is it necessary to use the superposition principle in order to solve a circuit?
Can any circuit with multiple independent voltage sources be solved without superposition?
Here is my paper. A criticism and other comments are welcome.
Abstract: The Lagrange-D'Alembert Principle is one of the fundamental tools of classical mechanics. We generalize this principle to mechanics-like ODE in Banach spaces.
As an application we discuss geodesics in infinite dimensional...
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...
Per the Heisenberg uncertainty principle, a particle does not have a precisely defined location. Does such uncertainty contribute to the transfer of thermal energy (i.e. entropy)? Is uncertainty the primary means for the transfer of thermal energy at the quantum level?
I am studying the general theory of relativity(GTR). Covariance and the principle of equivalence are foundational pillars for the theory. I can understand the need for covariance but I don't see why the need for the principle of equivalence (POE). What I have seen so far is that the...
A few days ago, I learned to make an AC to DC converter. One question is troubling my mind. How does a High Pass Filter Capacitor work? Going through some websites I got a sketchy idea.
As the current after passing through the bridge rectifier comes to capacitor, the capacitor starts charging...