> Materiae vis insita est potentia resistendi, qua corpus unumquodque, quantum in se est, perseverat in statu suo vel quiescendi vel movendi uniformiter in directum.
Is this "materiae vis insita" really a force? Does this suggest that Newton believed that it is a force?
> Lex I: Corpus omne perseverare in statu suo quiescendi vel movendi uniformiter in directum, nisi quatenus a viribus impressis cogitur statum illum mutare.
here in his First Law he uses "viribus impressis" (nom. sg.: vis impressus)
The first law is what happens when there is no force, the 2nd when there is a force, pretty sure it's wrong to try to use the 2nd law as a definition of force in any sense, if that's what you mean
@LeakyNun My perspective is, a force is something that causes a change in an object's velocity. Although this is dependent on the reference frame, coordinate system, etc., which determine whether a change in velocity is observed
Say I'm swinging a yoyo very fast. The ball breaks off. In my inertial frame, I can explain it perfectly as inertia, i.e. the ball's tendency to maintain its direction. But from the ball's frame, my trajectory suddenly spun out of control the moment the string snapped.
The ball couldn't explain this as "maintaining velocity" from its own measurements. In the ball's noninertial frame, it'd say there was a centrifugal force acting, whereas I'd say there was no force acting. We wouldn't agree on the forces.
Once you bring in quantum mechanics, even the idea of 4 dimensions might not be true :p
"In modern particle physics, forces and the acceleration of particles are explained as a mathematical by-product of exchange of momentum-carrying gauge bosons."
In physics, a force is any interaction that, when unopposed, will change the motion of an object. A force can cause an object with mass to change its velocity (which includes to begin moving from a state of rest), i.e., to accelerate. Force can also be described intuitively as a push or a pull. A force has both magnitude and direction, making it a vector quantity. It is measured in the SI unit of newtons and represented by the symbol F.
The original form of Newton's second law states that the net force acting upon an object is equal to the rate at which its momentum changes with time. If the mass...
Some of this is simply madness if taken seriously
Momentum exists but the idea of force and acceleration only arise as a by-product
The Vis Insita, or Innate Force of Matter, is a power of resisting, by which every body, as much as in it lies, endeavours to persevere in its present state, whether it be of rest, or of moving uniformly forwards in a right line.'
and in Law I he uses "vis impressa" and in Law II "vis motrix impressa"
and I as a modern reader would agree that "vis impressa" & "vis centripeta" & "vis motrix impressa" are really forces, but that "materiae vis insita" is questionable
Looks like definition 1 is defining mass, definition 2 is defining momentum (moving mass), definition 3 is defining inertia which is like the force a body would exert if interacting with another body, definition 4 is defining the idea of a force acting on a body to change it's motion (impressed force), a thing you couldn't define without having defined a body to carry with it the idea of a force in the first place, if objects are not defined to carry a force (inertia) how can forces even act
Inertia is like 'the empty set', and impressed force is like a set containing the empty set runs
This question has been on my mind for a while. Is quantum field theory an approximation, or a special case of quantum mechanics? Before I started physics I used to think that QFT was the more general or more correct one, simply because I had heard it was harder. However, now I am not sure if this is the case.
@user8718165 the video doesn't explain exactly what measurement is being done. For example it doesn't say whether the current is travelling with or against the flow. But it is measuring some current through the flowing water, which is what I would expect.
@JohnRennie I don't know but please correct me. I think the current will pass through the water from the fence, through the body of the person and then try to go to the ground through the feet if the fence is at higher voltage...so this makes the current flow upstream.
@JohnRennie In yesterday's problem we discussed that at one point cl- will be electrolysed to cl while at the other contact point na+ will be electrolysed to na.Though the water stream is neutral after the water leaves this point, will we get the original na+ and cl- ions?
@user8718165 what actually happens is that we get hydrogen and oxygen produced at the electrodes. That's because if neutral Cl atoms were produced they would immediately oxidise the water to oxygen and $H^+$. Likewise at the other electrode sodium atoms would reduce water to hydrogen and $OH^-$.
Sir, we've discussed that the video I linked didn't make much sense as it was not shown how the circuit was completed. But suppose if the person was standing bare feet and the fence was hot...would he receive the shock?
I mean if he completed the circuit through his body and feet.
Suppose the fence was at +6000V relative to ground. Then the current would flow from the fence, through the urine, through the person and then to ground. The shock the person would experience would depend on the resistance of the person and the resistances of the urine stream and the ground.
The unmoved mover (Ancient Greek: ὃ οὐ κινούμενον κινεῖ, translit. ho ou kinoúmenon kineî, lit. 'that which moves without being moved') or prime mover (Latin: primum movens) is a concept advanced by Aristotle as a primary cause (or first uncaused cause) or "mover" of all the motion in the universe. As is implicit in the name, the "unmoved mover" moves other things, but is not itself moved by any prior action. In Book 12 (Greek: Λ) of his Metaphysics, Aristotle describes the unmoved mover as being perfectly beautiful, indivisible, and contemplating only the perfect contemplation: self-contemplation...
@JohnRennie I got it but could you please tell me how does the electricity pass upstream through the water steam into the ground through the person . Won't the water just be electrolysed at the point where the stream touches the hot fence and the current won't flow?I'm not getting this thing.
I'm not sure it's helpful to start with the person peeing on a fence because there will be different conduction machanisms in the wires, urine, the person and the ground. It would be better to consider a simple setup like a battery with two wires dipping into a flowing stream of salt solution.
@JohnRennie Sir thanks a lot, I got this diagram. The circuit is completed just by electrolysis at points A and B so there is no need for the current to flow thro' the water...correct?
@user8718165 well, consider the situation when the flow velocity is zero. If the H+ and OH- ions didn't flow through the water then we'd get a buildup of H+ at A and a buildup of OH- at B. This buildup would eventually stop the electrolysis.
What happens is the H+ ions generated at A flow downwards towards B and the OH- ions generated at B flow upwards towards A. This flow stops the charge buildup so we get a continuous current. In the wire that current is carried by electrons while in the water it is carried by H+ and OH- ions.
@user8718165 the flow velocity will affect the ion motion, but the H+ and OH- ions flow in different directions. So the flow will speed up one ion and slow down the other. Regardless of the durection of flow we always get some current flowing through the water.
@user8718165 yes. The current depends on the voltage and the conductivity of the water. The conductivity of the water depends on the salt concentration.
what does "The eight gluons are identical except for their colors" mean? Aren't there only 3 fundamental colors, red, blue, green? But there are 8 gluons!
A gluon () is an elementary particle that acts as the exchange particle (or gauge boson) for the strong force between quarks. It is analogous to the exchange of photons in the electromagnetic force between two charged particles. In layman's terms, they "glue" quarks together, forming hadrons such as protons and neutrons.
In technical terms, gluons are vector gauge bosons that mediate strong interactions of quarks in quantum chromodynamics (QCD). Gluons themselves carry the color charge of the strong interaction. This is unlike the photon, which mediates the electromagnetic interaction but lacks...
@user400188 Yes, a QFT is just a big ol' QM system.
The undergrad QM you know is largely just the stuff people figured out before hitting on QFT, which is why it seems a little easier, but they're not different subjects.
That doesn't quite answer the question though. Is QFT a more general version of QM, or is QM a more general version of QFT? Are there any approximations in QFT that do not appear in QM?
If you mean the basic axioms then they apply to QFT as well as to non-relativistic QM.
QFT and non-relativistic QM are different because they quantise different things. QFT quantises fields while non-relativistic QM quantises particles. But they are both based upon the same principles. It isn't the case that one is a subset/superset of the other, but rather starting from the same basic principles they are two different forks.
@JohnRennie That's true when the NaCl concentration is low. But at high concentrations you get chlorine at the anode, and you get hardly any oxygen if the voltage is low. If you do the electrolysis with concentrated brine in 2 half-cells, you get NaOH solution on the cathode side, otherwise you get sodium hypochlorite. Or if you use a mercury cathode, you get sodium amalgam.
@CaptainBohemian yeah I believe QFT is just the quantization of those classical fields. Or at least that's where it seems to start as I haven't done much in detail. Amusingly, my understanding is that you can chain together QHOs to get a quantum field as an alternative to chaining together classical harmonic oscillators to get a classical field then quantizing it
You are mixing the properties of a point charge and that of a capacitor.
The formula you've written works perfectly for point charges and intuitively for two entities holding the same nature of charge and to be very precise, you should use $r$ instead of $d$ when dealing with point charges as th...
@user8718165 You can roll back their reversion. Or come here & explain the situation so someone with edit privileges can do it. If a post turns into an "edit war", after a few rollbacks, it will automatically raise a moderator flag, and the mods can lock it to prevent further edits.
Yeah you take the limit as the number of oscillators goes to infinity and their separation goes to zero. I'm feeling less certain about the case of putting QHOs together like that working out now that I think about it
@CaptainBohemian sorry that was in response to this
@user8718165 Qmechanic's edit did not inlcude your improvements. And now that I look at the post history, it seems they indeed reverted your edit but for some reason the system logs this as a rejection of the original suggested edit
@danielunderwood I have actually read a lot about classical field theories but haven't read much about quantization techniques. But I read in a book which claims these fields have been counted as quantum fields while a lot of books only call the fields under second quantization of them as quantum fields, which the book deems as improper.
I have only known the quantization techniques which have been taught in nonrelativistic quantum mechanics, I don't know much about the quantization techniques in quantum field theories.
Well canonical quantization is pretty simple. I think QFT often goes the path integral approach, which seems to be quite difficult to pick up (at least for me). There's also geometric quantization, which...exists?
@user400188 quantum field theory is relativistic quantum mechanics in the occupation number formalism where one works with the quantum field operators that arise naturally out of the occupation number formalism. There is a more direct way to get to quantum field operators without going through the occupation number formalism so it might not be so obvious how it's linked to QM, but you can also go through normal QM to get to it
@bolbteppa One should caution that the fields arising from the particle mechanics is "the Weinberg viewpoint", while it is equally valid to view "quantization of classical field theory" as the starting point and then get the particles from the mode expansions of the field. The formalism doesn't really care whether we take fields or particles as fundamental.
The more direct way being quantizing classical fields by replacing Poisson brackets with commutators, but one has to ask where does this idea come from, it comes from the same place you can start from to get to the occupation number formalism, the uncertainty principle...
'The next step in the construction of LQG is to decide what the dynamics are. Technically, this is done either (A) by choosing a "Hamiltonian constraint" in parallel with the Hamiltonian formulation of GR, or (B) in the spin-foam formalism, by postulating some sort of sum over histories assigning an action to each spin foam. It is here which we encounter the major problem: There is no agreement over how to implement the dynamics! There are many ideas, but no consensus on what to do. ...
I would say that LQG really doesn't exist yet as a well-defined theory. Unless you consider dynamics to be an unimportant part of a theory. And finding sensible dynamics is a really hard problem, perhaps impossible. ...
Yet, despite the lack of dynamics, there's no end of papers where people do specific applications, like count black hole entropy, or even attempt to do quantum cosmology (basically by truncating the theory to a finite number of degrees of freedom, and then quantizing those degrees of freedom in a way which is "loopy" in spirit). But all of these things are totally provisional until one can embed them in an actual theory with dynamics. '
Yikes
'One can put too much emphasis on quantizing gravity---really that's backwards, we need the classical theory to emerge from the quantum theory, not vice versa. When people calculate discrete area and volume spectra for spin network edges and vertices, they've got things backwards.'
I wonder how their approach relates to e.g. what Feynman tried to do
@knzhou There is a bit of a linguistic confusion where people use "QM" both for the axiomatic system encompassing QFT and "0-dimensional QFT" aka "ordinary QM" and for "ordinary QM" excluding any true QFT
I'm just being semi-prescriptive here. I think the word QM should be used so that QFT is a special case of it, because the first jump to QFT is one of the most jarring things when learning physics.
Anything that makes it feel more continuous would be better.
@user8718165 sort of. What the video shows is classical diffraction of light waves rather than an effect due to quantum mechanics. However the maths behind the broadening of the spot is basically the same as in quantum mechanics.
@user8718165 most things seem simple once you've learned them. To me Fourier transforms seem easy peasy because I learned them about forty years ago and have used them regularly ever since. I probably found them scary at first, but that was so long ago I've forgotten what it was like.
Even things like General Relativity seem easy once you've learned them. Though I'm unconvinced that anyone finds QFT easy even after they've learned it :-)
It will take me a long time just to get these QM stuff well along with the math behind it. Mastering anything requires dedication, intuition and practice :-)
@JohnRennie What does one study in QFT? Is it totally different from QM?
I recently came across an interesting explanation of diffraction through an aperture which does not use Huygens' Construction but instead relies on Heisenberg's Uncertainty Principle:
The Uncertainty Principle states that trying to pin a particle down to a definite position will create uncert...
BTW, back when I helped coach the US team for the IPhO the year it was in India, I was told to give them very long calculations with a very short time limit -- apparently that was how INPhO-style questions were supposed to be.
@TheEastWind I don't know QFT. I know only just enough about it to have an idea how it's constructed. But compared to GR QFT seems a mass of details and special cases. I know lots of people love GR for it's simplicity and elegance. I'm just not sure QFT is loved even by it's most skilled practitioners :-)
In reference to physics.stackexchange.com/questions/468998/… I bet it'd be hard getting the necessary experiments past an ethics committee... so we may never know how much gravity can a grizzly bear. ;)
@PranshuKhandal Nope. It's not going to happen. Many people have tried, both before & since Earnshaw's theorem, but all have failed. You may enjoy this site coolmagnetman.com/magindex.htm which has tons of amateur-level info on magnets, & heaps of magnetic gizmos you can make or buy. It even has a few sensor & control circuits for electromagnetic levitation.
@PranshuKhandal Yes, I noticed. And I've suggested a duplicate. ;)
You can do it with a spinning magnet, like the Levitron, but it's not easy to achieve stable levitation, so the Levitron wasn't much of a commercial success. Modern maglev gizmos have control circuitry that modulates the strength of the electromagnets thousands of times per second. And even those things can be fiddly to set up correctly. If you want truly stable maglev, you need a diamagnetic material, or a superconductor.
In physics, the exchange interaction (with an exchange energy and exchange term) is a quantum mechanical effect that only occurs between identical particles. Despite sometimes being called an exchange force in an analogy to classical force, it is not a true force as it lacks a force carrier.
The effect is due to the wave function of indistinguishable particles being subject to exchange symmetry, that is, either remaining unchanged (symmetric) or changing sign (antisymmetric) when two particles are exchanged. Both bosons and fermions can experience the exchange interaction. For fermions, thi...
' In Eq. (3), C is the Coulomb integral, B is the overlap integral, and Jex is the exchange integral. These integrals are given by:'
right, I've seen exchange in spatial coordinates, but I haven't seen it where we include spin, I think
I'm guessing the idea is the same
oh, it makes sense that all up-states yields the highest (spatial) exchange interaction, because they are symmetric, and thus yield an anti-symmetric spatial part, which we know has lower exchange interaction
In mathematical physics and mathematics, the Pauli matrices are a set of three 2 × 2 complex matrices which are Hermitian and unitary. Usually indicated by the Greek letter sigma (σ), they are occasionally denoted by tau (τ) when used in connection with isospin symmetries. They are
σ
1
=
σ
x
...
I have a question about some logic circuits (I have the Boolean functions and truth tables) that I would like to minimise. Where would I post a question about this? I was thinking Physics firstly but possibly somewhere else?