Anonymous at Mon, 14 Oct 2024 11:23:49 UTC No. 16430681
>>16430114
>performs a Legendre transformation
nothing personell kid
Anonymous at Mon, 14 Oct 2024 19:11:11 UTC No. 16431573
>>16430114
then two of them must be wrong
Anonymous at Tue, 15 Oct 2024 00:51:13 UTC No. 16432140
>>16430114
>are not equivalent
you can literally derive them from each other.
Anonymous at Wed, 16 Oct 2024 04:06:08 UTC No. 16433886
>>16432140
You can derive classical mechanics from Quantum Mechanics. Are you saying Quantum Mechanics and Classical Mechanics are equivalent?
Anonymous at Wed, 16 Oct 2024 04:14:13 UTC No. 16433890
>>16433886
>I'll try an apples and oranges thing and pretend it's a fair analogy.
Losing arguments much?
Quantum Mechanics isn't a single solution method. You should try reading a book some time.
Anonymous at Wed, 16 Oct 2024 04:16:27 UTC No. 16433891
>>16433890
>Being able to derive something from something else makes them equivalent
>Squares and rectangles are the same thing since I can derive the properities of a square from the properties of a rectangle
I thank God every day I wasn't born in India.
Anonymous at Wed, 16 Oct 2024 04:52:57 UTC No. 16433924
>>16433891
Squares are literally a subset of rectangles, retard.
A square, by definition, IS a rectangle.
Anonymous at Wed, 16 Oct 2024 07:31:07 UTC No. 16434044
>>16433886
You can’t derive QM from CM. It’s one-way. Lagrange-Hamilton is two-way. Learn what an if and only if statement is, retard
Anonymous at Wed, 16 Oct 2024 12:02:46 UTC No. 16434249
>>16433924
A special case is not an equivalence.
Anonymous at Wed, 16 Oct 2024 12:09:02 UTC No. 16434256
>>16430114
In the absence of non-conservative forces Newtonian, Lagrangian, and Hamiltonian mechanics are equivalent. In the presence of non-conservative forces they can be made equivalent through the use of dissipating functions, multipliers, etc.
Anonymous at Wed, 16 Oct 2024 12:10:26 UTC No. 16434257
>>16434256
>They are equivalent...in special cases
So not equivalent
Anonymous at Wed, 16 Oct 2024 12:12:47 UTC No. 16434261
>>16432140
Show your work
Anonymous at Wed, 16 Oct 2024 12:18:38 UTC No. 16434267
>>16434261
He can't. He is just parroting what his teacher, Dr. Srinivasan Ragachurrisar at IIT Bombai taught him.
Anonymous at Wed, 16 Oct 2024 12:25:18 UTC No. 16434277
>>16434256
In the absence of non conservative forces... well well well.
So what forces are exactly non conservative?
I can only use QM to predict non linear systems that's it. Notice I say predict and not precisely measure.
How did the interpretations in physics become so confusing
It makes people argue do to poor communication
Anonymous at Wed, 16 Oct 2024 12:33:57 UTC No. 16434288
>>16434257
Nigga, even Newtonian conservation of energy techniques aren’t equivalent to Newtonian force law techniques if you’ve got non-conservative forces. Adding in path-dependence to your dynamics requires adding in additional mathematical techniques regardless of which formalism you use.
But the fact is that any of the formalisms can be similarly and easily modified to deal with those cases further demonstrates that the underlying formalisms are equivalent.
>>16434277
Interactions that are path dependent (friction, drag, etc.). All your usual methods for solving Newtonian, Lagrangian, or Hamiltonian systems have to be altered to handle dissipate be forces.
Anonymous at Wed, 16 Oct 2024 12:58:47 UTC No. 16434315
>>16434288
>They can be modified to be made equivalent
>Therefore they are equivalent
I really wish we had like a skin tone check to post here.
Anonymous at Wed, 16 Oct 2024 13:01:00 UTC No. 16434318
>>16434315
Magic cups fallacy
Anonymous at Wed, 16 Oct 2024 13:05:52 UTC No. 16434321
>>16434288
Well in system sciences i Iearned conservative dynamic systems like the solar system are FRICTIONLESS.
Is a particle fictionless? What doesn't have FRICTION On earth? I'm confused by the definition.
Anonymous at Wed, 16 Oct 2024 17:59:53 UTC No. 16434820
>>16434315
Newtonian mechanics, Lagrangian mechanics, and Hamiltonian mechanics are all equivalent when there are no non-conservative forces - each dictates that the path an object will travel on is the path which minimizes the difference between the total work done on the system, and the work done by the conservative forces. The mathematical formalisms differ slightly - Newton approaches it through brute-force integration in coordinate space, Lagrange through optimization in coordinate space, and Hamilton through optimization in phase space. All three formalisms are built up from the same first principles and yield the same equations of motion, it's simply a matter of which approach is the simplest or yields the most insight.
All three approaches must be modified to deal with the complex statistical mechanics of interactions that take energy out of the system (or, more accurately, conserve energy, but render it no-longer-useful for macroscopic dynamics).
>OH SO THEY'RE NOT THE SAME!? *le smug reddit face*
Newtonian mechanics must be modified to deal with non-conservative forces, but it doesn't stop being Newtonian mechanics.
Lagrangian mechanics must be modified to deal with non-conservative forces,. but it doesn't stop being Lagrangian mechanics.
Hamiltionian mechanics must be modified to deal with non-conservative forces, but it doesn't stop being Hamiltonian mechanics.
These modifications differ slightly because the mathematical formalisms differ slightly, but they're still coming from the same first principles - having a motion-dependent interaction that does not conserve energy, and must therefore be worked out in terms of brute force integration (Newton) or incorporated into a dissipating function (Lagrange, Hamilton).
It's all the same shit, just dressed up in different mathematical formalism.
Anonymous at Wed, 16 Oct 2024 20:17:09 UTC No. 16435116
>>16434820
>all equivalent when...
Equivalent under certain conditions isn't equivalent.
Anonymous at Thu, 17 Oct 2024 00:15:42 UTC No. 16435524
>>16435116
Your statement is only true under certain conditions, though.
Anonymous at Thu, 17 Oct 2024 03:11:14 UTC No. 16435661
>>16435524
No, my statement is true generally.
f(x) = x and g(x)=x^2 aren't magically equivalent functions because they agree at x=0.
Anonymous at Thu, 17 Oct 2024 03:54:30 UTC No. 16435713
>>16434044
you can derive QM from classical mechanics when you add noise so we are talking about a classical stochsstic process. QM is the stochastic generalization of lagrangian mechanics.
3 assumptions gets you to QM:
1. The stochastic process is time-reversible and therefore non-dissipative / energetically conservative.
2. The form of the diffusion coefficient, which is assumed inversely proportional to particle mass: D = σ^2/2, σ^2 = h-bar / m.
3. Particles are following a stochastic Newton law that can be derived through variational principles analogously to classical mechanics. This essentially means that particles behave according to Newton's second law but for the fact they are being disturbed by noise.
Again, all of this adds up to is lagrangian mechanics plus noise, paying attention to the last assumption especially where we talking about newtons laws plus noise. obviously needs to conserve energy hence 1.
the whole procedure ?
its called the variational method of stochastic quantization
the theory?
stochastic mechanics
it is the CORRECT interpretation of QM
Anonymous at Thu, 17 Oct 2024 04:11:03 UTC No. 16435737
>>16430114
Show us several examples from Classical Mechanics for which they give non-equivalent answers!
I'll wait.
Anonymous at Thu, 17 Oct 2024 07:30:34 UTC No. 16435913
>>16435737
mass of the electron
Anonymous at Thu, 17 Oct 2024 11:52:29 UTC No. 16436136
>>16435661
If an operator A acting on a function f(x) yields a differential equation with a solution q(t) and an operator B acting on a function g(y) yields a differential equation with a solution r(t), where for the same initial conditions q(t) = r(t) for all t, it’s reasonable to state that A operating on f(x) and B operating on g(y) are equivalent processes, even though A and B are not equivalent and f(x) and g(y) are not equivalent.
Newtonian mechanics is not just finding a net force, it is the operation of combining net forces and Newton’s 2nd Law to derive a differential equation for the position of an object. Lagrangian mechanics is not just constructing the Lagrangian, it’s the operation of running a difference in net work and work due to different forces through the Euler-Lagrange equation to derive a differential equation for the position of an object.
Both methods yield identical results for the position and motion of objects in a system.
Anonymous at Thu, 17 Oct 2024 12:06:29 UTC No. 16436145
>>16436136
>Both yield the same results
Not for dissapative systems.
Anonymous at Thu, 17 Oct 2024 16:31:53 UTC No. 16436525
>>16436145
>Not for dissapative systems.
Even for dissipative systems.
Newtonian, Lagrangian, and Hamiltonian mechanics will all come up with the same equations of motion for the same system whether there are non-conservative forces or not. You just have to be careful and logically consistent converting your non-conservative forces into a dissipating function.