Quantum Mechanics- The Science of Absolute Connection

[steve_bank]

Jump over to philopshy and the thread I staed on enrgy and fileds.

Wjat is a fpc ield? It is a ,ap of the mahntude and drection of a partcle moved aroud the filed.


But a battery across two parallel plates and we say tere is an e;ecric filed between the two plates.

Move a theretcal unit charge around the plate and at each point the chrage exrences a force vector.

What an elecrc filed 'is' we do not know, but wat we calla field is a map.

Up through the 19th century one issue in physics was explaining 'action at a distance' for elecricicty and magnetism.

Some proposed a medium through which a mechanical force was transmitted.

Maxwell came up with the idea of a field. A propagating EM wave in space was modeled as orthogonal electric and magnet fields.

In my view it is more correct to say the construct of a field is a building block of scientific theory.

The map is not the countryside. Scientific models model reality but are not reality itself.

BTW I don't generally watch any of the videos people post, especially if there is no preface. I read books and used theory in my work.

As somebody else said post a summary of the point you are making along with a video.

 

[Thomas II]

 

[steve_bank]

I believe Shrodenger's cat problem he posed was to illustrate how QM can be misinterpreted.

In pop science there has been an endless stream of QM says this QM says that.

There is a late night radio show Coast To Coast AM. It is the follow up to the old Art Bell show.

I listen it sometimes when I go to bed for a laugh.

Pseudo science and woo with just a bit of real science.

QM proves life after death, and so on. QM proves mind is separate form body.

 

[lpetrich]

Quantum mechanics is very counterintuitive and it involves gruesomely complicated mathematics. Here is a table of mathematical formulations of it and their relation to classical-limit mathematical formulations.

Classical	Quantum
Plain Newtonian mechanics
Lagrangian formulation	Path integral (Feynman)
Hamiltonian formulation	Matrix mechanics (Heisenberg)
Hamilton-Jacobi formulation	Wave mechanics (Schrödinger)

 

[lpetrich]

I'll try to express these formulations relatively simply, but it's hard to do without partial differential equations.

First the classical formulations.

Plain Newtonian mechanics, one dimension for convenience, motion with mass m and position q in a potential V(q):

\( \displaystyle{ m \frac{d^2q}{dt^2} = - \frac{dV}{dq} } \)

Lagrangian formulation: L(q,dq/dt,t) is "Lagrangian"

\( \displaystyle{ L = \frac12 m \left( \frac{dq}{dt} \right)^2 - V ;\ \delta \int L \, dt = 0 ;\ \frac{d}{dt} \left( \frac{\partial L}{\partial (dq/dt)} \right) - \frac{\partial L}{\partial q} = 0 } \)

Hamiltonian formulation: H(q,p,t) is "Hamiltonian" with new variable p, the momentum

\( \displaystyle{ H = \frac{p^2}{2m} + V ;\ \frac{dq}{dt} = \frac{\partial H}{\partial p} ;\ \frac{dp}{dt} = - \frac{\partial H}{\partial q} } \)

Hamilton-Jacobi formulation: S(q,a,t) is an auxiliary function, with new variable a, which is held constant. Another one, b, is also held constant.

\( \displaystyle{ \frac{\partial S}{\partial t} + H = 0 ;\ p = \frac{\partial S}{\partial q} ;\ b = \frac{\partial S}{\partial a} } \)

These are all mathematically equivalent.

 

[lpetrich]

Quantum-mechanics formulations:

Wave mechanics (Schrödinger): wavefunction Ψ(q,t), operators p, H (with p as an operator in it)

\( \displaystyle{ p \Psi = - i \frac{\partial \Psi}{\partial q} ;\ H \Psi = i \frac{\partial \Psi}{\partial t} } \)

Quantum to classical:

\( \displaystyle{ \Psi = \Psi_0 e^{- i S} } \)

Matrix mechanics (Heisenberg): wavefunction fixed, q, p, H are all operators and functions of time: q(t), p(t), H(t), and in general, do not commute with each other. The "matrix" part is because each operator turns a quantum state into a linear combination of quantum states.

The "commutator" of operators A and B is [A,B] = A.B - B.A. For operator A:

\( \displaystyle{ \frac{dA}{dt} = i [H,A] + \frac{\partial A}{\partial t} } \)

Quantum to classical: commutators become "Poisson brackets"

\( \displaystyle{ [A,B] = i \{A,B\} ;\ \{A,B\} = \frac{\partial A}{\partial q} \frac{\partial B}{\partial p} - \frac{\partial A}{\partial p} \frac{\partial B}{\partial q} } \)

Path integral (Feynman): find weighted average over all paths through parameter space. Divide time into discrete times t_i, turn time derivatives into differences, and integrate over every possible value of q for each time:

\( \displaystyle{ Z(A) = \int A \cdot e^{i L} \prod_i d(q(t_i)) ;\ <A> = \frac{Z(A)}{Z(1)} } \)

Quantum to classical:

The integral is essentially an integral over all paths q(t), and the path that contributes the most is the one that causes the integral of L over that path to vary the least from that path and neighboring paths: the "method of steepest descent".

These are also all mathematically equivalent.

 

[pood]

I believe Shrodenger's cat problem he posed was to illustrate how QM can be misinterpreted.

My impression was he was offering a reductio of QM, to show that something about it must be amiss, because it seemed absurd to suppose that microscopic effects could propagate to macroscopic states. Others took it seriously and eventually we ended up with many worlds, in which the cat is alive in one reality and dead in another.

 

[pood]

Quantum many worlds is amazingly like Borges’s short story, The Garden of Forking Paths. When the writer was asked whether he was thinking about many worlds when he wrote it, he simply said, ”No.”

 

[lpetrich]

Quantum mechanics is grossly counterintuitive, and it must be noted that Newtonian mechanics also has its counterintuitive features, violations of "intuitive physics", as it is sometimes called. Do heavier objects fall faster than lighter ones? It may seem so, but when air resistance is insignificant, they fall at the same rate. It's easy to do the experiment for yourself. I dropped an ID card and a full water bottle onto my bed, and they both fell at the same speed to within my perception of their motions. The solution is that heavier objects have more inertia than lighter ones, and that the two effects cancel each other out.

QM has been enormously successful, sometimes to very high accuracy, like the extra magnetic moment of the electron. But there are difficulties, like collapse of the wavefunction.

A classic example of this collapse is the two-slit experiment, demonstrating diffraction and interference of light waves: the light arrives at the detector in parallel bands oriented in the slits' direction. That happens even at low intensities, when only one photon at a time is in the apparatus. So the photon went through both slits, but at the detector its energy became concentrated in one spot, exciting an electron there, one out of some huge number. This great shrinkage is wavefunction collapse.

Not only single photons, but also pairs of photons, can have wavefunctions that are correlated over long distances:  Bell test of  Bell's theorem In some cases of electronic excited states of atoms, the atom's electrons can move to a lower state by emitting two photons, photons with correlated wavefunctions. This long-distance coherence has been tested in several experiments, with the detectors doing wavefunction collapse when they detect these photons.

 Interpretations of quantum mechanics describes numerous attempts to resolve that conundrum.

The Copenhagen interpretation states that it is observation that causes wavefunction collapse. But what counts as observation? This is where the mystic-physics interpretation of QM gets started, the interpretation that it is our consciousnesses that collapse the wavefunctions.

This is sometimes illustrated with the thought experiment of Schrödinger's cat. It involves a cat in a box with a radioactive atom, a detector, and a poison-gas release mechanism that can release poison gas that kills the cat. If the mechanism detects a decay, it will kill the cat, and if it doesn't, the cat will live.

From the Copenhagen interpretation of quantum mechanics, the radioactive atom is in a mixture of initial and decayed states, and this mixture carries into the detector, the mechanism, and the cat. So the cat is in a mixed state, both alive and dead, until it is observed, and that observation collapses the cat's wavefunction, making it either alive or dead.

An alternative that I like is that the complexity of macroscopic systems is what causes the collapse. Thus the detector causes the atom's radioactive-decay wavefunction to collapse, and this collapsed wavefunction propagates to that cat. So when the detector detected the decay, the cat soon died even though it was not observed.

 

[pood]

Or the cat is both alive and dead in different branches of reality, each cat quantum-entangled with a different version of the observer. Weird as this is, all the other weirdness of QM goes away. The MW is local, determinstic and realist, with no spooky action at a distance. And no wave function collapse either, which otherwise is inexplicable.

 

[lpetrich]

Or the cat is both alive and dead in different branches of reality, each cat quantum-entangled with a different version of the observer. Weird as this is, all the other weirdness of QM goes away. The MW is local, determinstic and realist, with no spooky action at a distance. And no wave function collapse either, which otherwise is inexplicable.

Many worlds? Complete with branching into new worlds as time goes by? That's almost too much for me to take.

 

[pood]

Or the cat is both alive and dead in different branches of reality, each cat quantum-entangled with a different version of the observer. Weird as this is, all the other weirdness of QM goes away. The MW is local, determinstic and realist, with no spooky action at a distance. And no wave function collapse either, which otherwise is inexplicable.

Many worlds? Complete with branching into new worlds as time goes by? That's almost too much for me to take.

Why? It violates no known physics, including conservation principles, and it does away with indeterminism, nonlocality and antirealism.

 

[lpetrich]

Or the cat is both alive and dead in different branches of reality, each cat quantum-entangled with a different version of the observer. Weird as this is, all the other weirdness of QM goes away. The MW is local, determinstic and realist, with no spooky action at a distance. And no wave function collapse either, which otherwise is inexplicable.

Many worlds? Complete with branching into new worlds as time goes by? That's almost too much for me to take.

Why? It violates no known physics, including conservation principles, and it does away with indeterminism, nonlocality and antirealism.

It's the multiple coexisting universes that's the problem, universes that multiply as time goes on. If it's a finite number, then that number grows enormously over time, though if it's an infinite number, it stays infinite.

 

[pood]

Or the cat is both alive and dead in different branches of reality, each cat quantum-entangled with a different version of the observer. Weird as this is, all the other weirdness of QM goes away. The MW is local, determinstic and realist, with no spooky action at a distance. And no wave function collapse either, which otherwise is inexplicable.

Many worlds? Complete with branching into new worlds as time goes by? That's almost too much for me to take.

Why? It violates no known physics, including conservation principles, and it does away with indeterminism, nonlocality and antirealism.

It's the multiple coexisting universes that's the problem, universes that multiply as time goes on. If it's a finite number, then that number grows enormously over time, though if it's an infinite number, it stays infinite.

I’m not sure what you find problematic about that.

 

[steve_bank]

I thought Schrodinger posed his cat problem to illustrate how QM can be misinterpreted.

How is QM any more 'weird' than any thing else?

 

[lostone]

That is why I despise videos. POOD

 

[pood]

I thought Schrodinger posed his cat problem to illustrate how QM can be misinterpreted.

How is QM any more 'weird' than any thing else?

Spooky action at a distance, indeterminism, antirealism in Copenhagen … many worlds in Everett‘s relative state formulation … pretty weird to me!

 

[steve_bank]

I thought Schrodinger posed his cat problem to illustrate how QM can be misinterpreted.

How is QM any more 'weird' than any thing else?

Spooky action at a distance, indeterminism, antirealism in Copenhagen … many worlds in Everett‘s relative state formulation … pretty weird to me!

Lifting a rock and dropping it and it always goes down, now that's spooky.

Action at a distance? I throw a rock and it hits you in the butt, that is spooky.

People hear the word spooky associated with QM and it spreads.

Put a current through a wire near a compass ad the needle will deflect, spookiness to the max.

 

[pood]

I thought Schrodinger posed his cat problem to illustrate how QM can be misinterpreted.

How is QM any more 'weird' than any thing else?

Spooky action at a distance, indeterminism, antirealism in Copenhagen … many worlds in Everett‘s relative state formulation … pretty weird to me!

Lifting a rock and dropping it and it always goes down, now that's spooky.

Action at a distance? I throw a rock and it hits you in the butt, that is spooky.

People hear the word spooky associated with QM and it spreads.

Put a current through a wire near a compass ad the needle will deflect, spookiness to the max.

All those things are understood. Spooky action at a distance — i.e., nonlocality — is not like those things.

 

[pood]

Nor is a fifty-fity chance of spin up or down anythng like the 50-50 probability of a coin toss.