Why in Quantum Mechanics is about energy but no force

[JayKo]

In classical mech, we heard of force, but in quantum there is no force mentioned at all. why? I am rather puzzle by this fact.

 

[nismaratwork]

In classical mech, we heard of force, but in quantum there is no force mentioned at all. why? I am rather puzzle by this fact.

In QM you hear about forces in a completely different way, such as a force-field (non-scifi). If you're looking for force and work, that's Newtonian mechanics and about as far from QM as you can humanly get and still be working on the same rough subject.

Beyond that, QM is concerned with the world of the 'very small' and is built from new terminology and concepts than classical mechanics. Maybe I'm misunderstanding you however, because your initial question seems a bit like asking why you don't hear about cooking techniques in law school.

 

[Demystifier]

In classical mech, we heard of force, but in quantum there is no force mentioned at all. why? I am rather puzzle by this fact.

Energy is easier to measure than force, that's why it is mentioned more frequently. But force is mentioned in QM too, e.g., in the Heisenberg picture.

 

[dextercioby]

The classical concept of energy is much more useful than the concept of force, because we can speak about the energy in the absence of any interaction, while force, by definition, is interaction. Surely, in experiments we measure energy of a system through its possible interactions, but theoretically speaking <energy> is much more useful than <force>. That's why from the classical notions we take over to quantum mechanics and also to relativistic (special or general) the <energy/Hamiltonian> and <momentum> and
not <force>, nor <speed>, nor <acceleration>.

 

[nismaratwork]

The classical concept of energy is much more useful than the concept of force, because we can speak about the energy in the absence of any interaction, while force, by definition, is interaction. Surely, in experiments we measure energy of a system through its possible interactions, but theoretically speaking <energy> is much more useful than <force>. That's why from the classical notions we take over to quantum mechanics and also to relativistic (special or general) the <energy/Hamiltonian> and <momentum> and
not <force>, nor <speed>, nor <acceleration>.

Not to mention that when your measured "body" is 'smeared' like an electron, and the other problems which QM tackles, the notion of force exerted vs. energy moving around just makes no sense.

In the end, Demystifier bigbau make good points, so consider this: You could measure a laser in terms of the force it exerts against a very sensitive force-place, or you could consider it's power in terms of delivering X amount of energy in Y time.

 

[JayKo]

In QM you hear about forces in a completely different way, such as a force-field (non-scifi). If you're looking for force and work, that's Newtonian mechanics and about as far from QM as you can humanly get and still be working on the same rough subject.

Beyond that, QM is concerned with the world of the 'very small' and is built from new terminology and concepts than classical mechanics. Maybe I'm misunderstanding you however, because your initial question seems a bit like asking why you don't hear about cooking techniques in law school.

ok, don't mind to tell me the force field concept here? i know netwonian mech is not applicable in QM, but isn't we should have classical mech equivalent of Newtonian mech in QM although the force is super small.

cooking skill in law school is not a good example in my opinion for this subject.

 

[JayKo]

Energy is easier to measure than force, that's why it is mentioned more frequently. But force is mentioned in QM too, e.g., in the Heisenberg picture.

mind to tell me more? so far i have read Griffth's intro to QM but force is totally out of the picture. is it the Heisenberg principle or something else?

 

[JayKo]

The classical concept of energy is much more useful than the concept of force, because we can speak about the energy in the absence of any interaction, while force, by definition, is interaction. Surely, in experiments we measure energy of a system through its possible interactions, but theoretically speaking <energy> is much more useful than <force>. That's why from the classical notions we take over to quantum mechanics and also to relativistic (special or general) the <energy/Hamiltonian> and <momentum> and
not <force>, nor <speed>, nor <acceleration>.

i see, i getting a clearer picture now, but if physicist really want to measure expectation value of acceleration in QM, it can still be done right.

I remember few years back IBM published that they managed to manipulate some element's atom and measure the force required and it is about few nano Newton.

 

[JayKo]

Not to mention that when your measured "body" is 'smeared' like an electron, and the other problems which QM tackles, the notion of force exerted vs. energy moving around just makes no sense.

In the end, Demystifier bigbau make good points, so consider this: You could measure a laser in terms of the force it exerts against a very sensitive force-place, or you could consider it's power in terms of delivering X amount of energy in Y time.

yes, the uncertainty principle comes into play, i got it now, thanks for clearing my doubt ;)

 

[xepma]

You can always define a force in terms of the potential, through

F = -\nabla V.

You could say that in quantum mechanics Newton's equation of motion (F=ma):

\frac{d}{dt} p = -\nabla V

has been replaced by Heisenberg's equation of motion:

\frac{d}{dt} p = -ih[H,A].

If we write the Hamiltonian as a simple sum of the kinetic energy and the potential energy, H = p^2/2m + V(x), then indeed we obtain something similar to Newton's law:

\frac{d}{dt} p = -ih[p,V] = -\nabla V.

This is an operator equation -- there's no reference to the state of the system yet. But it's still Newton's law to some extent. Note that you can simply take the expectation value left and right of the equation, to obtain what is known as Ehrenfest's theorem:

\langle F \rangle = \langle -\nabla V\rangle = \frac{d}{dt}\langle p \rangle.

This is the statement that in the classical limit, the classical Newton's law emerges from quantum mechanics.

 

[nismaratwork]

yes, the uncertainty principle comes into play, i got it now, thanks for clearing my doubt ;)

It's my pleasure!

 

[nismaratwork]

ok, don't mind to tell me the force field concept here? i know netwonian mech is not applicable in QM, but isn't we should have classical mech equivalent of Newtonian mech in QM although the force is super small.

cooking skill in law school is not a good example in my opinion for this subject.

OK, first I should have clarified that term when I know you're new to this... that's my fault. A force field in QM isn't "Star Trek" in nature... it's just what it sounds like: forces exist as field quantized at every point in space. It is literally the Field (as in Quantum FIELD Theory), of the force involved (EM is a great example).

Remember, QM isn't a classical theory, so we just can't apply the view of the world Newton formulated and Einstein refined to this small world throughout the continuum of extremes (such as Black Holes). It's the hardest thing to realize that the mathematics of QM seem more and more to support a view of the world that is incompatible at small scales, with our view of reality, never mind classical physics.

 

[JayKo]

OK, first I should have clarified that term when I know you're new to this... that's my fault. A force field in QM isn't "Star Trek" in nature... it's just what it sounds like: forces exist as field quantized at every point in space. It is literally the Field (as in Quantum FIELD Theory), of the force involved (EM is a great example).

Remember, QM isn't a classical theory, so we just can't apply the view of the world Newton formulated and Einstein refined to this small world throughout the continuum of extremes (such as Black Holes). It's the hardest thing to realize that the mathematics of QM seem more and more to support a view of the world that is incompatible at small scales, with our view of reality, never mind classical physics.

i get it. the field as in light passes alongside massive object get bend, the field theory. why is that so when you said QM seemed more and more to support a view that is incompatible at small scale? QM is the explanation for ultra small scale.

GUT is still unable to combine ultra small with ultra large to date. thanks anyway.

 

[JayKo]

It's my pleasure!

you're must welcome, i learn more than a classroom can offer in here.

 

[JayKo]

You can always define a force in terms of the potential, through

F = -\nabla V.

You could say that in quantum mechanics Newton's equation of motion (F=ma):

\frac{d}{dt} p = -\nabla V

has been replaced by Heisenberg's equation of motion:

\frac{d}{dt} p = -ih[H,A].

If we write the Hamiltonian as a simple sum of the kinetic energy and the potential energy, H = p^2/2m + V(x), then indeed we obtain something similar to Newton's law:

\frac{d}{dt} p = -ih[p,V] = -\nabla V.

This is an operator equation -- there's no reference to the state of the system yet. But it's still Newton's law to some extent. Note that you can simply take the expectation value left and right of the equation, to obtain what is known as Ehrenfest's theorem:

\langle F \rangle = \langle -\nabla V\rangle = \frac{d}{dt}\langle p \rangle.

This is the statement that in the classical limit, the classical Newton's law emerges from quantum mechanics.

i see, i learned it in my QM1 course on ehrenfest's theorem, i can better appreciate QM now after the good insight you guy have shared with me, thanks folks :D