Are Quantum Physics & Classical Physics incompatible?

[Rolliet]

Is quantum physics closer to the truth than classical physics, or is it just a different way of looking at the same problem? For example, the rules of baseball explain the behavior of baseball players better than the rules of football, and vice versa. The rules of these two sports are not compatible. Is this a good way at looking physics? Thanks

 

[phinds]

Is quantum physics closer to the truth than classical physics, or is it just a different way of looking at the same problem? For example, the rules of baseball explain the behavior of baseball players better than the rules of football, and vice versa. The rules of these two sports are not compatible. Is this a good way at looking physics? Thanks

Classical physics is a good approximation of reality at certain scales (the ones we normally live in, for example) but it does not describe reality at small scales at all, you need quantum mechanics for that, and it does not describe reality at all well at high speeds or near very massive objects, you need relativity for that.

Also, "classical physics" includes a lot of stuff that is very solid, such as Newton's Laws of Motion.

 

[jfizzix]

Quantum physics and classical physics are not incompatible.
Quantum physics is more fundamental and accurate than classical physics, but not incompatible.

You can find classical physics as a limit of quantum physics for large objects, (i.e., objects much larger than or composed of many elementary quantum objects).

For large objects, classical physics offers a much simpler description for most things one might be interested in. You could describe a baseball quantum mechanically, but that's like using a chainsaw to make a toothpick, as far as power and difficulty goes.

 

[Doug Huffman]

Classical physics is a subset of quantum physics just as Newtonian physics is a subset of classical physics.

 

[rootone]

Quantum physics is the physics of very small entities and their behaviour cannot be described with something like Newton's mechanics.
However on macroscopic scales classical mechanics is still good for things such as building a bridge.
Introducing quantum mechanics to that would not result in a better bridge.

 

[abbas_majidi]

Every theory in physics have a job, this job is describing result of experiments before perform them. Experiments are nature answers to our questions. We don't have a general theory in physics which perform it's job perfectly. it is not good, but physicists every day try to find it. They can't find it but are closing to it. Like a Taylor expansion they try to find more term and more accurate. More accurate for a theory meaning answer to more questions. Classical theory can answer to many questions but Quantum answers much more(each question is answered by classical mechanics truly have a true answer in quantum mechanics but there is questions which only quantum can true answer to them) . We have 3 group questions:

1. Both theory have true answer to this group,answers with acceptable accurates.

2. Both theory have answer but classical answer is not true and only quantum can answer them.

3. Both have answer but they are false.

In other hand classical and quantum physics are approaches to nature's behavior.

 

[Jano L.]

Is quantum physics closer to the truth than classical physics, or is it just a different way of looking at the same problem?

People based in classical physics believe that physical phenomena happen and can be faithfully captured as events in space and time and the endeavour of physics is to study mathematical models of these phenomena and explain what is going on in the world. Things such as observation, measurement of these phenomena play no fundamental role in the theory of the phenomenon, since it is assumed that these are merely intrusions of people to get information and the phenomena themselves are occurring elsewhere even without these intrusions. For example, theory of orbital motions is based in classical physics and gives position of a satellite such as Moon or spaceship as a function of time. This function obeys fixed set of equations. Any influence of observation or measurement of the satellites is usually ignored since it is negligible. It could be taken into account according to the theory, but it would complicate the theory immensely.

People based in quantum physics believe that the best description and explanation of physical phenomena anyone can do is via $\psi$ function or density matrix. This function / matrix is an abstract mathematical device without immediate intuitive connection to what we can observe with our senses and is unlike the above function of time. What is it good for? Shortly, in quantum physics one does not calculate what happens in the model of the phenomenon to understand the phenomenon. Instead, for given physical quantity (positions, energy,...), one computes from $\psi$ probabilities that chosen values will be obtained as a result of measurement in future. So instead of modelling phenomena and developing explanations, we aspire for predictions of future. Abstracted concept of measurement and probabilistic fundamentalism play great roles in the quantum theory. For example, in Stern-Gerlach experiment, where silver atoms are passed through magnet and are subsequently captured on the screen placed in path of the stream, only probabilities for two preferred landing zones can be calculated. The atom lands in one of the two patches, but which one it will be cannot be found from the formalism of quantum physics. It could only be found from the formalism of classical physics, but I do not think we have achieved such classical model yet.

Historically, classical physics has been useful in the study of everyday macroscopic phenomena and phenomena on a large scale such as Earth, solar system, galaxy. There were always some phenomena that lacked satisfying explanation in terms of classical physics, like perturbations in the motion of the Moon and Mercury, or complicated behaviour of tides, but often good explanation was finally found. Only in 20th century the idea that the classical aspirations may not be legitimate on the scale of atoms took wind. What if atoms are not comprehensible with classical physics? Thus quantum physics developed, but it did not replace classical physics; it denounced its aspirations. Since this is not very useful in areas where classical physics has been succesfull, the quantum physics applications tend to concentrate in areas where there is no successful classical model yet.

So, to get back to your question, quantum physics is not that much a different way of looking at the same problem as it is a very different view on what are objectives of physics and what work is physicist supposed to do.

 

[rootone]

I like that. although it is a bit long.
QM is a different way to look at things, and although some stuff makes more sense seen that way, there is also stuff that QM does nothing to help our understanding.of what is happening.
It's a bit like asking if a picture made by Picasso, is a better picture than one made by Dali.
(or even some early cave painter)

 

[A. Neumaier]

Classical mechanics and quantum mechanics treat different aspects of the same reality. For processes that oscillate slowly enough in time and/or space, classical mechanics is fully adequate, while to resolve very high frequency processes (processes where something nontrivial happens at short distance or short time scales that cannot be ignored by averaging) one needs quantum mechanics. The two ways of looking at problems coexist in systems where the slow part is treated classically and the fast part is treated quantum mechanically. These quantum-classical processes are described by a combination of Hamiltonian classical mechanics and the Schroedinger equation. (On the most fundamental level, of course, arbitrarily fast processes must be taken into account, and this can only be done in terms of quantum mechanics - or rather quantum field theory).

 

[Q_Goest]

A more useful question might ask what the difference is between phenomena that can be described using classical physics versus phenomeona that must be described using quantum physics. Phenomena that must be described using quantum physics can't be described using classical physics, but phenomena that can be described using classical physics can also be described using quantum physics.

There is a very useful tool however that can be applied to phenomena that are describable using classical physics. They are "separable", meaning that there's an aggregate of atoms and molecules that produce the behavior that we attribute to the phenomenon; and any similar aggregate will produce essentially the same results. All finite element type computational analysis is based on this fact. Neuron interactions for example are said to be 'classical' in nature because they do not exploit any of the special features of quantum mechanics. Similarly, heat transfer, mechanics of materials, electromagnetic phenomena and many other classical scale phenomena are describable using classical physics and do not depend on specific interactions at the quantum level. Classical scale phenomena are easily modeled on computers using finite state numerical modeling techniques.

In contrast, quantum physics is nonseparable so that specific interactions between particles must be accounted for. Entanglement is a commonly used example of a phenomenon that is nonseparable. The type of analysis applied to entangled particles and other quantum phenomena is very different than the numerical analysis applied to classical phenomena.

 

[Jano L.]

A more useful question might ask what the difference is between phenomena that can be described using classical physics versus phenomeona that must be described using quantum physics.

You seem to believe that there are some phenomena that must be described by quantum theory, as if quantum theory was some ultimate truth about the world. Such absolute beliefs are not scientific. All knowledge is approximate and there are many theories that can accommodate the facts. Just because quantum theory was more fruitful in some investigations does not mean it is necessarily the last word on the subject. After all, quantum theory has its serious deficiencies.

Classical scale phenomena are easily modeled on computers using finite state numerical modeling techniques. In contrast, quantum physics is nonseparable so that specific interactions between particles must be accounted for. Entanglement is a commonly used example of a phenomenon that is nonseparable.

What do you mean by "classical scale"? What do you mean by "quantum physics is nonseparable"? What are "specific interactions"?

In classical physics, many-particle systems also require consideration of inter-particle interactions. There can also be long-distance correlations of states of different particles.

The type of analysis applied to entangled particles and other quantum phenomena is very different than the numerical analysis applied to classical phenomena.

If by analysis you mean computer aided calculations, both classical and quantum models use the same kind of computer with finite number of possible states. It is not clear at all what you meant by your statements.

 

[DrewD]

You seem to believe that there are some phenomena that must be described by quantum theory, as if quantum theory was some ultimate truth about the world. Such absolute beliefs are not scientific. After all, quantum theory has its serious deficiencies.

Ultimate might be a bit strong, but more precise yes. While it has not been proved in general, most quantum systems do behave classically when you consider classical size scales. Certainly our current understanding of QM is not perfect and, for many problems, it is unnecessarily cumbersome, but it is a more fundamental theory. By "more fundamental" I mean that classical motion follows from quantum rules, not the other way around.

What do you mean by "classical scale"? What do you mean by "quantum physics is nonseparable"? What are "specific interactions"?

Classical scale is the scale over which classical physics works. This usually starts around the distance scales of large molecules. Entangled states are non separable. This means that the wave functions of particles cannot be written as a product of the wave functions of the constituent parts. This does not happen in classical physics.

In classical physics, many-particle systems also require consideration of inter-particle interactions. There can also be long-distance correlations of states of different particles.

The correlations are different. Classical correlations obey Bell's inequality.

 

[Jano L.]

... but it is a more fundamental theory. By "more fundamental" I mean that classical motion follows from quantum rules, not the other way around.

Can you provide a reference explaining how classical motion follows from quantum rules? That would be interesting.
The problem with this often expressed idea is that quantum theory is a scheme to compute probabilities of results of experiments. Classical motion means we have coordinates of particles as functions of time. I doubt it is possible to get these coordinates as functions of time from quantum rules. If you know a source that demonstrates that, I'd be glad to hear about it.

Classical scale is the scale over which classical physics works. This usually starts around the distance scales of large molecules. Entangled states are non separable. This means that the wave functions of particles cannot be written as a product of the wave functions of the constituent parts. This does not happen in classical physics.

It does not happen in the same form because in classical physics there are no $\psi$ functions to begin with.
It does happen in the sense there are used non-factorizable probability distributions in probabilistic description of many-particle systems. For example, classical statistical physics model of interacting gas molecules.

I'd like to hear Q_Goest's explanation of those terms since he introduced them first. What do you mean by "classical scale"? What do you mean by "quantum physics is nonseparable"? What are "specific interactions"?

 

[vjacheslav]

Sorry, bit waste, Us try to build classical theory of electrodynamics, any help will be appreciated :)

 

[DrewD]

Can you provide a reference explaining how classical motion follows from quantum rules?

Ehrenfest's Theorem shows that, on average, quantum objects follow classical trajectories. In the classical limit, where the uncertainties much smaller than the scale of the object, the average is (approximately) all that is left.

It does happen in the sense there are used non-factorizable probability distributions in probabilistic description of many-particle systems. For example, classical statistical physics model of interacting gas molecules.

The state of the system at a moment can always be separated (as far as I know) into the individual momenta and positions of particles. Classically, there is no reason to believe that this can't be done in an interacting gas. It ISN'T done because it would be terribly difficult to do. That doesn't mean that velocity of a certain particle no longer has a real value, it just means that it isn't important to the computation. In standard QM, the state of entangled particles is fundamentally non-separable.

I'd like to hear Q_Goest's explanation of those terms since he introduced them first. What do you mean by "classical scale"? What do you mean by "quantum physics is nonseparable"? What are "specific interactions"?

Apart from "specific interactions", the other terms are very common (although "classical scale" is not terribly precise) in the literature.

 

[Jano L.]

Ehrenfest's Theorem shows that, on average, quantum objects follow classical trajectories. In the classical limit, where the uncertainties much smaller than the scale of the object, the average is (approximately) all that is left.

Ehrenfest's theorem, for one particle in a given conservative field with potential energy $V(\mathbf r)$, is the equation

$$
\frac{d}{dt}\int \psi^*(\mathbf r,t)i\hbar \nabla \psi(\mathbf r, t) \, d^3\mathbf r = -\int \psi^* \nabla V \psi\,d^3\mathbf r.
$$

This equation does not occur in classical physics. It determines what is the evolution of expected average of $\mathbf r$ in the given potential field. One can easily have $\psi$ that spans the whole configuration space. The concept of trajectory is not present and I do not see how one could introduce it here.

 

[DrewD]

Ehrenfest's theorem pretty much directly states that the laws of classical mechanics follow the average quantum behavior. On the scale that we see, we couldn't notice the deviations. The other direction does not work.

The concept of trajectory is not present and I do not see how one could introduce it here.

Quantum mechanically there is not a classical trajectory, but on average, a particle follows a classical trajectory (the position is governed by the same laws a classical particles). On large scales we can ignore the deviations from this average motion because they are many orders of magnitude less than the size of the object. That is what it means to say that we can recover classical mechanics from quantum, not that the exact equations are contained in QM.

Similarly, Galilean Relativity is recovered from Special Relativity when $v<<c$ (Caveat: I do think relativity implies classical kinematics more cleanly). The important thing is that Classical Mechanics can follow as an approximation to both Relativity and QM, but it does not work the other way.

 

[Rolliet]

when a photon is viewed as a particle does it exhibit mass and gravity? Likewise, when electrons are viewed as a wave does it behave like a photon (i.e.: causing an electron to jump an energy level) ?

 

[Jano L.]

Ehrenfest's theorem pretty much directly states that the laws of classical mechanics follow the average quantum behavior.

It is not possible it states anything about classical mechanics, because it follows from the Schroedinger equation, which is not part of classical mechanics. It only states something about expected average values and about the Schroedinger equation.

Quantum mechanically there is not a classical trajectory, but on average, a particle follows a classical trajectory (the position is governed by the same laws a classical particles).

If there is no trajectory, particle cannot follow trajectory, classical or not classical. Following particular trajectory on average makes no sense if particle never follows particular trajectory at all.

 

[A. Neumaier]

If there is no trajectory, particle cannot follow trajectory, classical or not classical. Following particular trajectory on average makes no sense if particle never follows particular trajectory at all.

But in standard QM (except in the copenhagen interpretation) there are trajectories, they are just not described by a path in spacetime but by a small diameter tube whose mean width can be computed from the expectations. It is precisely like the paths of a classical extended particle, which also has no precise world line. Only its center of mass has. But the center of mass is a fictitious point only. For a ring shaped extended object it is even outside the object!

 

[DrewD]

If there is no trajectory, particle cannot follow trajectory, classical or not classical. Following particular trajectory on average makes no sense if particle never follows particular trajectory at all.

Sorry, I'm not going to keep arguing this. The topic was covered in the 30's and is part of most introductory QM texts. A perfect example are the trajectories of cosmic rays in bubble chambers. Certainly there is a lot of discussion about whether or not decoherence solves the measurement problem and whether or not all of classical mechanics could be derived from QM, but the fact that the classical behavior of many systems follows from quantum mechanics in the classical scale approximation is something that was worked on quite a bit in the early days of QM.

 

[Gaz]

I seen a program that described physics advancements pretty well. The presenter said imagine a onion with its layers one on top of the other.
New advancements build up on top of the old ones to improve upon them. So I guess QM could be classed as a improved way of looking at things that better explains the outcome.

However hopefully future layers will improve upon QM a bit because I'm not a fan =) I prefer classical because it is easyer to understand. QM on the other hand has to many it works we just don't know why's in it for my liking.

 

[Jano L.]

Sorry, I'm not going to keep arguing this. The topic was covered in the 30's and is part of most introductory QM texts. A perfect example are the trajectories of cosmic rays in bubble chambers. Certainly there is a lot of discussion about whether or not decoherence solves the measurement problem and whether or not all of classical mechanics could be derived from QM, but the fact that the classical behavior of many systems follows from quantum mechanics in the classical scale approximation is something that was worked on quite a bit in the early days of QM.

I agree with that. However, "classical behaviour" seems to me is a rather foggy concept with many different uses. If we stick to your original statement about classical mechanics being some kind of limit of quantum theory, I believe that is not correct. I do not think trajectories of particles can be derived from the Schroedinger equation.

 

[Jano L.]

But in standard QM (except in the copenhagen interpretation) there are trajectories, they are just not described by a path in spacetime but by a small diameter tube whose mean width can be computed from the expectations. It is precisely like the paths of a classical extended particle, which also has no precise world line. Only its center of mass has. But the center of mass is a fictitious point only. For a ring shaped extended object it is even outside the object!

That is a different concept of trajectory. The common meaning is coordinates of a point as functions of time. In classical mechanics, body itself has no single trajectory, but the material points it consists of do have trajectories.

The centroid of coordinate probability distribution could be used to define a trajectory. If the $\psi$ function of a particle is sufficiently localized for a long time, the Ehrenfest equation restricting this trajectory comes close in description of configuration to what one would have from classical physics.

It would be interesting to see some kind of limit made for a specific model in quantum theory that would lead to description where $\psi$ function remains factorized into particle terms in the course of time and these terms remain concentrated with very small interval of coordinates. Do you know any references that would have such a limiting process?

 

[vjacheslav]

When quantum mechanic just appeared, there arised a question: what concept (and equation as well) must be chosen from classical mechanic as fundamental, particles as field or particles as point objects. Currently field concept has won. Is it correct solution?

 

[A. Neumaier]

That is a different concept of trajectory. The common meaning is coordinates of a point as functions of time. In classical mechanics, body itself has no single trajectory, but the material points it consists of do have trajectories.

The centroid of coordinate probability distribution could be used to define a trajectory. If the $\psi$ function of a particle is sufficiently localized for a long time, the Ehrenfest equation restricting this trajectory comes close in description of configuration to what one would have from classical physics.

It would be interesting to see some kind of limit made for a specific model in quantum theory that would lead to description where $\psi$ function remains factorized into particle terms in the course of time and these terms remain concentrated with very small interval of coordinates. Do you know any references that would have such a limiting process?

There is no reason to think that classical concepts have direct meaning in the quantum domain. But in the limit where $\hbar\to0$, the tube becomes a classical trajectory. This is the meaning of the classical limit, and it is well-understood. You can easily workout everything for yourself.

In classical field theory (elasticity theory describing a deformable body), there are no material points, hence no trajectories.

One gets approximate trajectories from Maxwell's equations, say, by considering the geometric optics approximation. Something similar can be done for quantum fields. Only in this approximation, the concept of a particle makes sense.

 

[Jano L.]

But in the limit where $\hbar\to0$, the tube becomes a classical trajectory. This is the meaning of the classical limit, and it is well-understood.

Please give references to your claims. I hardly can work out this for myself, since I do not think this is what Schroedinger's equation leads to. I may be wrong, but I need more specifics about those tubes and how the limit is made in a specific model.

In classical field theory (elasticity theory describing a deformable body), there are no material points, hence no trajectories.

The deformable body in elasticity theory is a continuum of points and each can be ascribed trajectory. This is what Lagrangian description of continuum is about.

One gets approximate trajectories from Maxwell's equations, say, by considering the geometric optics approximation. Something similar can be done for quantum fields.

Please give a reference to a paper or a book that does that and we can discuss that.