Difference between CM and QM

In summary: The "final version of quantum theory" is about the current state of the theory, with the understanding that there may be a final version that we don't yet have.
  • #1
shalu
8
0
what is the difference between classical mechanics and quantum mechanics??

other than that classical mechanics dealing with macroscpic particles while quantum mechanics with microscopic particles
 
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  • #2
shalu said:
what is the difference between classical mechanics and quantum mechanics??

other than that classical mechanics dealing with macroscpic particles while quantum mechanics with microscopic particles

Quantum mechanics allows for the simultaneous existence of several classical states. It is the content of the superposition principle. If classically, a certain system can be in state A or in state B or in state C, then quantummechanically, the system can be in any combination of A, B and C, with complex coefficients to A, B and C.

If you do a measurement on the system, to find out whether it is in the classical state A, the classical state B, or the classical state C, then you will find one of these states, with a probability proportional to the absolute square of those complex coefficients.
 
  • #3
shalu said:
what is the difference between classical mechanics and quantum mechanics?
Classical mechanics already exists. Physicists understand it.
Quantum mechanics does not exist yet. Physicists do not understand it. But they may use it... like cave man may use cell phone. :smile:
 
  • #4
jdg812 said:
Classical mechanics already exists. Physicists understand it.
Quantum mechanics does not exist yet. Physicists do not understand it. But they may use it... like cave man may use cell phone. :smile:

It sounds a bit silly to say that an 80-year old theory doesn't exist (but we can nevertheless use it - even though its non-existence ?).

You are probably referring to the interpretational problems of quantum theory. But let us not forget that we've given up interpreting classical physics, exactly because of the advent of quantum physics!
 
  • #5
vanesch said:
It sounds a bit silly to say that an 80-year old theory doesn't exist (but we can nevertheless use it - even though its non-existence ?).
Words in human language may have several meanings. We may use one meaning in one sentence and another meaning of the same word in another sentence.

For example:
(FINAL VERSION OF) "quantum mechanics" does not exist yet.
Physicists may use (PRELIMINARY VERSION OF) "quantum mechanics"

vanesch said:
You are probably referring to the interpretational problems of quantum theory.
Not only to the interpretational problems, but to other not solved problems as well
 
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  • #6
jdg812 said:
Words in human language may have several meanings. We may use one meaning in one sentence and another meaning of the same word in another sentence.

For example:
(FINAL VERSION OF) "quantum mechanics" does not exist yet.
Physicists may use (PRELIMINARY VERSION OF) "quantum mechanics"

But we do have a final version of classical physics ?
 
  • #7
vanesch said:
But we do have a final version of classical physics ?
We believe we do have a final version of CM, but actually we do not. Because tomorrow somebody may prove a new theorem about Lagrangian and we will get a new "final version" of CM. :smile:

As for QM, we believe we don't have a final version of QM and we indeed do not have it.
 
  • #8
How do we define "final version" of a theory. How do we know that a theory is a "final version" of a previous theory.
 
  • #9
jdg812 said:
We believe we do have a final version of CM, but actually we do not. Because tomorrow somebody may prove a new theorem about Lagrangian and we will get a new "final version" of CM. :smile:

As for QM, we believe we don't have a final version of QM and we indeed do not have it.

I think you're confusing "final theory" and "final version of quantum theory".

Classical theory has its problems, but it also has a rich body of "working" machinery, and we leave it at that. Probably the problems will never be solved entirely within its scope (like the radiation reaction and so on). That doesn't stop people to add stuff to the edifice.

You can say exactly the same about quantum theory. I don't think that its fundamental problems will ever be solved within its own scope.

Tomorrow, we might have a new theoretical paradigm. But there's no reason to call it "new quantum physics". We may also stay stuck with our present tools for a long time to come. Who knows ?

So I don't see any fundamental difference between the state of current quantum theory, and the state of classical theory, except for the fact that, because as of now, we don't have as of yet an underlying, newer theory, we seem to make more fuzz about the problems quantum theory has than we are making of the problems classical theory has.

But I'd say that quantum theory is "up and running" just as much as was classical physics, when it was still thought to be "fundamental".
 
  • #10
vanesch said:
I think you're confusing "final theory" and "final version of quantum theory".
I don't think so.
The "final theory" is about EVRYTHING (including gravitation, soul, God and many other undiscovered yet phenomena)
The "final version of quantum theory" is about atomic, nuclear, particle etc. phenomena ONLY

vanesch said:
So I don't see any fundamental difference between the state of current quantum theory, and the state of classical theory".
I understand your point of view... thanks...
but my point of view is different...

It is like a possibility to choose one or another coordinate frame in the theory of relativity... any would be good... :smile:
 
  • #11
jdg812 said:
I don't think so.
The "final theory" is about EVRYTHING (including gravitation, soul, God and many other undiscovered yet phenomena)
The "final version of quantum theory" is about atomic, nuclear, particle etc. phenomena ONLY

Mmm, but quantum physics as of today does a very good job at most of that already...

Just like Newtonian physics does a very good job at describing the orbit of the Earth around the sun, and the tides, as well as falling apples.

However, look at the tiny deviation of mercury's orbit: is general relativity then the "final version of Newtonian physics" because we now have a quasi perfect description of the solar system, which is "Newtonian physics" ?

So if ever we discover new principles underlying atomic, nuclear etc... phenomena, which have nothing to do with the superposition principle or unitary operators, is that then "final quantum theory" ?

I make a distinction between certain categories of phenomena (solar system, atoms, galaxies, nuclear physics, GeV-level elementary particle physics, lasers, ...) on one hand, and theoretical paradigms (Newtonian, general relativistic, quantum theory, ...) on the other.

You seem to associate "quantum physics" to whatever paradigm is going to adress best atomic and nuclear phenomena. So, 120 years ago, "quantum physics" was Newtonian physics when it was the best tool available to describe microscopic physics ?

Quantum physics to me is the application of the superposition principle, and the linearity of time evolution. Whether this paradigm works for atoms, quarks, molecules, planets or galaxies is a different matter.
 
  • #12
vanesch said:
Mmm, but quantum physics as of today does a very good job at most of that already...
Yes, absolutely! It does a VERY good job, but NOT ALL job!

vanesch said:
Just like Newtonian physics does a very good job at describing the orbit of the Earth around the sun, and the tides, as well as falling apples.

However, look at the tiny deviation of mercury's orbit: is general relativity then the "final version of Newtonian physics" because we now have a quasi perfect description of the solar system, which is "Newtonian physics" ?
No, GR is not the "final version of Newtonian physics" and GR is not even a "version of Newtonian physics".

vanesch said:
So if ever we discover new principles underlying atomic, nuclear etc... phenomena, which have nothing to do with the superposition principle or unitary operators, is that then "final quantum theory" ?
If only new principles , probably not yet.
If ALL principles , probably yes.
:smile:
 
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  • #13
what is the difference between classical mechanics and quantum mechanics??
I’d be interested in hearing what others think of this particular explanation, good, bad or otherwise.

Any phenomena (ex: such as vortex shedding from an aircraft wingtip or even the coupling of fluids and solids that may create nonlinear phenomena) which are seen to be explainable at the classical mechanical level, can be both physically and analytically reduced to their individual parts such as is done using finite element analysis or computational fluid dynamics for example. This is a type of reductionism which allows one to consider what is occurring within some small volume of space, contingent only on the local affects of aggregates of molecules.

In contrast, phenomena which are produced at a quantum mechanical level are not physically nor are they analytically reducible to small volumes of space which are contingent only on the local affects of particles. In quantum mechanics, molecules and molecular interactions must be considered in some holistic sense. Instead of examining local interactions, a quantum mechanical system must be described using a single wavefunction, “and this wavefunction must be a function of the different position coordinates of all the separate particles.” (Penrose)
 
  • #14
shalu said:
what is the difference between classical mechanics and quantum mechanics??

other than that classical mechanics dealing with macroscpic particles while quantum mechanics with microscopic particles

The Lie algebra of the Galilean group is the Lie algebra of symmetry of both CM & QM. Therefore, one can say that CM & QM are two different realizations of a single mathematical formalism. To see what I mean, consider the Lie bracket;

[tex]\left( a , b \right) = - \left( b , a \right)[/tex]

which satisfies the conditions

[tex]\left( ab , c \right) = a \left( b , c \right) + \left( a , c \right) b[/tex]

[tex]
\left( a , \left( b , c \right) \right) + \left( c , \left( a , b \right) \right) + \left( b , \left( c , a \right) \right) = 0
[/tex]

Now assume that

1) under the time translation [itex]t \rightarrow t + \delta t[/itex], the physical state, [itex]P(t)[/itex], changes according to;

[tex]\delta P(t) = - \left( H , P(t) \right) \delta t[/tex]

where [itex]H = p^{2} + V(q)[/itex] is the Hamiltonian. In particular

[tex]\delta H = ( H , H ) \delta t = 0[/tex]

gives the Lie algebra of the 1-parameter group of time translation. We also have

[tex]\dot{q}_{i} = ( q_{i} , H )[/tex]
[tex]\dot{p}_{i} = ( p_{i} , H )[/tex]

2) space translations; [itex] q_{i} \rightarrow q_{i} + \delta q_{i}[/itex], induce the following change;

[tex]\delta P(t) = - \left( p_{i} , P(t) \right) \delta q_{i}[/tex]

Hence

[tex]\delta p_{j} = - ( p_{i} , p_{j} ) \delta q_{i}[/tex]

assuming that [itex]\delta p_{i}[/itex] and [itex]\delta q_{i}[/itex] are independent, we find the algebra

[tex]( p_{i} , p_{j} ) = 0 \ \ \ (1)[/tex]

Letting [itex]P(t) = q_{j}[/itex], we find the bracket

[tex]( q_{i} , p_{j} ) = \delta_{ij} \ \ \ (2)[/tex]

3) for the "translations" [itex]p_{i} \rightarrow p_{i} + \delta p_{i}[/itex], we take

[tex]\delta P(t) = - \left( q_{i} , P(t) \right) \delta p_{i}[/tex]

which gives

[tex]( q_{i} , q_{j} ) = 0 \ \ \ (3)[/tex]

No more assumptions needed to complete Galilean invariance, since the fundamental brackets (1), (2) and (3) together with the definition of the angular momentum, [itex]J_{i} = \epsilon_{ijk}q_{j}p_{k}[/itex], are sufficient to derive the Lie algebra of the rotation group so(3);

[tex]( J_{i} , J_{j} ) = \epsilon_{ijk} J_{k}[/tex]

Therefore, rotational invariance of the system is guaranteed once the dynamical variabes satisfy the fundamental brackets.

Now, if the Lie bracket is given by (Poisson's):

[tex]
( a , b ) = \frac{\partial a}{\partial q_{i}} \frac{\partial b}{\partial p^{i}} - \frac{\partial a}{\partial p^{i}} \frac{\partial b}{\partial q_{i}} \equiv \{ a , b \}
[/tex]
the above formalism gives you CM. But, when Lie bracket is realized by commutator;

[tex]( a , b ) = i(ba - ab) \equiv - i [ a , b ][/tex]

then, you are talking QM: since [itex]pq \ne qp[/itex], the dynamical variables cann't be ordinary numbers. Therefore, in QM, these variables are represented by operators and matrices. This means that the space of all possible physical states in QM is different from that in CM. The dynamical equations in both theories are linear. This leads to the fact that (in both theories) superposition of physically possible states is also physically possible. However, in QM ( again because of [q,p]=i ), the principle of superposition has a classically-weird meaning; While it is impossible for a classical (macro) object to be in two places at the same time, a quamtum (micro) object seems to be able to accomplish such classically-impossible task.

regards

sam
 
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  • #15
correction

samalkhaiat said:
3) for the "translations" [itex]p_{i} \rightarrow p_{i} + \delta p_{i}[/itex], we take ...

the correct equation is

[tex]\delta P(t) = \left( q_{i} , P(t) \right) \delta p_{i}[/tex]



regards

sam
 

What is the difference between classical mechanics (CM) and quantum mechanics (QM)?

Classical mechanics and quantum mechanics are two different branches of physics that describe the motion and behavior of particles and objects in the universe. Classical mechanics is based on Newton's laws of motion and can accurately predict the behavior of macroscopic objects, while quantum mechanics describes the behavior of particles on a microscopic level.

How do the principles of CM and QM differ?

Classical mechanics is based on the principle of determinism, meaning that the future state of a system can be determined from its present state. On the other hand, quantum mechanics is based on the principle of probability, where the behavior of particles is described by wave functions and can only be predicted in terms of probabilities.

What are some key concepts in CM and QM?

In classical mechanics, key concepts include force, mass, and energy, as well as concepts like velocity, acceleration, and momentum. In quantum mechanics, key concepts include wave-particle duality, uncertainty principle, and quantum entanglement.

How do CM and QM differ in their approach to measuring and observing particles?

In classical mechanics, particles are seen as distinct objects with definite properties that can be measured and observed without affecting their behavior. In quantum mechanics, the act of measuring or observing a particle can actually change its behavior, as the act of measurement collapses the particle's wave function and determines its state.

What are some practical applications of CM and QM?

Classical mechanics is utilized in many engineering and technological applications, such as designing bridges and buildings, as well as in the development of machines and vehicles. Quantum mechanics is used in fields such as quantum computing, quantum cryptography, and quantum teleportation, and is also essential in understanding the behavior of atoms and molecules in chemical reactions.

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