Fundamental difference between quantum physics and classical physics

[shounakbhatta]

Hello,

There has been lot many articles, write up(s) pointing out the difference between classical and quantum physics. Well, I know that there has been thousand and one articles written on the topic, but my point is to find out the basic fundamental difference.

One point is quiet evident is that of energy. In classical mechanics we have energy varying up to any level, whereas in quantum mechanics we have energy using up to discrete level. But there is one clarification?

When we are using statistics in classical field like Maxwell-Boltzmann statistics or otherwise thousand instances where we are using statistics to find out the behavior of the system, there also we are trying to find out the predictability or the degree of randomness in that particular system. In quantum mechanics, also we are using statistics to find out the degree of randomness.

So where lies the fundamental difference?

If anybody can explain with some example, it will be very helpful.

Thanks

 

[ddd123]

It's not true that energy is always on discrete levels in quantum physics, in fact, loosely speaking, that's true only for bound states.

The fundamental difference lies in the fact that states in quantum physics are represented with a Hilbert space, whereas in classical physics they are represented by the generalized coordinates of the phase space or configuration space.

In fact, both representations can be used to write the partition function in statistical mechanics, but the Hilbert space is more apt here in that particles in a box are bound states and thus have already discrete energy levels!

 

[bhobba]

The fundamental difference is QM is basically one of the two most reasonable probability models for modelling physical systems - probability is built right into its foundations:
http://arxiv.org/pdf/quant-ph/0101012.pdf

Classical physics has definite values for all its properties - nothing is probabilistic.

The dynamics however is, and quite interestingly, determined by the same thing - symmetries.

Thanks
Bill

 

[kith]

There is a number of ways to state the fundamental difference between QM and classical mechanics. An important one (discovered by Heisenberg in his 1925 paper) is that we have non-commuting observables in QM.

In both theories, given an initial state with incomplete knowledge, you can prepare a state of maximal knowledge by measuring some physical quantities. In classical mechanics, this allows you to calculate the outcome for all future measurements in principle. In QM, there are quantities which are not compatible with the ones you have measured to prepare the state. If you measure them, you forget what you knew about the old ones (this is quantified by Heisenberg's uncertainty principle). For example, if you know your particle's position and measure the momentum, a subsequent position measurement may yield a different position.

 

[Demystifier]

I like the following formulation of the difference. Both quantum and classical mechanics can be described by a wave function obeying a superposition principle and determining the probability amplitude. The difference is that wave function is complex for quantum mechanics, but real and positive for classical mechanics:
http://lanl.arxiv.org/abs/quant-ph/0505143 [Found.Phys.Lett. 19 (2006) 553-566]
http://lanl.arxiv.org/abs/0707.2319

 

[dauto]

One important difference is that in classical physics you add probabilities to find the total probability of some event. So if an event can happen in two different ways with probabilities p₁, and p₂, the total probability is just p = p₁ + p₂. In quantum physics, you actually add amplitudes of probability M = M₁ + M₂ where M can be a complex number and than calculate the probability as the magnitude of the amplitude p = |M|². That's where interference comes from in quantum mechanics giving it's wave-like properties.

 

[Maui]

In classical mechanics you learn about the properties of classical matter. In quantum mechanics you learn that there is no classical matter as such.

 

[Jilang]

I think the main difference is that quantum mechanics demands that a state evolves in a unitary way. Classical mechanics involves some rather problematic discontinuities (consider for example spontaneous decay). The compromise is that wavefunctions need to evolve in imaginary time, but there's no such thing as a free lunch!

 

[ChrisVer]

Already posted...
If you'd like one more, I'd say is in the path integral formalism. Whereas in classical mechanics, when you want to see how would a particle travel from point A to point B, you get a classical determined path- in quantum mechanics this changes. In fact all paths contribute in this...

 

[shounakbhatta]

Hello All,

Thank you everyone for their wonderful and lucid answers. Actually, I was listening to a lecture of Prof.Susskind at Stanford University. What I could understand is that energy which comes in discrete packets is a major factor in quantum mechanics. Also, in a classical system you can detect the position looking at it, whereas in QM once you look at the system (even gently) you disturb the whole system and increase the randomness of the entire system.

 

[Naty1]

The following is an explanation I like which combines several of those already posted:


From Roger Penrose celebrating Stephen Hawking’s 60th birthday in 1993 at Cambridge England...this description offered me a new insight into quantum/classical relationships:

..Either we do physics on a large scale, in which case we use classical level physics; the equations of Newton, Maxwell or Einstein and these equations are deterministic, time symmetric and local. Or we may do quantum theory, if we are looking at small things; then we tend to use a different framework where time evolution is described... by what is called unitary evolution...which in one of the most familiar descriptions is the evolution according to the Schrodinger equation: deterministic, time symmetric and local. These are exactly the same words I used to describe classical physics.

However this is not the entire story... In addition we require what is called the "reduction of the state vector" or "collapse" of the wave function to describe the procedure that is adopted when an effect is magnified from the quantum to the classical level...quantum state reduction is non deterministic, time-asymmetric and non local...The way we do quantum mechanics is to adopt a strange procedure which always seems to work...the superposition of alternative probabilities involving w, z, complex numbers...an essential ingredient of the Schrodinger equation. When you magnify to the classical level you take the squared modulii (of w, z) and these do give you the alternative probabilities of the two alternatives to happen...it is a completely different process from the quantum (realm) where the complex numbers w and z remain as constants "just sitting there"...in fact the key to keeping them sitting there is quantum linearity...

and he goes on to relate this linearity and superposition to the double slit experiment.


Since no one mentioned it, I will: another way to look at quantum versus classical is via 'locality':

...The Schrodinger equation is certainly deterministic; there is no doubt about it. However, the question whether it is also local is more subtle. Since the wave function lives in the configuration space and not in the ordinary 3+1 space, what does it even MEAN to be "local"?

In other words, classical physics is local and does not admit the 'entanglement' of quantum theory.

 

[bhobba]

These have all been very good replies - I learned a bit from every one.

One thing I want to add is an elaboration of my comment about the dynamics.

Classical physics is determined by the Principle Of Least Action and symmetries via Noethers Theorem.

Quantum Physics is determined by the principles in the paper I linked to on 5 reasonable axioms - which implies the Principle of Least Action, and the same symmetries as in Classical Physics.

Thanks
Bill

 

[Naty1]

I found several other related viewpoints in my notes, from various sources:

Physical action at the sub atomic scale is quantized.

In QM some observables don't commute giving rise to the uncertainty principle and a statistical/probabilistic formulation of theory.

The telltale difference between quantum and classical notions of probability is that the former is subject to interference and the latter is not. Brian Greene.

 

[Naty1]

I like demystifier's brief statement best, but with a one word addition:

Both quantum and classical mechanics can be described by a DETERMINISTIC wave function obeying a superposition principle and determining the probability amplitude. The difference is that wave function is complex for quantum mechanics, but real and positive for classical mechanics:

 

[shounakbhatta]

Hello All,

Thank you very much for all your responses.

Naty1, can you please send the original link for Roger Penrose's statement.

Thanks.

 

[Determinism89]

The evolution of the wave function is deterministic at all times, including the probability distribution of the Schrodinger Equation.

 

[ddd123]

What I could understand is that energy which comes in discrete packets is a major factor in quantum mechanics.

Quantization occurs as a consequence of the particle-wave duality. When a particle has a wave probability function associated to it, the wave's frequency determines the particle's kinetic energy. If the particle is bound by a potential, the wave is, loosely speaking, tied at the ends like a vibrating guitar string: this imposes a constraint on the possible energy values, they will be discrete; in the case of a box potential the energies that correspond to the normal modes of vibration.

If there is no potential, the wave is free so continuous energy values apply, as I've said in my first post.

 

[Annihilator]

It is not a difference!

one is wrong
both are wrong
or it is something else

 

[Naty1]

Wikipedia has a decent, short explanation:
http://en.wikipedia.org/wiki/Energy_..._energy_levels

...Quantized energy levels result from the relation between a particle's energy and its wavelength. For a confined particle such as an electron in an atom, the wave function has the form of standing waves. Only stationary states with energies corresponding to integral numbers of wavelengths can exist; for other states the waves interfere destructively, resulting in zero probability density.

Naty1, can you please send the original link for Roger Penrose's statement.

I replied offline, did not see the request here...for those interested...

As noted, it is from Roger Penrose lecture "Celebrating Stephen Hawking 60th birthday included in the book, THE FUTURE OF THEORETICAL PHYSICS AND COSMOLOGY, 4.6 The Measurement Paradox.