# Fundamental difference between quantum physics and classical physics

1. Dec 10, 2013

### 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 writen 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

2. Dec 10, 2013

### 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!

3. Dec 10, 2013

### Staff: Mentor

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

4. Dec 10, 2013

### 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.

5. Dec 10, 2013

### 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

6. Dec 10, 2013

### 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.

7. Dec 10, 2013

### 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.

8. Dec 10, 2013

### 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!

9. Dec 10, 2013

### ChrisVer

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...

10. Dec 11, 2013

### 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.

11. Dec 11, 2013

### 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:

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':

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

12. Dec 11, 2013

### Staff: Mentor

These have all been very good replies - I learnt 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

13. Dec 12, 2013

### 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.

14. Dec 12, 2013

### Naty1

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

15. Dec 13, 2013

### 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.

16. Dec 13, 2013

### Determinism89

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

17. Dec 15, 2013

### ddd123

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.

18. Dec 15, 2013

### Annihilator

It is not a difference!

one is wrong
both are wrong
or it is something else

19. Dec 15, 2013

### Naty1

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

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

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

Last edited by a moderator: May 6, 2017