# Can Newton's laws be explained by Quantum Physics? [duplicate]

I have only basic knowledge of physics. Could you please explain to me if a "Quantum" laws can theoretically (perhaps in the future?) be used to explain everything in macro levels?

I'm having problems to understand how we can have "two physics" at the same time. are Newton's laws only a simplification?

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## marked as duplicate by Ben Crowell, Waffle's Crazy Peanut, Qmechanic♦May 26 '13 at 15:46

Ideally, Newton's laws would result from taking a "classical limit" of QM, but it's surprisingly tricky - see this question and the links therein physics.stackexchange.com/questions/32112/… –  twistor59 May 26 '13 at 12:09
Possible duplicates: physics.stackexchange.com/q/17651/2451, physics.stackexchange.com/q/32112/2451 and links therein. –  Qmechanic May 26 '13 at 13:12
voting to close as a duplicate of physics.stackexchange.com/q/32112/4552 –  Ben Crowell May 26 '13 at 14:05

You already have several excellent answers, but from your question I suspect you are hoping for an answer that is a bit less mathematical and more about just how the transition between quantum physics and ordinary large-scale physics takes place.

For most everyday phenomena, including chemistry and the way behaves and interacts with matter light (radio, light, X-rays, gamma rays), quantum mechanics already predicts classical phenomena with exquisite precision, as best we can tell.

QED

The "as best we can tell" qualifier is because the computational cost of doing so is horrendous and grows larger so quickly that you have to start approximating very early in the process. The theory that provides this level of precision -- arguably the most precise predictive theory ever developed -- is something with the ungainly moniker of Quantum Electrodynamics, or QED for short. The variant of QED that Richard Feynman co-received a Nobel Prize for is the one that led to Feynman diagrams, those little stick-figure diagrams that show electrons as arrows and light particles (photons) as squiggles.

QED also shows beautifully how such odd physics can lead to our ordinary world: Through probabilities. Many very strange things are possible in quantum mechanics, including for example light moving around in random loops and turns instead of in a straight line. QED even allows you to calculate the probability of such things, and then build experiments to very that such oddities really do exist!

Reasonable Probabilities

But what happens on the scale of ordinary humans is that these oddly quantum scenarios quickly become so incredibly minute that they simply don't happen, at least not within the life span of the universe. So light, for example, seems to go in straight lines for the most part (even on our scale that's not entirely true) because the probabilities for all those odd paths, or even paths slightly off from straight, become vanishingly small.

Added all together, this collection of "reasonable probabilities" for many, many atoms and particles of light becomes what we think of as ordinary or classical physics. Surprisingly, the transition between the two via probabilities is quite smooth and not abrupt in any way. We just don't notice that transition much because, except for certain large-scale phenomena such as metallic mirrors that seem "classical" only because we have simple rules to approximate how they work, all of these transitions from strange quantum physics to the comparative simplicity of classical physics take place at very small scales, typically near the size and mass scale of atoms and their constituent particles.

QCD: Going Nuclear

For nuclear phenomena, a similar theory that by intentional analogy called QCD (for Quantum Chromodynamics) does a pretty good job of predicting why particles like protons and neutrons -- and many other less common particles -- behave like they do. That theory is even more difficult to compute than QED, however.

The Standard Model

Beyond that is the Standard Model, an intensely quantum-based model that ties together the entire zoo of particles that we see coming out of particle colliders. Although the Standard Model addresses only a very narrow and exotic range of predictions of phenomena that we never encounter directly in everyday physics, it nonetheless is critical for explaining much of how the large-scale structure of the universe emerges. Through this roles in defining the universe in which we exist, the Standard Model also helps explain how quantum phenomena lead (much less directly!) to what we call the classical world.

Gravity

So what's missing? Gravity!

Gravity remains ornery and uncooperative in terms of its quantum description providing precise predictability. That's not from any lack of trying! Speculations on quantum gravity are in fact the darling of many popular programs and ideas about physics. But because the original theory of general relativity by a fellow named Einstein was a purely geometric theory without a shred of quantum anything to it, it remains to this day a theory that is difficult to fold into the kind of pure-quantum framework exemplified by the spectacular success of QED. That might not be a problem if general relativity was an inaccurate or approximate theory, but that's not the case: Like QED for its domain of electrons and light, general relativity for its domain of the overall structure of a universe with gravity remains spectacularly effective and predictive for what we can see.

Conclusion

So, for much of the world, and all of the parts of it that we see and interact with on a daily basis, the transition between quantum physics and ordinary physics is already surprisingly well understood from a mathematical perspective, even if philosophical views are far from being in agreement: It's all just a matter of probabilities, with very small things allowing more (and more strange) things to go on, and classical physics just being the sum of probabilities that begin to get very specific and very selective at larger scales. There are holes still, sure, but it seems likely that even when those holes are someday filled, that theme of higher probabilities providing the transition will remain.

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I'm having problems to understand how we can have "two physics" at the same time. are Newton's laws only a simplification?

To start with Nature does not have "two physics" . The underlying substrate of all physics is quantum mechanical. Depending on the dimensional regimes of measurement different mathematcal frameworks have been validated to work to the necessary accuracies.

The term " two physics" should be modified to "different physical frameworks for observational data", because they are not even two, they are many more.

classical mechanics to quantum mechanics

classical electrodynamics to quantum electrodynamics.

classical statistical mechanics to quantum statistical mechanics

and a number more esoteric formulations for special cases like fluids and superfluids, plasma, etc.

In some cases it is simple or doable to show how the classical emerges from the quantum level and in some cases harder or not yet done.

What an educated person with some knowledge of modern physics should keep in mind is that the underlying foundation of all is quantum mechanical. Heisenberg's Uncertainty Principle defines the regions of validity

When distances times momenta are large enough, the quantum mechanical framework is irrelevant and the modeling of the data with the various classical mathematical tools is valid. In regions where the numbers are small, quantum mechanical models have to be used.

One has to keep in mind that all physical theories are mathematical models of our data, and are valid as long as they predict new phenomena and are not invalidated by any. Thermodynamics emerges from statistical mechanics and quantum statistical mechanics, the regions of overlap are defined and known. This does not mean that there are two physics. Just that there are two physical theories appropriate for the region of validity of the variables studied.

Currently physicists believe that the ultimate level is the quantum mechanical level because of various very strong consistency laws that would be violated if there existed a level below the QM level. All other theories are emergent and based on the QM substructure and laws.

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Nice answer. I am just wondering if since it also depends on the scale one considers, which laws describe the physics observed, if in some cases classical limits can be obtained from coars graining or renormalizing the microscopic quantum laws ...? This is just a potentially very stupid thought :-) –  Dilaton May 26 '13 at 13:14
@Dilaton well, as twistor says it is not that simple. One can also think of the poisson brackets, physics.stackexchange.com/questions/19770/… classical and quantum, but when one wants to look at the mathematics it needs elbow grease. –  anna v May 26 '13 at 13:38
@Dilaton a very readable account of what you're alluding to (coarse grained decoherent histories) is in Jonathan Halliwell's paper –  twistor59 May 26 '13 at 15:07
Thanks @twistor59, that looks interesting! –  Dilaton May 26 '13 at 19:40

Indeed, classical mechanics emerge from quantum mechanics. Newton formulated the mechanics as the Newtons laws at first, people only later showed their equivalence to more fundamental laws - the Lagrange principle, Hamilton principle and principle of least action. It is still the same mechanics, but formulated in a more profound way.

The quantum mechanics were as well formulated in an unique way at first, and only in later years of 20th century Richard Feynmann realized the path integral formulation, which is actually analogous to principle of least action and finally showing the direct link between quantum mechanics and classical mechanics.

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Classical mechanics (point particle) can follow via Ehrenfest Theorem:

$$\vec{p}=m\vec{v}$$

$$\vec{F}=-\nabla V$$

holds for a system with a (quantum mechanical) Hamiltonian

$$H=\frac{p^2}{2m}+V(\vec{r},t)$$

via expectation values

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