What is the Definition of Quantum Physics?

[zastras]

TL;DR Summary

"Physics of the small" is rather vague.

Is there a precise definition for the field? That is what I am after, since I am rather annoyed by the fact I currently do not have an unified view of the theory; having a one-liner helps me a lot in better understanding. So far there seems to be a split between an "old" quantum physics, which began with Max Planck when he used the word "quanta" in "quanta of matter and electricity", in 1901; and a "new" quantum physics that appears to use the word "quantum" to refer to quantities of even more "things", like energy. Wikipedia defines quantum as "a quantum (plural quanta) is the minimum amount of any physical entity (physical property) involved in an interaction"; which is perhaps the best I could find so far, but the issue I have with it are the words "physical entity"; is this part of the terminology of this field?

A lot of results in .edu sites points to articles attempting to simplify the concept for an intuitive understanding of the field, which works in a classroom but doesn't work when studying the subject on your own. The best I can derive from the little I have read is that quantum physics is the field that studies the phenomena of the smallest quantities of "something" found in nature, but that does not give anything that specifies what the "somethings" are, nor what are studied about them.

 

[vanhees71]

Today quantum physics is all of physics except gravity. It describes the known matter as consisting of fundamental constituents of the Standard Model (quarks and leptons as the "matter particles", the gauge bosons of the strong and the electroweak interaction, and the Higgs boson).

 

[fresh_42]

Today quantum physics is all of physics except gravity. It describes the known matter as consisting of fundamental constituents of the Standard Model (quarks and leptons as the "matter particles", the gauge bosons of the strong and the electroweak interaction, and the Higgs boson).

Is it valid to summarize it as
$$
\operatorname{QM} \text{ (framework) } \subseteq \left.\begin{align*}
\operatorname{QED}\\\operatorname{QCD}
\end{align*}\right\} \subseteq \operatorname{QFT} \subseteq \text{relativistic} \operatorname{QFT}
$$
?

 

[PeroK]

Summary:: "Physics of the small" is rather vague.

To give some specific examples of things studied in QM:

There are atoms (Hydrogen, Helium, Lithium etc.) They are quantum mechanical systems and one of the main things that is studied is the spectrum of each atom (and molecule):

https://en.wikipedia.org/wiki/Emission_spectrum

Electrons are one of the most important elementary particles and they are studied using the Schroedinger and Dirac equations. Of particular interest is that of electron spin:

https://en.wikipedia.org/wiki/Spin_(physics)

This is also a quantum mechanical theory of light, called QED (Quantum Electrodynamics). Richard Feynman wrote a popular book about this:

https://en.wikipedia.org/wiki/QED:_The_Strange_Theory_of_Light_and_Matter

Those are perhaps three of the most important things studied in QM, but there are hundreds of others.

 

[Dale]

Summary:: "Physics of the small" is rather vague.

Is there a precise definition for the field? That is what I am after

I would say that the precise definition of modern QM is the Wightman axioms (https://en.m.wikipedia.org/wiki/Wightman_axioms) and the associated mapping between the math and experiments.

having a one-liner helps

I don’t think that “precise” and “one-liner” are compatible desiderata

 

[zastras]

Thank you for the answers so far. This helped me come up with something not as loose but still points to its sub-fields, and that satisfies me. Point out if there are errors here; I appreciate any extra pointers.

Quantum physics is the field that studies the quanta in a physical system (where elements defined in the Standard Model might be present). This physical system is mathematically defined in Quantum Field Theory.

 

[PeroK]

Understanding what Quantum Mechanics is involves more than finding a soundbite. There are no prizes for describing quantum mechanics in thirty words or fewer.

 

[Frabjous]

There are no prizes for describing quantum mechanics in thirty words or fewer.

I thought that Schrodinger and Dirac did for doing it in less than 30 characters

 

[dextercioby]

Is it valid to summarize it as
$$
\operatorname{QM} \text{ (framework) } \subseteq \left.\begin{align*}
\operatorname{QED}\\\operatorname{QCD}
\end{align*}\right\} \subseteq \operatorname{QFT} \subseteq \text{relativistic} \operatorname{QFT}
$$
?

It would rather be:
$$
\operatorname{QM} \text{ (framework) } \subseteq \begin{align*}
\operatorname{Theoretical Standard Model of Particle Physics}
\end{align*} \subseteq \text{relativistic} \operatorname{QFT} \subseteq \operatorname{QFT}
$$

So SM (and its subtheories, EW + QCD) is the most famous example of relativistic QFT. The last inclusion (opposite of yours) is needed to allow the existence of the so-called „non-relativistic (finite temperature) QFT” which aims to describe physics at a non-elementary level and in a non-relativistic regime using methods of relativistic QFT (i.e. creation and annihilation operators, for example).

 

[Frabjous]

It would rather be:
$$
\operatorname{QM} \text{ (framework) } \subseteq \begin{align*}
\operatorname{Theoretical Standard Model of Particle Physics}
\end{align*} \subseteq \text{relativistic} \operatorname{QFT} \subseteq \operatorname{QFT}
$$

So SM (and its subtheories, EW + QCD) is the most famous example of relativistic QFT. The last inclusion (opposite of yours) is needed to allow the existence of the so-called „non-relativistic (finite temperature) QFT” which aims to describe physics at a non-elementary level and in a non-relativistic regime using methods of relativistic QFT (i.e. creation and annihilation operators, for example).

I thought that beyond the standard model was still an empty set …

Apologies for two snarks in a row.

 

[dextercioby]

I thought that beyond the standard model was still an empty set …

Apologies for two snarks in a row.

Yes, but he is a mathematician, so this reply was meant in the same vein as his. We have the set of QF theories, which we partition in two (specially relativistic and non-specially relativistic). From the specially relativistic, we select the SM and leave out some Chern-Simons, non-linear QED, perturbative (linear) quantized gravity, etc.

 

[mpresic3]

I have never found Wikipedia helpful in cases like this one, where a large organized body of knowledge is digested and compressed until most of it is at best, misleading and at worst, completely wrong. For example, Chemistry can be said to be the "physics" of the small. Doesn't chemistry study atoms, the smallest building blocks of matter? Why aren't atoms considered quanta. They fit the definitions provided by wikipedia.
I also take issue with the definition that physics today except for gravity is all quantum mechanics. For one thing, there are efforts to give gravity a quantum treatment. Alternatively, there are many papers in physics in transport theory, and plasma physics, and chaos where the treatment is not quantum mechanical.

One possible interpretation which may or may not be helpful is the quantum is not the minimum amount of matter, or the minimum amount of energy, but it is the minimum amount of action. You will need to know more physics to get an idea of what the action means. As they said in thse 1960's go where the action is.

The best way to start learning quantum physics, is to find a elementary textbook, or a tutor. Most books I am acquainted with will give you a better idea after the first chapter, than can be obtained through wikipedia. After studying a few more chapters, you will know even more. After studying a few more textbooks some more advanced, you will learn enough to see why the wikipedia article is awful.

In general, I have known subject experts who have corrected Wikipedia with accurate information and their contribution has lasted a day or two, only to be taken down later, with incorrect information. Fifty years ago, my high school teacher said do not ever use an encyclopedia article as a reference as it is not a scholarly source of information. I think this is true to this day. Encyclopedias (including Wikipedia) are OK (perhaps) to get background information, nothing more.

 

[vanhees71]

To give some specific examples of things studied in QM:

There are atoms (Hydrogen, Helium, Lithium etc.) They are quantum mechanical systems and one of the main things that is studied is the spectrum of each atom (and molecule):

https://en.wikipedia.org/wiki/Emission_spectrum

Electrons are one of the most important elementary particles and they are studied using the Schroedinger and Dirac equations. Of particular interest is that of electron spin:

https://en.wikipedia.org/wiki/Spin_(physics)

This is also a quantum mechanical theory of light, called QED (Quantum Electrodynamics). Richard Feynman wrote a popular book about this:

https://en.wikipedia.org/wiki/QED:_The_Strange_Theory_of_Light_and_Matter

Those are perhaps three of the most important things studied in QM, but there are hundreds of others.

That's of course true, but one must not forget that QT also includes many-body physics, describing matter from the usual one around us (condensed-matter physics, mostly non-relativistic many-body QM, although some topics like the chemistry of the heavier atoms also need relativistic corrections) as well as matter "under extreme conditions" such as neutron stars and the strongly interacting matter created in heavy-ion collisions (both very closely related).

QT is the overarching conceptual framework of all of physics, and not only for the most fundamental level of elementary particles. The only thing it cannot yet satisfactorily describe is the gravitational interaction. IMHO I think the reason for this is that we have no clear hints from observation what quantum effects in this context really are, because the classical description with general relativity applies to all phenomena, where the gravitational interaction plays a significant role, i.e., mostly with astronomical objects from stars, galaxies, and finally cosmology.

 

[vanhees71]

It would rather be:
$$
\operatorname{QM} \text{ (framework) } \subseteq \begin{align*}
\operatorname{Theoretical Standard Model of Particle Physics}
\end{align*} \subseteq \text{relativistic} \operatorname{QFT} \subseteq \operatorname{QFT}
$$

So SM (and its subtheories, EW + QCD) is the most famous example of relativistic QFT. The last inclusion (opposite of yours) is needed to allow the existence of the so-called „non-relativistic (finite temperature) QFT” which aims to describe physics at a non-elementary level and in a non-relativistic regime using methods of relativistic QFT (i.e. creation and annihilation operators, for example).

I would put QFT to the very left, because it's the most general formulation of what I'd call QT for both relativistic and non-relativistic QT. I'd reserve QM for non-relativistic QT in the first-quantization approach.

 

[PeroK]

It would rather be:
$$
\operatorname{QM} \text{ (framework) } \subseteq \begin{align*}
\operatorname{Theoretical Standard Model of Particle Physics}
\end{align*} \subseteq \text{relativistic} \operatorname{QFT} \subseteq \operatorname{QFT}
$$

You need a Venn diagram ...

 

[gentzen]

I'd reserve QM for non-relativistic QT in the first-quantization approach.

This is probably why dextercioby and fresh_42 explicitly wrote "QM (framework)" to make it clear what they mean. So I guess you prefer to write "QT (framework)" for what they mean. Or do you want to exclude the framework itself entirely, because it doesn't yet include physical notions like energy, momentum, time, space, action, or angular momentum?

 

[vanhees71]

You can formulate QT without a spacetime model first, although it's hard to make physical sense of its operations. E.g., you can just use a 2D Hilbert space with the corresponding self-adjoint operators. Some modern textbooks do this and refer to the spin observable of spin-1/2 particles or polarization observables of a single photon. Of course to get the underlying physical intuition you need a spacetime model to make sense of what spin means physically. As a purely mathematical scheme of course you don't need this intuitive part.

 

[Demystifier]

Is it valid to summarize it as
$$
\operatorname{QM} \text{ (framework) } \subseteq \left.\begin{align*}
\operatorname{QED}\\\operatorname{QCD}
\end{align*}\right\} \subseteq \operatorname{QFT} \subseteq \text{relativistic} \operatorname{QFT}
$$
?

No. Relativistic QFT is a subset of QFT, not the other way around. Furthermore, QM as a framework is even bigger, it entails nonrelativistic particle QM, all kinds of QFT, quantum gravity, string theory ...

 

[f95toli]

It is perhaps worth pointing out that the fact that there is no general agreement of what we mean by "quantum physics" is not just a "philosophical "problem" but has practical implications. It also means that the definition of "quantum technology" (which usually is understood to mean "applications of quantum physics") is unclear.
There are many practical reasons for why this actually matters; one obvious example is that different funding agencies define "quantum" in different ways so if there is a call for proposals in the area of "Quantum technology", what type of proposals are eligible? A more recent problem has been companies that claim to be selling products which utilise "quantum" somehow; which -in some cases- could be classified as false advertising.
"Quantum materials" such as 2D materials (e.g. graphene) and topological insulators are also a of a grey area.

Sometimes you see applications of quantum physics being divided into "1.0" which refers to things like transistors, lasers and "2.0" which uses entanglement and/or superposition of states. I am not convinced that this distinction is helpful since "2.0" also strictly speaking includes e.g. atomic clocks which are "old" technology; but I have seen funding calls specifically refer to "2.0".

There are now attempts to start coming up with internationally accepted "official" definitions (I am involved in some of these efforts) but in reality these are mainly meant for things like technical specifications and standards; I seriously doubt that they will have any impact on how the terms are uses in everyday situations.

 

[A. Neumaier]

the fact that there is no general agreement of what we mean by "quantum physics"

This is not a fact but fiction, of the same kind as claiming there is no general agreement of what biologists mean by "life".

All physicists know what is meant by "quantum physics", though it is difficult to give a comprehensive definition of it in a single sentence.

 

[f95toli]

All physicists know what is meant by "quantum physics", though it is difficult to give a comprehensive definition of it in a single sentence.

In my experience that is not true. There are numerous examples of people "defining" it as "the physics of atoms" or something similar; presumably because that is how quantum physics is often taught in undergraduate courses.

In practice, if you talk to people working on e.g.. quantum materials they will often have a very different understanding of the "scope" of quantum physics than if you speak to someone working on quantum computing.

So yes, coming up with simple definitions is one issue, but the "problem" does go deeper than that.

 

[PeroK]

In my experience that is not true. There are numerous examples of people "defining" it as "the physics of atoms" or something similar; presumably because that is how quantum physics is often taught in undergraduate courses.

In practice, if you talk to people working on e.g.. quantum materials they will often have a very different understanding of the "scope" of quantum physics than if you speak to someone working on quantum computing.

So yes, coming up with simple definitions is one issue, but the "problem" does go deeper than that.

There's not necessarily a problem. Different people in IT will give very different definitions of what computers do. Things as broad as QM and IT are too complex to be encapsulated.

 

[A. Neumaier]

In practice, if you talk to people working on e.g.. quantum materials they will often have a very different understanding of the "scope" of quantum physics than if you speak to someone working on quantum computing.

This is because the true scope is so large that hardy any physicist knows the whole scope. So people repeat the 1-line approximations to a definition that they learned when they were introduced to quantum physics, modified by their own experience. This is not unlike what happens for the definition of any other complex subject.

 

[Dale]

This is because the true scope is so large that hardy any physicist knows the whole scope. So people repeat the 1-line approximations to a definition that they learned when they were introduced to quantum physics, modified by their own experience. This is not unlike what happens for the definition of any other complex subject.

Which is why "precise" and "one liner" are incompatible.

 

[f95toli]

There's not necessarily a problem. Different people in IT will give very different definitions of what computers do. Things as broad as QM and IT are too complex to be encapsulated

I completely agree that it is usually not a problem when say speaking to other scientists; but it does become a problem when e.g. a company want to persuade an investor that their product is a "quantum technology".

I spend quite a lot of time talking about applications of quantum physics/technology to non-scientists and the fact that it is so hard to pin down what the "scope" is does cause problems. For example, I am currently involved in planning a meeting for companies and people from academia working on "quantum components". People no familiar with the UK "quantum ecosystem" have (for obvious reasons), very different ideas of what a "quantum component" is.

Again, I am not saying that this problem has a solution; all I wanted to highlight that it IS a problem.

 

[vanhees71]

Then my coffee mug is also quantum technology, because it's a pretty stable piece of matter and that can only be explained by quantum mechanics. A good old light bulb s then also quantum technology, because it's thermal spectrum can only be explained with quantum mechanics. ;-)).

But it's indeed a problem in communication. E.g., once I looked for a book on quantum optics, went to the library and, being in a hurry not looking into the books, I've also borrowed one with the title "Photonik" (German for "photonics" of course). To my surprise it was just a book on classical wave optics ;-)).

 

[A. Neumaier]

it does become a problem when e.g. a company want to persuade an investor that their product is a "quantum technology".

well, across the street where I live there is someone selling some form of quantum therapy... The buzzword 'quantum' sells well, independent of what is actually behind!

 

[mpresic3]

I think I am paraphrasing Feynman correctly when he said something like, No one understands really quantum mechanics.
Most physicists use QM as a tool. It is easy to get too caught up in the philosophy. I understand the idea to read every sentence and not move on until you understand everything, whether in wikipedia or in many textbooks. In QM, I think it is more useful to get on with the business to learn QM in a workman's fashon. In my case, I started with a physical chem course, and that course emphasized the Hydrogen atom, and some spectroscopy. My physics courses emphasized mathematical formalism as well as the atomic structure.
In looking at the Wikipedia again, I find you can get a lot out of it, as long as you do not read every sentence too literally. I suppose many articals inside and out of wikipedia should not be read too literally, so I have softened my attitude towards the wikipedia article in question.
(I still think it treats the action very lightly, hardly even mentioning the action, and h, after all has units of action. So do energy-time and position-momentum, and angular momentum-angle, all of which have units of action)
My recommendation if you are intent on learning QM is to learn through classes, textbooks, and go lightly on the philosophy at least in the beginning. I find most classes have no problem in this regard, because the limited time in the semester causes the students and professors to be goal-oriented, and not hung up in matters that are hard to settle.
Otherwise, you can always find a grandmother. There are no shortage of students who were instructed to demonstrate their understanding by explaining these most complicated subjects to their grandmother.

 

[DennisN]

Summary:: "Physics of the small" is rather vague.

Is there a precise definition for the field? That is what I am after, since I am rather annoyed by the fact I currently do not have an unified view of the theory; having a one-liner helps me a lot in better understanding.

I find it very difficult to summarize it in a one-liner (or a couple of one-liners).

Sometimes a picture is worth a thousand words, and sometimes that picture also contains a lot of words.

Like this picture (from http://hyperphysics.phy-astr.gsu.edu/hbase/quacon.html):

As you may understand from this picture quantum physics is a pretty complicated and big topic.

 

[DennisN]

Summary:: "Physics of the small" is rather vague.

Is there a precise definition for the field? That is what I am after, since I am rather annoyed by the fact I currently do not have an unified view of the theory; having a one-liner helps me a lot in better understanding.

I find it very difficult to summarize it in a one-liner (or a couple of one-liners).

I suddenly got inspired to give it a try anyway:

Quantum physics is the study of nature at the currently most fundamental level (including particles, particle systems, atoms, fields etc). The behavior of quantum systems also have significant implications for other fields of science above this fundamental level, e.g. chemistry.

 

[vanhees71]

I find it very difficult to summarize it in a one-liner (or a couple of one-liners).

Sometimes a picture is worth a thousand words, and sometimes that picture also contains a lot of words.

Like this picture (from http://hyperphysics.phy-astr.gsu.edu/hbase/quacon.html):

View attachment 289930

As you may understand from this picture quantum physics is a pretty complicated and big topic.

The picture gets much more clear and consistent when you eliminate outdated precursors of modern quantum theory.

The shortest characterization is: Quantum Physics encompasses all of the known physics today except the gravitational interaction.

 

[Morbert]

Throwing my soundbite on the pile

"Quantum" is the generalising of the event algebra of a theory. A theory of mechanics of a system is made more general with a theory of quantum mechanics. A theory of statistical mechanics is made more general with a theory of quantum statistical mechanics. A field theory is made more general with a quantum field theory. A theory of gravity is made more general with a quantum theory of gravity. In each case, we move from a less general algebra to a more general algebra. More specifically, abelian algebras are generalised to non-abelian algebras. This is the primary distinction between classical and quantum theories.

This generalising is typically associated with particular scales and discretisations of phenomena. but is not a necessary condition. If a theory of finance modeled with some abelian event algebra is made more general with a non-abelian event algebra, you would have a theory of "quantum finance".

 

[vanhees71]

"Quantum economics" is a buzzword you already find here and there ;-)).

https://en.wikipedia.org/wiki/Quantum_economics

 

[CelHolo]

This generalising is typically associated with particular scales and discretisations of phenomena. but is not a necessary condition. If a theory of finance modeled with some abelian event algebra is made more general with a non-abelian event algebra, you would have a theory of "quantum finance".

A good example is quantum cognition used in studying survey statistics or other psychological data where the event algebra is generalised to a non-commutative one.

 

[A. Neumaier]

A good example is quantum cognition used in studying survey statistics or other psychological data where the event algebra is generalised to a non-commutative one.

Please give a key reference which explains why the noncommutative setting is useful.