Understanding Quantum: The Particle/Number Duality

[Quotidian]

I am watching a good introductory account of quantum physics for a lay audience. I’m up to the part where it explains how Einstein introduced the idea of the quantum as the description of the particulate nature of light, as opposed to the generally-assumed wave nature of light. The narrative says that the quantum was conceived as ‘a stream of tiny bullet-like particles’.But the meaning of ‘quantum’ is clearly related to ‘quantity’, is it not? I seem to also recall that when Bohr discovered the discrete orbits into which electrons could jump, that these values were always in some way correspondent with whole numbers.

So, I’m wondering if the nature of ’quanta’ might not be better conceived as being like numbers, than like particles or objects, as such. It might seem a quibble, except for the fact that the reality of particles is object-like, but the reality of number is noetic i.e. only perceptible to an intelligence capable of counting. So in this sense, quanta are not really ‘particles’ of something, but ‘measures’ of something.

 

[Ibix]

The point Einstein was making is that light does not deliver energy continuously, but that there are discrete packets of energy delivered. The idea that these quanta are "bullet-like particles" is (at best) hopelessly antiquated, if not just wrong.

My knowledge of quantum physics isn't good enough to help with what the modern picture actually says. I'll report the thread and suggest it be moved to the quantum forum.

 

[Quotidian]

Thanks - although the expression ‘wave-particle duality’ still seems current.

 

[Wrichik Basu]

But the meaning of ‘quantum’ is clearly related to ‘quantity’, is it not?

Not quite. Say you have $100 in $1 denominations. Then each $1 note is a quantum, and 100 such quanta make up the total money.

Similarly, energy in the world comes in such discrete "packets". These packets are the quanta. A number of quanta make up the energy.

These will become clear when you study QM. For example, in the Harmonic oscillator, the energy of each level comes as integral multiple of some value. This value is the quanta of energy in this case, in a naive sense. The energy of each state is some integer multiple of this energy quantum.

In QFT, we have particles carrying fields, like the photon for EM field, gluon for strong interactions, Higgs boson for the Higgs field, and the not-yet-discovered graviton for gravity. These are the quanta of their respective fields.

 

[Borek]

Note: for a given system (harmonic oscillator, atom, molecule, something like that) energy is quantized and can take only well defined values. However, for other system these allowed energy values will be completely different, so if you look at the thing form other perspective for each energy you can find a system for which this energy is perfectly OK.

People sometimes think quantization is related to energy in general, which is not true.

 

[Wrichik Basu]

People sometimes think quantization is related to energy in general, which is not true.

Of course it's not true, but I used it as a simple example. The OP is currently at the layman level:

I am watching a good introductory account of quantum physics for a lay audience.

So I tried to make things simple.

 

[vanhees71]

Thanks - although the expression ‘wave-particle duality’ still seems current.

Unfortunately the expression is still used, particularly in popular-science writing. The big breakthrough (for almost all physicists at the time but not Einstein by the way) was the discovery of modern quantum mechanics by three different people (or in one case a collaboration):

(a) Heisenberg (with the vague idea, found famously on the island of Helgoland in summer 1925), Born and Jordan (with the worked-out math in terms of "matrix mechanics")

(b) Schrödinger 1926 (finding the same theory in terms of "wave mechanics"; he also very soon proved that the two formulations are equivalent)

(c) Dirac 1926 (writing down the theory in the most elegant form in a pretty representation independent way).

This modern quantum theory is the only one valid today and it once and for all got rid of pretty unsatisfying concepts like "wave-particle duality". The prize one has to pay is a pretty abstract formalism and the unavoidable introduction of a probabibilistic description of what's going on in nature, and it's not probabilistic as in classical statistical physics, where the probabilities only come into describe the incompleteness of our knowledge. In QT the probabilistic aspect is inherent in nature itself, and in fact a quantum system can never be in a state, where all possible observables on this system take definite values.

One of the most flawed ideas was Einstein's initial idea of "light quanta". The only thing still correct is that electromagnetic radiation of frequency $\omega$ can be absorbed and emitted by matter made of charged particles in "portions" or "quanta" of the size $E=\hbar \omega$. For electromagnetic fields a particle interpretation is very far from correct. A photon in the modern sense is a certain state of the electromagnetic quantum field, and it is not possible to define anything like a position observable for it.

This is different for massive particles, where you always can define a position observable, and under certain circumstances a particle picture becomes a good description.

 

[Quotidian]

Not quite. Say you have $100 in $1 denominations. Then each $1 note is a quantum, and 100 such quanta make up the total money.

Similarly, energy in the world comes in such discrete "packets". These packets are the quanta. A number of quanta make up the energy.

That is pretty well what I said - that a quantum is a ‘measure’ more than it is a ‘particle’. To extend your analogy, if currency was denominated against an actual unit - say, a gold coin of a particular weight - then you could say that this $1.00 coin is an object with a given value. But a quantum is not ‘an object’ in that sense; a $10.00 bill is a token of value, it too is not an object per se, or rather, the paper object only denotes a value. Maybe it really is more like a number, which is, so to speak, an object of thought.

As it happens, there was another Einstein quote at the end of that program, along the lines of ‘I have been thinking about what the quantum is for fifty years, and I still don’t know’. And if *he* didn’t know... ;-)

 

[Quotidian]

Unfortunately the expression is still used, particularly in popular-science writing...

Thanks. I have read Manjit Kumar’s Quantum, David Lindley’s Uncertainty, and several other books on the subject, which covers the history of the period quite well.