Why Must Quantum Physics Involve Discrete Quanta?

[TGlad]

Hello, I am fairly new to quantum physics, I am trying to understand where discrete quanta come from...

I think that energy levels and particle angular momenta (and momentum?) are all quantised in quantum theory. Is there a simple explanation of why there must be discrete levels... is it some sort of unavoidable property of classical physics that it must be quantised at small scales... or is quantum theory just matching observed data at small scales?

I'm looking for a sort of intuitive and simple explanation of the core reason why there must be quanta and not a continuum.

Thanks for any help.

 

[Einj]

Questions like yours usually don't have an answer. Hustorically speaking, physicists (actually, Planck was the very first) needed to introduce quanta in order to explain some incoherencies in classical theories (for example the black body radiation and the ultraviolet catastrophe).
But this is just the way quanta were introduced in physics, the real reason of existence of the quanta is just that nature is like that! Nature has no "need" to be like it is, is our problem to understand how it works.

 

[TGlad]

OK, but there is certainly some degree to which quanta just have to exist (otherwise we get infinite power in certain calculations).

I wonder if both relativity and quantum theory could be derived from computability of the universe... special relativity at least basically derives from the need for a maximum speed of information flow (i.e. a computable universe), and if you get the ultraviolet catastrophe without quanta then maybe black-body radiation isn't computable.
Hmmm... anyway, thanks for the answer.

 

[ZapperZ]

You need to learn a bit more of quantum mechanics.

One of the FIRST thing we teach students in an intro QM class is to solve the Schrodinger equation for a "free particle". Try it if you can. You'll notice that the energy that the particle can attain is NOT quantized at all! It can have a continuous amount of energy.

Yet, this is what we obtain using a common formalism of QM, using the Schrodinger equation itself!

Secondly, do not make speculative posts such as deriving something "from computability of the universe..." This is in violation of the PF Rules that you had agreed to.

Zz.

 

[TGlad]

You need to learn a bit more of quantum mechanics.

That should be clear from my first sentence.
I am trying to learn what the root cause of quanta is, and if it is explainable to a person like me with interest in the area, but who isn't a QM student. There is a lot of material out there, but some questions just need a discussion.

Secondly, do not make speculative posts such as deriving something "from computability of the universe..." This is in violation of the PF Rules that you had agreed to.
Zz.

I'm not proposing a new theory, just wondering something to aid in my understanding. The point was by analogy, that if special relativity could be derived from some principle (rather than the observation that light speed is the same in all inertial frames) then similarly, is there some principle which indicates that there must be quanta of energy in a universe, rather than just observational evidence.

Einj I think answered this by pointing out the ultraviolet catastrophe, so thanks Einj.

 

[Zarqon]

The quantization is usually a result of a particular boundry condition. For example, the frequency of a photon is not quantized when it's free, but if you put it into a cavity, you enforce additional boundry conditions, and you get quantized frequencies, the ones that are compatible with the length of the cavity.

It's the same for energy levels in an atom. A free electron has no space quantization, but when it is bound to an atom, only paths where its wavefunction interfere constructively with itself upon "roundtrips" are allowed (the others have zero probability due to destructive intereference of the probability amplitudes). This is a periodic boundry condition that causes quantization and descrete energy levels.

 

[TGlad]

Ah I see. So, hmmm, quanta are only arising in this explanation when there is a cavity / boundary condition... and photons are normally quantised because they are only released from an electron jumping between these quantised energy states.

Now I understand what ZapperZ was saying.

 

[ZapperZ]

Ah I see. So, hmmm, quanta are only arising in this explanation when there is a cavity / boundary condition... and photons are normally quantised because they are only released from an electron jumping between these quantised energy states.

Now I understand what ZapperZ was saying.

Actually, your understanding is still incorrect:

1. Photons are created NOT just from "electron jumping between quantized states". If that is true, your incandescent light bulb won't work, and the synchrotron light sources will go dark!

2. Light still comes in discrete quanta - photons.

3. The RANGE OF ENERGY that this light can have is the one that can either be quantized, or not.

Zz.

 

[TGlad]

1. OK, I didn't mean that electrons jumping between states was the only way they could be generated

2. In other words it is a small 'wave packet' rather than a continuously emitted wave... I assumed this was simply because the electron jumping energy state takes tiny amount of time (or perhaps better to say it occurs at an uncertain time within a small time window).

3. Yes, agreed

 

[Naty1]

Hello TGlad...

I'm looking for a sort of intuitive and simple explanation of the core reason why there must be quanta and not a continuum.

There is no 'fundamental' final explanation of the exact sort you seek...it's what we observe!
but we can offer rather keen insights that have been developed over the years. It does take some time to adapt from classical to quantum thinking. For one thing, the quantum mathematics that best describes what we observe has discrete probabilities...based on 'h'.

You've already discovered that the Schrödinger equation, which describes the continuous time evolution of a system's wave function, is deterministic. However, the relationship between a system's wave function and the observable properties of the system appear to be non-deterministic…

Max Planck discovered physical action at small scales takes place in discrete steps, not continuous ones...hence the 'h' Planck's constant. Action at the sub atomic scale is quantized... For example, the wave function of an electron in free space can take on continuous values, but when in an atomic orbital [or an atom in a lattice for example] is constrained to discrete values...quantized energy states...This is one of the 'weird' aspects of quantum mechanics. Not only is the energy discrete, but it changes energy in different settings...the electron reflects the constraints imposed by the system it inhabits...we say the degrees of freedom change from structure to structure.

Here is a way to visualize that classically: take a loose string and dangle it around and it moves continuously...moves in wave form without any particular frequency. Now string it in a violin and stretch it tight...it's movement is constrained and it takes on only resonant frequencies..many frequencies are 'eliminated'...cannot appear. Tighten the string and the resonances change! This means the energy of the vibrations is constrained...limited. The following quote is from Roger Penrose [the mathematical physicist] celebrating Stephen Hawking’s 60th birthday in 1993 at Cambridge England...he was addressing the elite of the physics world...this description offered me a new perspective 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"..

So key differences between the classical and quantum world are superposition and complex numbers in our models. This 'strange procedure' describes what we observe!

As Richard Feynman says: " We have to accept nature as she is, absurd."