I receive much crackpot email. There is a very common misunderstanding often central, one I have not seen a good answer to anywhere. This is partially due to that few who write about physics counter crackpot theories well. Allow me to explain this point with a new personal story before explaining why energy seems quantized, why photons seem to be little packets of energy rather than a concept that describes quantum interactions more or less well.

Bad answers feed the perception of establishment conspiracy. I supplied many examples over the years. For yet another example: Joy Christian’s nonsense is still actively argued against by established scientists wasting their time on internet forums, but their own theories are worse than Joy’s at a crucial point. Ask: “How many parallel worlds does your theory imply?” Joy’s answer would be that there is only one “real” world and that is also the number that his (for many other reasons idiotic) theory implies.

At least two or three of the scientists who argue against Joy also publicly support my own work and the Quantum Randi Challenge for example, so it may seem that we are on one team. However, those scientists, more established than me, refuse to think about how many worlds their theories imply (I asked them several times). Some claim that it is only a single world, but their theory implies either multiple worlds or solipsism.

Crackpots like Joy sense this mistake more or less clearly, because they are obsessed with certain realisms. In a well defined sense, Joy’s nonsense is at the most crucial point less nonsensical than what established scientists who support me counter with. Why should people like Joy take them seriously?

Usually, physics crackpots are anti-quantum nowadays; they do no longer refuse Einstein’s relativity, but instead, Einstein is their hero now, because Einstein did also not understand the core of quantum mechanics in those early days of that theory, and it is quantum mechanics that seems to destroy realism worse than the relativity of time already destroyed it (not true, but it seems to most that way).

Einstein would have come around soon to understand ‘Everett relativity’ (which roughly means something like “parallel worlds”), because Everett relativity is the straightforward extension* of his own space-time relativity if you include not just all times but also all possibilities into the theory of everything.

But life is short, Einstein died, so quantum crackpots think that Einstein is on their side. Great, because Einstein’s relativity tells us that light is red-shifted relative to systems that move away from the light source. This implies that if there is even just the tiniest motion between two atoms, the light emitted by one atom could never be absorbed by the other, not if energy were quantized into little packets that cannot be divided.

Think about it: Assume one sodium atom emits an amount Delta = (E2 – E1), where E1 and E2 are the precise energies of the relevant energy levels of sodium atoms (in case energy is fundamentally quantized, the atom’s energies would be too!). The other sodium atom can thus also only receive precisely such an amount Delta. Then the atoms would have to be absolutely still relative to each other, or else the amount of energy Delta is slightly blue or red shifted for the second atom and could not be absorbed, because where is the tiny amount of difference in energy going to go if energy is thought of as occurring in little packets, especially if they are thought to have a fundamental minimum size?

Also, the visible lights’ wavelength (or its coherence length if you like that better) is a thousand times larger than the atom. The absorbing atom cannot know whether the whole length has a shape and thus energy that it can absorb. Once the whole wave has zipped by with light velocity, the atom may know that this photon could have been absorbed, but now it is too late.

Sure, you can describe a situation where all atoms absorb all photons and then spit them out immediately if they do not fit, and this is kind of what leads to the slow down of light in materials like glass, but that would not be what crackpots-for-naive-realism would enjoy (they want a simple reality) and the main problem is just pushed to somewhere less obvious in such a description. The problem is: If every part were a certain precise way, the way it “really happens to be”, nothing would ever fit with anything else perfectly enough to interact. The world could not be happening.

Here are the proper relevant explanations:

1) Only interaction is quantized by quantum mechanics. There are other types of quantization (e.g. string winding number, atoms), but they are not the quantization of quantum mechanics. Anything that appears quantized because of quantum mechanics, like for example energy in equations like Delta(E) = h * Frequency, is a manifestation of the quantization of interaction, and that is what the constant h is about. Usually, there is some periodicity of a parameter that supplies a boundary condition; here for example it is time that is periodical via the involved frequency. This periodic boundary condition is responsible for that the interaction-quantum shows up as if energy is quantized. Angle is always periodic; you are back where you started after turning around once. Therefore, angular momentum is quantized, *not* because it happens to be *also* quantized, but because the momentum along the circle reflects the interaction quantization (the momentum kind of interacts with itself as it is smeared along the circle, bumping into itself).

Interaction is not quantized into some god-given amount h either. That odd value this constant happens to have is due to our odd traditional units. Interaction is quantized simply because either two things interacted or not. Information is in some sense the fundamental substance of our stories, bits that are either 1 or 0, Yes or No. You cannot have half an interaction.

2) There are no “really existing” photons; according to Einstein, photons do not even have time to exist! Photons are fundamental in that they are almost not existing, not because they are little packets of fundamental energy; energy is not fundamental.

The “Delta” in the formula Delta = (E2 – E1) seems to indicate that Delta is no more but the difference between two levels, that is, a certain amount, a packet. That is often a convenient way to see it, but Delta comes ultimately from the quantum uncertainty relation. It is fundamentally not a difference, but a measure of uncertainty, often very close or equal to the standard deviation like in the following expression: E = (50 +/- 0.3) Joule. 50 Joule is here the average, sometimes written <E>, and 0.3 Joule is the standard deviation, sometimes written Delta(E).

Think of Delta as always deriving from an uncertainty like in E = <E> +/- Delta(E), even if it can be conveniently interpreted as a difference. Delta = (E2 – E1) is the uncertainty in the atom’s energy during emission.

3) Naïve realists say:

“The real world as such is precisely in some certain way, and the uncertainty is ours while the photon for example has whatever energy it happens to have and no other”.

Here is how that naïve worldview arises: The absorbing atom is very likely to move a little in some direction relative to the first atom. Nevertheless, there is a finite probability for it to absorb energy from the emitting atom, *because* the amount of energy is fuzzy (uncertain) and the velocity is fundamentally uncertain and the states of the atoms when emitting or absorbing, are fundamentally uncertain. Also the problem with the photon’s coherence length being thousands of atomic diameters is resolved by that the time of emission and the time of absorption and thus all positions are uncertain.

The coherence length is nothing but the position uncertainty of the light. All these parameters are fuzzy, because all the possible interpretations in terms of a classical “real” world, many possible worlds so to speak (no, I do not support a naive many world view!), are all involved in the quantum interaction. The correlations between the potentially observed outcomes restricts what is ultimately possible, thus leading to what appears to be physical “law” as if it is obeyed in spite of there being fundamentally no time to obey anything.

Now you may say: “How could energy ever be conserved if it is all that fuzzy?”

You must make measurements on the whole system including both atoms, in order to see how much energy may have been lost. All these measurements are all interactions that change uncertainties. Since you design the measurements to reduce the uncertainty about energy, the more accuracy you obtain, the more you cut out ever more possible worlds from the direct involvement in your uncertainty of interest (while uncertainty hugely grows somewhere else of course, just like entropy, in most other parameters that you are not interested in at that point).

The measurement interaction when measuring conserved quantities (like energy in this example, which is in general not conserved) is such that your reducing of uncertainty about the energy of the overall system selects those potential parts that are consistent with a conservation law. From all the possibilities for the emitting atom and all the possibilities of states for the absorbing atom, those that together do not conserve energy well enough are not going to show up together; they are no longer both together possible after your measurement.

Here an easier example: An experiment (the EPR setup) is constructed so that Alice always gets the opposite result of Bob's, but without there being a classical common cause like a pair of socks, where Alice would get the left sock whenever Bob gets the right sock. Here is what happens instead: Those Alice worlds that measure 1 will find themselves together with a Bob who measured 0. Those Alice worlds that measure 0 find themselves later with a Bob that measured 1. The result 0+1 = 1+0 is conserved to be 1, but not because Bob’s or Alice’s outcome is certain.

On the contrary, it can be conserved because they are both uncertain, because only then can the possible outcomes all pair up so that conservation appears with all possible pairs! (If Alice = 1 and Bob = 1 were actually certain, the result would be 1+1=2 instead; there would be no longer a way to conserve the sum to be 1 every time.)

* I have shown this to be the case by analysis of the EPR paradox [see
here and here], and Einstein would have seen this eventually, because he understood the light-cone formulation and was not obsessed with space-time foliations.

quantum light front page image credit: IOP