If you know a bit about quantum physics, you might have heard that everything is made out of particles. Mass comes from Higgs particles, gravity from graviton particles, and light and electricity and magnetism from photon particles. The particles are the “quanta”, the smallest possible units of stuff.
This is not really how quantum physics works.
You might have heard (instead, or in addition), that light is both particle and wave. Maybe you’ve heard it said that it is both at the same time, or that it is one or the other, depending on how you look at it.
This is also not really how quantum physics works.
If you think that light is both a particle and a wave, you might get the impression there are only two options. This is better than thinking there is only one option, but still not really the truth. The truth is there are many options. It all depends on what you measure.
Suppose you have a particle collider, like the Large Hadron Collider at CERN. Sometimes, the particles you collide release photons. You surround the collision with particle detectors. When a photon hits them, these particle detectors amplify it, turning it into an electrical signal in a computer.
If you want to predict what those particle detectors see, you might put together a theory of photons. You’ll try to calculate the chance that you see some specific photon with some specific energy to some reasonable approximation…and you’ll get infinity.
You might think you’ve heard this story before. Maybe you’ve heard people talk about calculations in quantum field theory that give infinity, with buzzwords like divergences and renormalization. You may remember them saying that this is a sign that our theories are incomplete, that there are parameters we can’t predict or that the theory is just a low-energy approximation to a deeper theory.
This is not that story. That story is about “ultraviolet divergences”, infinities that come from high-energy particles. This story is about “infrared divergences” from low-energy particles. Infrared divergences don’t mean our theory is incomplete. Our theory is fine. We’re just using it wrong.
The problem is that I lied to you a little bit, earlier. I told you that your particle detectors can detect photons, so you might have imagined they can detect any photon you like. But that is impossible. A photon’s energy is determined by its wavelength: X-rays have more energy than UV light, which has more energy than IR light, which has more energy than microwaves. No matter how you build your particle detector, there will be some energy low enough that it cannot detect, a wavelength of photons that gives no response at all.
When you think you’re detecting just one photon, then, you’re not actually detecting just one photon. You’re detecting one photon, plus some huge number of undetectable photons that are too low-energy to see. We call these soft photons. You don’t know how many soft photons you generate, because you can’t detect them. Thus, as always in quantum mechanics, you have to add up every possibility.
That adding up is crucial, because it makes the infinite results go away. The different infinities pair up, negative and positive, at each order of approximation. Those pesky infrared divergences aren’t really a problem, provided you’re honest about what you’re actually detecting.
But while infrared divergences aren’t really a problem, they do say something about your model. You were modeling particles as single photons, and that made your calculations complicated, with a lot of un-physical infinite results. But you could, instead, have made another model. You could have modeled particles as dressed photons: one photon, plus a cloud of soft photons.
For a particle physicists, these dressed photons have advantages and disadvantages. They aren’t always the best tool, and can be complicated to use. But one thing they definitely do is avoid infinite results. You can interpret them a little more easily.
That ease, though, raises a question. You started out with a model in which each particle you detect was a photon. You could have imagined it as a model of reality, one in which every electromagnetic field was made up of photons.
But then you found another model, one which sometimes makes more sense. And in that model, instead, you model your particles as dressed photons. You could then once again imagine a model of reality, now with every electromagnetic field made up of dressed photons, not the ordinary ones.
So now it looks like you have three options. Are electromagnetic fields made out of waves, or particles…or dressed particles?
That’s a trick question. It was always a trick question, and will always be a trick question.
Ancient Greek philosophers argued about whether everything was made of water, or fire, or innumerable other things. Now, we teach children that science has found the answer: a world made of atoms, or protons, or quarks.
But scientists are actually answering a different, and much more important, question. “What is everything really made of?” is still a question for philosophers. We scientists want to know what we will observe. We want a model that makes predictions, that tells us what actions we can do and what results we should expect, that lets us develop technology and improve our lives.
And if we want to make those predictions, then our models can make different choices. We can arrange things in different ways, grouping the fluid possibilities of reality into different concrete “stuff”. We can choose what to measure, and how best to describe it. We don’t end up with one “what everything is made of”, but more than one, different stories for different contexts. As long as those models make the right predictions, we’ve done the only job we ever needed to do.
4 gravitons 
I think there is one problem when speaking about quantum physics. This is that we describe what “is” photon, in what stat “is” the state of a system, but that is not what quantum physics tells us. The quantum physics tells us what we know about photon, what we know about the state of a system. I believe that changing this wording how we describe quantum physics would remove a lot of misunderstandings of it. We have to realise all time that quantum physics does not describe what is the world, but what we know about it.
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I agree, though I’d go a bit farther and say that’s true of all science. “Is” is just a shorthand for a set of tools for a person to make decisions. Quantum physics just makes it especially inconvenient to pretend otherwise.
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That is the fundamental difference between the classical and quantum physics: The classical physics has the intention to describe a system as it is. The quantum physics realised that this goal is unphysical; there is no way to verify any prediction about the system as it is, because any measurement changes the system. So the quantum physics predicts “only” result of measurement, not the state of the system. The state of the system is not an observable, cannot be verified, and any speculation about is is only philosophical gibberish (this includes all so called interpretation of quantum mechanics that try to resurrect the state of a system as valid observable).
Speaking about state vector as description of system state makes an expectation that something like state of a system exists. I believe that this is source of misunderstanding of quantum mechanics – the contradiction between the theory and words that are used to describe it.
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This is the best of your posts I’ve read recently, and in addition the elaboration in reply to Pavel. There are widely held misconceptions about the power of science to expose ‘truths’, rather than recognising it as a modelling process that has had some considerable success in predicting measurable outcomes in the physical world, but not really able to say what anything is.
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Pavel,
“That is the fundamental difference between the classical and quantum physics: The classical physics has the intention to describe a system as it is. The quantum physics realised that this goal is unphysical; there is no way to verify any prediction about the system as it is, because any measurement changes the system. ”
Let’s assume, for the sake of the argument, that electrons are classical particles, correctly described by classical electromagnetism. Can you propose an experiment where you can measure position/momentum of an electron without disturbing the electron?
The fact that measurements disturb the system does not imply that describing the system is not possible. The measurement still tells you what the properties of that system were before. You may not be able to predict the future of that system but you can deduce its past.
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Such experiment doesn’t exists, that’s what I wrote.
In addition, its not true, that by a measurement you measure state of a system before the measurement. It may be state before the measurement, during the measurement or after the measurement and you never know what of these states you measured. That’s the reason why the state of a system is not something well defined in quantum mechanics and any speculation about it is just a gibberish.
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Pavel,
“Such experiment doesn’t exists, that’s what I wrote.”
If no such experiment exists in classical physics it follows that ” any measurement changes the system” in classical physics just like in QM. So, from this point of view there is no distinction between classical and quantum physics.
” its not true, that by a measurement you measure state of a system before the measurement.”
If you prepare the system in a known state (say momentum on X is -1) and then measure the X momentum you get the same result. So, we know that the measurement returns the pre-measurement state. If a measurement would just return some random state it would be useless as it would not give you any relevant information about the system.
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There is in classical physics one hidden axiom, that the state of the system is well defined and may be measured. This axiom is wrong and realising that this is the reason for all the strange observation (black body radiation, stability of atom, …) lead to the advent of quantum physics.
Classical physics works on the macroscopic dimensions, where the system change caused by the measurement is negligible. You will probably never measure the speed of your car with the precision of several tens of digits – and only by so precise measurement you can observe quantum effects even in the macro world. If you will try such precise measurement, you will need so much energy that your car would be evaporated and you would not know its position.
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Pavel,
“There is in classical physics one hidden axiom, that the state of the system is well defined and may be measured.”
I’ve never heard of this axiom. Classical physics does not say anything about measurements since they are treated in the same way as any other interactions. Hence, there is no axiom, hidden or not about what can be measured. What classical physics implies is that you can in principle measure anything if you have complete knowledge of the initial state. But since such knowledge cannot be practically obtained you are going to have errors. I would be curios to see if those errors have been rigorously evaluated and how they compare with the quantum uncertainty.
” This axiom is wrong and realising that this is the reason for all the strange observation (black body radiation, stability of atom, …) lead to the advent of quantum physics.”
Black body radiation has been nicely explained classically:
Boyer, Timothy. (2017). Blackbody Radiation in Classical Physics: A Historical Perspective. American Journal of Physics. 86. 10.1119/1.5034785.
Click to access 1711.04179.pdf
The absence of atomic collapse has also been explained classically. The explanation is that atoms are in a dynamic equilibrium between radiated and absorbed energy. The work on a classical model of the atoms is ongoing:
“Relativity and radiation balance for the classical hydrogen atom in classical electromagnetic zero-point radiation”
Timothy H Boyer 2021 Eur. J. Phys. 42 025205 DOI 10.1088/1361-6404
Click to access 2103.09084.pdf
“Classical physics works on the macroscopic dimensions, where the system change caused by the measurement is negligible.”
There is no such limitations. And classical physics has been checked at microscopic scale. For example, the tracks in particle accelerators are interpreted assuming that charged particles obey classical electromagnetism (Lorentz force law in principle). Here we are not speaking about cars but about elementary particles, like electrons.
I think you can determine the velocity of a car very accurately using interferometry (similar with LIGO). You don’t need very energetic particles to do that so you are not going to evaporate your car.
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And I thought I was confused about quantum physics before. But very well written to the extent I can understand this field.
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