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Let's say there is a process of scattering of a photon by an electron. The process has a certain amplitude, the square of the modulus of which determines the probability that the measurement will result in a result corresponding to the final state of this process. And if the interaction was not recorded, then what? does it mean that the interaction did not happen at all, or in the intermediate state we have a superposition <interaction did not happen / interaction occurred>, and if the amplitude of the first term is much larger, then the output will be negative?

Arman Armenpress
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    We don't know, quantum field theory provides a nice way to calculate scattering amplitudes, it does not attempt to say what actually happens during the interactions. – Charlie Jan 09 '21 at 13:46
  • @Charlie But the process is described as a superposition of states <particles did not interact / particles interacted>. Is it physically impossible? After all, in quantum mechanics, the superposition of states is common. – Arman Armenpress Jan 09 '21 at 15:25
  • You're touching on an important point, but the answer is that this is in fact a very general statement about physics as a field. Our models are designed to accurately predict mathematical relationships that exist between real world measurable quantities, it is a mistake to go a step further and imply that our mathematical models are telling us something objective about the exact nature of the real world (i.e. physics tells us how the world works, not why it happens to work that way). I talk about that here. – Charlie Jan 09 '21 at 15:30
  • @ChiralAnomaly Let's say no one measures anything. Somewhere in space, an electron and a photon are flying towards each other. There are three variants of events: particles did not interact exactly, particles interact exactly, or they find themselves in a superposition <do not interact + interact>. What option will happen?The question is more related to the fact that there is certainty in the quantum world without observation or not? Or is the superposition a real physical phenomenon independent of observation? – Arman Armenpress Jan 09 '21 at 16:10
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    @ArmanArmenpress It sounds like you might be asking a metaphysical question, so let me try this: Why would it matter? If two different-looking theories both correctly predict everything that we can observe, and if both theories are equally "simple" (whatever that means), then how would we decide which of those two theories is better? Which one more accurately describes what happens between measurements? Is that question even meaningful? – Chiral Anomaly Jan 09 '21 at 16:36
  • @Chiral Anomaly you are right, from a practical point of view it does not. if you need to describe the process of scattering of a photon by an electron, then the first diagram, that is, the zero approximation is the absence of interaction, right? After all, all possible stories are needed, including those in which particles do not notice each other. – Arman Armenpress Jan 09 '21 at 16:46
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    From Landau vol. 4 sec. 1: "The momentum can figure in a consistent theory only for free particles; for these it is conserved, and can therefore be measured with any desired accuracy. This indicates that the theory will not consider the time dependence of particle interaction processes. It will show that in these processes there are no characteristics precisely definable (even within the usual limitations of quantum mechanics); the description of such a process as occurring in the course of time is therefore just as unreal as the classical paths are in non-relativistic quantum mechanics." – bolbteppa Jan 09 '21 at 17:04
  • @bolbteppa as I understand it, this also applies to the case of lack of interaction, since this is also one of the stories. – Arman Armenpress Jan 09 '21 at 17:09
  • The point is, trying to describe what goes on during relativistic interactions is as impossible as trying to describe the path of a non-relativistic particle, however the momentum of a free particle is in principle measurable, so no it does not apply to the lack of interaction - this is why scattering processes involve incoming and outgoing free particles, it's not some deficiency in our current ability to solve a math problem it's a physical reality as fundamental as the rejection of classical paths. I recommend you read the section I referenced above for a simple way to think about all this – bolbteppa Jan 09 '21 at 17:16
  • @bolbteppa I formulated my idea incorrectly. I mean, the sum of the Feynman diagrams contains diagrams in which the particles are free and do not interact (zero approach), in which one interaction occurs (first approximation), and so on. I – Arman Armenpress Jan 09 '21 at 17:24

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What happens in between is everything and nothing. There is no privileged clearcut answer what happened that would be physically meaningful. It's really the very basic point of quantum mechanics that only results of measurements are physically meaningful facts or observables; all other data are fictitious or uncertain. By the very definition of your problem, no measurement took place in the intermediate states which means that no sharp answers to any questions were generated, no answers or values became real or privileged or facts.

Feynman's path integral formalism is the most explicit method to answer the question "what happened in between". In this approach, the only physically meaningful answer involves the summing over all possible intermediate histories that are weighted by $\exp(iS/\hbar)$ where $S$ is the action of each history. So what happens is the complex superposition of all conceivable intermediate histories with the given initial and final conditions.

Not only that. The absolute value of this exponential is always the same (namely one in my normalization) so all histories, whether they are close to an intuitive or classically allowed history, contribute equally. The nearly classical histories are favored in the classical limit due to the positive interference. The phase $S$ (an angle) is almost constant near the minimum of the action (note that the classically allowed history have the stationary or minimal action) and that is why their contribution to the final observed results is greatest. In a combination, these nearly classical histories contribute more than other combinations where much of the interference is destructive.

It's important to notice that the intermediate histories are indeed superpositions of qualitatively different histories. This point is made very explicit by the Feynman diagrams. The probability of a given processes is calculated from a sum of Feynman diagrams, each of which may have a different shape or even the number of virtual particles. All these diagrams contribute so "all the corresponding histories had some likelihood to happen" in between. But unlike classical physics, quantum mechanics says that not only the probabilities of each history matter. All the relative phases matter, too. As I said, most of the decisions "what looks real according to a quantum mechanical theory" boils down to the question whether the interference between the contributions is constructive or destructive.

Luboš Motl
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  • Thank you. But let's say no one measures anything. Somewhere in space, an electron and a photon are flying towards each other. There are three variants of events: particles did not interact exactly, particles interact exactly, or they find themselves in a superposition <do not interact + interact>. What option will happen?The question is more related to the fact that there is certainty in the quantum world without observation or not? Or is the superposition a real physical phenomenon independent of observation? – Arman Armenpress Jan 09 '21 at 16:13
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    Dear Lubos, I was just informed by a reader that your blog is by invitation only, and I can understand why. Unfortunately I have very often given the link to the eye opening blog https://motls.blogspot.com/2011/11/how-classical-fields-particles-emerge.html in answers to relevant questions. Is the content in another site ? Thanks and hope you are well. I am sorry to miss your physics posts. – anna v Apr 06 '22 at 03:56
  • Dear Anna, sorry, this is just a technical realization of the basic event that I was basically forced to shut down the blog by escalating censorship requests from the terrorists harbored by Google. I just ran out of patience, to be the last scientist on Earth who fights against this scum was too exhausting. – Luboš Motl Apr 07 '22 at 04:20
  • @LubošMotl maybe you should have stuck to writing about Physics than advocating for the enslavement of ethnic Russian or the toppling of the 2020 elections. – Daniel Apr 08 '22 at 22:35
  • Your comment proves that you are both a liar and a fanatical Stalinist warrior against basic human rights who belongs to jail or worse. – Luboš Motl Apr 10 '22 at 03:56
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    Have you considered the alternative of creating a subscription-only site for your content? You might be surprised at the number of people prepared to pay say $10 a year making it possibly worth your while. Also, please be careful with wrestling with individuals who might get you suspended; as happened to a certain talented individual who's banned until 2292 ;) – Larry Harson Apr 22 '22 at 21:36
  • No, sorry, I haven't. If it were just ten dollars a year, I would need close to a thousand than hundreds payers and I feel certain that number wouldn't register. – Luboš Motl Apr 24 '22 at 04:05
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    @LubošMotl I think you could easily charge ~$20/mo for your content. Substack has openly rejected requests for censorship, and has yet actually gained mainstream popularity. – Abhimanyu Pallavi Sudhir Nov 22 '22 at 17:59
  • Lubos, I was also a regular reader of your blog. I would also be ready to pay like 10 $/mo. – Mikael Aug 02 '23 at 18:39
  • Dear Mikael, are you THE Mikael whom I remember as a commenter? I really stopped blogging and the hiding of the website is my preferred way of reversible deletion. I and 2 people in the world have access to the website. There is nothing new there. It is possible that I could collect the average income, a nice amount, from the 100 or so of people who complained that the blog is gone and who offered comparable things like you. But given the threats of astronomical lawsuits and stuff like that, it just isn't enough for me to overcome the repulsion. – Luboš Motl Aug 03 '23 at 10:03
  • The immediate reason to cancel the blog was a triplet of new censorship requests from Google, justified by the placement of AdSense, over articles that had already been previously deleted. They just violate every rule and litmus test of decency and went straight after my neck. I resisted for an unnaturally long time but it was time for a good bye. – Luboš Motl Aug 03 '23 at 10:04