# Spacetime of a quantum measurement

In a classical(or wave) picture, when we measure a doppler effect from a receding galaxy, we are working on two wave crests essentially. Therefore, there are two events in spacetime for such detection.

In the quantum (or particle) picture, since there is only a photon, then there should be only one event. The detector seemingly just "sucks" the photon.

I found this inconsistency rather strange. The spacetime interval of such two events should not be changed by simply "switching" picture (resuting in some "interval $$> 0$$" to "$$0$$ or undefined"). I am guessing if receiving the photon is to be counted as one event, then "wavefunction collapse" is the second event? Even so, I don't think wavefunction collapse has "direct" correspondence to the second wave crest. I am left more confused.

How to resolve this (presumable) paradox?

Or more generally: is a quantum measurement one event in spacetime?

• downvoter, care to explain? Nov 13 '21 at 9:48
• I don't know the reason for the downvote, but variants of this question comes up often. The problem comes from picturing a photon as a pointlike object. That's how lots of pop-sci sources describe photons, but that's not what quantum theory says, at least not without a very liberal redefinition of "pointlike." I wrote another answer that reviews what quantum theory really says. Nov 13 '21 at 14:52
• @ChiralAnomaly Thanks for reply. I think your answer there will be very insightful and helpful, but since I don't know QFT, so I don't understand it. Meanwhile, I came up with this question while studying Alan Guth's The Early Universe on MITopencourse. I won't call it pop-sci. Furthermore, photon is never really well defined in non-relativistic QM (as far as I am aware of), it seems you suggesting assuming photon as point-like object is wrong? But even it is not point-like object, during the measurement, how many events occur? Nov 13 '21 at 16:39
• Personally, I feel quite uncomfortable sticking with one formalism. After all, I think it is Physics that matters most, not formalism. That's why I like to switch from one picture to another. Nov 13 '21 at 16:40
• Good point about the label "pop-sci." That label wrongly suggests a dichotomy between popular and technical sources, but it's a continuum, not a dichotomy. Helpful sources exist at all levels of (non)rigor, and also unhelpful sources exist at all levels of (non)rigor. Our current understanding of physics can't be accurately conveying using only words, though. Math isn't just for doing calculations. We need math to express the concepts on which everything is based. Still, inaccurate translations can still be helpful. Without their help, none of us would have been able to get started at all. Nov 13 '21 at 17:46