Can Multiple Routes in Wave-Particle Duality Be Observed?

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Wave-particle duality suggests that particles can take multiple routes simultaneously, as proposed by Richard Feynman. Observations, however, collapse these multiple potential paths into a single route, as demonstrated by the two-slit experiment. When not observed, particles exist in a superposition of states, leading to interference patterns; when observed, they appear to take only one path. The reason for this collapse during observation remains a topic of debate, with some considering it a "fact without reason." The discussion highlights the complexities and ongoing uncertainties in understanding quantum mechanics.
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As many people here will know, particles have wave-particle duality. A American scientist, Richard Feyman, suggested that when a particle move from a point to another, the particle can move through every possible route, not only one route (or history) as described in classical theory. The route we observed is the only possible route.
The question is, if more than one route is possible will we observed more than one route?

p/s: I am still learning quantum mechanic, please correct me if I am wrong.
 
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No, we will not observe more than one route.

The particle will follow every possible route - all states will be superposed - as long as it is not *observed*. When observed, the states all collapse to one, which we observe.

This is what the two-slit experiment shows so clearly. If we do not observe which slit the photon passes through, then it passes through both, interferes with itself, and we see an interference pattern. If we put detectors at the slits, thus observing the photon, it is seen to pass through only one slit, and we get no interference pattern.

Thus, when not observed, the photon has experienced multiple superposed histories. When observed, it has experienced only one history.
 
Thanks, I think I know what you meant. But why must all states collapse to one when oberved? Is there a reason for this? Or this is just a fact without reason?
 
The nature of measurment is that!
When you say that the system is in one specified state , it means that if you make another measurment, you will find the system in that state again. If not, your measurment is not reasonable! and you can not trust on it. So every measurment put the system in the eigen state of the measured value
 
"But why must all states collapse to one when oberved? Is there a reason for this? Or this is just a fact without reason?"

I believe 'fact without reason' is about right.

I don't know if anyone knows the physics behind this yet - we undestand so little in this realm. It is only one interpretation of the observed data, afterall, and a hotly debated one at that. As we get farther and farther into QM, we find that the only meaningful answer is that there are no real-world explanations, and that it's all a matter of mathematical formulae.
 
I think it is not just "a fact without reason"
The argument behind it is about clear . Or maybe I think so!
 
Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?

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