# Exploring Wave Function Collapse and Measuring Particles

• I
• Sciencemaster
In summary, exploring wave function collapse and measuring particles involves examining the behavior of particles at the quantum level and how they change when observed or measured. This phenomenon is a fundamental principle of quantum mechanics and plays a crucial role in understanding the behavior of particles in the microscopic world. By studying wave function collapse, scientists are able to gain insight into the nature of particles and their interactions with the environment, leading to advancements in fields such as quantum computing and communication. Measuring particles also allows for the detection and manipulation of individual particles, providing a deeper understanding of their properties and potential applications. Overall, these explorations into wave function collapse and particle measurement have significant implications for our understanding of the universe and the development of future technologies.
Sciencemaster
Hello!
Let's say we have a wave function. Maybe it's in a potential well, maybe not, I think it's arbitrary here. This wave function is one-dimensional for now to keep things simple. Then, we use a device, maybe a photon emitter and detector system where the photon crosses paths with the wave function of our other particle at some point. If the photon does not reach the detector, that's where are particle is. As such, we know where it is to some finite region. There is going to be some uncertainty in our measurement, so I don't imagine it's simply a delta function. Additionally, if our detector does not measure the particle, what happens to the wave function? I would imagine that the new wave function is the same as the pre-collapse wave function, except for in the region with the detector, where the probability drops to zero in a piecewise fashion.
Essentially, my question is the same as the tagline. Once we collapse a particle's wave function to a finite region, or measure it to not be in a finite region, how do we mathematically model its wave function?

Demystifier
I assume at least you need to change and renormalize wavefunction with the information of area where particle does not exist by your observation.

In the special setting that particle go though gates A or B and you observe no passing at B we may deduce that wavefunction collapse to pass gate A though no direct observation is done there. This example suggests to me that wavefunction is not more than information we have for the special setting we prepare. It does not seem physical entity to me. I know it is a controversial issue.

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anuttarasammyak said:
I assume at least you need to change and renormalize wavefunction with the information of area where particle does not exist by your observation.

In the special setting that particle go though gates A or B and you observe no passing at B we may deduce that wavefunction collapse to pass gate A though no direct observation is done there. This example suggests to me that wavefunction is not more than information we have for the special setting we prepare. It does not seem physical entity to me. I know it is a controversial issue.
Regardless of what is happening behind the scenes, our mathematical models should be able to predict reality. As such, we should be able to model a wave function post-collapse that can time-evolve and describe measurements. I'm hoping to learn how to model this given a measurement done on a given particle's wave function.

physika
I thought you could predict the probability of an event happening (at t=0) regardless at what time it happens in the future or what happened beforehand. As such, superposition evolves into superposition, entanglement may occur etc.

Sciencemaster said:
we should be able to model a wave function post-collapse that can time-evolve and describe measurements.
You may be interested in learning how particle wave function evolves after passing slits, i.e. position observation allowing width, and goes to screen for full position observation in Young double or other slit experiments.

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Sciencemaster said:
As such, we know where it is to some finite region. There is going to be some uncertainty in our measurement, so I don't imagine it's simply a delta function. Additionally, if our detector does not measure the particle, what happens to the wave function? I would imagine that the new wave function is the same as the pre-collapse wave function, except for in the region with the detector, where the probability drops to zero in a piecewise fashion.
Yes, this is described by projectors to the region to which the wave function collapses. A projection is needed even if the detector does not click, because it also brings new information about position of the particle. For mathematical details see e.g. my recent paper https://arxiv.org/abs/2107.08777.

vanhees71
anuttarasammyak said:
You may be interested in learning how particle wave function evolves after passing slits, i.e. position observation allowing width, and goes to screen for full position observation in Young double or other slit experiments.
I mean, this seems at the very least similar to what I was looking for, I think that would help!

Demystifier said:
Yes, this is described by projectors to the region to which the wave function collapses. A projection is needed even if the detector does not click, because it also brings new information about position of the particle. For mathematical details see e.g. my recent paper https://arxiv.org/abs/2107.08777.
Alright, so a projector can be used to model a new wave function post-collapse. However, I'm talking about spatial collapse, not arrival time like in your paper. So, for a particle whose position is being measured, would it still use projectors? How would that work?

Sciencemaster said:
However, I'm talking about spatial collapse, not arrival time like in your paper.
My paper also talks about spatial collapse, you just need to read more than title and abstract. See in particular Sec. 3.

physika and vanhees71

## 1. What is wave function collapse?

Wave function collapse is a fundamental concept in quantum mechanics that refers to the phenomenon of a particle's wave function collapsing into a definite state when it is observed or measured. This means that the particle's properties, such as position or momentum, become fixed and no longer exist in a state of superposition.

## 2. How is wave function collapse related to the measurement of particles?

The measurement of particles involves interacting with them in some way, which causes their wave function to collapse. This is because the act of measurement involves obtaining information about the particle, which forces it into a definite state. Therefore, wave function collapse is an essential aspect of measuring particles in quantum mechanics.

## 3. Can wave function collapse be predicted?

No, wave function collapse is a random and unpredictable process. According to the Copenhagen interpretation of quantum mechanics, the collapse of a particle's wave function is a result of the observer's interaction with the particle, and it cannot be predicted beforehand.

## 4. How is wave function collapse different from other theories of measurement?

There are several interpretations of quantum mechanics, and each has a different explanation for the phenomenon of wave function collapse. For example, the Many-Worlds interpretation suggests that wave function collapse does not occur, and instead, all possible outcomes of a measurement exist in parallel universes. However, the Copenhagen interpretation remains the most widely accepted theory of measurement in quantum mechanics.

## 5. Can we directly observe wave function collapse?

No, wave function collapse is an invisible process that occurs at the quantum level. We can only observe its effects, such as the definite state of a particle after measurement. However, there are ongoing efforts in quantum technology to develop devices that can indirectly observe wave function collapse in action.

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