From Indistinguishable to Completely Identical Particles

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Discussion Overview

The discussion revolves around the possibility of taking two identifiably different particles of the same type and manipulating them to achieve completely identical quantum states in every respect, specifically within the framework of quantum mechanics (QM) without invoking measurement or collapse. Participants explore the implications of quantum state evolution, the role of phase transitions, and the distinction between manipulation and measurement.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants question the feasibility of making two different particles completely identical in quantum states without measurement or collapse.
  • There is a discussion about the implications of the Pauli exclusion principle for fermions, which prevents them from being in identical states, while bosons can achieve this through Bose-Einstein condensation.
  • Participants inquire whether Bose-Einstein condensation involves measurement or collapse, with some asserting it does not and is a reversible process.
  • Questions are raised about how physical operators can differentiate between identical quantum states over time without measurement.
  • Some participants suggest that manipulating the Hamiltonian of a system can lead to different outcomes for initially identical quantum states, while others seek clarification on how this differs from measurement.
  • There is a specific inquiry into the Stern-Gerlach experiment and whether it provides examples of manipulating identical quantum states into different states without measurement or collapse.

Areas of Agreement / Disagreement

Participants express differing views on the nature of quantum state manipulation, the role of phase transitions, and the definitions of measurement versus manipulation. No consensus is reached on the feasibility of achieving completely identical quantum states through the discussed processes.

Contextual Notes

The discussion highlights the complexity of quantum state evolution, the conditions under which phase transitions occur, and the implications of manipulating quantum systems. Limitations include the dependence on specific definitions of measurement and manipulation, as well as the unresolved nature of certain mathematical and physical claims.

ObjectivelyRational
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Is it possible to take two identifiably different particles of the exact same type (I previously called them indistinguishable in error?) which have different quantum states (say a different distribution in position or momentum Hilbert space) and physically cause them to have identical states, i.e. exactly the same momentum states and position states and spin states etc. so that they are in physical reality completely identical in absolutely every QM respect?

By possible, I mean is there a mechanism in reality which in principle could do this?

For clarity, I'm wondering about this when the process to remains in QM time evolution without any "measurement" causing any "collapse", just straight forward evolution of QM states... and only secondarily do I wonder the possibility of this using "measurement" or "collapse" in order to do it.
 
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ObjectivelyRational said:
take two identifiably different indistinguishable particles
What do you mean? If they are identifiably different, they are by definition distinguishable!
 
A. Neumaier said:
What do you mean? If they are identifiably different, they are by definition distinguishable!

Sorry I mean to say two different particles of the same type having different quantum numbers... like starting at different places in an experiment.

Corrected the OP, thanks!
 
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ObjectivelyRational said:
Sorry I mean to say two different particles of the same type having different quantum numbers... like starting at different places in an experiment.
This is impossible for fermions because of the Pauli principle. It happens for bosons in Bose-Einstein condensation.
 
A. Neumaier said:
This is impossible for fermions because of the Pauli principle. It happens for bosons in Bose-Einstein condensation.
OK so Bosons only.

Does Bose-Einstein condensation involve any "measurement" or "collapse" or is it only according to standard QM time evolution that the two Bosons originally from different positions can undergo Bose-Einstein condensation?
 
ObjectivelyRational said:
Does Bose-Einstein condensation involve any "measurement" or "collapse"
No. It is a collective effect that happens under certain conditions (zero temperature phase transition) and is reversible.
 
A. Neumaier said:
No. It is a collective effect that happens under certain conditions (zero temperature phase transition) and is reversible.

By reversible do you mean that starting with the completely identical particles in the Bose-Einstein condensate, hypothetically, reversing time would separate the distinguishable particles back to their original states (different Hilbert space distributions corresponding to "starting at different places" in the experiment)?

What kind of physical operators can take completely identical quantum states and cause them to become different quantum states through time evolution (here reversed time) without any "measurement" or "collapse"?
 
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So I think this is coming down to:

How could any physical operators take completely identical quantum states and cause them to become different quantum states through time evolution (here reversed time) without any "measurement" or "collapse"?

IF true for some operator, what does it mean for quantum states to be "completely identical".

IF simply false, how can completely identical quantum states ever be achieved with a reversible process from two non-identical quantum states (assuming no measurement or collapse)?I'd appreciate hearing any "insight" from anyone who has the answers.
 
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ObjectivelyRational said:
By reversible do you mean that starting with the completely identical particles in the Bose-Einstein condensate, hypothetically, reversing time would separate the distinguishable particles back to their original states (different Hilbert space distributions corresponding to "starting at different places" in the experiment)?
Reversible is meant in the sense of thermodynamics.
ObjectivelyRational said:
What kind of physical operators can take completely identical quantum states and cause them to become different quantum states through time evolution (here reversed time) without any "measurement" or "collapse"?
Not an operator, but a zero temperature phase transition. This is the technical term.
 
  • #10
You state that "a zero temperature phase transition" can take completely identical quantum states and cause them to be different quantum states through time evolution without "measurement" or "collapse".Can you explain how the process of "phase transition" differentiates between "completely identical quantum states" to cause, as time evolves, different quantum states (without any measurement or collapse)?
 
  • #11
ObjectivelyRational said:
You state that "a zero temperature phase transition" can take completely identical quantum states and cause them to be different quantum states through time evolution without "measurement" or "collapse".Can you explain how the process of "phase transition" differentiates between "completely identical quantum states" to cause, as time evolves, different quantum states (without any measurement or collapse)?
Just design a temoral evolution that changes the parameters to cross the phase transition. https://en.wikipedia.org/wiki/Bose–Einstein_condensation
 
  • #12
A. Neumaier said:
Just design a temoral evolution that changes the parameters to cross the phase transition. https://en.wikipedia.org/wiki/Bose–Einstein_condensation

I've taken a look at this.

How do you design a quantum mechanical process that can "change parameters" over time of "completely identical quantum states" in ways which result with different quantum states (absent measurement or collapse)?

Isn't thought QM evolution deterministic (absent measurement or collapse)?

If we look at one of the particles in the "completely identical quantum state" and assuming QM works the way reality does, we apply the Hamiltonian on that state and get a resulting QM state (no collapse) with whatever its probabilities and eigenstates, how can we apply the same Hamiltonian "completely identical quantum state" of another particle with the exact same completely identical quantum state and get a resulting QM state (no collapse) which is different from the first?
 
  • #13
ObjectivelyRational said:
Isn't thought QM evolution deterministic (absent measurement or collapse)?
The evolution of closed systems, yes. But people manipulate open systems, and every manipulation of knobs and buttons changes the Hamiltonian of the manipulated system. This is the key for all applications of quantum mechanics. Without being able to manipulate the dynamics, quantum mechanics would be completely useless and esoteric.
 
  • #14
A. Neumaier said:
But people manipulate open systems, and every manipulation of knobs and buttons changes the Hamiltonian of the manipulated system. This is the key for all applications of quantum mechanics.

How does this manipulation by people differ from "measurement" or "collapse" of the particles in the completely identical QM state?
 
  • #15
ObjectivelyRational said:
How does this manipulation by people differ from "measurement" or "collapse" of the particles in the completely identical QM state?
Changing the direction of a magnetic field in a Stern-Gerlach experiment does not constitute a measurement. but it changes the dynamics (and later measurement results) of systems passing the magnet. Similarly for other manipulations.
 
  • #16
A. Neumaier said:
Changing the direction of a magnetic field in a Stern-Gerlach experiment does not constitute a measurement. but it changes the dynamics (and later measurement results) of systems passing the magnet. Similarly for other manipulations.

I like the Stern-Gerlach experiment... is there any example in that experiment where "completely identical quantum states" are "manipulated" (as you put it) so as to evolve into different quantum states (without measurement or collapse)? I cannot recall anything like that in the experiment...
 
  • #17
ObjectivelyRational said:
I like the Stern-Gerlach experiment... is there any example in that experiment where "completely identical quantum states" are "manipulated" (as you put it) so as to evolve into different quantum states (without measurement or collapse)? I cannot recall anything like that in the experiment...
No. I just gave it as the simplest example of how human manipulations change the dynamics of a unitary process.

Now it is up to you to generalize and put the pieces together.
 
  • #18
A. Neumaier said:
No. I just gave it as the simplest example of how human manipulations change the dynamics of a unitary process.

Now it is up to you to generalize and put the pieces together.

I understand if you do not want to continue discussing this. You have replied many times. I appreciate it.I am still searching for how a unitary process acting on a set of "completely identical quantum states" could possibly cause them to evolve differently from each other (absent any measurement or collapse).

If anyone else can answer that I would greatly appreciate it.
 

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