Wigners Friend where is the paradox?

  • Thread starter ManyNames
  • Start date
  • Tags
    Paradox
In summary: It's a paradox of knowledge.In summary, the conversation discusses the concept of quantum entanglement between an observer and an observed system, and how the measurement of one can lead to a collapse in the other. Two equations are presented to illustrate this concept, with one leading to a real positive value solution and the other not. The role of the observer and the observed is explained, and it is stated that they can only collapse if they have specific values. The conversation also delves into the paradox of Wigner's friend, where the friend's lab does not seem to collapse despite the observer seeing an outcome. This is explained as a paradox of knowledge and can be resolved by choosing a specific interpretation of quantum mechanics.
  • #1
ManyNames
136
0
So i try and try to understand why physics should suggest a quantum entanglement of wigner friend and the observed system, because instantaneous measurement makes a collapse in the system, there should be no question when the wave function is determined.

Suppose we consider two equations:

[itex]\zeta_{\delta^{\alpha=i}_{\beta=i}} |\psi (t)>=\sum_n |\psi_n (\alpha_{\delta}, \beta_{\delta*} (t))|^2[/itex]

and

[itex]\zeta_{\delta^{\alpha=j}_{\beta=j}} |\psi (t)> \ne \sum_n |\psi_n (\alpha_{\delta}, \beta_{\delta*} (t))|^2[/itex]

It's destinctive immediately that eq. 1 has a squared modulus value solution, whereas the equation with the subscripts containing [itex]j[/itex] in eq. 2 shown here as [itex]\delta^{\alpha=j}_{\beta=j}[/itex] do not lead to a real positive value of 1. The Dirac Delta is used trivially to express when both equations can be valid. In these equations, [itex]\alpha[/itex] is the observer and [itex]\beta[/itex] is the observed. Reference of the states of [itex]\alpha[/itex] and [itex]\beta[/itex] is given by the association of the collapse when both [itex]\alpha[/itex] and [itex]\beta[/itex] converge in a collapse.

If the observer and the observed have not collapsed, then the remain in a superpositioning in a joint state with the observed system:

[itex]|\psi \alpha_{\delta_{t_1}} ... ... \psi \alpha_{\delta_(t_2)}> + |\psi \beta_{\delta_{t_1}}... ... \psi \beta_{\delta_{t_2}}>[/itex]

The joint state can be seen as evolving linearly, and being in a superpositining state then by:

[itex]\zeta_{\delta^{\alpha=i}_{\beta=j}} |\psi (t)>=|\psi \alpha(t)> + |\psi \beta(t)>[/itex]

Remember that iff [itex]\alpha[/itex] and [itex]\beta[/itex] have values of [itex]i[/itex] can they collapse -interaction between the scientist and the state happens - no question of when the wave function truely has collapsed as the scientist holds it as an absolute fact of the exeriment.

Let's take [itex]\alpha*[/itex] as the second observer. If [itex]|\psi \alpha_{\delta_{t_1}} ... ... \psi \alpha_{\delta_(t_2)}> + |\psi \beta_{\delta_{t_1}}... ... \psi \beta_{\delta_{t_2}}>[/itex] converges into a collapse (the collapsed states as the observer and the observed) in an earlier time than which the second observer measures the experiment, then [itex]\alpha*(t)<\alpha (t)[/itex]. Information on the state of [itex]\beta[/itex] is then assertained in an early period. The description of:

\zeta_{\delta^{\alpha=i}_{\beta=i}} |\psi (t_1)>=\sum_n |\psi (\alpha, \beta(t_1)|^2

states that the wave function of the observed system has collapsed, and time has been expressed in a past time sense [itex]t_1[/itex]. Since one of the questions of Wigners Friend is if the first observer and the system are themselves in a state of quantum superpositioning?

How could it be though, if not vanishingly small, since we can state that the observers wave function and the observed wavefunction coheres, and the observed system has observable attributes; it seems valid to state the wave function collapsed when the meaurement was first taken, not whether or not a second observer is required.
 
Last edited:
Physics news on Phys.org
  • #2
The supposed paradox is that the friend's lab does not seem to settle down into a collapsed state. If you actually model the evolution they remain superposed, despite that the friend should see an outcome. So it seems Wigner's description of his friend contradicts the definite observation of an outcome. The convergence to collapsed state that you describe does not occur.

However it isn't really a paradox for two reasons.

Firstly the friends observation of an outcome is related to the state of his measuring device. If Wigner traced over the environment within the lab, he would see even his superposed state describes decoherence of the device pointer observable and thus it is fine to take an ignorance based view of its statistics (i.e. there is an outcome but I don't know it).

An even deeper reason it isn't a paradox though is that one can arrange the paradox exactly as it is in Classical theories with an epistemic limit like Spekkens toy model and you can see Wigner's superposed state is just a result of him tracking the environment. His maximum information state isn't as "tight" as that of the friend who only tracks the device.

There's nothing Quantum about Wigner's friend as these Classical theories have it.
 
  • #3
Wigner friend, like Schrodinger cat or delayed choice, is a paradox only if you are not sure which of the "official" quantum interpretations you use (be it collapse, many worlds, Bohmian or whatever). Once you fix the interpretation and stick to it consistently, there is no paradox.
 
  • Like
Likes DarMM
  • #4
Demystifier said:
Wigner friend, like Schrodinger cat or delayed choice, is a paradox only if you are not sure which of the "official" quantum interpretations you use (be it collapse, many worlds, Bohmian or whatever). Once you fix the interpretation and stick to it consistently, there is no paradox.
And it's also not even a Quantum paradox really.
 

Related to Wigners Friend where is the paradox?

1. What is the Wigner's Friend thought experiment?

Wigner's Friend is a thought experiment proposed by physicist Eugene Wigner in 1961. It explores the concept of observer-dependent reality in quantum mechanics.

2. Where is the paradox in Wigner's Friend?

The paradox arises from the conflict between the observer's perception of reality and the actual state of the system being observed, as described by quantum mechanics.

3. How does the Wigner's Friend paradox challenge our understanding of reality?

The paradox challenges the idea that there is an objective reality that exists independent of observation. It suggests that reality is created by the act of observation and is therefore subjective.

4. What solutions have been proposed to resolve the Wigner's Friend paradox?

Some possible solutions include the many-worlds interpretation, where every observation creates a new universe with a different reality, and the quantum decoherence theory, which explains how macroscopic systems appear to have definite states even though they are governed by quantum mechanics.

5. How does the Wigner's Friend thought experiment relate to the measurement problem in quantum mechanics?

The Wigner's Friend thought experiment is one of the many examples used to illustrate the measurement problem in quantum mechanics. It raises questions about the role of the observer and the collapse of the wave function, which is a central issue in the measurement problem.

Similar threads

  • Quantum Physics
Replies
8
Views
753
Replies
2
Views
607
Replies
1
Views
768
Replies
4
Views
822
  • Quantum Physics
Replies
1
Views
976
Replies
4
Views
1K
  • Quantum Interpretations and Foundations
Replies
14
Views
2K
Replies
5
Views
2K
  • Quantum Physics
Replies
4
Views
1K
Replies
5
Views
2K
Back
Top