How to Shut Up and Calculate a Delayed Choice Outcome

In summary, the conversation discusses the concept of Quantum Mechanics in an Evolving Hilbert Space and its potential use in delayed choice experiments. The speaker asks if there is a simplified way to apply the principle to toy problems without fully understanding the formalism. They provide an example of a two-photon source with optical elements that can control interference effects. They also ask how to calculate expected statistics such as coincidence counts.
  • #1
Swamp Thing
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Googling for some unrelated topic, I stumbled upon Quantum Mechanics in an Evolving Hilbert Space.

A lot of the math in this paper is beyond my present level, but some of the more descriptive passages made intuitive sense to me.

Based on this, my question is, is the formalism of an evolving Hilbert space a useful tool to describe (and calculate!) delayed choice experiments?

And if so, is there a simplified way to apply the basic principle to toy problems with one or two particles, without necessarily mastering the formalism in its entire awful majesty?
 
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  • #2
For example, say we have a two-photon source as shown below. U1A, U2A and U1B are optical elements (transforms) that could modify the prepared state in some way -- they would control the phases of various Feynman paths and thus control various interference effects.

But the world lines of U1A and U2A are such that we have effectively a delayed substitution of one for the other. If all the world lines are defined, how do we calculate the expected statistics such as coincidence counts etc which we know to be functions of U1A, U2A and U1B?

delayed.png


P.S. I think I know how to shut up, but I really don't know how to calculate.
 
  • #3
Or, simpler and better, assuming electrically (classically) modulated U1A and U2A devices:

delayed2.png
 

Related to How to Shut Up and Calculate a Delayed Choice Outcome

1. What does it mean to "shut up and calculate" a delayed choice outcome?

Shutting up and calculating a delayed choice outcome is a concept in quantum mechanics that refers to the practice of simply performing calculations and making predictions about the outcome of an experiment without trying to understand the underlying physical mechanisms or interpretations.

2. How does the delayed choice experiment work?

In a delayed choice experiment, a particle is fired through a beam splitter and is then faced with two possible paths. The experimenter can choose to observe which path the particle takes or not. If they choose to observe, the particle will behave like a particle and will only go through one path. If they do not observe, the particle will behave like a wave and will go through both paths simultaneously. This shows the importance of the observer's choice in determining the behavior of the particle.

3. What is the significance of the delayed choice outcome in quantum mechanics?

The delayed choice outcome challenges our understanding of the fundamental nature of reality and the role of the observer in shaping it. It suggests that the behavior of particles is not determined by their physical properties alone, but can also be influenced by the observer's actions and choices.

4. Can the delayed choice outcome be explained by any existing theories?

There are various interpretations and theories that attempt to explain the delayed choice outcome, such as the Copenhagen interpretation, the many-worlds interpretation, and the transactional interpretation. However, there is still much debate and no consensus on which interpretation is the most accurate.

5. How does the delayed choice outcome impact our understanding of causality?

The delayed choice outcome challenges the traditional notion of causality, which states that an event can only be influenced by events that occurred before it. In the delayed choice experiment, the observer's choice seems to have a retroactive effect on the behavior of the particle, suggesting that causality may not be as straightforward as we once thought.

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