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In quantum mechanics, non-direct interaction with the system can itself be interpreted as measurement.

This is known as interaction-free measurement. Here, the absence of a detection on one path provides information. i.e., the photon must have taken the other path, and it is this information that causes wavefunction collapse.

According to the Copenhagen interpretation, the wavefunction evolves in a superposition until a measurement occurs. Though a "measurement" includes any interaction or "interaction like" inference, such as the observation of no clicks on one path.

The absence of physical detection updates information about the state and therefore collapses the wave function. i.e., the photon is now known to take the other path.

See the Renninger negative-result experiment$^1$ and counterfactual quantum communication that has been demonstrated$^2$.

$^1$ From source

In quantum mechanics, the Renninger negative-result experiment is a thought experiment that illustrates some of the difficulties of understanding the nature of wave function collapse and measurement in quantum mechanics. The statement is that a particle need not be detected in order for a quantum measurement to occur, and that the lack of a particle detection can also constitute a measurement. The thought experiment was first posed in 1953 by Mauritius Renninger. The non-detection of a particle in one arm of an interferometer implies that the particle must be in the other arm. It can be understood to be a refinement of the paradox presented in the Mott problem.

$^2$ The first experimental verification of counterfactual quantum communication was completed in 2012 by Liu, Ju, Liang, Tang, Peng, Pan, et. al. They implemented a (counterfactual) quantum cryptography protocol, achieving high visibility (over $98\%$) in their interferometers

Even more recently (this month of this year, 09/2025), researchers presented an on-chip quantum photonic implementation of counterfactual communication using the quantum Zeno effect (with probabilities of about $74\%$ for transmitting a $0$-bit and $85\%$ for a $1$‑bit, while detecting only $\approx 0.17\%$ of photon leakage).

In quantum mechanics, non-direct interaction with the system can itself be interpreted as measurement.

This is known as interaction-free measurement. Here, the absence of a detection on one path provides information. i.e., the photon must have taken the other path, and it is this information that causes wavefunction collapse.

According to the Copenhagen interpretation, the wavefunction evolves unitarily in a superposition until a measurement occurs. When the systems state becomes definite (eigenstate), we say measurement has occurred. So, a "measurement" includes any interaction or "interaction like" inference, such as the observation of no clicks on one path.

The absence of physical detection updates information about the state and therefore collapses the wave function. i.e., the photon is now known to take the other path.

See the Renninger negative-result experiment$^1$ and counterfactual quantum communication that has been demonstrated$^2$.

And how much time it takes for the wavefunction to collapse to the other path?

In most standard interpretations of quantum mechanics, the wavefunction collapse is considered instantaneous (though this notion comes with important subtleties).

$^1$ From source

In quantum mechanics, the Renninger negative-result experiment is a thought experiment that illustrates some of the difficulties of understanding the nature of wave function collapse and measurement in quantum mechanics. The statement is that a particle need not be detected in order for a quantum measurement to occur, and that the lack of a particle detection can also constitute a measurement. The thought experiment was first posed in 1953 by Mauritius Renninger. The non-detection of a particle in one arm of an interferometer implies that the particle must be in the other arm. It can be understood to be a refinement of the paradox presented in the Mott problem.

$^2$ The first experimental verification of counterfactual quantum communication was completed in 2012 by Liu, Ju, Liang, Tang, Peng, Pan, et. al. They implemented a (counterfactual) quantum cryptography protocol, achieving high visibility (over $98\%$) in their interferometers

Even more recently (this month of this year, 09/2025), researchers presented an on-chip quantum photonic implementation of counterfactual communication using the quantum Zeno effect (with probabilities of about $74\%$ for transmitting a $0$-bit and $85\%$ for a $1$‑bit, while detecting only $\approx 0.17\%$ of photon leakage).

In quantum mechanics, non-direct interaction with the system can itself be interpreted as measurement.

This is known as interaction-free measurement. Here, the absence of a detection on one path provides information. i.e., the photon must have taken the other path, and it is this information that causes wavefunction collapse.

According to the Copenhagen interpretation, the wavefunction evolves in a superposition until a measurement occurs. Though a "measurement" includes any interaction or "interaction like" inference, such as the observation of no clicks on one path.

The absence of physical detection updates information about the state and therefore collapses the wave function. i.e., the photon is now known to take the other path.

See also counterfactual quantum communication that has been demonstrated$^1$.

$^1$ The first experimental verification of counterfactual quantum communication was completed in 2012 by Liu, Ju, Liang, Tang, Peng, Pan, et. al. They implemented a (counterfactual) quantum cryptography protocol, achieving high visibility (over $98\%$) in their interferometers

Even more recently (this month of this year, 09/2025), researchers presented an on-chip quantum photonic implementation of counterfactual communication using the quantum Zeno effect (with probabilities of about $74\%$ for transmitting a $0$-bit and $85\%$ for a $1$‑bit, while detecting only $\approx 0.17\%$ of photon leakage).

In quantum mechanics, non-direct interaction with the system can itself be interpreted as measurement.

This is known as interaction-free measurement. Here, the absence of a detection on one path provides information. i.e., the photon must have taken the other path, and it is this information that causes wavefunction collapse.

According to the Copenhagen interpretation, the wavefunction evolves in a superposition until a measurement occurs. Though a "measurement" includes any interaction or "interaction like" inference, such as the observation of no clicks on one path.

The absence of physical detection updates information about the state and therefore collapses the wave function. i.e., the photon is now known to take the other path.

See the Renninger negative-result experiment$^1$ and counterfactual quantum communication that has been demonstrated$^2$.

$^1$ From source

In quantum mechanics, the Renninger negative-result experiment is a thought experiment that illustrates some of the difficulties of understanding the nature of wave function collapse and measurement in quantum mechanics. The statement is that a particle need not be detected in order for a quantum measurement to occur, and that the lack of a particle detection can also constitute a measurement. The thought experiment was first posed in 1953 by Mauritius Renninger. The non-detection of a particle in one arm of an interferometer implies that the particle must be in the other arm. It can be understood to be a refinement of the paradox presented in the Mott problem.

$^2$ The first experimental verification of counterfactual quantum communication was completed in 2012 by Liu, Ju, Liang, Tang, Peng, Pan, et. al. They implemented a (counterfactual) quantum cryptography protocol, achieving high visibility (over $98\%$) in their interferometers

Even more recently (this month of this year, 09/2025), researchers presented an on-chip quantum photonic implementation of counterfactual communication using the quantum Zeno effect (with probabilities of about $74\%$ for transmitting a $0$-bit and $85\%$ for a $1$‑bit, while detecting only $\approx 0.17\%$ of photon leakage).

In quantum mechanics, not seeing something can itself be interpreted as a measurement.

This is known as interaction-free measurement. The absence of a detection on one path provides information. That is, the photon must have taken the other path, and it is this information on its own that causes the wavefunction to collapse.

According to the Copenhagen interpretation, the wavefunction evolves unitarily in a superposition until a measurement occurs. Though a "measurement" includes any interaction or "interaction like" inference, such as the observation of no clicks on one path.

The absence of physical detection updates information about the state and therefore collapses the wave function. i.e., the photon is now known to take the other path.

See also counterfactual quantum communication that has been demonstrated$^1$.

$^1$ The first experimental verification of counterfactual quantum communication was completed in 2012 by Liu, Ju, Liang, Tang, Peng, Pan, et. al. They implemented a (counterfactual) quantum cryptography protocol, achieving high visibility (over $98\%$) in their interferometers

Even more recently (this month of this year, 09/2025), researchers presented an on-chip quantum photonic implementation of counterfactual communication using the quantum Zeno effect (with probabilities of about $74\%$ for transmitting a $0$-bit and $85\%$ for a $1$‑bit, while detecting only $\approx 0.17\%$ of photon leakage).

In quantum mechanics, non-direct interaction with the system can itself be interpreted as measurement.

This is known as interaction-free measurement. Here, the absence of a detection on one path provides information. i.e., the photon must have taken the other path, and it is this information that causes wavefunction collapse.

According to the Copenhagen interpretation, the wavefunction evolves in a superposition until a measurement occurs. Though a "measurement" includes any interaction or "interaction like" inference, such as the observation of no clicks on one path.

The absence of physical detection updates information about the state and therefore collapses the wave function. i.e., the photon is now known to take the other path.

See also counterfactual quantum communication that has been demonstrated$^1$.

$^1$ The first experimental verification of counterfactual quantum communication was completed in 2012 by Liu, Ju, Liang, Tang, Peng, Pan, et. al. They implemented a (counterfactual) quantum cryptography protocol, achieving high visibility (over $98\%$) in their interferometers

Even more recently (this month of this year, 09/2025), researchers presented an on-chip quantum photonic implementation of counterfactual communication using the quantum Zeno effect (with probabilities of about $74\%$ for transmitting a $0$-bit and $85\%$ for a $1$‑bit, while detecting only $\approx 0.17\%$ of photon leakage).