Why no position operator for photon?

In summary, the photon does not have a position operator in quantum mechanics. This is because in the context of relativistic quantum theory, the position operator leads to violations of causality. Therefore, quantum field theory dispenses with the position operator altogether, relegating position to the role of a parameter. This means that there is no spatial representation for relativistic quantum mechanical states, but rather a quantum field that creates/annihilates particles at different points in space and time. Although a position operator can be defined for massive particles in QFT, it still leads to causality violations. Some authors suggest that not assigning any meaning to the notation |x\rangle can avoid these paradoxes, but ultimately, the model's predictions should not depend on the
  • #36
Elemental said:
To me it suggests that momentum is a more fundamental property than position, but I'm not sure why that would be the case. Any other insights welcome.
Or, perhaps, non-relativistic QM is more fundamental than relativistic QFT. See the paper linked in my signature below.
 
<h2> Why is there no position operator for photons?</h2><p>The position operator is a mathematical tool used in quantum mechanics to describe the position of a particle. However, photons are massless particles that do not have a defined position in space. As a result, the concept of a position operator does not apply to photons.</p><h2> Can't we measure the position of a photon using a detector?</h2><p>While we can detect the presence of a photon using a detector, the position of a photon cannot be precisely measured due to the uncertainty principle. This principle states that the more precisely we know the position of a particle, the less we know about its momentum, and vice versa. As photons have no mass, their momentum is always uncertain, making it impossible to accurately measure their position.</p><h2> How do we determine the position of a photon in an experiment?</h2><p>In experiments involving photons, their position is usually determined indirectly by measuring the position of the detector where they are detected. The position of the detector can then be used to infer the position of the photon at that moment. However, this does not give us a precise measurement of the photon's position, only an estimation.</p><h2> If photons have no position, how do they travel in a straight line?</h2><p>While photons do not have a defined position in space, they do have a defined direction of travel. This direction is determined by the momentum of the photon, which is always in the direction of its propagation. As photons have no mass, they are not affected by external forces and can travel in a straight line.</p><h2> Are there any exceptions where a position operator can be applied to photons?</h2><p>No, there are no exceptions where a position operator can be applied to photons. The concept of a position operator only applies to particles with mass, and photons are massless particles. Therefore, the position of a photon cannot be described using a position operator.</p>

FAQ: Why no position operator for photon?

Why is there no position operator for photons?

The position operator is a mathematical tool used in quantum mechanics to describe the position of a particle. However, photons are massless particles that do not have a defined position in space. As a result, the concept of a position operator does not apply to photons.

Can't we measure the position of a photon using a detector?

While we can detect the presence of a photon using a detector, the position of a photon cannot be precisely measured due to the uncertainty principle. This principle states that the more precisely we know the position of a particle, the less we know about its momentum, and vice versa. As photons have no mass, their momentum is always uncertain, making it impossible to accurately measure their position.

How do we determine the position of a photon in an experiment?

In experiments involving photons, their position is usually determined indirectly by measuring the position of the detector where they are detected. The position of the detector can then be used to infer the position of the photon at that moment. However, this does not give us a precise measurement of the photon's position, only an estimation.

If photons have no position, how do they travel in a straight line?

While photons do not have a defined position in space, they do have a defined direction of travel. This direction is determined by the momentum of the photon, which is always in the direction of its propagation. As photons have no mass, they are not affected by external forces and can travel in a straight line.

Are there any exceptions where a position operator can be applied to photons?

No, there are no exceptions where a position operator can be applied to photons. The concept of a position operator only applies to particles with mass, and photons are massless particles. Therefore, the position of a photon cannot be described using a position operator.

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