Pair production via Quantum Tunneling has negative Kinetic energy?

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Discussion Overview

The discussion centers on the concept of pair production via quantum tunneling, specifically examining the conditions under which a photon could convert into a positron-electron pair when the energy is insufficient (hv<2Me*c^2) and the implications of this scenario on the energy of the resultant pair.

Discussion Character

  • Exploratory, Debate/contested

Main Points Raised

  • One participant questions whether a photon can produce a positron-electron pair when the energy is below the threshold, suggesting that tunneling might allow for this under certain conditions.
  • Another participant references Hawking radiation as a related concept, implying a connection to the original question.
  • A third participant asserts that a single photon cannot produce a pair in free space due to conservation laws, indicating that two photons would be necessary instead.
  • There is confusion regarding the term "uncertainty amount," with a participant seeking clarification on what this refers to in the context of energy levels.
  • A later reply challenges the initial premise by stating that pair production cannot be viewed merely as overcoming a potential barrier, indicating a misunderstanding of the process involved.

Areas of Agreement / Disagreement

Participants express differing views on the feasibility of pair production under the specified energy conditions, with no consensus reached on the possibility of tunneling or the implications for the energy of the resultant pair.

Contextual Notes

The discussion highlights limitations in understanding the role of energy conservation and the nature of quantum tunneling in the context of pair production, with unresolved definitions and assumptions regarding the "uncertainty amount."

Superposed_Cat
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If we have a photon being converted to a positron-electron pair, but we lack enough energy for this to happen (hv<2Me*c^2) but the difference is smaller than the uncertainty amount, such that tunneling may be possible, would the resultant pair have net negative energy? Would tunneling even be possible in this case? Any help appreciated.
 
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Hawking radiation would be one along your idea.
 
Superposed_Cat said:
a photon being converted to a positron-electron pair

A single photon can't do this in free space, because there is no way for this to happen without violating energy or momentum conservation. You would need a pair of photons.

Superposed_Cat said:
we lack enough energy for this to happen (hv<2Me*c^2) but the difference is smaller than the uncertainty amount

What "uncertainty amount"?
 
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Superposed_Cat said:
If we have a photon being converted to a positron-electron pair, but we lack enough energy for this to happen (hv<2Me*c^2) but the difference is smaller than the uncertainty amount, such that tunneling may be possible, would the resultant pair have net negative energy? Would tunneling even be possible in this case? Any help appreciated.

This is very puzzling. You're making it sound as if pair production is nothing more than matter-antimatter pair already there and only need to overcome some potential barrier to be liberated. It is no such thing.

Zz.
 
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