Heisenberg's uncertainty principle
I keep seeing Heisenberg's uncertainty principle described in popular journalese as allowing a temporary violation of the law of energy conservation (or of the law of momentum conservation). The argument goes that HUP allows you to lend or borrow energy as long as settlement is made very soon, and that this arrangement represents a temporary violation of the law of energy conservation.
The truth is that there is no violation of the law of energy conservation.
The lending or borrowing of energy (and momentum) is done in a way that always respects energy (and momentum) conservation. How can this be? Just as with financial transactions where you lend to someone or borrow from someone, with energy transactions you lend to something or borrow from something. What is that something? The details depend on the precise circumstances, but I can illustrate one of the possibilities with the diagrams below.
Walk through these diagrams:
- A: This shows a particle going along all by itself conserving energy (and momentum) as per usual.
- B: This shows a particle that goes along as in A, but then it emits another type of particle (shown as the dashed line), after which the energy (and momentum) of the original particle have changed. Call these particles of type 1 (solid line) and type 2 (dashed line).
- C: This shows particles of types 1 and 2 going along, but then the type 2 particle is absorbed by the type 1 particle, after which the energy (and momentum) of the type 1 particle have changed.
- D: This shows diagrams B and C combined. The type 1 particle goes along all by itself, emits a type 2 particle, later on it reabsorbs the type 2 particle, and then goes along all by itself again.
That is the basic structure of how particles behave in physics. Energy (and momentum) conservation are always respected, so moving along each of the lines in the above diagrams each particle conserves its energy (and momentum), and at each of the vertices where a particle is emitted or absorbed the sum of the energies (or momenta) over all particles coming into the vertex is the same as the sum going out of the vertex.
Thus in diagram B the incoming type 1 particle's energy (and momentum) are shared between the outgoing type 1 and type 2 particles. This sharing between the type 1 and type 2 particles has to respect only the fact that the sum of the energies (or momenta) have to add up to the energy (or momentum) of the incoming type 1 particle. That means that one of the particles can have a negative energy and the other a positive energy, as long as the sum has the correct value.
The notion of a negative energy is counterintuitive. What does it mean? The physicist's definition of "energy" is the "frequency of oscillation" of the wave that is associated with the particle. Frequency can have any value (positive or negative) just as the rate of advance of a clock can be anything (forwards or backwards), so analogously energy can have any value.
Conservation of energy and momentum at the vertex where a particle is emitted or absorbed means that the particles don't have complete freedom to choose whatever energy and momentum they want to have, because their sum is constrained to be the same as whatever it was at the start. When a particle is going along all by itself (as in diagram A) there is a definite relationship between its energy and its momentum. After the particle has emitted another particle (as in diagram B), although the total energy and momentum are conserved the individual particles have energy and momentum that do not have the harmonious relationship that exists when the particle is going along all by itself. The physical consequence of this conflict in each particle is that they cannot not travel very far before they have to get their energy and momentum back into a harmonious relationship, and this requires the further emission or absorbtion of a second particle (as in diagram C). Diagram D brings it all together, where energy (and momentum) are conserved everywhere in the diagram (i.e. along each line, and passing through each vertex), and the conflict between each particle's energy and momentum in the "loop" part of the diagram means that the loop cannot be very large.
I think that this conflict between the energy and momentum of each particle, which is caused by the exact energy (and momentum) conservation everywhere in diagram D, is what is wrongly referred to (in popular journalese) as a temporary violation of energy (and momentum) conservation.
The relationship between the size of the conflict between each particle's energy and momentum and extent of the loop in diagram D is given by Heisenberg's uncertainty principle. The greater the conflict the smaller the loop. A particle going along all by itself has perfect consistency between its energy and momentum, so it is not part of a finite-sized loop.