Regarding conservation of mass-energy Wikipedia says: "this is an exact law, or more precisely, has never been shown to be violated."

However, regarding quantum fluctuations, Wikipedia says here: "That means that conservation of energy can appear to be violated, but only for small times".

I thought to resolve the two conflicting statements by proposing that the virtual particles from quantum fluctuations are created/destroyed from the "noise energy" of the uncertainty principle. Hence, the energy is already there. Is this correct?

If this is incorrect, how can we resolve the two?

  • 2
    $\begingroup$ The uncertainty principle limits us from actually observing these violations. Either the energy is too small to detect or the time for which it exists is too fast. $\endgroup$
    – David H
    Jun 16, 2013 at 12:41
  • 7
    $\begingroup$ Long before virtual particles were imagined, the Bohr-Kramers-Slater theory proposed that energy and momentum were only conserved statistically, on the average. This was disproved in 1925 in a series of experiments by Bothe and Geiger. This is the kind of experimental evidence that the first WP quote refers to, and that quote is correct. The second WP quote is of a qualitatively different nature. The word "appear" refers to an optional philsophical interpretation of a mathematical construct -- not to the results of actual experiments. $\endgroup$
    – user4552
    Jun 16, 2013 at 15:45
  • 1
    $\begingroup$ @BenCrowell Emphasis on the optional. :) $\endgroup$
    – Michael
    Aug 26, 2013 at 6:19

1 Answer 1


In the four dimensional spacetime of field theory, which is where virtual particles live, Energy is one of the four momentum components: p_x, p_y,p_z,E . In this fourvector space , actually a pseudovector space because a minus sign enters between the fourth and the rest of the coordinates:

four momentum dot

the dot product of the vector with itself is its scalar measure, analogous to the length of the three dimensional vector in the normal three dimensional space. This scalar number in "real" space is fixed and unchangeable. In "virtual" space it can change according to the mathematical formulations of the Feynman diagrams describing the interaction.

Virtual space is a mathematical tool for complicated calculations and is constrained only by mathematics, not physics laws like energy conservation. This is because one can never do an experiment in virtual space, by construction.

As @DavidH comments to you the HUP is another story, it is a general uncertainty in the possibility of measuring some pairs of variables, well defined, as for example energy and time. If you measure the energies before an interaction well the energy should be conserved after the interaction. The HUP would just constrain the knowledge of how long the interaction took within the uncertainty limits. It is not the HUP that is generating virtual particles, but the specific calculations of interactions.

You may be thinking of vacuum fluctuations, but these are virtual, unless there is an interaction, i.e. energy is supplied by an interacting particle. Otherwise we would be able to get energy out of the vacuum :).


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.