Take the time-energy uncertainty relation, $\Delta$$E$$\Delta$$T$$\ge$$\hbar/2$.

My question is based on my confusion about the effect this relation may have within the interior of a highly compressed object such as a neutron star:

Would it:

  • provide a source of repulsive energy, albeit over a very short time span?
  • or would it actually represent effective mass, increasing the inward directed gravitational force?
  • or would it average out as in the flatspace metric, producing no overall effect?

My background is at beginner GR level, but I do appreciate that this relation can have a large effect at very short scales, I'm just not sure if these are relevant, even within a highly compressed object such as a neutron star, although a black hole is a different matter.

EDIT: I have posted an answer myself below.

  • 1
    $\begingroup$ Obligatory reading: This question and its answers. $\Delta t$ is probably not what you think it is, and this uncertainty relation probably doesn't mean what you think it does. $\endgroup$
    – ACuriousMind
    May 21, 2015 at 12:15
  • $\begingroup$ @ACuriousMind thank you very much for that advice. I had started reading a John Baez article based around the fact that time is not an operator (and the consequences of that for the above relation) and I will approach it again with that in mind. $\endgroup$
    – user81619
    May 21, 2015 at 12:35

1 Answer 1


In light of the comments above, regarding the time energy relation, I would need to read more about the time energy relation and later rephrase this question.

Normally I would delete the question, but it may be of value to other newbies like myself, making the same wrong assumption that the time energy relation is equivalent to the position momentum relation.

This article by John Baez is ,imo, very helpful in clarification of the difference between the relations, as well as the link provided by ACuriousMind in the comments above.


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