[tex]\Delta E \Delta t \geq \frac{\hbar}{2}[/tex].(adsbygoogle = window.adsbygoogle || []).push({});

If I understand well, if I measure the energy of a particle (or system of particles) with a great precision, I cannot know well at all when the system had this energy... right?

My doubt is: The system had (or will have?!) the energy I measured, but when? Well, it could be long ago, a few seconds ago, or... in the future?

I don't really know how to form my question.

Say I measure with a 100% accuracy the energy of a particle. I will have a 0% accuracy in the time the system had this energy. However I know it can't be in future (right?), so there's a restriction in time. It can only be present or past, but not future... unless I'm wrong.

My common sense tells me I can't measure an energy the system never had if I measured with a perfect accuracy (or almost perfect). However from Heisenberg principle, all seems to indicate that I can measure very accurately an energy that the system will have within say [tex]10 ^9[/tex] years, which makes no sense to me.

Can someone explain clear my doubts?

In a sketch, say I have the "time axis" on the real numbers. Delta t would be an interval. On another real line I could put the value I measured for the energy. The interval being very small or even vanishing if I measured perfectly. So I know "the" value of the energy of the system. In this case, the Delta t interval would be the whole real numbers axis. However if the positive t's means future, I know I can't have measured the energy the system will be in the future! So I can reduce the interval from [tex]-\infty[/tex] to [tex]0[/tex]. And so writing [tex]\Delta E \Delta t \geq \frac{\hbar}{2}[/tex] is wrong although [tex]\Delta x \Delta p \geq \frac{\hbar}{2}[/tex] is correct.

I hope you can understand what I mean. In case not, I'll try to clarify but please let me know.

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# Heisenberg principle, about time

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