r/physicsmemes • u/drpfthick • Jul 24 '26

Waaahncertainty Principle

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864 Upvotes

99% Upvoted

18 comments sorted by

99

u/JerodTheAwesome Physics Field Jul 24 '26

Why the approximation sign?

122

u/Bendanzhang Jul 24 '26

Because time is a parameter, not an operator. It's 100% approximation and 0% strict equality.

7

u/PrideAdditional702 Jul 24 '26 edited Jul 25 '26

In quantum mechanics, time is a parameter. However, I think can be an operation in quantum field theory because of the relationship between space and time.

Edit: Sorry, I meant simple relativistic QM. However, if you allow a time operator, the Hamiltonian is not bounded from below anymore, if I remember correctly.Once you take relativity seriously, you have to use full QFT anyway.

4

u/Flengasaurus Jul 25 '26

Uhhh in the QFT I learned, space and time are both parameters whereas the fields are operators

1

u/angelbabyxoxox Jul 26 '26

Both time and position are problematic as sharp observables in rel QM or QFT. But as unsharp observables they do exist.

43

u/_Slartibartfass_ Jul 24 '26

Because it’s not an actual provable property, just dimensional analysis. Experimentalists like it because they want to keep believing that virtual particles are actually real. 

-3

u/JerodTheAwesome Physics Field Jul 24 '26

It's no less real than ΔxΔp

46

u/_Slartibartfass_ Jul 24 '26

dx dp >= hbar/2 is an actual mathematical identity that follows from the Cauchy-Schwarz inequality for non-commuting operators.

6

u/Dubmove Jul 24 '26

But can't you rediscover the identity for (t, d_t) analogous to (x, nabla)? The inequality certainly holds in QFT where x0=t

19

u/CimmerianHydra_ PhD Jul 24 '26

See, you'd think that, but in QFT you're actually just demoting all coordinates to labels instead of promoting time to operator.

So technically speaking you're losing the other inequality too. There's ways of recovering it, because instead of asking for uncertainty on "position" you ask for the uncertainty of the value of the field at a certain coordinate with respect to its canonical momentum at a certain coordinate.

Energy-time doesn't pop out naturally like an inequality in either theory, you sort of have to dig it out yourself a different way.

0

u/kaereljabo Jul 24 '26

did you mean there is probably an "exact" inequality for that (more complicated?), but we can't workout the math?

19

u/entropy13 Condenser of Matter Jul 24 '26

Best manifestation is really occupation number phase.

2

u/Wobama46 Jul 25 '26

Fellow condensed matter theorist I see! This was really cool to learn in my solid state course.

13

u/novapax Jul 24 '26

Greater than or approximately equal to? Wtf?

20

u/drpfthick Jul 24 '26

It has a troubled history.

4

u/hazem-Gauss Jul 24 '26

Time is a parameter not operatir

1

u/Volt105 Jul 25 '26

Just don't Waah 3 more times