I had long thought (erroneously, apparently) that the Heisenburg uncertainty principle was just the observer effect applied to quantum mechanics (i.e., our inept attempts at observation were affecting the quantum scene and making the measurements unreliable).
My question is – how were they able to determine this? Was there some a-ha mathematically miraculous moment when they realized, “It’s not the limits of our technology! It’s a basic property of quantum systems! Wowzers!”?
I do not know the answer to your question, but i will say that as Heisenberg set it up, it was never a matter of ineptness or “limited” technology that might one day be overcome or superseded. Heisenberg argued that, in the light of fundamental physical laws and logic, it was and would always remain an absolute impossibility to make measurements at the quantum level that would not disturb the system and so introduce the relevant uncertainty.
A WAG: Perhaps it has to do with entangled particles. If two electrons are entangled, a measurement of the spin of one determines completely the spin on the other even though no observer has directly interacted with the latter. Other than that, I am not sure how you could distinguish even in principle between the inherent nature of the indeterminacy and the observer effect.
A particularly useful analogy when considering the Heisenberg Uncertainty Principle is to imagine a wave pulse (like tugging quickly on a rope or a slinky and watching the wave go down the length of it). The quicker you make the pulse, the more defined its position will be, but the less defined its wavelength will be. The slower you make the pulse, the more spread out it will be (hence its position becomes a fuzzy concept), but its wavelength is more accurately measurable. So if you increase information about a wave’s position, you inherently destroy information about its wavelength. Heisenberg’s Uncertainty Principle is essentially this property as applied to quantum mechanics. It’s not about disturbing a system with measurements so much as it is that the more you pin down one property, the more information is necessarily “given up” about the other property.
In essence, I can send a pulse down a rope that is very short and has a well defined position as it travels down the rope, but if you tried to measure the wavelength of the pulse you just couldn’t do it very well (and if it is a perfect spike pulse then it has no wavelength at all). Or, I can send a long gradual pulse down the rope that makes a nice beautiful wave, but if I asked you “where” that wave is, the best you could say would be that it starts in one place and ends in another, so it’s really not in any given one position, is it?
ETA: Scooped by flight! Damn it!!! With a nice simple video… That’s what I get for not reading the whole thread.
So I read both the other thread and this one, including the video.
What I get from that is: we don’t know where ordinary waves are, either? But don’t waves have speed?
Like it starts here: /////_______
Then a few seconds later it gets over there:
______/////_
If so, isn’t the wave (considered as a whole) constrained between its start and end crests, and can’t we say that any a given moment the wave is “there” and not “here”?
And aren’t we able to measure the movements of different waves through different mediums?
Isn’t that position and velocity, both?
ETA: I guess I’m thinking in terms of elementary-school physics, where you make a sine wave in a rope. You can clearly see it go from one end to the other, and if you took a video of it you could measure its position at any moment in time and also how quickly it’s moving towards the other end of the rope. I’m obviously missing something…
In QM theoretically if you repeatedly measure two non commuting observables A and B, one after the other, repeatedly and ‘instantaneously’ (meaning with such a short time between each measurement that there is no significant evolution of the wavefunction) such ABABABABABAB… for enough measurements you will find the result of each subsequent measurement can only be predicted as a probability distribution. However if you measure a single observable AAAAAAAAAAA… repeatedly and instantaneously you will find it always returns the same result (indeed this can even be used to keep a system in a certain state a la quantum Zeno effect). This is not the uncertainty principle per se, rather the quantum uncertatinty form which it is derived.
The observer effect doesn’t have an inbuilt distinction between which measurements are being made, but quantum uncertainty does, that’s one illustration of their difference.
More like it starts out here: /////_________________________
And a few seconds later it gets to:
_///////////_
(ok, that’s a horribly flawed picture for several reasons, but there’s a better one here)
Because the wave packet is finite, it doesn’t have a certain momentum (only an infinite wave train does) and that uncertainty results in a more spread-out wave packet later on.
Physical waves are a total red herring, we can always measure a particles (and quantum mechanics is a theory about physical particles, not physical waves) position or momentum with arbitrary accuracy in theory.
Yes not both, but my point is if you measure one if those waves where the position is spread out you can still obtain arbitrarily accurate value for the position of the particle, it’s your ability to predict the result of the measurement that is uncertain.
Of course immediately after the measurement (and you can’t ignore measurement because the UP is about what happens when measurements are made) the wave would change into one with arbitrarily well-defined position, but that is spread out in momentum space. But why should that be? Because the measurement apparatus interferes with the wave in some way? Which is certainly true, but without clarification it’s conflating the UP with the observer effect.
What about entangled particles, as all particles surely are to some degree? Then each particle is either described by a density matrix or a wave function that doesn’t obey the Schrodinger wave equation and the wave function/ wave function that does obey the S. equation is the wave function of the entire universe.
The old quantum view of particles also being waves is not as straightforward as it might seem to carry over in to quantum mechanics.
But don’t waves have speed?