The uncertainty in this principle is talking about uncertainty of measurement or particle itself?
They HUP has nothing to do with our ability to measure things, it is a fundamental characteristic of nature.
But is it the act of observing it that creates the uncertainty or is the uncertainty always there, regardless of whether we're observing it or not?
The uncertainty is always there, in the sense that it is impossible to prepare a quantum system in such a way that two incompatible observables both have definite values.
The uncertainty created by the act of observation is called the observer's effect. That has nothing to with uncertainty principle. The observer's effect may affect experiments whether Classical or Quantum in nature. The uncertainty principle is talking about an intrinsic uncertainty in a quantum system.
Simply put, it is not possible to both know where a particle is and how fast it moves about.
But i wonder what constraints the HUP poses for colliders where you know the location of the particle because you are guiding it so you can collide it with other particles while you know its speed/momentum and energy/time. And since the momentum is very high, its wavelength must be very low and some interpret this as a prerequisite for little to no wave bahavior(position uncertainty).
Does the HUP apply in the same manner to a massive accelerated particle as it does to an electron bound in an H atom? Or is there a semi classical situation of an acclerated particle where the HUP gradually fades away giving way to classicality?
In the LHC and other colliders, you don't aim individual particles at each other. You prepare two beams, each of which contains many particles and has a small but nonzero diameter, and arrange for them to intersect (overlap). In the intersection region, some particles in one beam just happen, randomly, to come close enough to particles in the other beam that they can interact. Most of the particles in both beams go right through the intersection region without interacting.
'Uncertainty principle' is a term I'd rather not use. As a result of the mathematical formalism of Quantum Mechanics, this is a theorem about the bounds of mean square deviations of 2 observables described through self-adjoint operators. The virtual statistical ensemble theory links the matrix elements appearing in the theorem to the results of perfect/unperturbed measurements of the 2 observables on the virtual statistical ensemble via the Born rule.
Please read this thread:
Its a theorem about observables and the outcome of observations. What a particle is etc when not being observed is anyone's guess because the theory is silent about it.
And I don't like it either, but like wave-function is enshrined - sigh.
No, not really. You CAN know that for a single particle. What the HUP says is that you have not discovered something deterministic the way that classical physics would say you have, you've just found it for one particle. When you do EXACTLY the same experiment with another particle, classical physics says that it will do the exact same thing as the first one, but that isn't what happens and THAT is what the HUP is all about. This is discussed in the link that zapperz provided.
I am not sure you can know both position and momentum for a single particle as this would imply a classical trajectory and afaik this only happens for very massive accelerated particles or as approximation of millions of detections. The relationship is given as delta x.delta p=h/2 and is a fundamental limit to the precision that these two observables can be known simultaneously for a particle. What you say seems to me an oversimplification and in qm there are plenty of them but seldom capture the essence.
What you can know about a single particle(measurement) will always be probabilistic as the particle doesn't have a well defined position and momentum.
It does as soon as you detect it. Once it is detected it has no more probability.
The uncertainty principle is about predicting the momentum and position of a particle prior to detection. You can predict either the momentum or the position with an arbitrary precision, but not both. It is also about determining the position and momentum of successive identical particles.
See this post: https://www.physicsforums.com/showthread.php?t=737543#post4656668
That is what I was saying - you need a measurement which as a process falls outside the formalism of qm to assert that a single particle has both well defined x and p. Prior to that the particle obeys the HUP and does not have these attributes.
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