Question on uncertainty Principle

[balabanscott]

I had a quick question on the uncertainty principle. I'm not a physicist but I'm familiar with the basic theories. I've never had anyone explain it to me like this, but this seems to be an intuitive way to look at it. So I need to know if I'm framing this right.

In classical, you start from point A and after undergoing the laws of nature you end up at point B. This also works perfectly valid in reverse: You could also say that given you are only allowed to end up at B, it means you must start at point A. Quantum mechanics seems to be the same thing except that instead of there being only one allowed state in the future, multiple states are allowed.

So if you have a "particle" that can end up at either A, B, or C say 1 second in the future any of which are perfectly valid, what would you expect to see when observing the particle right now? The answer would be exactly what we are seeing. If you fix the objects position, you have no way of knowing where it's going, since it is allowed to freely move to A, B, or C. If you measure its motion, let's say it is moving south, then the particle would appear to be exactly north of all three spots A, B, and C. Where a quantum particle is allowed to be in the future, determines what we observe now in the present.

Is this a proper way to frame what we are looking at with the uncertainty principle?

 

[Naty1]

Hi Scott:
'quick questions' here often go for pages and pages and weeks and weeks...

Where a quantum particle is allowed to be in the future, determines what we observe now in the present.

that's not the uncertainty principle, but this statement is I believe correct and does relate:

There is no known argument or experiment that can completely rule out the possibility that particles have well-defined positions at all times.

Try here for a start on Heisenberg uncertainty:

http://en.wikipedia.org/wiki/Uncertainty_principle

Here is the 'advanced course' from my notes of an excruciating long discussion here:

Synopsis: Is it possible to simultaneously measure the position and momentum of a single particle. Apparently not: The HUP doesn't say anything about whether you can measure both in a single measurement at the same time. That is a separate issue.

What we call "uncertainty" is a property of a statistical distribution. The HUP isn't about a single measurement and what can be obtained out of that single measurement. It is about how well we can predict subsequent measurements given the ‘identical’ conditions. The commutativity and non commutivity of operators applies to the distribution of results, not an individual measurement. This "inability to repeat measurements" is in my opinion better described as an inability to prepare a state which results in identical observables.

The uncertainty principle results from uncertainties which arise when attempting to prepare a set of identically prepared states. The wave function is associated not with an individual particle but rather with the probability for finding particles at a particular position.What we can't do is to prepare an identical set of states [that yields identical measurements]. NO STATE PREPARATION PROCEDURE IS POSSIBLE WHICH WOULD YIELD AN ENSEMBLE OF SYSTEMS IDENTICAL IN ALL OF THEIR OBSERVABLE PROPERTIES. ‘Identical’ state preparation procedures yield a statistical distribution of observables [measurements].

The uncertainty principle restricts the degree of statistical homogeneity which it is possible to achieve in an ensemble of similarly prepared systems. A non-destructive position measurement is a state preparation that localizes the particle in the sense that it makes its wavefunction sharply peaked. This of course "flattens" its Fourier transform, so if the Fourier transform was sharply peaked before the position measurement, it isn't anymore.

Don't recall where I got this, but it explains some of the details in a "Graduate level explanation" :

In quantum mechanics, measurement of observables exhibits some seemingly unintuitive properties. Specifically, if a system is in a state described by a vector in a Hilbert space, the measurement process affects the state in a non-deterministic, but statistically predictable way. After a measurement is applied, the state description by a single vector may be destroyed, being replaced by a statistical ensemble.

Hope you are confused just a bit: then you can join the 'uncertainty' club!

 

[balabanscott]

Thanks for the reply. I was looking for an easy way to explain this and and a way to understand it conceptually. Admittedly I get a little lost when going through the complex math. I think what you are saying about state prep matches what I was saying. So if:

1. Quantum "particles" have multiple possible future states and
2. The allowable future states of a "particle" determine what you see in the present

I get conceptually what's going on if that's true. And it makes perfect sense to me everything I've read on HUP so far (except for the complex math).


I used to have the hardest time with special relativity until I realized that the time dilation equations were really just the pythagorean theorem (for some reason none of my profs explained it like this). Time is just another dimension like the other three and if you use up your motion moving through space, you don't move along the time axis as quickly (just like if you fire a ball out of a cannon at an angle to the ground, it doesn't move horitontally as quickly as if you fire it straight along the ground.) And the speed of light is basically motion at a right angle to the time axis (so time stands still).

 

[Naty1]

1. Quantum "particles" have multiple possible future states and
2. The allowable future states of a "particle" determine what you see in the present

not sure what YOU mean by 'states'...

if you are searching for a really simple introductory explanation ...like the one you explain for special relativity ...that explantion of 'future states' might be ok, but it is not related to Heisenberg uncertainty.

if you are using a definition like this:

In physics, a quantum state is a set of mathematical variables that fully describes a quantum system. For example, the set of 4 numbers...defines the state of an electron within a hydrogen atom and are known as the electron's quantum numbers.

http://en.wikipedia.org/wiki/Quantum_statethen

In quantum theory, even pure states show statistical behaviour. Regardless of how carefully we prepare the state ρ of the system, measurement results are not repeatable in general, and we must understand the expectation value of an observable A as a statistical mean.

http://en.wikipedia.org/wiki/Quantum_stateSo what you 'see in the present' is a statistical distribution of measurement results...that's Heisenberg uncertainty...

Further I would argue that the possibility of an electron being in some other energy level in the future has nothing to do with it's current energy level. It's current energy level in an atom is determined by the degrees of freedom of that atomic assembly now, not in the future. The would imply things are predetermined and they are not. For example, the 'present electron' doesn't know I'm going to bombard its atom with electromagnetic energy tomorrow...and boost it's energy level. Or if it's radioactive, it might decay. But we can't predict with accuracy when it will decay: that too is a statistical phenomena applicable to large numbers of similar atoms. [I don't think it's specifically Heisenberg uncertainty??]

Most important: if YOU like your explanation, keep it and as you learn more, test it against what you learn. See if it gives you insights you seek. Einstein reportedly got started by wondering what would happen if he caught up with light...we know you can't, but that didn't stop him from developing some insights that changed science forever.

 

[Naty1]

Here is a paper whose introduction you might find of interest:

https://www.physicsforums.com/showthread.php?t=551554

I only read the intro...but I'll guess some experts will wrangle..and that's helpful in understanding different viewpoints...

edit: another explanation of Heisenbergg uncertainty:
" Physical systems which have been subjected to the same state preparation will be similar in some of their properties, but not in all of them. Indeed the physical implication of the uncertainty principle is that no state preparation procedure is possible which would yield an ensemble of systems identical in all their observable properties..."
which is very similar to one already posted.