H.U.P. = prng, loss of precision, early return?

[s19n]

I don't like the uncertainty principle. Who's with me? Since I don't fully understand it (and I don't think I fail to comprehend the jist of it, I just don't know why it's happening..), I search the net for crazy untestable theories for why the U.P. exists.

Psuedo random number generator - reality is one big function of time. That'd be fun /ttiforum/images/graemlins/smile.gif

Loss of precision - like when representing double presision and floats in most programming languages, there will be a loss of presion when you convert from a double to a float. So if information about position and momentum must be stored in a shared and fixed number of "bits", you would need more bits to store position when making a very accurate measurement and thus, you would loose precision when it came time to store momentum. A random value is chosen instead...?

Early return - A realtime system: measuring position very precisely might take more time than the universe alots. Position and momentum share the allotment of "cpu" cycles avaible when taking a measurement so when you measure one very precisely, the other one ends up being a random value.


Are there different methods of measuring position and momentum of small particles? Is the act of bouncing photons off one another the only method we know about?

 

[Darby]

s19n,

don't like the uncertainty principle. Who's with me? Since I don't fully understand it (and I don't think I fail to comprehend the jist of it, I just don't know why it's happening..), I search the net for crazy untestable theories for why the U.P. exists.

Quantum uncertainty can be fairly well understood in terms of classical physics. In those terms the uncertainty principle makes perfect sense.

In QM we're dealing with subatomic particles or at least particles that are ultra-tiny. We can't see them with ordinary visible light. So we have to use electrons or high energy/short wavelength photons to detect the particles.

Now we want to determine simultaneously both the position and momentum of, say, an electron that we are curious about. To do that we shoot it with a photon.

Photographers know that to focus a subject in the lens you have to use light that has a shorter wavelength than the diameter of the subject that you're going to photograph. The same applies to detecting the particle. The wavelength of the photon has to be less than the diameter of the electron (and you have to forgive the loose use of the term "diameter" when talking about electrons - it would be more precise to say "the wavelength of the electron").

But we also know that there is a relationship between the wavelength of a particle, in this case our photon, and the momentum of the particle. The relationship is inverse. Changing the wavelength changes the momentum in the opposite direction.

So, we decrease the wavelength of the detector photon so that its significantly smaller than the diameter of the electron but at the cost of significantly increasing its momentum. It strikes the electron and we very precisely determine its location. But in doing so we imparted some large undetermined momentum to the electron (it's underermined but we know that its a function of the wavelength of the photon). The electron's path is changed and we don't know what it's actual momentum was at the instant that it was struck by the photon.

We can go the other way by trying a gentler approach. We increase the wavelength so that its significantly larger than the diameter of the electron thus decreasing the momentum of the photon. This time when the photon collides with the electron we very precisely measure the momentum - but the electron isn't in focus. We don't know its exact position.

Next we split the difference between the two wavelengths. In that case we have both a fuzzy electron that also receives a momentum kick from the photon. Both position and momentum are uncertain.

This is a fundamental law of quantum physics and it has been experimentally verified. It has nothing to do with having better, more precise instruments. No matter how accurate the instruments are this uncertaintly relationship between ultra-tiny particles, wavelength,momentum and position will always be there. There's no way to "observe" the electron without disturbing it.

 

[reactor1967]

There's no way to "observe" the electron without disturbing it.

And they use to say there was no way to travel to the moon too but we did it. But, it is accurate to say that to day there is no known technology that can observe an atomic particles with out disturbing them. But, I say what if we could set up an experiment to exactly shoot the electron in the same path, same energy, and same spin every time. We could measure it then re-set up the experiment then measure the electron at a different time and a different position. Since the electron is being sent the same way every time at the same energy level and the same spin with all conditions being the same every time could we not have the ability to have are cake and eat it too. I wonder and I question.

 

[Darby]

But, I say what if we could set up an experiment to exactly shoot the electron in the same path, same energy, and same spin every time. We could measure it then re-set up the experiment then measure the electron at a different time and a different position.

No problem doing that. I showed you how to do it above. You can measure one or the other to a very high degree of precision.

The issue is the inability to make both measurements simultaneously with the same degree of accuracy for both as is the case of measuring just one.

But, it is accurate to say that to day there is no known technology that can observe an atomic particles with out disturbing them.

That's accurate in a sense. We don't have a technology today that allows one to observe a particle without disturbing it. But it suggests that tomorrow we will (or at least might). That's not accurate.

It's not at all a matter of better technology. It's not the lack of technology that prevents observing particles without disturbing them. It's the act of observation itself, by whatever means, that disturbs the particle.

 

[s19n]

This time when the photon collides with the electron we very precisely measure the momentum - but the electron isn't in focus. We don't know its exact position.

Darby! You've finally given me the ability to understand why position and momentum can't be measured together by using the term "focus". Now, I am left wondering about the difference between the observer effect and the H.U.P. edit: I should say it was a lot more than the word focus, I really appreciate you taking to the time explain it, but that was when the AHA moment struck and I understood why position and momentum were "linked".

I've read that the observer effect is independed of the HUP, meaning that no matter what kind of rig you build, we are still going to end up with a random element when taking a measurement. Is what I've understood about the observer effect accurate? If so, it's this independence that will not let my curiosity rest...

 

[satown]

thats not all true, once you observed time as a fourth dimension you start to look for a fifth dimension that exists outside anything physics can explain. this dimension will be imaginary and complex just as Abraham de Moivre.

 

[Darby]

s19n,

I've read that the observer effect is independed of the HUP, meaning that no matter what kind of rig you build, we are still going to end up with a random element when taking a measurement. Is what I've understood about the observer effect accurate?

Yes, that's accurate.

Now I do want you to keep very clearly in mind that the description of uncertainty I gave you was stated in terms of classical physics. It's accurate but it doesn't completely define the situation. A lot of quantum physics, and that includes uncertainty in it's complete form, doesn't have a classical analog.

You can do a lot more investigation into uncertainty to get a clearer understanding. The bottom line is that as far as we know uncertainty is a fundamental part of the description of reality that doesn't depend on mechanisms or frames of reference. Like any other well stated scientific theory it is defined in terms that allow for it to be nullified through experiment, observation and verification. Scientific theories cannot be proven to be true. They can only be shown to make accurate predictions or nullified as untrue. What is true is that scientists accept that all scientific theories are approximations of reality that have limits to their domains of validity (even if the limit has not been discovered yet).

A good example of a nullified scientific theory is Newtonian Mechanics. It's wrong. But - it makes very accurate predictions over a very large and general set of circumstances. Those circumstances go from bouncing billiard balls off each other to predicting the evolution of the orbital mechanics of planets and celestial bodies like entire galaxies. It's the most successful "failure" of a scientific theory in the history of humanity. We just happened to have discovered the limits of its domain of applicability about 100 years ago.

 

[s19n]

The bottom line is that as far as we know uncertainty is a fundamental part of the description of reality that doesn't depend on mechanisms or frames of reference.

Ahh, that's what bugs me. And "nullification" of uncertainty is irrisistable to me for some reason /ttiforum/images/graemlins/smile.gif


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

Laplace strongly believed in causal determinism, which is expressed in the following quote from the introduction to the Essai:

“ We may regard the present state of the universe as the effect of its past and the cause of its future. An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed, if this intellect were also vast enough to submit these data to analysis, it would embrace in a single formula the movements of the greatest bodies of the universe and those of the tiniest atom; for such an intellect nothing would be uncertain and the future just like the past would be present before its eyes

Even if the HUP was nullified it would still have to abide by the existing rules at some level ( I think..) so there's probably no mechanism to be discovered that will give us full determinism, but I'm drawn to the subject regardless.

2D image created from a single pixel sensor

http://arxivblog.com/?p=762

They shoot a beam at a single photon detector, another entangled beam at a CCD. From this they are able to see a 2d image. They did that in '95. Now, they have reconstructed the 2nd beam virtually using math and they are able to see a 2d ghosted image of an object with only a SINGLE photon detector. Very nice. Now they gotta build a bigger one ;-)

 

[Angleochoas]

A geniune question (forgive ignorance - you may have to fill in my own blanks)

That's accurate in a sense. We don't have a technology today that allows one to observe a particle without disturbing it. But it suggests that tomorrow we will (or at least might). That's not accurate.

Our perceptions is our reality right? Therefore our proofs?

5 senses;
is only one mainly used or two/? I'm thinking two...
- Optical/light = sight
- vibrations = sound ... but doesn't that get tricky? Isn't everything a vibration?
Color / light / energy / mass ?

So in dealing with observing subatomic particles are we trying to use two senses at once, or one at a time - or just one in reality?

If optics is just shades of light / then vibrations are these... then sight is just really sound (vibration)...Now you have me thinking too deep b/c;
touch would be micro/macro friction sensing? IE; vibration...again ...all sensed by sound?
3 = 1 ??? (I won't try the other two)

The other two just don't/cannot make sense???

Or does it not really matter anyway because it's just the 'receptor' ?

(I really can't imagine a LHT - Large Hadron Taster lol ... I think you get my erratic drift) Feel free to educate me,
I'm curious.

- Could electomagnetic fields be built to observe 'touch' (the disturbances around the suspended subject within the field)?
...Hrm if a 'collider' is 'touch' ... are we trying to incorpate all the senses...except smell/taste ?

/ttiforum/images/graemlins/confused.gif


OMG I think we're too late...it appears china has the "LHT"

 

[Einstein2087]

Ahh, that's what bugs me. And "nullification" of uncertainty is irrisistable to me for some reason

Well... you can get your wish, by changing your perspective a bit. The uncertainty principle does not forbid you to give a completely accurate description of a quantum system.

Remember that in quantum mechanics, particles are described as a waves travelling through space (actually this is an over-simplification, but it will do for the moment). And you can describe any wave PRECISELY, with a wave-function that tells you the amplitude of the wave at every point in space.

When you look at it in this way, the uncertainty principle becomes a non-issue. When you draw the graph of a wave on a piece of paper, it's obvious that the thing cannot be pin-pointed to single point. And if you had a wave confined into a very small space (giving you a relatively precise location), it would have to be a very chaotic wave - hence the uncertainty in momentum.

Similarly, the momentum of a wave is given (roughly) by its wavelength. So if the wave has any shape other than a perfect sine wave, there will be some uncertainty in momentum. And the closer the wave is to a perfect sine, the longer it must spread out - hence the uncertainty in position.

It's all a matter of simply geometry. And the entire thing can be perfectly understood in terms of classical wave mechanics. The only hard thing to swallow here, is the idea that electrons behave as waves. But believe me: over time, you get used to this idea.

 

[Einstein2087]

- vibrations = sound ... but doesn't that get tricky? Isn't everything a vibration?

Yup.

All the 5 senses are, in essense, wave (or particle) detectors. Indeed, every measuring instrument you can dream of, will be - in essense - a wave detector.

But note how, in the daily-life world, the 5 senses compliment one another. Your eyes give you a completely different input than your ears. Both may be sensing vibrations, but they are giving you very different information about the world around you.

So if we want to emulate the success of the 5 senses in the subatomic world, we should look for the same kind of idea: Look for ways to measure as many different aspects of the system in question, so we can learn as much as we can about it.

And ideed, that is exactly what particle physicists do. Every particle accelerator has lots and lots of detectors. Some look for photons. Others look for charged particles such as electrons. Still others look for particles in a specific energy range, or a specific combination of particles.

These detectors are our eyes, ears, nose, mouth and fingers. A casual observer might think that all these devices do exactly the same thing. But in the eyes of a trained professional, each type of detector serves as a completely different "sense".