Uncertainty principle and information theory

[jadrian]

does the fact that there is a limit on how much can be observed on electrons location and momentum have anything to do with the finiteness and conservation of information?

is the total momentum plus location of an electron unknown to us or is it also unknown to the universe?

meaning, does an electron posess the information of both its location and momentum in the universe, and can that full information be propagated?

 

[Drakkith]

The usual interpretation of the wavefunction is that a particle doesn't have a set momentum and position at the same time and isn't capable of having one.

 

[pbuk]

In simple terms (avoiding the concept of wave functions)...

The finiteness of information is the same concept that there is a limit on how much can be observed on electrons location and momentum.

The concept of conservation of information states that if there is a limit on how much is knowable about an electron's location and momentum then the same limit applies to how much can be observed on that information, so again it is roughly equivalent to the concept of the finiteness of information.

The total momentum plus location of an electron is not only unknown, these quantities together do not have any meaning. In other words an electron which has a given momentum does not exist at any location, and vice versa.

The non-existence of information about specific quantum states (as opposed to the mere unknowability of such information) was highlighted by the EPR (Einstein-Podolsky-Rosen) Paradox, and Alain Aspect's experiments confirming the 'resolution' of that paradox.

 

[jadrian]

In simple terms (avoiding the concept of wave functions)...

The finiteness of information is the same concept that there is a limit on how much can be observed on electrons location and momentum.

The concept of conservation of information states that if there is a limit on how much is knowable about an electron's location and momentum then the same limit applies to how much can be observed on that information, so again it is roughly equivalent to the concept of the finiteness of information.

The total momentum plus location of an electron is not only unknown, these quantities together do not have any meaning. In other words an electron which has a given momentum does not exist at any location, and vice versa.

The non-existence of information about specific quantum states (as opposed to the mere unknowability of such information) was highlighted by the EPR (Einstein-Podolsky-Rosen) Paradox, and Alain Aspect's experiments confirming the 'resolution' of that paradox.

damn this website is cool
so the maximum amount of information an electron can propagate is I am just guessing somewhere in between knowing an electrons momentum plus location and knowing only its momentum or only its location?

also is this the basis for knowing what the smallest packet of information that can be propagated is?

also, can a photon carry any information other than its wavelength etc, or can you tell from a photon where (where is probly the wrong word) the electron was when it emmited the photon?

 

[Naty1]

hi jadrian...I see one of your areas of personal interest is information theory, so I'll attempt to go a bit further here. I am NOT an expert, but am also interested. [and I see you just posted more interesting questions while I am typing this]


First of all, I like Mr Anchovy's summary above, but am not sure how widely accepted all the the replys will be...If he could supply some links to sources that would help understand the context.

Let's start with just what the Heisenberg uncertainty releation means, irrespective of 'information' was the subject of a painfully confusing, contradictory and lengthy discussion here: [I'm not at all sure all participants would agree with my summary but there sure were a lot of experts arguing/discussing.]

https://www.physicsforums.com/showthread.php?t=516224

My own summary notes from that thread:

Synopsis: [Trying to figure out IF]: It is possible to simultaneously measure the position and momentum of a single particle. [Apparently not.] The HUP doesn't actually say anything about whether you can measure both in a single measurement at the same time. That is a separate issue.

What we can't do is to prepare an identical set of states. NO STATE PREPARATION PROCEDURE IS POSSIBLE WHICH WOULD YIELD AN ENSEMBLE OF SYSTEMS IDENTICAL IN ALL OF THEIR OBSERVABLE PROPERTIES.

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.

Next, here is an observation from DECODING THE UNIVERSE BY Charles Seife which I found to
have very interesting explanations of 'information'. This book is for the general public, no math.

...the paradox of Schrödinger's cat comes from trying to store a quibuit on a classical object...Something weird happens when you try to transfer a quibit from a quantum object to a classical object...from say an electron to a cat...Heisenberg's uncertainty principle is a problem of information transfer. The mathematics of quantum theory says you cannot gather information about two complementary attributes of a quantum object at the same time...You can't know a particle's position and momentum,simultaneously, for example. When you gather information about a particle's position, you lose information about its momentum...

This seems rather different than Mr Anchovy's post...but I have no idea if Seife's view
is accurate or not.

Also Seife, points out the quantum Zeno effect that if you keep rapidly 'measuring' a nucleus
you can prevent it from decaying:
:

[It]...shows that the act of measurement-the transfer of information-is intimately related to real, physical phenomena like nuclear decay.

and when I checked it Wikipedia,

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

you'll never guess the name that popped up with a neat quote: Alan Turing!

I have often wondered about what isgoing on between information residing
in quantum systems and their inherent superposition, just how multiple simultaneous quantum states are reflected in quibits which can take on those contradictory values...

Also, you might use the search function at the top of each page here for 'informaton' if
interested and see what's been discussed previously ...I mention that because I spent well over a year on these fourms before I noticed it...

 

[Naty1]

jadrian: one caution...lots gets posted which is later refuted, people realize they did not post what they meant,etc,etc...so
take replies with 'a grain of salt'...mine included!

so the maximum amount of information an electron can propagate is I am just guessing somewhere in between knowing an electrons momentum plus location and knowing only its momentum or only its location?

You seem to have two issues here (a) what information exists, you use the term
'propagates', and (b) what information can be extracted, what we can observe/measure.

THIS should be interesting! I'm guessing: Get ready for some debates if the experts latch
on to this discussion...one never knows if a discussion ends in 3 or 5 posts or goes on and on for weeks, even months!

This is one way to describe what happens:

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. In particular, after a measurement is applied, the state description by a single vector may be destroyed, being replaced by a statistical ensemble.

http://en.wikipedia.org/wiki/Observable_(quantum_computation)#Quantum_mechanics

[I have yet to relate my limited communication engineering perceptions of information with
those bubbling from quantum mechanics, but I can tell this description relates to my prior post about Heisenberg uncertainty: state preparation produces a statistical ensemble!.]

 

[jim hardy]

I still think the doggone thing is someplace, just we can't measure it.

 

[jadrian]

jadrian: one caution...lots gets posted which is later refuted, people realize they did not post what they meant,etc,etc...so
take replies with 'a grain of salt'...mine included!



You seem to have two issues here (a) what information exists, you use the term
'propagates', and (b) what information can be extracted, what we can observe/measure.

THIS should be interesting! I'm guessing: Get ready for some debates if the experts latch
on to this discussion...one never knows if a discussion ends in 3 or 5 posts or goes on and on for weeks, even months!

This is one way to describe what happens:



http://en.wikipedia.org/wiki/Observable_(quantum_computation)#Quantum_mechanics

[I have yet to relate my limited communication engineering perceptions of information with
those bubbling from quantum mechanics, but I can tell this description relates to my prior post about Heisenberg uncertainty: state preparation produces a statistical ensemble!.]

my perception of information is something that is propagated or can be propagated. information that can't be propagated should not have any effect on the universe, therefore unpropagatable information could be regarded as having no existence correct?

wow this **** is addicting

 

[jadrian]

I still think the doggone thing is someplace, just we can't measure it.

yeah I am with einstein on the dice thing. randomness and causality don't get along

 

[Naty1]

my perception of information is something that is propagated or can be propagated...information that can't be propagated should not have any effect on the universe,...therefore unpropagatable information could be regarded as having no existence correct?

not that simple...for example, information beyond your timelike light cone has no effect on you, but affects all the universe within it's timelike lightcone...How about encoded information which we cannot decipher? [see below]

Have you thought about information from the big bang...and that which 'disappears' into
a black hole?

I've collected some insights into information...none is complete but I found each to have an interesting perspective:

In general, information as the answer to some question should reduce your uncertainty about which among possible answers is correct.

A source of a message should have HIGH uncertainty, otherwise you'll know what the message contains before it is sent...we say it has high entropy, yet we want a received message to have LOW uncertainty...so we can understand it!

So the rule for objectivity is not that everyone lives in the same reality, it is that no two observers' realities can be inconsistent with each other. This also means that "complete" information does not imply a unique description of the reality, it merely implies access to all the information that is locally available to that observer in principle. The locality of the information is what preserves causality…”

an example:

Let's say I want to gather some "information" about local particles: Accelerated detectors will register different particle counts than an inertial detector! This is called the Unruh Effect. So how many local particles and the energies (temperature) I observe is not so simple...the 'information' depends not only on locality but frame of reference.

General relativity and quantum mechanics is fundamentally about information.

... Charles Seife

... at the end of the universe entropy is at a maximum...information will be at a minimum.

The holographic principle is a property of quantum gravity and string theories which states that the description of a volume of space can be thought of as encoded on a boundary to the region—preferably a light-like boundary like a gravitational horizon.

[The prior one is especially weird: just where is information 'stored'...everytime I expand the horizon that's where the information resides...on the enclosed area not within the volume as intuition would suggest.]

Leonard Susskind in his book THE BLACK HOLE WAR (his controversy with Stephen Hawking)
has some really interesting insights on information and horizons...like

the horizon of a black hole is "stringy"...it can be described in terms of quantum strings...hidden information is proportional to the total LENGTH of a string!... Hawking radiation can be viewed as string bits breaking loose from just outside the horizon...due to quantum fluctuations...

a perspective akin to virtual particles causing the Hawking radiation with its release of irretrievably scrambled information.

Also, you have to wonder if according to digital sampling theory in which periodic samples of a continuous message at an appropriate sample rate can completely reproduce the information content, we really understand what is around us. Add 'compression' techniques to that, and it becomes more interesting...what is it about our universe that causes it to have 'unnecessary' [redundant] information...like maybe we have in our genes?? [I strongly suspect those 'unnecessary' genes have a LOT to tell use when we can decode their purposes.]

I found a [peer reviewed] paper for another discussion which proclaimed:

at submicroscopic scales there is no distinction betwteen analog and digital...they are one and the same...

finally, have you tried to tackle this:
http://en.wikipedia.org/wiki/Entropy_(information_theory)

If information isn't difficult enough to get a firm grasp, entropy is worse.

Maybe the rule is that instead of entropy inevitably increasing we should be looking more
closly at its analog, that information is inevitably decreasing.

 

[Naty1]

randomness and causality don't get along

And yet the universe continues to function just fine...
the problem is us, not nature!

 

[jadrian]

this is why i hold the belief that reality (information transfer) be defined/communicated at a point.

 

[jadrian]

And yet the universe continues to function just fine...
the problem is us, not nature!

randomness implies that events occur as if the events themselves had free will.