"which-way" information in quantum particles

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"which-way" information in quantum particles

Postby hyksos on September 12th, 2015, 2:34 am 

Prerequisites and suggested preparatory material :

(It is strongly suggested. Look over only the beginning and ending sections of the MWI article at stanford. Don't bother reading the whole thing. The Feynman lecture was broken up at a really bad section which straddles part 3 and part 4. For brevity, watch the end of part 3 and the beginning of part 4.)




In this thread I will be investigating the consequences an outlandish claim about the nature of the universe. In a nutshell, the claim goes :

All particles in the universe are as large as the universe. However, we experience particles as tiny, located points because the speed of light induces a spacetime lag between them.

That claim is so absurd that it feels like it should be abandoned without a second glance. However, as this article progresses, we will see that its consequences will (ironically) dovetail nicely with how quantum mechanics describes fundamental particles. In all situations where you say "Well this claim can't be true because..." eventually explain some known aspect of quantum weirdness.

This article is not introductory physics. It is not for the untrained. The motivation is to produce a theory for entangled photons, whose entanglement is dependent on the destruction of the "which-way" information in the lab.

If two photons are sent through mirrors in an optics lab, and a partially-silvered mirror sends them into an unknown path, it is said that the "which-way" information of the photon has been destroyed. The formalism of quantum mechanics then dictates the two photons are entangled. This phenomenon is also observed in the famous double-slit. Lacking the "which slit" information, the photon acts as if it took both slits and "interfered with itself". This is as much spoon-fed explanations as I will provide. It is expected that the reader will be familiar with the materials linked.


From modern formulations of quantum information theory, we get a coherent picture of how the universe around us never destroys any information. The "unexpected" correlations in the boxes described by Feynman can be explained mechanistically by a universe that never lets us poor humans destroy any information. Nor does the universe allow us to change the total number of bits of information in the universe. (see Esalen lectures above) Because we humans live our daily lives in a macroscopic world where things are forgotten, lost, destroyed and so on, our intuitions are (temporarily) confused by this. Our attempts to duplicate a quantum state exactly will be foiled by the universe. ("No Cloning theorem"). Our attempts to broadcast a quantum state exactly will be foiled by the universe. ("No broadcast theorem"). The universe is not malicious, its just that it never forgets anything (..it never "loses information").

So the information the quantum state of an isolated particle is largely resolved ; laid to rest. Isolated immobile particles contain 'information' in them like Feynman's three boxes do. See part 4 of the lecture vid starting around minute 13:00.

The remaining problem (hopefully addressed by this article) is that mere information-in-box picture does not help at all in resolving the fact that a particle also contains "which-way" information about its location in space and time. The entanglement seen in the "Feynman boxes" also extends to direction a photon was sent through an optics lab. Worse, the photon could be sent down long distances, whole city blocks, and still exhibit both entanglement as well as "self interference".

We could comfortably sleep at night if the weird quantum stuff was isolated snugly into the nucleus of tiny atoms. With the funny stuff inside boxes, we could keep the weirdness at arms length. But if entangled photons are sent down city blocks, or transmitted across water to a distant lab, we can no longer rely on those comforting illusions.

The essential sentence from the stanford article on MWI reads :
The Schrödinger equation itself does not explain why we experience definite results in quantum measurements.

This is a neat summary of the whole drama swirling around various interpretations of quantum mechanics. When the Schroedinger equation is extended to "city blocks" where photons travel, or don't travel, or go both ways, the problem rears its head in a more dramatic way.

The idea that we should give up on the photon ever having any position in space is not new. It was first posited seriously by a physicist named Nevill Francis Mott in the 1920s. It was then reiterated again more formally in Matrix Mechanics. From the PDF above, page 3 :
As a consequence, Matrix Mechanics appears as an abstract algebraic formalism where any visualized or intuitive description of a microscopic object is abandoned.

The emphasis was added by me. Mott knew that when a nucleus decayed and emitted a particle , that the Schroedinger equation was describing a spherical wave with the mother nucleus at the center. But in real physical bubble chambers, that never happens. The emitted particle always chooses a particular direction, and then traces out a straight line. In the presence of magnetic fields, the particle will trace a curved path. In all cases the observed trajectory is 'classical' -- as if the particle were exactly like a very tiny object moving in space.

The formalism contains no "tiny balls moving in space" (remember we abandoned all intuitive descriptions), and yet this is what is always observed in the lab. I believe a resolution can be obtained. I first propose an equivalence between emitted alphas exhibiting classical trajectories, and photons containing which-way information as a "kind of" quantum state. In other words, the phenomenon underlying classical trajectories emerging from alphas is the same phenomenon that erases the decoherence of photons whose which-way information is resolved by measurement. A simple example is placing a detector on a slit, which immediately removes the interference pattern.

Now that the "which-way" is a quantum state, it should be emphasized that we cannot rely on the stuff-in-boxes picture, nor will my theory ever resolve into it. Instead whenever a photon chooses a particular pathway, or an alpha moves in a classical trajectory, that position/state is not intrinsic to the alpha or the photon itself. To understand my theory, imagine that the position of a particle in spacetime is not "inside" the particle itself. Abandon such notions, as difficult as that might be right now.

Instead the quantum state which we have formerly named the "position" of a particle or the "trajectory" of a photon is stored in an ensemble of perceiving physical systems separated from that position in spacetime. But the separation is not intrinsic to quantum mechanics. Instead it is induced by the fact that observers are causally lagged from those positions by the speed of light. For all intents and purposes, we perceive a "particle at a place" but this is not actually happening. The particle is everywhere. It's not crazy because the Schroedinger equation says this exactly.

I empathize that the reader may be recoiling in horror from this idea. But look at how this theory fairs against what we actually observe in experiment. When the "ensemble of causally separated observing systems" is not storing the "position-state" of a photon, the photon will go through both slits. If the causally-separated-ensemble does something to leak the position-state (i.e. grad student places a detector) the photon's position/state is resolved for that ensemble. That's precisely what physically happens!

Analogously, the ultra-cooled alcohol in a bubble chamber acts as the causally-separated-ensemble for the alpha. The speed of light acts as a universal lag for quantum-state copying , and the alcohol atoms perceive a universe where the alpha is moving like a microscopic thing at a location. Formerly we believed this happens because the alpha particle intrinsically "carries around its own location". That's backwards. All particles are the size of the universe, and only appear as particles-at-a-place because the ensemble-of-measurers all have the same speed of light in their reference frames. That's why they all see the same thing -- not because they are all getting copies of the reality of the location of the (alleged) actual location that is actually out there.

I will be extending and summarizing this article later on. Time permitting, and depending on levels of interest in this thread.
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Re: Good Start

Postby Faradave on September 12th, 2015, 10:30 am 

hyksos wrote:All particles in the universe are as large as the universe.


I'm a little busy at present but I think you're off to a good start hyksos. What is a particle without its fields? The fields have indefinite span but are lightlike in spacetime orientation from a given location on a particle's world line (occupying a light cone).

There has been a trend recently to consider particles as "particular" disturbances of a common, universal field. To me, that's like the result of taking a sound level meter into a noisy room full of people. Measures could be taken at many locations and a map created of the common sonic field. I'd call that a "composite field", which fills the room.

I think more fundamental knowledge is gained from isolating an individual and mapping that person's "native field". It yields the radial (Gaussian) morphology that allows us to characterize the particular source at its center.
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Re: "which-way" information in quantum particles

Postby hyksos on September 12th, 2015, 12:11 pm 

I think more fundamental knowledge is gained from isolating an individual and mapping that person's "native field". It yields the radial (Gaussian) morphology that allows us to characterize the particular source at its center.

Yes. I was looking at this stuff earlier this morning. There are other people who have already followed this path of inquiry, but luckily not very many. The verbiage they tend to use for "characterizing a radial morphology" is something called Projective Spaces.

To review some of the basic food groups ,


Regarding this issue of characterizing a field's source "at its center", I would point your attention to the Grassmanians. The set of all lines passing through the origin has really grabbed my imagination in the past few days. (I don't have time to make fancy graphics right now,) but let me show you something quite surprising about this.

Consider a large set of lines passing through the origin on a chalkboard plane. We orient ourselves with the origin and then zoom in. Look what happens here. After zooming in by a factor of 100 , we still see exactly the same lines. This would continue with successive zoomings-in. ( to sound like stuffy grad students,) we declare that the positive Grassmanian is "invariant" under scaling transformations. Also, it is wildly NOT INVARIANT under translation.

That's neat and all, but where am I going with all this? Consider the picture of fundamental particles I gave earlier in my original post. I declared that all particles are as big as the universe, but the speed of light causes an ensemble of measurers to perceive them "at a location". We could ask if this is crazy, or we could ask : Does there exists a structure which is (1) invariant under scaling (2) not invariant under translation?

The answer is yes : it is the positive Grassmanian. (..!)

Anyways. I'll say a couple things that open the door to further discussion, without jumping off the deep end.

Textbook quantum mechanics introduces its concepts by having the reader consider a universe containing 1 particle at its lowest energy state (/temperature). ( "Consider a single electron trapped in a potential well with infinite sides, then blah blah blah" ) The reader can properly digest the material. Of course, we understand that we don't live in that universe. We don't live in a universe with 3 particles all cooled near absolute zero kelvin. We live in a warm universe full of lots of particles. And further that matters. In other words, the formalism in our book does not contain a so-called "ensemble of measurers separated at the speed of light" , but the world we live in does.

Second thing : everything you and I discussed on this forum considers the world as if it is made up of particles that exist eternally. That's another comforting illusion. Unfortunately, we live in the universe were E = mc^2 , and particles collide, annihilate, and reform, and decay. So there are people who have faced this issue already. They are trained physicists who make theories for the creation and destruction of particles. Notice that they talk about Grassmanians and twistors a lot. I don't believe this is a coincidence.
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Re: "which-way" information in quantum particles

Postby Braininvat on September 12th, 2015, 5:21 pm 

Great thread. Will need to brush up on QT a bit, so the biblio is appreciated, H. I've never been much for the ontic status of point particles, so I will follow with much interest.
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Re: The Incredible Lightness of Being (a Field)

Postby Faradave on September 12th, 2015, 10:50 pm 

hyksos wrote:The verbiage they tend to use for "characterizing a radial morphology" is something called Projective Spaces. ... Grassmanian is "invariant" under scaling transformations. Also, it is wildly NOT INVARIANT under translation.


Thanks for the references. I like the radial line analogy as would the real Faraday. But if you value invariance , instead of imagining the lines on a spatial surface, consider a lightlike surface (e.g. a future light cone). That's where a particle's native field would lie. It's the realm of any forces (or force carriers) with which it influences another particle.

Spatial cross-sections are more popular but describe composite fields of many particles. Like the roar of a crowd at a world cup soccer match. It can be difficult to know even what language is being spoken, let alone individual words.
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Re: "which-way" information in quantum particles

Postby bangstrom on September 13th, 2015, 6:03 am 

hyksos » September 12th, 2015, 1:34 am wrote:[size=85]
All particles in the universe are as large as the universe. However, we experience particles as tiny, located points because the speed of light induces a spacetime lag between them.

I prefer to think of particles as having the ability to function as coupled harmonic oscillators with remote particles anywhere in the universe rather than think of the particles themselves as being as large as the universe. This would be a connection similar to impedance matching in electronics where two and possibly more charged particles can momentarily share a common Schroedinger wavefunction as if they were side-by-side even though they may be galaxies apart. In other words, a particle here can "entangle" with a particle over there wherever "there" may be.

Hugo Tetrode suggested this possibility in 1922 as a mechanism for the transmission of light. If charged particles can share a wavelike connection across great distances, we have no need for the photon particle to explain how light works.
hyksos » September 12th, 2015, 1:34 am wrote:[size=85]
If two photons are sent through mirrors in an optics lab, and a partially-silvered mirror sends them into an unknown path, it is said that the "which-way" information of the photon has been destroyed. The formalism of quantum mechanics then dictates the two photons are entangled.

This statement sounds questionable to me. There is no “which-way” information for the original photons so there is no “which-way” information to be destroyed. A partially silvered mirror will not create an entangled pair. You may be thinking of a “spontaneous parametric down converter” (SPDC) where one photon enters and two entangled photons emerge.
hyksos » September 12th, 2015, 1:34 am wrote:[size=85]
In other words, the phenomenon underlying classical trajectories emerging from alphas is the same phenomenon that erases the decoherence of photons whose which-way information is resolved by measurement. A simple example is placing a detector on a slit, which immediately removes the interference pattern.
I know charged particles such as electrons or alphas can be detected at a slit but are you saying it can also be done with photons? I find that impossible.
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Re: "which-way" information in quantum particles

Postby Braininvat on September 15th, 2015, 12:27 pm 

It's helpful to bear in mind that Schrodinger's spherical wave is a probability distribution. The vapor in the cloud chamber registers more probable areas of field strength of the spherical field. The cloud chamber setup basically recruits individual atoms in the vapor of the chamber as detection devices - I like the way Figari and Tetra's paper trace the various historical lines of thinking on whether the cloud chamber atomic interactions are part of the quantum system or part of the classical readout of the chamber to the observer. Mott certainly anticipates decoherence theory in his analysis of what happens there.

For me, a universe-sized electron seems to violate a kind of basic intellectual parsimony in describing our measurements of particle events. I had the same reaction to John Wheeler's infamous "one electron" conjecture, which Feynman received one day in a phone call and reportedly had his mind blown. If you're not familiar with it, it basically suggests that all electrons have precisely equal mass and charge because they are actually just one electron. The universe just has one electron, which appears all over by means of intricate passage both backwards and forwards through spacetime. When it's moving in a T-negative path, it looks like a positron. And it's charge is reversed, of course. Yep.

Personally, I don't know which is ontologically more migraine-inducing, explaining a universal humongous electron field or explaining a point particle. I think people cling to the latter because it feels better causally.

I believe Bangstrom is correct, that you need a SPDC to obtain entangled photons. Had not heard about Tetrode and his wavelike connection, BTW, but I will seek out more information on that. Eliminating the photon strikes me as a theoretical path worth pursuing. The trick, I guess, is preserving quantization in a wavelike connection.
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Re: "which-way" information in quantum particles

Postby Braininvat on September 15th, 2015, 12:51 pm 

Come to think of it, photons are the size of the universe, because for a photon there is no time and no linear dimension length to the universe. Time dilation and Lorentz contraction gone mad! Photons, just from a relativity perspective, don't really exist. But if we say they do, then the photon would see itself and the universe as the same size and every trip would be, ha, instantaneous. They say, to realllly know a particle, you have travel along with it in its frame of reference. The only reason we think photons exist is that we can't travel with them and really get to know their non-entity-ness.
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Dimension Matters

Postby Faradave on September 15th, 2015, 2:32 pm 

Braininvat wrote:Come to think of it, photons are the size of the universe, because for a photon there is no time and no linear dimension length to the universe.

True enough, in the direction of motion. That covers one of four dimensions of size. One might argue that "direction of motion" is also ray-like (e.g. ray of light) from an origin within the universe (the emitter), the path then covering "size" from that point outward. If we add the opacity of the absorber, the path is limited further to a finite segment.

You might do better to abandon the light quantum as a red herring. The prior electric field of the emitter has indefinite span from its center outward in all directions and forward in time. That's where the universe filling electron notion arises. hyksos is correct to point out the limitations involved with creation and annihilation events for a particular particle.

Remember that a particle without fields is an empty event, no particle at all. Better to consider a "particle" as simply the vertex of a light cone field, the latter being the essential aspect. The "particle" with its field can have a timeline, which gives a stack of snow cones model.
Image
The "particle" might correspond to a creation event, and the vertex of the topmost cone annihilation. The cones, as fields, would all be indefinite in extent. The field of an annihilated particle can thus, still effect future events, in the same way earth would receive light from the sun for 8 minutes after its vanishing.
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Re: "which-way" Indeed!

Postby Faradave on September 15th, 2015, 3:05 pm 

Braininvat wrote:When [an electron is] moving in a T-negative path, it looks like a positron. And it's charge is reversed, of course.


I'll make it simple. While Wheeler and Feynman intuited something important, they never made it all the way to realization. This because, like everyone else, they completely ignore the dimension of time as providing a 4th independent spin coordinate, the one which sustains "intrinsic" spin (my chronaxial spin).

This is critical because time is unidirectional. That means chronaxial spin can be absolutely right-handed or absolutely left-handed (wrt to the future). When Feynman identified positrons as like electrons going backward in time, it was naïve and silly for others to take it literally. We can easily trap positrons and continuously observe them going forward in time with us.

What's different about a positron is that its chronaxial spin is going the opposite direction to that of an electrons. That's why it seems like an electron going backward in time. A positron has the opposite spin wrt to the future (as an electron would have wrt to the past). Of course if a positron and electron collide, chronaxial spins cancel, the fields collapse.
Good by particles!

electron positron posi-electron.png
Being unidirectional, temporal axes provide two opposite absolute spin directions, corresponding to positive and negative electric charge (left conjugate pair). If an electron could flip over to travel backward in time, its chronaxial spin would match the positron's (right)!
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Re: "which-way" information in quantum particles

Postby bangstrom on September 16th, 2015, 5:45 am 

Braininvat » September 15th, 2015, 11:51 am wrote:Come to think of it, photons are the size of the universe, because for a photon there is no time and no linear dimension length to the universe. Time dilation and Lorentz contraction gone mad! Photons, just from a relativity perspective, don't really exist. But if we say they do, then the photon would see itself and the universe as the same size and every trip would be, ha, instantaneous. They say, to realllly know a particle, you have travel along with it in its frame of reference. The only reason we think photons exist is that we can't travel with them and really get to know their non-entity-ness.

I suspect we live in a universe of waves and it is the waves that connect all things. Even “solid” particles like protons may be nothing more than standing waves in a sea of waves and it is this environment of waves “the fabric of space” that is the size of the universe.

There is a recent English translation of Tetrode's 1922 article where he describes how two electrons can exchange energy via a two way resonance that extends both forward and backwards in time.
http://nonloco-physics.0catch.com/interaction.pdf

The same idea can be found in some modern theories of light such as John Cramer's Transactional Interpretation of Quantum Mechanics (TIQM).
http://arxiv.org/pdf/1503.00039.pdf
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Re: "which-way" information in quantum particles

Postby Braininvat on September 16th, 2015, 12:14 pm 

I like Cramer's thinking, as it builds upon the old Wheeler-Feynman handshake theory of transaction between emitter and absorber. It deals handily with violations of Bell inequality. I need to revisit Cramer more often, and I thank you for the link, Bang. The passage below will no doubt resonate with DaveOblad, and other Tegmarkian fellows, as it acknowledges the wavefunction has the ontological status of a mathematical encoding of the possibility of a quantum process.

The wave functions ψ of the wave-mechanics formalism are the offer
waves. In some sense they are real waves traveling through space, but in another
sense they are not real because they represent only a mathematical encoding of
the possibility of a quantum process. The transaction that forms after the emitter-absorber offer-confirmation exchange process goes to completion is the real object, what we would call the “particle” that has been transferred from emitter to absorber. In that sense, the real objects in our universe are waves, while particles are an illusion created by the boundary conditions that must be observed at the vertices of the wave-exchange transactions.

What happens to the offer and confirmation waves that do not result in the formation of a transaction? Since the formation of a transaction produces all of the observable effects, such waves are ephemeral, in that they produce no observable effects, and their presence or absence has no physical consequences. However, in explaining seemingly paradoxical quantum phenomena such as interaction-free
measurements, such waves can be viewed as “feeling out” components of
the system....


I think it's interesting that one can postulate such non-transactional wave events....they seem to belong to a computed universe where you can have the system monitoring things without any actual energy transfer. Sort of like people all stopping at ATMs to just check their balance, but not actually withdrawing money or sending it anywhere or leaving any observable trace that they have checked their account. I can hear Einstein's head exploding, again, in the Bardo or wherever he might find himself.
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Re: "which-way" information in quantum particles

Postby hyksos on September 16th, 2015, 4:56 pm 

I know charged particles such as electrons or alphas can be detected at a slit but are you saying it can also be done with photons? I find that impossible.

"The experiment utilizes a Mach–Zehnder interferometer, and visually demonstrates the loss of interference fringes when a which-way measurement is imposed, and the restoration of that pattern when the which-way information is destroyed."

http://www.optics.rochester.edu/workgroups/lukishova/QuantumOpticsLab/homepage/snyderlapuma.pdf
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Re: "which-way" information in quantum particles

Postby hyksos on September 16th, 2015, 5:48 pm 

Hugo Tetrode suggested this possibility in 1922 as a mechanism for the transmission of light. If charged particles can share a wavelike connection across great distances, we have no need for the photon particle to explain how light works.


Come to think of it, photons are the size of the universe, because for a photon there is no time and no linear dimension length to the universe. Time dilation and Lorentz contraction gone mad! Photons, just from a relativity perspective, don't really exist. But if we say they do, then the photon would see itself and the universe as the same size and every trip would be, ha, instantaneous.


This should serve as a response to both Hugo Tetrode and Braininavat.

The key part of this puzzle that you are missing (and that Tetrode was missing) is the two Feynman lectures above. Please watch them carefully. Feynman tends to be longwinded, and even the grad students off camera take an hour to finally get what he is trying to communicate. Let me try to communicate the basic idea as much as this probably won't pan out well.

Our universe must preserve the total amount of information it contains in every interaction. All the weirdo behavior you see in the Feynman boxes is a consequence of that underlying law. One way to really understand what this means is to first consider the universe as it was conceived at the time of Isaac Newton. In the "newtonian" universe, an event would happen in spacetime and all parts of the universe would receive its consequence at the same time. Nobody found this strange, because that's what we see in our daily lives. One man talks in front of a crowd and the whole crowd hears his voice. When a bonfire is lit, all participants nearby see their own copy of that fire. An event in spacetime E is broadcast to all nearby observers.

But fundamental particles cannot do this. Nothing about them can be broadcast to the rest of the universe. They can only reveal their current quantum state to 1 other particle somewhere else. Feynman describes in the videos above what happens when you try to "game the system" into making correlated copies of a quantum state. For a red lightbulb he gives the example "He see's that its red. And that guy over there sees that it's red, and I can see that it's red." The only way this can happen is that lightbulbs are macroscopic objects composed out of gazillions of fundamental particles. For each "observer who sees red" there must be at least one atom of lightbulb emitting red.

Look at what Susskind says starting at 1:00

[youtube]https://www.youtube.com/watch?v=tpjUtQxKjQ4?t=1m[/youtube]

In summary, we aren't going to recover Tetrode-like wave mechanics in a universe like this one.
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Re: "which-way" information in quantum particles

Postby Braininvat on September 16th, 2015, 6:17 pm 

I tend to do better with papers than videos. That said, I will watch, but ask you to bracket with url rather than youtube, which makes for a dead link here.
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Re: "which-way" information in quantum particles

Postby bangstrom on September 18th, 2015, 4:00 am 

hyksos » September 16th, 2015, 3:56 pm wrote:
I know charged particles such as electrons or alphas can be detected at a slit but are you saying it can also be done with photons? I find that impossible.

"The experiment utilizes a Mach–Zehnder interferometer, and visually demonstrates the loss of interference fringes when a which-way measurement is imposed, and the restoration of that pattern when the which-way information is destroyed."

http://www.optics.rochester.edu/workgroups/lukishova/QuantumOpticsLab/homepage/snyderlapuma.pdf
The phenomena you mentioned were familiar more than a century ago and they have nothing to do with items in the quote- electrons, alpha particles, or identification at the slits. There are no slits or entangled pairs in Mach–Zehnder demonstration.
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Re: "which-way" information in quantum particles

Postby hyksos on September 18th, 2015, 10:48 am 

This thread is getting derailed into semantics. If you find some clerical error in my post, mark it up as erratta. That's fine. Yes photons have to be treated slightly differently to remove which-way information, as is done in the Mach-Zehnder. Your claim that imposing which-way information on photons, and erasing that information is impossible. I have provided a link to a simple well-known experiment which does both. I'm not here to get pulled into minutiae of experimental apparatuses.

The central points in this thread remain unassailed.
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Re: "which-way" information in quantum particles

Postby hyksos on September 18th, 2015, 12:32 pm 

Braininvat » September 17th, 2015, 2:17 am wrote:I tend to do better with papers than videos. That said, I will watch, but ask you to bracket with url rather than youtube, which makes for a dead link here.

Alright, I understand this complaint regarding popular science. Yes, I did link to Susskind speaking in a popular science TV program (about ink being dropped into a sink of water.)

Let me first tell you what I am trying to look for regarding a "paper" on conservation of information in quantum states. Prior to quantum information science being born (roughly the early 1980s) QM as a discipline already had a handful of physical laws which presaged it. One of them is called unitarity. The other one was a law that stated the evolution of a quantum system was reversible in time. (I believe this was called Louiville's theorem , or the Quantum Louiville Equation )

Unitarity meant that the sum total of all the probabilities of a quantum measurement will always be 1.0

The Quantum Louiville Equation was a quantum version of the classical Louiville equation. The Louiville is a result from a branch of physics called Hamiltonian mechanics. It's a description of a system made up of many (billions) of coupled particles.

Quantum Louiville is pointedly reversible, meaning the time could be reversed and all the old trajectories can be recovered completely. This is only possible (theoretically possible) if the dynamics are not destroying/forgetting something the system did during its actual evolution in time. In other words, it is "conserving information".

Anyways! That was the picture QM had up to about 1979. But lets get back on track. You want a paper and I want to give you one. Alright. So first of all, I will say that I have googled for over 30 minutes in a feverish hunt for a paper. The only one I could find that is low-level enough to follow was
http://www.bimanbagchi.com/courses/ss207/notes/Lecture_note_1.pdf

This is literally the simplest paper I could find on this topic. (I'm not even kidding.) It looks like a wall of mathematics, but I will point you to the final sentence of the PDF.
But in quantum statistics, the quantities wnn gives the probability of finding the system in a particular quantum state with no indication of coordinates and momenta of the particles of the system.


Here is another PDF if you want to a more thorough formulation of Classical Louiville. (Quantum Louiville is toyed with on the last page only)

http://inside.mines.edu/~tohno/teaching/PH505_2011/liouville_dvorak.pdf

Outside these walls of math , googling produces people talking on forums saying things like:
"Conservation of information" is quantum unitarity, the law that the quantum mechanical wavefunction always evolves coherently, no pure state ever turns into a mixed state. These are clean google terms. The classical analog is Liouville's theorem.

But the above quote is not from a "paper" so you can take it with a grain of salt.
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Re: "which-way" information in quantum particles

Postby Braininvat on September 18th, 2015, 12:59 pm 

I (and hopefully other lurkers about) will read, thanks. I'd also add that many physics papers that seem quite daunting can be handled by reading the abstract, the intro, and the concluding paragraphs which are usually the least walled with equations. Then, if one wants the challenge, you can sometimes follow a bit of the math (looking up things as you go) and, even if you can't quite get how some equations were derived, you get a feel for what are the constants, what are the variables, which side has which sort of energy, how things get summed up, where negative values are welcomed or verboten, where things go absurdly to infinity, etc. Stretching one's college calculus is good, albeit painful for most. If you skipped or slept through matrix theory, tensor analysis, and other fun stuff, then it can be very painful. What I always tell myself (and usually I'm not lying to myself) is that the math is simpler than it looks and it's often possible to verbally describe equations in a manner that you can carry away with you, e.g. "on this side, we have total energy density, on that side, we have spacetime curving...."

And I certainly don't discount videos, especially when they are very lucid and engaging fellows like Leonard Susskind talking about how we all are projected from information on a 2-dimensional film at the edge of the universe. That gets a foot in the door.
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Re: "which-way" information in quantum particles

Postby bangstrom on September 19th, 2015, 1:55 am 

hyksos » September 18th, 2015, 9:48 am wrote:This thread is getting derailed into semantics. If you find some clerical error in my post, mark it up as erratta. That's fine. Yes photons have to be treated slightly differently to remove which-way information, as is done in the Mach-Zehnder. Your claim that imposing which-way information on photons, and erasing that information is impossible. I have provided a link to a simple well-known experiment which does both. I'm not here to get pulled into minutiae of experimental apparatuses.

The central points in this thread remain unassailed.
I have never made any statement that, “that imposing which-way information on photons, and erasing that information is impossible” because clearly these things are possible. I find it to be more than a matter of “semantics” that your answers don't resemble my questions.

If I have more questions, I will try to make them more clear and I hope you will try to read them more carefully.
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Re: "which-way" information in quantum particles

Postby bangstrom on September 20th, 2015, 5:24 am 

hyksos » September 12th, 2015, 1:34 am wrote:[size=85]
The formalism contains no "tiny balls moving in space" (remember we abandoned all intuitive descriptions), and yet this is what is always observed in the lab. I believe a resolution can be obtained. I first propose an equivalence between emitted alphas exhibiting classical trajectories, and photons containing which-way information as a "kind of" quantum state. In other words, the phenomenon underlying classical trajectories emerging from alphas is the same phenomenon that erases the decoherence of photons whose which-way information is resolved by measurement. A simple example is placing a detector on a slit, which immediately removes the interference pattern.

Now that the "which-way" is a quantum state, it should be emphasized that we cannot rely on the stuff-in-boxes picture, nor will my theory ever resolve into it. Instead whenever a photon chooses a particular pathway, or an alpha moves in a classical trajectory, that position/state is not intrinsic to the alpha or the photon itself. To understand my theory, imagine that the position of a particle in spacetime is not "inside" the particle itself. Abandon such notions, as difficult as that might be right now.
I see the alpha particle and photon as two different conditions, so for simplicity, consider the case the a photon.

This is my question: If the position/state is “not intrinsic” to the photon, then where is it?

I think your explanation that the photon is as large as the universe is kind of on the right track and that is where the answer should lie but it needs some clarification. And, if the the photon is as large as the universe, then the position/state would be intrinsic to the photon.

There are experiments where placing a detector on a slit removes the interference pattern for charged particles like electrons. The detector detects the charge without disturbing the path of the particle which gives us which-way information but photons have no charge to detect and any detection of a photon would annihilate the photon ending its path. Also, if the photon acts as though it goes through both slits, a detector could not give us which-way information because the path for a photon is both ways.

To repeat the question, Where is the position/state of the photon?
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Re: "which-way" information in quantum particles

Postby hyksos on September 21st, 2015, 2:08 am 

And, if the the photon is as large as the universe, then the position/state would be intrinsic to the photon.

My theory is claiming the position (which-way) of a photon is stored in the ensemble of measuring observers.


The detector detects the charge without disturbing the path of the particle which gives us which-way information but photons have no charge to detect and any detection of a photon would annihilate the photon ending its path.

(Pun intended) I have detected that a consistent complaint you are giving is : that no information about a photon can be obtained, lest we destroy it by absorption.

Ironically, there is a end-around backdoor to avoiding this issue that the photon must be destroyed. See for example,

http://www.nature.com/nature/journal/v512/n7515/abs/nature13586.html

See also http://physics.illinois.edu/people/kwiat/interaction-free-measurements.asp
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Re: "which-way" information in quantum particles

Postby bangstrom on September 24th, 2015, 5:24 am 

hyksos » September 21st, 2015, 1:08 am wrote:
My theory is claiming the position (which-way) of a photon is stored in the ensemble of measuring observers.

I would go even farther and claim that all of the information of a photon is stored in the ensemble of measuring observers. The information we gather about photons is derived from observations of the total ensemble and the changes we observe as electrons gain and lose energy.
Photons and the paths they take are all conjecture based on these observations. Photons are a narrative we use to explain how energy leaves one electron and arrives at another. We have no need for the photon if the cause for the energy exchange lies in the nature of the total ensemble and a wavelike connection between an electron in the light source and an electron in the receiver (entanglement).

hyksos » September 21st, 2015, 1:08 am wrote:
(Pun intended) I have detected that a consistent complaint you are giving is : that no information about a photon can be obtained, lest we destroy it by absorption.

Ironically, there is a end-around backdoor to avoiding this issue that the photon must be destroyed. See for example,

http://www.nature.com/nature/journal/v512/n7515/abs/nature13586.html

See also http://physics.illinois.edu/people/kwiat/interaction-free-measurements.asp
To be specific, I don't think we can detect the photon between signal and receiver because it doesn't exist.

The experiments you cited are are some I haven't seen before and they were amazingly clever. There are also other experiments where “impossible” things can be done with photons such as quantum erasure, quantum teleportation, or entanglement between photons that don't exist at the same time.

I think the common explanation for all of these “impossibilities” is that the entanglement is between electrons in the source and electrons in the receiver and the photon explanation is just an imaginary distraction.
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Re: "which-way" information in quantum particles

Postby hyksos on September 24th, 2015, 5:23 pm 

We only really observe the energy going down in electron Alice, and then later on, the energy of electron Bob goes up. We deduce (presume?) that a little thing "carried" the energy there in a packet of some kind.

(On a personal note here). Honestly, I had reached your conclusion about photons being a convenient fiction. I remember that I first had the thought some time in my senior year of high school. One fateful day I tried to communicate this to my high school physics teacher. However, being a teenager at the time, I was not articulate enough or trained enough in the special "physics lingo" words to explain this to him clearly.

I remember the exchange quite clearly from decades ago. The best my teenage wisdom could do is bring up Heisenberg Uncertainty Principle. This caused my poor teacher to basically bark me down by explaining to me what the Uncertainty Principle really meant. However, what I wanted to say to him was that :

  • "Photons are a convenient fiction."
  • "I'm not referring to the Uncertainty Principle, I'm making an analogy with it."
Alas, my teen mouth was not articulate enough to say things as clever as "convenient fiction". Or "I am making an analogy here".
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Re: "which-way" information in quantum particles

Postby bangstrom on September 26th, 2015, 5:52 am 

hyksos » September 24th, 2015, 4:23 pm wrote:I remember the exchange quite clearly from decades ago. The best my teenage wisdom could do is bring up Heisenberg Uncertainty Principle. This caused my poor teacher to basically bark me down by explaining to me what the Uncertainty Principle really meant. However, what I wanted to say to him was that :

  • "Photons are a convenient fiction."
  • "I'm not referring to the Uncertainty Principle, I'm making an analogy with it."
Alas, my teen mouth was not articulate enough to say things as clever as "convenient fiction". Or "I am making an analogy here".
I like your statement, "Photons are a convenient fiction."
A. F. Kracklauer has this to say:
“In any case, this writer holds, the optimum tactic to improve the paradigm for ‘light’ is to hew as close as possible to directly experienced, empirical data, without introducing hypothetical constructions. Historically, it has been these hypothetical constructions that eventually led to both contradictions and constraints on imagination impeding progress. Such hypothetical notions in the course of time take on in the folklore a sense of ‘reality’ altogether undeserved but vivid, so that eventually it becomes the implicit goal of science to explain these constructions, in place of nature herself. ‘Fields’ and ‘photons’ are prime examples; both have lead to the idea, now very widely spread, that radiation can detach from its source and exist independently, as if it were a kind of ethereal matter. This is nowhere supported by evidence,”
http://nonloco-physics.0catch.com/paradigm.pdf

hyksos » September 24th, 2015, 4:23 pm wrote:We only really observe the energy going down in electron Alice, and then later on, the energy of electron Bob goes up. We deduce (presume?) that a little thing "carried" the energy there in a packet of some kind.
I see more similarity to Schroedinger's cat than to the Uncertainty Principle. Instead of the electron (cat) being dead or alive, its location is indeterminate. If electrons Alice and Bob momentarily entangle, they share a common wavefunction and they are essentially no longer separated by space and time. They are like a single particle but their locations can no longer be said to be either here nor there. Their locations are “indeterminate” like Schroedinger's indeterminate dead/alive cat. When the wavefunction collapses, their locations again become determinate and, if electron Bob is now the one with the energy we deduce that a “something” must have carried the energy from one location to the other but the electrons have swapped identities including energy levels.
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Re: "which-way" information in quantum particles

Postby Braininvat on September 26th, 2015, 10:17 am 

Can one really say electrons, in an emitter/absorber interaction, swap identities, Bang? Do the electron in the photosphere of the sun, and the electron of a selenium atom in the PV panel on my roof, swap? Just trying to sharpen our sense of this type of emission/absorption.
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Re: "which-way" information in quantum particles

Postby hyksos on September 26th, 2015, 4:48 pm 

After some 'refresher course' on this Quantum Louiville stuff. It seems to me wobbly to put so much faith into the consequences of this theory, particularly regarding conservation of quantum information. It does not make a strong case about this, since the equation itself is formulated in a statistical context. Also, Stephen Hawking was (once) very comfortable with the idea that black holes destroy information. It seemed for a while that either scenario, destroyed information or conserved information, was tenable in physics.
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Re: "which-way" information in quantum particles

Postby bangstrom on September 27th, 2015, 4:07 am 

Braininvat » September 26th, 2015, 9:17 am wrote:Can one really say electrons, in an emitter/absorber interaction, swap identities, Bang? Do the electron in the photosphere of the sun, and the electron of a selenium atom in the PV panel on my roof, swap? Just trying to sharpen our sense of this type of emission/absorption.

The electrons exchange “information” and information is the thing that gives particles their “identity.” Quantum information is conserved in the exchange.

I understand the transfer of light energy among remote electrons to be no different from quantum entanglement where two remote particles share the same coupled harmonic oscillation and, when the wavefunction collapses, their identities can be redistributed as if properties of one have swapped places with the other. So an electron in your solar panel can gain energy as an electron in the sun loses energy.

There is no photon particle carrying energy as it travels through the space between and there is no time interval between emission and absorption. In the dimension of light there is no space or time but in our dimension of spacetime we see any two remote points separated by space to also be separated by an interval of time equal to one second for every 300,000 km of space as described in SR. In this view, c is a dimensional constant and not the speed of light or even a speed of any kind. The speed of light is essentially instant or at least too fast to measure but we can never see it as such.
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Re: "which-way" information in quantum particles

Postby hyksos on September 28th, 2015, 11:20 am 

To a large degree, I made this thread to talk about the Mott Problem.

We have a situation where the abstract equation for the emitted alpha particle is spherically symmetric. On a chalkboard it would be radially symmetric. This equation is the Schroedinger Wave. However, back in the real world in the lab, we always ever see an alpha choose a particular direction and fly off in a straight path.

For centuries, the normal flow of investigation (the modus operandi) of discovering the secrets of physical systems was to look closer at their parts. To "open them up and look inside to see what makes them work". In the context of the Mott problem, this would mean we proceed with our investigation by probing more deeply into the inner workings of the nucleus which emitted the alpha. If we just look close enough at its inner parts, we hope to uncover the answer as to why the radiation always chooses a direction (or so we thought).

Instead, a rather different approach is required for making real progress. Instead of probing deeper inside, we need to ask a question. : what is the difference between the abstract formulation of the Schroedinger wave on the chalkboard and the actual atom sitting in our lab? Immediately the answer is that the real atom in the lab is surrounded by a sea of nearby , adjacent atoms. The 'abstract nucleus' on our chalkboard is sitting alone in an impossible universe all by itself. This thinking opens up the exciting possibility that is not something inside the inner gears of the nucleus that resolves the Mott problem, rather, the resolution is to be found in the adjacent nearby atoms. In earlier posts, I referred to the group of nearby atoms as the "ensemble of measurers"

The first line of attack claims the outside atoms, (being situated in some asymmetric configuration in space,) send something into the emitter nucleus, which by cause-and-effect makes the nucleus select a particular direction for its emitted alpha. That scenario is fine, but not investigated by me in this thread. That idea lends support to the Transactional Interpretation of quantum mechanics. Others forum posters have expressed personal support for the Transactional Interpretation.

My theory suggests a different mechanism. We view the location of the particle as if it were another quantum state (analogous to spin, polarization, or wavelength). The intuition is to give up the idea of a particle having a size. Then the ensemble of measurers induce a collective agreement on its location, in the same manner that particles would "agree upon" a measured quantum state. The last part of the mechanism is that it proceeds at the speed of light in space. This is why the particle seems so small to us. This also explains why the alpha moves in a track away from the emitter. Those adjacent molecules in the bubble chamber who are "first in line" to receive causal information about the nucleus will be the "initial ensemble" for establishing the physical reality of the alpha's location.

In summary the disagreement between the equations of particles versus the experimental behavior of particles is due to the fact that all real atoms in our universe are surrounded by a sea of other atoms. Each nearby atom is a 'measurer' and they lend their collective support in piecemeal at the speed of light.
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Re: "which-way" information in quantum particles

Postby Braininvat on September 28th, 2015, 11:40 am 

Just to be clear, I like the creative thrust of the Transactional Interp, but that shouldn't be construed as "personal support," as I remain fairly agnostic on any specific QT. Your ensemble of measurers (which caused a joking reference to Wisdom of the Crowd to pop into my head, for better or worse) has some merit, but I find confusion in taking away size from a particle in one breath, and saying that it has a spatial relationship to other particles in the next - as you put it, "...surrounded by a sea of other atoms." If one can speak of atoms surrounding other atoms, or of "nearby" atoms which comprise the initial ensemble, then it seems as if scale is sneaking back into the description. Observation seems to uncover a Lego universe made up of Planck lengths, but as you point out, such a "length" is really a description based on the speed of light (or what I like to call, the rate at which the universe happens) and not a scale in the classical sense.
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