How Does Counterfactual Computation Work?

[selfAdjoint]

They can all be found in

* simulation study of aspects of the classical hydrogen atom interacting with electromagnetic radiation : circular orbits, Daniel C Cole and Yi Zou
*Analysis of orbital decay time for the classical hydrogen atom interacting with circulary polarized radiation, Daniel C Cole and Yi Zou
* quantum mechanical ground state of hydrogen obtained from classical electrodynamics, Daniel C Cole and Yi Zou

The last of these papers (or at least another with the same title) is on the arxiv at http://arxiv.org/abs/quant-ph/0307154

From the paper, describing "Stochastic Electrodynamics":

SED is really a subset of classical electrodynamics. However, it differs from
conventional treatments in classical electrodynamics in that it assumes that if thermodynamic equilibrium of classical charged particles is at all possible, then a thermodynamic radiation spectrum must also exist and must be an essential part of the thermodynamic system of charged particles and radiation.
As can be shown via statistical and thermodynamic analyses [1], [10], if thermodynamic equilibrium is possible for such a system, then there must exist random radiation that is present even at temperature T = 0. This radiation has been termed classical electromagnetic zero-point (ZP) radiation, where the “ZP” terminology stands for T = 0, as opposed to “ground state” or “lowest energy state”.

 

[Careful]

The last of these papers (or at least another with the same title) is on the arxiv at http://arxiv.org/abs/quant-ph/0307154

Yep, but actually one should go through the old Phys Rev papers of Boyer and Marshall first, something which is still partially on my ``to read´´ list but a human life is just too short sometimes ! Actually, another cute thing to do would be to study how an accelerated gravito-electromagnetic electronmodel would behave (say an accelerated spinning charged configuration). As said before, GR changes drastically EM on the Compton scale of the particle (equal charges attract and so on...) what happens with the radiation field here? I think Will Bonnor (a good oldie ) has been looking into this...

 

[Hurkyl]

What you say is the following: one should just take any stationary current for an equation of motion which does not contain a radiation vector potential and solve the Maxwell equations with respect this current. But in this way, I can claim that the classical Bohr atomic model is stable too !

The Bohr model posits an orbiting point charge, and not a stationary charge/current distribution.

The point is that the electron will not only radiate energy, it will also *extract* energy from an an external radiation field. The question being whether this could be a stable process. Again, it probably makes no sense in speaking about a stable atom in vacuum. You should read the textbooks more critically.

Surely you'd admit that hypothesizing an all-pervasive background radiation field which acts as a supplier of energy to electrons is a rather major change to EM, né?

But this is the sort of response about which I was talking -- a research path that addresses the traditional problems with classical methods. This is far superior to expressing disbelief that physicists thought that had proven anything, when some formula had not yet been worked out.

Of course, our miscommunication about the papers didn't help -- since you weren't providing new links or references, I had been assuming that it was related to the links you already provided. (Which were on backradiation)

I am trying to be patient with you here, I would appreciate it if you would even just consider to think about what I say.

I do -- the problem is that much of what you say seems to be irrelevant to the questions I want to hear answered! When I hear someone saying CM is adequate, I don't want to hear all the reasons why QM is inadequate! (and besides, it conveys a perception that the arguer thinks CM is adequate simply because he finds QM inadequate)

 

[Careful]

The Bohr model posits an orbiting point charge, and not a stationary charge/current distribution.

Ok fine, I meant something like a rotating string, or a shell or something else alike . (you must have felt happy here )
To be absolutely clear about what I want to say: you want to uphold a realistic interpretation about the wave function (q psi^2 = charge distribution). But then you should take into account the self interactions of the charged ``fluidum´´ and so on, which is not done at all (evidently, the stationary wave functions as being realistic charge distributions are not stable at all). What one does in the textbook derivation however is to POSIT that any solution to the Schroedinger equation - one which does not allow for a dynamical electromagnetic self coupling - EXISTS. But allowing myself such liberties, a classical rotating charged string, will also do the job - simply consider a planar circular current. Now, to get out the quantum behavior here (and to make the model stable !) you might add a new type of force field which balances out radiation when the string is brought out of equilibrium (which is of course an undesirable thing to do).
Voila, such line of thinking is entirely CLASSICAL - from our ``misunderstandings´´ it seems that you interpret this word as ``textbook material´´- and does the job. The problem with such strategies is that we do not learn anything since we just shift it to the next level : ``what is the field theory behind this new mysterious force and what are its charge carriers ?´´. Obviously, if a new problem shows up at the next level, we can apply the same strategy and so on and so on... Of course, any rigid stationary object or any configuration alike does not radiate, but through what fundamental interactions does it *exist* ? In QM this comes at the price of a new strange ``force´´ and a very strange equation for it. This is one of the things I like about Einstein-Maxwell theory, here you have a chance of getting out a realistic stable charged spinning fluidum without introducing any new forces at all. Moreover, in both cases you still have to study stability of these configurations (which is the coupling to QED for QM) and that is a *very* non-trivial part.


**
Surely you'd admit that hypothesizing an all-pervasive background radiation field which acts as a supplier of energy to electrons is a rather major change to EM, né? **

No, it is actually very natural if you think about it, it is simply a well posed problem within EM, albeit one people don't speak about too often. It is actually not anything ``new´´ (in the sense of new physics) either.

**
But this is the sort of response about which I was talking -- a research path that addresses the traditional problems with classical methods. This is far superior to expressing disbelief that physicists thought that had proven anything, when some formula had not yet been worked out.**

My dear friend, I have mentioned these papers before in other threads as well as many other things. And as I said: other routes are also possible. It is just that you cannot imagine anymore that there is a pleithoria of classical possibilities (all well within EM and GR) to explain so called mysterious QM phenomena. Even nonlocality could be retrieved - I think- if you give up GR and go back to Newton, but so far I see no reason for that. Actually, an interesting paper in that line of thinking was written recently by Peter Holland, it teaches you how the Lorentz symmetry in EM could be an effective phenomenon (within the context of Galileian fluidodynamics), rather than a fundamental one:
`` constructing the electromagnetic field from hydrodynamic trajectories, peter Holland, November 2004 ´´
I think that one was published in the proceedings of the London Royal society, but I am not sure anymore.

**
Of course, our miscommunication about the papers didn't help -- since you weren't providing new links or references, I had been assuming that it was related to the links you already provided. (Which were on backradiation) **

But I said a few times that I mentioned these before, or in another thread.

The reason why I don't say ``you should look for that and that kind of specific classical model to explain quantum phenomena´´ and provide plenty of references for all of them, is that I am not sure myself what the ``right´´ way to go is. It seems to me there are some few distinct possibilities from which SED is one. Therefore, it is always useful to treat less ambitious (but still very difficult) problems first, like studying details of the radiation mechanism within Einstein Maxwell theory - say - before you embark in one path. You seem to want too much right away Hurkyl, that is NOT the good strategy to solve a difficult problem The result of such action would indeed be a theory like QM or something alike, but that is precisely what we do not want. We want genuine unification of forces, charge(s?) and matter.

As long as there is not a candidate theory present which does achieve that - and even after that - you shoud be open minded for the more rational alternative, and I always find it a pitty when young eager minds (well I am not old actually :-)) want to go for the quick bite.


Cheers,

Careful

 

[Chronos]

**Of course -- that's by definition. But, that implies all the things that come with being an eigenfunction of the Hamiltonian -- such as all physical quantities (e.g. charge and current distributions) being time independent. And since stationary charge/current distributions don't radiate, there's no need to bother with considering radiation in the Hamiltonian) **

Come on, there is no straigthforward *good* prescription at all for the radiation field determined by the wave function (actually, there exists an obvious candidate, but this one does not seem to give stationary states) ! In the Hamiltonian we are talking about, you just put in BY HAND that there is NO correspondence between the wave function and the radiation vector potential. The Schroedinger equation - as it stands there - does not allow for a dynamical coupling between charge and radiation. It is easy to ``solve´´ the problem like that in classical mechanics too you know

What you say is the following: one should just take any stationary current for an equation of motion which does not contain a radiation vector potential and solve the Maxwell equations with respect this current. But in this way, I can claim that (correction!) a classical atomic model with electrons as rotating strings is stable too !


**
It feels silly that I have to explain the textbook argument to you, but alas...

The atom continuously radiates energy. Due to conservation of energy, in order to remain "stable", it must have an external source that is continuously pumping energy into it. (Does that even qualify as "stable"?) **

The point is that the electron will not only radiate energy, it will also *extract* energy from an an external radiation field. The question being whether this could be a stable process. Again, it probably makes no sense in speaking about a stable atom in vacuum. You should read the textbooks more critically.

**
None of the papers you've "linked" have been by either of them, which makes it difficult. **

True, I gave them in another thread as I mentioned specifically. They can all be found in

* simulation study of aspects of the classical hydrogen atom interacting with electromagnetic radiation : circular orbits, Daniel C Cole and Yi Zou
*Analysis of orbital decay time for the classical hydrogen atom interacting with circulary polarized radiation, Daniel C Cole and Yi Zou
* quantum mechanical ground state of hydrogen obtained from classical electrodynamics, Daniel C Cole and Yi Zou


**Only if I was trying to argue something to the effect that QM solves them.
But given the assumption that QM maintains the classical property that stationary charge/current distributions do not radiate, the textbook solution of the (Hydrogen) atom clearly solves that problem.**

Not really, the textbook treatment does not teach you anything of that kind; the STABILITY of this configurations is a more advanced (partial !) recent result - check out another thread where I have posted the relevant papers.


** And, of course, the EPR experiments are not a problem for QM. **

Neither are they for CM, apart from some restrictions it puts on local realism.

I am trying to be patient with you here, I would appreciate it if you would even just consider to think about what I say.

Cheers,

Careful

I sense a few contradictions in your . . . arguments. Apparently your textbook is pushing the envelope. Do you have any citations in mind?

 

[Careful]

I sense a few contradictions in your . . . arguments. Apparently your textbook is pushing the envelope. Do you have any citations in mind?

As long are you cannot specify your ``feeling´´, how can I react? My argumentation is correct and the QM bibles I had to learn in my student time are very standard - as were the devoted high priests conveying them to me. Perhaps you can go straight to the content of the matter - such as Hurkyl partially did - that usually simplifies the discussion.

 

[Hans de Vries]

Come on, there is no straigthforward *good* prescription at all for the radiation field determined by the wave function (actually, there exists an obvious candidate, but this one does not seem to give stationary states) ! In the Hamiltonian we are talking about, you just put in BY HAND that there is NO correspondence between the wave function and the radiation vector potential. The Schroedinger equation - as it stands there - does not allow for a dynamical coupling between charge and radiation.

Correct, It gives you a charge density and momenta but wat is missing
is the velocity of the charge.

This however can be solved with SR. Velocity means relativistic mass
increase, Such an increase doesn't show up in the Energy eigenstate
which hasn't any relativistic mass increase at all (Neither for Schroedinger
nor Dirac solutions). The solutions would not be stable.

The relativistic mass increase,and thus E, are dependent on r because
of the quantisation of angular momentum:

<br /> \mathbf{p} \times \mathbf{r}\ =\ \sqrt{l(l+1)} \hbar<br />


Only Quantum mechanics can produce a negative radial term p_r^2 which
counterbalances the relativistic mass increase to make E the same
everywhere and independent of r:

E^2= p_r^2 c^2 + p_\theta^2 c^2 + p_\phi^2 c^2 + m_0^2 c^4\ = (\ m_0 c^2 - 13.6eV)^2

(Simplifying out the all potential energy terms here except the 13,6 eV )

It's the radial term:

\frac{l(l+1)}{r^2}\hbar^2 c^2

Which enters the radial equation of the Laplacian which accounts exactly
for the "missing" relativistic mass. I gave the prove here:

https://www.physicsforums.com/showthread.php?p=864642#post864642

What you say is the following: one should just take any stationary current for an equation of motion which does not contain a radiation vector potential and solve the Maxwell equations with respect this current. But in this way, I can claim that (correction!) a classical atomic model with electrons as rotating strings is stable too !

Yep, It's a wide general class which wouldn't radiate.

The point is that the electron will not only radiate energy, it will also *extract* energy from an an external radiation field. The question being whether this could be a stable process.

You realize that for a single point particle electron this would mean that
you would have to send in radiation from all over the "edge of the universe"
at exactly the right time to get the correct compensation...

It would get somewhat easier if the vacuum's dielectricum is viewed as
as consisting out of virtual particle/anti-particle pairs responsible for
the displacement current (But then this is a QFT idea... )


Regards, Hans

 

[Careful]

**
You realize that for a single point particle electron this would mean that
you would have to send in radiation from all over the "edge of the universe"
at exactly the right time to get the correct compensation...

It would get somewhat easier if the vacuum's dielectricum is viewed as
as consisting out of virtual particle/anti-particle pairs responsible for
the displacement current (But then this is a QFT idea... )


Regards, Hans **

Hi Hans,

I don't think the radiation has to come from all over the edge of the universe ; one can reasonably expect equilibrium to settle in more locally - but that remains to be seen (there is some robustness you could expect - but that is a guess at the moment).

In some sense, this idea is very much alike to QED - with that difference that it is classical (and therefore deterministic). Just for clarity: the point is not that QM offers you a stationary configuration - you can reach that classically as well (if you give up the notion of point particle - like many stringy theorists do these days ); the entire difficulty is to show that this configuration remains stable under background radiation (noise). This is a problem with backcoupling which has to be treated nonperturbatively and that is exactly what SED does from the start.

As mentioned before, the first thing to do is to get rid of the POINT particle and see if our theories GR + EM could produce a stable, non-distributional, charged dust configuration. In that respect, you might want to look for doughnut-like configurations (the Kerr singularity being a ring ).

Cheers,

Careful

 

[Careful]

***

This however can be solved with SR. Velocity means relativistic mass
increase, Such an increase doesn't show up in the Energy eigenstate
which hasn't any relativistic mass increase at all (Neither for Schroedinger
nor Dirac solutions). The solutions would not be stable. **

Hi, a quick scan makes clear that you still do not account for the electron Coulomb self interaction - this is always a problem if you try to give realist explanations for the mechanism behind the Schroedinger equation - which is something I stopped trying :-)

Cheers,

Careful

 

[selfAdjoint]

In some sense, this idea is very much alike to QED - with that difference that it is classical (and therefore deterministic). Just for clarity: the point is not that QM offers you a stationary configuration - you can reach that classically as well (if you give up the notion of point particle - like many stringy theorists do these days ); the entire difficulty is to show that this configuration remains stable under background radiation (noise). This is a problem with backcoupling which has to be treated nonperturbatively and that is exactly what SED does from the start.

And the nonperturbative regime in SED seems to be just as frustratingly hard as that in quantum field theories. Hence the simulation approach in the latest paper.

As mentioned before, the first thing to do is to get rid of the POINT particle and see if our theories GR + EM could produce a stable, non-distributional, charged dust configuration. In that respect, you might want to look for doughnut-like configurations (the Kerr singularity being a ring ).

Note that topologically, a torus is the only 2-manifold which can support a vector field that is non-zero everywhere. This doesn't matter in a quantum theory, but in your classical theory it should.

[/quote]

 

[Careful]

** And the nonperturbative regime in SED seems to be just as frustratingly hard as that in quantum field theories. Hence the simulation approach in the latest paper.**

Right, but the computations involved are still much less intensive as a full QED treatment would demand (ask that to Patrick ).

**
Note that topologically, a torus is the only 2-manifold which can support a vector field that is non-zero everywhere. This doesn't matter in a quantum theory, but in your classical theory it should.**

Sure, but that is precisely what one would like no? That the dust can freely rotate ``at the same speed´´, without clumping up at some poles.

Cheers,

Careful

 

[selfAdjoint]

**
Note that topologically, a torus is the only 2-manifold which can support a vector field that is non-zero everywhere. This doesn't matter in a quantum theory, but in your classical theory it should.**

Sure, but that is precisely what one would like no? That the dust can freely rotate ``at the same speed´´, without clumping up at some poles.

Indeed, I wasn't criticising the idea, just pointing out a nice property it has. Are you looking at a finite torus or the limit, a circle or "closed string" if you will?

 

[Careful]

Indeed, I wasn't criticising the idea, just pointing out a nice property it has. Are you looking at a finite torus or the limit, a circle or "closed string" if you will?

Ah, by dougnut I mean ``filled up´´ torus I just don't like distributional matter configurations - seems very unphysical to me (I could give better reasons here if you want to - but these are somewhat more speculative). But don't misunderstand me: I think that classical string theory - spiced up with SED - could be a very nice thing to look at - in a sense, it would be easier to start with.

Cheers,

Careful

 

[selfAdjoint]

Ah, by dougnut I mean ``filled up´´ torus I just don't like distributional matter configurations - seems very unphysical to me (I could give better reasons here if you want to - but these are somewhat more speculative). But don't misunderstand me: I think that classical string theory - spiced up with SED - could be a very nice thing to look at - in a sense, it would be easier to start with.

Cheers,

Careful

Uh-huh. My limited experience with bosonic string theory suggests it's very hard to derive it from an action principle without allowing closed strings and open strings to interact and change their topology. Recent work has shown ways to get fermions out of this simple bosonic model without going to supersymmetry and superstrings. You might also want to look at string field theory which has had some good news recently, noted over at Lubos Motl's blog.

 

[Careful]

**Uh-huh. My limited experience with bosonic string theory suggests it's very hard to derive it from an action principle without allowing closed strings and open strings to interact and change their topology. **

Where did I mention collisions between different *particles* (I was talking here about interaction between one particle and a classical EM field) ? Obviously, you would expect topology change to occur IF one could find such a configuration in the first place.

** Recent work has shown ways to get fermions out of this simple bosonic model without going to supersymmetry and superstrings. **

Ah, that's interesting, similar work being done ``recently´´ in Einstein-Maxwell theory, I think by Bonnor (that is how the spin-spin interaction behaves for rotating rods - at least I think it was that).

** You might also want to look at string field theory which has had some good news recently, noted over at Lubos Motl's blog. **

You are speaking here about classical string field theory I presume ? That is fine (I would believe interesting results to emerge from that), but as I mentioned before, I have reasons *not* to start from an a priori assumption that matter is given by a string.

Cheers,

Careful

 

[Hurkyl]

There's an arXiv paper on counterfactual computation:

http://arxiv.org/abs/quant-ph/9907007

(which can be found by searching wikipedia, and running into the possible copyright violation notice. )

A quantum computer is modeled as having an input consisting of three components:

(1) A switch that controls whether the computer is to be run or not.
(2) The output register to which the result of computation is added.
(3) Additional registers that are the inputs to the algorithm. (And are left unchanged by the computer)

For the analysis, only the switch and output registers really matter. The computer enacts the transformation:

|0> |j> --> |0> |j>
|1> |j> --> |1> |j+r>

j is the initial value in the output register, and r is the result of the computation. (Both are either 0 or 1. And, of course, 1+1=0)

Let t² = 1/2, to make things pretty.

A rotation is the (unnormalized) transformation that sends:
|0> --> t|0> + t|1>
|1> --> -t|0> + t|1>


Our protocol is this:

(1) We start with |00>.
(2) We rotate the switch bit, putting us in the state t|00> + t|10>
(3) We feed this state into the computer, and wait. (Give it enough time to run, if it were to actually run)
(4) Measure the result. (If we get a 1, we know r=1 and quit)
(5) Rotate the switch bit again.
(6) Feed the state into the computer, and wait.
(7) Measure both the switch and the result.

For an example of what might happen, consider a basis possibility when r = 0
(1) We start in |00>
(2) We rotate to t|00> + t|10>
(3) The computer doesn't run, leaving us in |00,f>
(4) We observe a 0, leaving us in |00,f0>
(5) We rotate to t|00,f0> + t|10,f0>
(6) The computer does run, leaving us in |10,f0n>
(7) We observe a 10, leaving us in |10,f0n10>

As you can see, I've appended additional labels denoting what has actually happened or was measured. "f" for "off", and "n" for on.

In the case of r = 0, the full state evolves as:

(1) |00>
(2) t|00> + t|10>
(3) t|00,f> + t|10,n>
(4) t|00,f0> + t|10,n0>
(5) t²|00,f0> + t²|10,f0> - t²|00,n0> + t²|10,n0>
(6) t²|00,f0f> + t²|10,f0n> - t²|00,n0f> + t²|10,n0n>
(7) t²|00,f0f00> + t²|10,f0n10> - t²|00,n0f00> + t²|10,n0n10>

But it is important to note that the "f" and "n" are not actually measured, and are not actual components of the physical state -- the final state is actually

t²|00,000> + t²|10,010> - t²|00,000> + t²|10,010> = |10,010>

due to interference! However, the observation "010" is known to arise only from histories in which the computer has run. So, when r=0, we can be absolutely certain the computer runs, and that we will observe "010".

When r=1, it evolves as:

(1) |00>
(2) t|00> + t|10>
(3) t|00,f> + t|11,n>
(4) t|00,f0> + t|11,n1>
(5) t²|00,f0> + t²|10,f0> + t|11,n1>
(6) t²|00,f0f> + t²|11,f0n> + t|11,n1>
(7) t²|00,f0f00> + t²|11,f0n11> + t|11,n1>

Of course, as before, the final state is
t²|00,000> + t²|10,010> + t|11,1>

So we can list all the possible results of our experiment:

"010" -- we know that r=0 and that the computer ran.
"000" -- we know that r=1 and the computer did not run.
"011" -- we know that r=1 and the computer did run.
"1" -- we know that r=1 and the computer did run.

The important thing to how this works is that the "000" cases when r=0 destructively interferred, so that it was an impossible outcome.

 

[KAckermann]

There should be fines for publishing drivel like that article.

The first clue that it was B.S. was the fact that they never really said what they succeeded in doing. What does 'successfully search a database' mean?

Ultimately, I'm certain it means nothing, because if they had truly extracted information without using energy, then Ted Koppel would come out of retirement to report it, and Obama would rearrange his inauguration to rejoice in the gift of infinite wealth for all the world.

This is the kind of useless stuff that comes from publish or perish.

 

[Hurkyl]

You did notice the article in the OP was in a newspaper, not a scientific journal, right?