Foundations of Quantum Mechanics and Physical Chemistry » Quantum Mechanics Research

003 Early models of the Atom

Bryan — Wed, 03 Aug 2011 19:15:59 +0000

Models for the atom

http://www.youtube.com/watch?v=zRtRAeGuO7M

Once atoms were found, it became evident that atoms were composed of protons, neutrons and electrons. The first model, due to J.J. Thomson, was the plum pudding model. This suggested that the atom was a positively charged cloud with electrons floating in it. This model is incorrect.

All models in science have to be consistent with experiment. While at McGill University in Montreal, Ernest Rutherford did a series of scattering experiments that proved the Plum pudding model was incorrect.

Rutherford fired alpha particles at a thin sheet of metal foil. Alpha particles are He nuclei or He 2+ atoms. If the Thompson model was correct, all the alpha particles would pass right through the atom. In fact most did.

However, a small number of alpha particles bounced right back. This could only happen if they hit a very dense part of the atom. Rutherford was surprised at this and said:

“It is as if you fired a 15-inch shell at a piece of tissue paper and it came back and hit you.”

The only way to explain this result is that a very dense nucleus exists in the center of the atom and this is surrounded by electrons. This dense nucleus was occasionally hit by the alpha particles and deflected. When the nucleus was not hit, the alpha particle went straight through the atom. The model of the atom with a dense nucleus at the center and surrounded by electrons is called the Rutherford model of the atom.

The Bohr model states that electrons exist in various orbitals and the energy corresponds to the energy level diagram on the left. Electrons of higher energy occupy Bohr orbitals of greater radii.

The statistical interpretation of quantum mechanics is one of the most profound aspects of science. It was developed in Copenhagen between 1925 and 1930 and was not fully accepted by Einstein who said

“God does not roll dice.”

But today most scientists agree Heisenberg was right. There is an inherent fundamental error to measurement.

009 Disproof of Bell’s Theorem

Bryan — Thu, 17 Feb 2011 16:08:35 +0000

Blog 009: Bye-Bye Bell: the end of an era.

Hello anyons: the new era

Blog 009: INTRODUCTION

httpvh://www.youtube.com/watch?v=A9VCmryD34I

Han Geurdes Disproves Bell’s Theorem

httpvh://www.youtube.com/watch?v=kIysfrByZHE

Joy Christian Disproves Bell’s Theorem Parts 1 and 2

httpvh://www.youtube.com/watch?v=Rq1vXQTrtSg

httpvh://www.youtube.com/watch?v=ABnIvcvn2bc

My Sub-quantum 2D spins are Anyons

httpvh://www.youtube.com/watch?v=PcwQWa-rV9Y

INTRODUCTION

Bryan Sanctuary

In this entry I will present the evidence that shows that Bell’s inequalities have no consequences for understanding quantum vs. classical correlations. I will also show that spin is a two dimensional anyon.

After a summary, two recent proofs are presented that show BELL’S INEQUALITIES are incorrect due to an over simplistic treatment of spin by Bell. Finally I relate these approaches to my sub-quantum 2D spins.

One of the proofs is by Han Geurdes in Holland and the other by Joy Christian in England. These conclusions support my LHV Local Hidden Variable theory that I have presented in blog entries 006 and 007.

I am going to state it unequivocally right at the beginning of this entry what we have found:

Bell’s Theorem is wrong.

His famous inequality, derived in this paper of 1964, upon which Bell’s theorem is based has finally been shown to be incorrect. Bell’s Inequalities certainly tell us nothing about quantum mechanics or Local Hidden Variables. They have misled the physics community for the past 50 years. It is the end of an era.

Recall: Bell’s theorem states:

“No physical theory of local hidden variables can ever reproduce all of the predictions of quantum mechanics”.

This statement is wrong.

Why do people believe Bell’s Inequalities are correct?

As much as scientists have tried to disprove Bell’s theorem, no one has been able to find any errors, at least until now. In my blog 007a I discussed the EPR coincidence experiments upon which the concept of non-local connectivity between EPR pairs is established.

No one understands non-locality.

And no one has been able to find a non-local hidden variable theory to explain the data, and no one ever will. Therefore people are left to accept that quantum mechanics as the most fundamental theory. Hence physicists accept that Nature is random and non-local.

Non-locality is supposed to be the basis for quantum teleportation. But all this goes against our basic intuition. Intuition alone, however, is not enough to reject BELL’S INEQUALITIES. We need a logical proof and alternate ways to explain the data.

Can you understand how “teleportation” works? Bye the way, sorry to all you pop science fiction buffs, Scotty cannot beam you up, and no one ever will.

We all have trouble understanding Nature. Unless you feel comfortable with non-locality, and it makes sense to you, you should keep the question open. One of my goals here is to dispel those concerns.

However, today many people state that non-locality as an example of quantum weirdness. As I mentioned in Blog 006 this word has moved into physics, especially quantum information theory. It is a word that sums up the confusion of the physics community on this issue.

Here is an example in the prestigious journal Nature written by by Gregor Weihs who in 1998 produced the most definitive EPR coincidence experimental data. Let us see what he says in the Nature paper:

“Unsurprisingly for connoisseurs of quantum weirdness, entanglement—the mysterious holism in which the state of one quantum object is tied to the state of a second, separate object—is the key to the trick”

Weirdness, mysterious, tricks are words that should not be used to describe a physical phenomenon.

There are no tricks in Nature, only our ignorance as to how Nature works. Well finally we can banish quantum weirdness and its associated tricks to the annals of Science Fiction forever. This is why:

Well look at the next part of this entry, 009a in which I describe what Han Geurdes has found.

Blog 009a: Bye-Bye Bell: the end of an era.

Hello anyons: the new era

Blog 009a Han Geurdes disproves Bell’s Theorem

Bryan Sanctuary

In this entry that follows 009, I present the evidence that shows that Bell’s inequalities have no consequences for understanding quantum vs. classical correlations. Han Geurdes has published a paper (Adv. Studies Theor. Phys., Vol. 4, 2010, no. 20, 945 – 949) which shows usual classical probabilities lead to violation of Bell’s Inequalities. I will say it again, Classical probabilities, not quantum, violate BI. That is a change.

Han has found that classical probabilities are not restricted to classical physics. They work for quantum mechanics too. If it is all classical, where are the quantum correlations BI are supposed to quantify? There are none.

Here’s the abstract:

“Mathematics equivalent to Bell’s derivation of the inequalities, also allows a local hidden variables explanation for the correlation between distant measurements.”

That could not be clearer. He has proved non-local correlations are not needed. He talking about “ LOCAL hidden variable, not non-local ones.

And let us look at the first paragraph:

“To many the experimental verification of the violation of inequalities is sufficient evidence for completeness of quantum theory. Here it will be demonstrated that Bell’s form of local hidden correlation can be transformed to violate Bell’s inequalities. “

Han’s results are totally against what Bell obtained. We can conclude from Geurdes’ paper that:

“Bell’s inequalities do not differentiate between local realism and quantum mechanics. Hence the experiments of Aspects, Weih’s etc. do not differentiate either.”

That is, Bell’s Theorem is wrong. It is a major result.

Bell is supposed to have showed that the correlation between classical events cannot exceed 2.

But qm violates them, why? Because Bell made an error, and I will discuss that error in due course.

In the end, it is shown that quantum spin satisfies the corrected version of BI. In fact the correct form of BI has a limit of 2√2 for spin not 2. Even this is only a special case and BI might take some entirely different value because it fundamentally depends upon the geometry of the data. I will be clearer on that point in later on in this blog: 009b and c. But 2√2 is correct of spin ½ not 2.

However when things are simpler than the spin data, the version of BI with a limit of 2, does work. For example, correlation between different sets of numbers satisfy BI. They do work in our macroscopic classical world. They have been tested many times.

For example, think of a set of classically correlated properties: a population of people have lots of correlation: say, color of skin; color of eyes and color of hair. If there are correlations between these properties, then they will satisfy BI. No classical correlations, according to Bell, can exceed the value of 2.

But it is well known that if the filters are set as shown here in the EPR coincidence experiments then these quantum results violate Bell’s Inequalities. (Here I use a spin ½ not photons of spin 1 whence the angles are halved).

No one has been able to explain that “quantum” correlation of 2√2-2=0.828 except to surmise it is due to entanglement: that “mysterious holism in which the state of one quantum object is tied to the state of a second, separate object—is the key to the trick”

Well no, entanglement is NOT key to the trick. Han Geurdes has shown that classical probabilities do the trick.

Quantum mechanics for spin ½ then satisfies the modified BI and so Bell’s theorem is toast.

LHV can exist and can complete quantum mechanics. Einstein was right:

“He does not play dice!”

However you can be sure that Han Geurdes paper will be scrutinized because there are a lot of people out there who will not like this result. Unfortunately like and dislike are subjective comments and of little consequence. People will have to show there are objective errors.

But where did Bell go wrong? The results of Geurdes are consistent with those of Joy Christian at Oxford, and my LHV model, so we turn to his work now.

In my next entry 009b we will find the reason for Bell’s error, and Christian’s elegant way of correctly account for the elements of physical reality that Bell missed.

Blog 009b: Bye-Bye Bell: the end of an era.

Hello anyons: the new era

Blog 009b: Joy Christian disproves Bell’s Theorem Part 1

Bryan Sanctuary

Now that the problem has been stated in entry 009 and the published results of Geurdes reviewed, along with some consequences in entry 009a, we now turn to the beautiful way in which Joy Christian formulated Bell’s error.

In his disproof of Bell’s theorem, Christian indeed derives the correct value of 2√2 without quantum mechanics and for classical systems. This is what Bell should have got. Christian and Geurdes have found Bell’s errors in two independent studies.

Bell’s error was made in his first equation: lets look .

This equation of Bell’s does not adequately account for all possible elements of physical reality of a spin. It simply says a spin can take values of +1 and -1, but that ignores the fact that spin is oriented in some way.

Notice here that Bell says that a product of these two components should agree with quantum mechanics, but that, he says, is impossible. That statement is wrong. Christian showed this by the use of Geometric algebra, also known as Clifford Algebra, to categorize the elements of physical reality of a spin. Bell missed a lot as we will see.

In a nut shell, all that BELL’S INEQUALITIES show is that the correlation between two points on a line is different between two points on a sphere. The points on a line could represent the data from hair, eye and skin color all right, but not if the data comes out in a sphere like spin data does. Nonetheless, classical probabilities work on spheres as well as lines, but with a different algebra.

Bell’s first Equation misses important elements of physical reality by ignoring the sphere of data in favour of scalar data. Spin indeed can take 2 values of +1 and -1 when measured, but these values can point anywhere on the unit sphere, not just along a line.

Let us read the main points of his abstract:

“It is shown that Bell’s theorem fails for Clifford algebra ……. This is made evident by exactly reproducing quantum mechanical expectation value….by means of .. local, deterministic …….variables, …….. Since Clifford product of multivector variables is non-commutative in general, the spin correlations ………violate the CHSH inequality just as strongly as their quantum mechanical counterparts. “

We’ll come back to multi-vectors.

The most important point is that there are situations when classical variables do not commute, whereas Bell’s always do. Christian finds more elements of physical reality, and these are exactly the ones that Bell missed.

And yes, he has had critics too, and he has replied to them all.

Now Clifford algebra is also called geometric algebra and is concerned with the algebra in different geometric spaces. However the point I want to make is that Bell’s beables are geometrically a unit sphere of zero dimension, denoted by S⁰. That is just two points of +1 and -1 on a line. That is all Bell’s uses.

In contrast to Bell, Christian realized that spins can point in two directions over the surface of the usual unit sphere in the real world and this is called a 2-sphere S² .

Bell’s choice has no orientation, nor left and right handedness, while the 2 sphere of Christian does. I’ll get to that soon.

To see this more clearly, if you look at the standard EPR experiments then each spin has a data set that forms a sphere S². At each filter, the spin is pointing in some direction on that unit sphere. EPR experiments seek the correlation between the two to give a coincidence data set. Now that data, obtained by correlating the spin data from two 2-spheres giving the coincidence data set that obeys the geometry of a 3-sphere, S^3. This is quite different from Bell:

The data set used by Bell in his first equation has too few elements of physical reality whereas Christian has counted them correctly. Bell misses S²-S⁰ elements of physical reality.

What does this lead to?

It makes sense that the algebra on different spheres is different. You know that from when planes fly polar routes. An S² sphere corresponds to Clifford Algebra Cl(3,0) and this is represented by the Pauli spin matrices. Bell’s beables are 0-spheres, or scalars. What are Christian’s?

Christian’s beables are Bell’s Inequalities-vectors and tri-vectors relevant to the 2-sphere, not scalars like Bell used. These two cases can be compared and contrasted. It is the Bell’s Inequalities-vector choice that makes the difference.

An example of a Bell’s Inequalities-vector is given by the product of two Pauli spin matrices, and a tri-vector is the product of three vectors in terms of the 2×2 Identity matrix. Note these play important roles in this approach, and the LHV theory I discussed in blogs 006 and 007.

Just a brief primer on Algebraic geometry. Let’s drop the indices on A and B.

They are still Bell’s Inequalities-vectors. Take the product of two and get this equation that exploits symmetry between Bell’s Inequalities-vectors in terms of the dot and wedge products defined here. The wedge operator is a generalization of the vector cross product. Whereas the scalar beables of Bell commute, the Bell’s Inequalities-vector beables of Christian’ on a sphere do not commute. This is an important difference.

Now I mentioned that the Pauli spin operators represent the Clifford Algebra Cl(3,0). This general expression reduces to the well known relationship between Pauli spin operators, in terms of the Kronecker delta function (i must equal j) and the Levi-Civita totally antisymmetric third rank tensor where if any two components , i,j,k are equal, then epsilon is zero. I,j,k can take values of x,y,z. Epsilon is equal to +1 for an even permutation of i,j,k, and -1 for an odd permutation, i,k,j.

This can also be written as a tri-vector ±I.

This double valued identity operator points in all direction over the unit 2-sphere, so it has direction and orientation. Let’s remove the sphere to see things a Bell’s Inequalitiest more clearly.

Equatorial planes are element of a 1 sphere S¹. It follows easily that the identity has two values of +1 and -1 and these two tri-vectors lie along the spin direction. Look at a different orientation of spin

Once again we get two values, but for a spin now pointing in a different direction. That is, the elements of physical reality chosen by Christian corrctly specify the possible values a spin can take in different directions. It makes a lot of sense.

Now we are ready to look at one of Christian’s paper where he discusses this approach. Let us jump to the relevant part,

Ok, well it looks a Bell’s Inequalitiest complicated but it really is not. First we see the CHSH form of Bell’s Inequalities which can be written in terms of the non-commuting Bell’s Inequalities-vectors and the filter angles used in EPR experiments, a and b. Now A and B describe spins that are far apart, so since we are dealing with LHV, then A and B must commute. That is a locality assumption.

However A does not commute with A, and B does not commute with B. If we were using Bell’s scalars, then everything commutes, but not here. Working out the details, that I skip, an expressions is found in terms of the filter settings, a and b for Bell’s Inequality. These are the usual vector dot and cross products and they make the difference by giving the correct value of 2√2. Clearly if those terms did commute, then the answer is what Bell got, 2. The correct answer is 2√2 for spin ½ .

Let us look for the filter settings that maximize the square root term. It is clear that a must be perpendicular to a’, and b must be perpendicular to b’. So far so good. We see this in the filter settings that are experimentally found that maximize the CHSH form of BELL’S INEQUALITIES. But we can go further.

We can write this expression another way using a Bell’s Inequalitiest of vector algebra. The only way to choose the angles to maximize the correlation is shown here and they are exactly the settings found experimentally and indeed from quantum mechanics. Note we have used NO quantum mechanics here: only classical algebraic relations on a sphere. So let us put this together:

Plug in the angles to give the second term of cross products equal to 1. Christian gets the correct value of 2Ö2 that quantum mechanics predicts and experiments confirm. In addition the relationship between the filter settings are consistent to the settings that maximize the correct form of BELL’S INEQUALITIES.

Bell’s error was to make the incorrect assumption about spin, thinking it can only take two real values of +1 and -1, where in fact it can take +1 and -1 anywhere on the surface of a sphere. So now we can understand my earlier statement.

Bell’s Inequalities tell us simply that the correlation between two point on a line is different than from between two points on a sphere; respectively 2 and 2√2 .

Finally I will relate my 2D LHV model to Geurdes and Christian’s work, and show that spin is fundamentally an anyon.

Bye-Bye Bell: the end of an era
Hello anyons: the new era

Bryan Sanctuary

Sub-quantum spins are anyons

The repudiation of Bell’s Theorem is a result of a three pronged attack. First Han Geurdes has shown from a fundamental mathematical approach that quantum correlations do not exist. BELL’S INEQUALITIES can be violated using classical probaBell’s Inequalitieslities.

Second, Joy Christian has demonstrated that Bell missed a lot of elements of physical reality of a spin. Including these led to the correct form of BELL’S INEQUALITIES for spin, using no quantum mechanics. Both of these theories also show that a LHV theory MUST exist to complete quantum mechanics.

My 2D spin discussed in this blog serves as completing quantum mechanics in the sense that EPR envisioned in 1935. So in this last part of blog 008, I will show how my LHV theory is consistent with Geurdes and Christian, and shows that spin at the most fundamental level is an anyon.

To see the connection to my LHV theory, let us start with the 2 sphere as Christian did, and we see an equatorial planes which are 1-spheres, S¹. Now the unit tri-vectors of Christian define the two spin values as we have seen. But this can point in any direction in that sphere

There are an infinite number of planes and if you have read my blogs 006 and 007 then each change of coordinates corresponds to a different spin orientation and a different spin microframe x,y,z.

Topologically the 2-sphere, S²,is made up of equatorial planes which are 1-spheres, S¹. So let us look at one plane of the infinite number possible.

I am going to write this slightly differently. Whereas Christian used a tri-vector in S² to orient a spin, the 2D sub-quantum spin I have talked about in blogs 006 and 007, uses a Bell’s Inequalities-vector in S¹ like this:

So now we see the 2D spin oriented in its microframe. I have used a right hand rule here so we see that this system has handiness, as well as magnitude, the plane zx, and orientation, by the Bell’s Inequalities-vector is

These are exactly my 2D spins. In that 2D plane and when no interactions are present, the two components of angular momentum are indistinguishable, and this produces the new state of matter, the exchange √2 spin.

This relates my sub-quantum LHV method to Christian’s and is consistent with Geurdes conclusion that classical probaBell’s Inequalitieslities work.

Let us just rotate them again.

I was talking about this with my colleague in Physics at McGill, Keshav Dasgupta whose field is String Theory, and in our discussion he said that these look a lot like Anyons—anyons exist in a plane (my spin is 2D is in a plane), show fractional or irrational quantum numbers (mine is √2) and display a phase (one spin can be rotated to the other and their orientations differ by a phase, so that when two anyons are interchanged, the phase is neither +1 (bosons) nor -1 (fermions) but any phase, so they are called anyons.

A lot is already known about them, but I will defer that to my next entry. We can summarize the difference between quantum mechanics and sub-quantum local hidden variables of anyon spins.

The quantum view of a spin is a point particle described by the three components of a spin vector that exists both in the presence and absence of a probe. Sub-quantum mechanics replaces this with an anyon spin with a 2D structure that has area, magnitude and handiness.

Bye-Bye Bell: the end of an era Hello anyons the beginning of a new era.

So ok, all this is a Bell’s Inequalitiest of a disaster for Bell, but good news for Einstein. He deserves to look smug, he told us all this must be true in 1935 and finally he has been shown to be correct. Of course Bell’s error has nonetheless helped to focus our understanding, but don’t feel bad for him. We all make errors, I make a lot, and we should learn from them.

Bell found an error in the work of the famous and brilliant mathematician, John von Neumann, who is also called the father of the modern computer and made enormous contributions to our understanding of quantum mechanics. But von Neumann did make a Bell’s Inequalitiesg error in his assumptions in an important paper of 1936 which basically incorrectly concluded that no hidden variables of any kind can complete quantum mechanics. This dashed EPR’s conclusions the year after EPR was published in 1935, and swayed many into believing that quantum mechanics is complete.

Bell found his error in 1966—so there were 30 years of confusion. But let us be reminded of what Bell said about von Neumann’s error:

“The von Neumann proof, if you actually come to grips with it, falls apart in your hands! There is nothing to it. It is not just flawed, it is silly! …When you translate (his assumptions) in terms of physical disposition they’re nonsense. You may quote me on that: The proof of von Neumann is not merely false but foolish!”

Von Neumann was no fool, and neither was Bell.

Welcome to Flatland.

008 The Sub-quantum spin

Bryan — Sat, 04 Sep 2010 13:41:54 +0000

The sub-quantum spin
By
Bryan Sanctuary
Department of Chemistry
McGill University

Part 1

http://www.youtube.com/watch?v=xDQBnWtj3bQ

Part 2

http://www.youtube.com/watch?v=r83R_uFRbnw

The discussion in blog 007 expresses the main concepts of sub-quantum mechanics for spin. In these next few entries I will explain the physical insight sub-quantum mechanics gives.

It is important to be able to use mathematics, which is the logic of the LHS of the brain, to visualize what is going on, using the RHS of the brain. The two must be consistent. Heisenberg said that we observe our natural surroundings and intuitively develop a visualization of what is going on. We do not need a mathematical description macroscopically, unless we need precision, and Classical Mechanics works extremely well.

However down at the microscopic world, we must be guided by the mathematics that allows us to visualize what is going on. If one accepts that sub-quantum mechanics is local (which is of course contrary to Bell’s Theorem) then EPR showed that quantum mechanics is incomplete.

The only real criticism of their findings concerns their locality assumption which is questioned solely on the basis of Bell’s Theorem and one type of experiment. If EPR is correct, than there must be a sub-quantum theory.

Of course John Bell did a lot more than deduce his theorem, in particular clarifying the incorrect conclusion by von Neumann that appeared to rule out hidden variable theories was one. Indeed one of the reasons that Bell developed a sub-quantum theory for spin was to show it was possible, in contrast to what von Neumann had mistakenly deduced. we have seen Bell’s most famous paper before. Let’s see what he did regarding sub-quantum mechanics.

He simply assumed that a pure spin state is described by a single polarization vector p, and a hidden variable lambda. Now all I do is assume that at any instant, spin is not one dimensional, but two dimensional. This makes a lot of difference.

Bell of course was just using the usual quantum model for a spin ½ as being a point particle with intrinsic angular momentum. In contrast, a 2D spin is assumed to have two axes of spin quantization. That is it has structure and is not a point particle. This simple extension of spin, which cannot be described by quantum mechanics, resolves the difficulties with quantum mechanics (that is it removes non-locality, makes new predictions).

In addition the singlet correlations formed from two spins can be written as a product without entanglement, is a local model (showing Bell’s theorem must be wrong); and gives a basis for the anomalies found in the EPR data as I discussed in blog 007.

As many earlier physicists like Lorentz and Einstein wanted, the 2D spin restores determinism and causality to the microscopic treatment of spin.

But is it correct? Since it agrees with experiment, whereas qm does not, then it seems worth pursuing. So to start from the very basic assumption, a spin in the 2D theory frozen in time at some instant is assumed to look like this. It is a real object.

The magnetic moment of an electron, for example, is known to great accuracy and obtaining this value theoretically is a great success of QED. Since the magnetic moment describes a magnetic field, this field is so well defined it is a real property of the spin.

Let us think about an electron for illustrative purposes. Please keep in mind that I am thinking of low energies much less than the electron mass. Since it now has structure, we need a convenient frame of reference, x,y,z, called the spin microframe. It is related to the laboratory frame by a simple rotation in 3D space.

This model says that it has a magnetic moment along the z and x axes and it is assumed that the magnetic moments are of the same magnitude as that of the usual magnetic moment of an electron. At this stage, the small arrow along the y axis is just to define a RH coordinate frame. So the total magnetic moment for a particle is given by the vector sum. The unit vector bisects to spin mircro frame and gives the magnetic moment as square root 2 greater than the usual spin ½ lying along that direction.

That is about all there is to it.

So to summarize, a structure spin, cannot be described by quantum mechanics, and is oriented somewhere in space which defines its unique microframe, one for each spin. Since the usual spin ½ has magnetic moment of magnitude mu, and it is assumed that each of the two magnetic axes has the same magnitude and these sum to give a net magnetic moment of square root two greater than the usual spin. This is directed along a unique axis called n (hat).

spin_1

However, as soon as a two D spin encounters an EM probe, like a magnetic field, then one axis lines up and the other averages to zero. (insert movie) It is impossible to tell the difference between a 1D spin and the 2D spin when a field is present. Since we must have a probe to measure a spin, clearly the root two magnitude cannot be directly observed. That is why the coincidence experiments are so important for photons: they are sensitive to the 2D spin structure. Without these experiments, the 2D spin would be a mathematical curiosity and nothing more.

But it does agree with all experimental data:

describes the correlation that leads to the violation of BI without entanglement;
Agrees with the experimental results of the Stern Gerlach experiment;
Restores locality to Nature
Gives a basis for explaining the Anomalies in EPR experiments
Restores determinism and causality to Nature—He indeed does not roll dice!

In the 2D spin model. The magnetic moment of an electron is given in terms of the Electron g-factor which is accurately known to 11 significant figures, the Bohr magneton and the spin ½ operator is given in terms of the Pauli Spin vector. Therefore up to a constant, the magnetic moment is a quantum mechanical operator being proportional to the Pauli spin vectors.

Therefore, back to our 2D spin. we assume that the magnetic moments are represented by these two Pauli Spin matrices. So let us write the 2D spin in terms of these two Pauli spin componets. Where the magnetic moments are replaced by two components of the Pauli spin matrix. These operators are attributes of the system which describe its state:

So what are the possible observables for a spin ½? We always have the Identity and three components of the Pauli spin vector. There are no more because the any other product of the observables can always be written in terms of only one by the commutation relations. Looking at all such combinations of observable is like saying that the attributes of a system are determined by its Algebra of Observables. What this means for a spin ½ is that only these four operators, and no others, are needed to fully describe a spin, but in what combination.

Let us have a look and see how to proceed.

If you think about it, the only macroscopic property from spin ½ is when they align in a magnetic field giving a paramagnetic polarization in the direction P. Hence the spin ½ density operator was discussed by Fano in 1957 and is given here.

Note that before I used lower case xyz for the spin microframe. Here I am using the laboratory frame upper case XYZ.

A system containing statistically many spins can give rise to a net macroscopic polarization. Its magnitude is proportional to P measured in the laboratory frame. The microframe and the laboratory are related by a rotation.

When P=1, all the spins are lined up in the direction of P;
When P<1, not all the spins are lined up and
When P=0, the spins are randomly oriented and have not net polarization.

This is a statistical treatment and the spin density operator gives the state of an ensemble of spin ½ . But what if the spins are polarized along the Z direction, so P_Z is not zero but P_X and P_Y are both zero. Note that there is no error associated with the Z component (it is a pure state) but complete dispersion (no knowledge) for the other two components. This is a consequence of the Heisenberg Uncertainty Principle which states that if the spin is polarized along one direction, say Z, then it cannot be polarized in any other direction.

The system is in a pure state defined by the Z axis. This gives us the usual spin picture from qm. Each spin is a point particle with a permanent magnetic moment pointing in one direction. As mentioned several times, I have no difficulty with this model except when a field is removed and the spins cannot couple to it and align with.

This is a good place to stop. It is now time to discuss the Stern-Gerlach experiment with the goal of showing that qm is a statistical theory about measurement and that spin polarization is a result of the net number of spins pointing up and down.

007 Anomalies in coincidence probabilities in EPR data

Bryan — Thu, 17 Jun 2010 00:27:02 +0000

Anomalies in the coincidence probabilities in EPR data.

Part 1: Quantum Limit

httpvh://www.youtube.com/watch?v=Z4KsOHhWNnk

Part 2: Sub-quantum results

httpvh://www.youtube.com/watch?v=_ydEn4XC7W4

Part 3a: Non-hermitian states (part 1)

httpvh://www.youtube.com/watch?v=jF_mKLaXmqM

Part 3a: Non-hermitian states (part 2)

httpvh://www.youtube.com/watch?v=GD_vG29yEmY

Part 4: Sub-quantum ensembles

httpvh://www.youtube.com/watch?v=pHFuXzpfi2I

Part 5: Conclusions

httpvh://www.youtube.com/watch?v=LyJOmWWCfjc

Part 1: Quantum Limit

The theme of the conference where I presented this paper in Torun Poland, held in June of 22010 is

“Quantum Channels, Quantum Information – Theory & Applications“.

It is often stated that all of quantum information theory rests upon the validity of Bell’s theorem and in this talk I will give an alternate explanation for long distant communication and quantum channels.

In particular I will show that a sub-quantum theory reproduces all the correlations of as well as accounting for the anomalies. This sub-quantum theory is both local and realistic and it is definitely not classical.

From quantum mechanics it is only possible to calculate the EPR coincidence probabilities using an entangled state. I will do it from a sub-quantum product state.

So that are the anomalies? Adenier and Khrennikov re-analyzed the 1998 data of Gregor Weihs. They find that whereas the overall correlation agrees with experiment, the joint probabilities display anomalies. Since quantum mechanics is used to calculate these, and they do not agree with quantum mechanics, then the whole of Bell’s theorem is cast into doubt. Adenier and Khrennikov conclude:

“If we follow Bell’s reasoning then both classical and quantum models should be rejected on the basis of the present experimental statistical data.”

In this talk I will present a new sub-quantum theory which resolves the anomalies found in coincidence EPR experiments. This is the experiment that Clauser Horne Shimony and Holt devised to test Bells’ theorem and to specifically show that quantum mechanics predictions are correct.

Let’s review this experiment again.

A source of two spins in a singlet state remains correlated upon separation. One spin moves to Alice and the other to Bob who both have filters at specific orientations, angles theta (a) and theta(b). Sometimes the photons pass the polarizers and sometimes they do not pass. If both pass, the coincidence is recorded as two clicks as ++. Likewise is neither pass the filters the coincidence is –, etc. Over a run of many thousands of coincidences their frequency gives their probabilities.

A particular sum of the coincidences give the correlation and it is this correlation that violates BI. a and b are the angles of the polarizers at Alice and Bob. Usually Alice’s polarizer is set to zero and Bob’s is rotated through 2pi radians.

A significant result of the sub-quantum theory is it agrees with the experimental results as a product state, with no quantum channels; no entanglement; predicts a new state of spin that quantum mechanics cannot predict and which is supported by the experimental agreement.

Not only does it agree with quantum mechanics, but it also is consistent with the anomalies found.

This experiment is the only one upon which the validity Bell’s theorem rests.

Let’s look at the results from quantum mechanics. They are obtained from the density operator that describes an entangled singlet. It is the outer product of the usual singlet state and it is straightforward to calculate the well known results for the correlation and the coincidences to give the usual –cos(theta) and expressions for the coincidences.

But it appears that the experimental data suggests that the coincidences do not agree with quantum mechanics even though in the sum the anomalies tend to cancel. Contrast that with the results from the sub-quantum theory for the coincidences which are presented here (without proof for now). It is important to accept that this is not a quantum state but a sub-quantum calculation based upon one pair of spins. It does not correspond to an ensemble, just two particles with spin.

For comparison, the quantum mechanics result is just ½ which is obtained by ignoring entanglement. It fails to agree with experiment and must be incorrect. The quantum result says that the single probabilities are an incoherent superposition of many spins ½ which average to ½. That is, there is no coherence between them if we take quantum mechanics as a product state.

This expression as a product of two spins is called a bi-particle because the two members have the same orientation and carry the same hidden variables. That is, when the singlet state was produced at the source, the two entangled spins share common elements. These hidden variables are:

Nz and nx, both of which are integers with values of +1 and -1.

The angle theta orients a sub-quantum structured spin in 3D space relative to the laboratory frame where the polarizers, Alice’s theta a and Bob’s theta b are oriented.

Let us maximize the probability at Alice. It is easy to differentiate the trig terms so we need (theta(a) minus theta) =45 degrees, giving a probability of 1 for Alice’s side. That is, for any setting of Alice’s polarizer, we pick out, or filter, only one sub-ensemble of spins.

But unless Bob’s filter is the same as Alice’s, which it generally is not, then Bob’s probability will not be maximized because his spin must have the same hidden variables, nz, nx and theta, as Alice. So we substitute the expression from Alice, (Theta(a) –theta)=45 in Bob’s probability and we agree with the result of quantum mechanics.

Let’s plot them.

Compare again with quantum mechanics. Alice’s filter is set to zero and bob’s is varied from –pi to +pi. Both the sub-quantum and quantum mechanics agree but the sub-quantum theory used a specific set of hidden variables.

However it is important to note that to date, no product state, or disentangled state, has ever been able to reproduce all the quantum effects. Since this is a local hidden variable theory, it shows that Bell’s theorem is incorrect.

There are other settings of the hidden variables other than the one that maximizes the probabilities and gives the quantum result. Let us look at the anomalies.

These are the joint probabilities and the full correlation as extracted by Khrennikov from Gregor Weihs’ data. Note that P++ and P- – do not coincide as quantum mechanics predicts. Also the maxima and minima are shifted, even though these difference cancel when summed appropriately.

Now I should point out that these anomalies were noted by A. Aspect but since the interest was in the full correlation and not the coincidences, and the full correlation agrees with quantum mechanics, it took Khrennikov’s re-analysis to discover these. Specific experiments to measure the coincidences were not performed. The agreement is therefore qualitative and more experimental data is needed to be quantitative. Therefore I just want to show the trends.

The most dramatic anomaly is shown in the marginal probabilities which is given by P++ + P+-, and P-+ + P– which from sum each adds up to 0.5 .

We see that there is a marked difference between quantum mechanics and experiment.

So how does my sub-quantum theory account for the anomalies? Well in a very simple and physically reasonable way which I will discuss next.

Part 2: Sub-quantum results

Now for the second part of the talk I show how the sub-quantum theory resolves the anomalies. The resolution is very simple and physically reasonable.

As the sub-quantum particles separate, they become misaligned due to spurious local interactions or instrumental effects. Imagine an entangled source and two sub-quantum particles separate: they are correlated only by their common orientation with no quantum channels. As the two beams pass through prisms, pass mirrors and are filtered by polarizers, the two bi-particles can get misaligned.

Recall I call the product state of two particles a “bi-particles” if they come from the same singlet state. In that case they must have the same values of their hidden and therefore are correlated from their source.

Now the hidden variable theta orients a structured spin in 3D space. The anomalies arise when spurious effects misalign them.

This means that Alice’s and Bob’s orientation can get out of sync a bit which gives a small asymmetry between the two. Let us take this as symmetric just for the sake of example.

For point zero five pi radians we see that the coincidences become separated and shifted and the marginal shows structure. The total correlation however remains close to the quantum result.

Now with 0.1 pi radians mismatch, it can be seen that P++ and P- - are similar to experiment. The P+- and P-+ coincide quite well which means there is little misalignment in those arms of the experiments. Clearly the trends are correct.

On the other hand, with a little effort encouraging agreement is found. Here in an angle range of up to 2 pi the trends are reproduced. P++, P–, P+- and P-+.

Finally, most dramatically, the marginals qualitatively agree with the sub-quantum results. This data supports the sub-quantum theory and, as we will see, is experimental evidence for a new state of matter.

So let us look at this sub-quantum theory in more detail.

I have mentioned before (blog 004) that I adhere to the statistical interpretation of quantum mechanics which means that although we might observe single events, we can only calculate the outcome statistically by averaging over many individual particles, i.e. over sub-ensembles.

In fact I will show that the filters in the EPR experiments pick out different sub-ensemble of spins and these sub-ensemble accounts of all the anomalies.

The statistical interpretation is the only one that considers a sub-quantum theory could complete quantum mechanics, but what are these sub-ensembles composed of?

Quantum states are composed of ontic particles. These particles are governed by the sub-quantum theory:

A quantum state is an ensemble of sub-quantum particles usually all prepared in a similar way for experiment-that is the statistical ensemble interpretation of the wave function.
The sub-quantum particles have a 2 dimensional structure rather than the point-particle quantum spin
Isolated sub-quantum particles display a new state of matter
Entanglement is resolved into product states

When considering the sub-quantum concepts, it is necessary to put your interpretation of quantum mechanics aside. The sub-quantum theory is totally different.

Spin arises from the Dirac equation. The free particle Dirac equation is obtained by linearizing the relativistic energy from which spin emerges as a Lorentz invariant and therefore an intrinsic property of matter. However you cannot get the magnetic moment, say for an electron, from the free particle Dirac equation. You have to add a probe. In the second form of the Dirac equation, the scalar and vector potentials from the EM force are introduced.

This means that the basic symmetry of the free particle Dirac equation and the particle in the presence of a probe is different. In the free particle case the environment is isotropic while in the presence of a probe it is anisotropic.

The magnetic moment of an electron is only obtained by using a probe and it successfully gives the correct Landé g-factor of 2 for the magnetic moment. This leads to the view that intrinsic angular momentum is as a vector quantity carrying angular momentum along a single axis of quantization.

It is assumed in quantum mechanics that the intrinsic angular momentum found in the presence of a probe also exists in the absence of a probe. The point of divergence between and this sub- is recognizing that it is not valid to assume that the anisotropic solution is valid for the free particle solution. That is, the vector spin angular momentum determined by a probe does not carry over to the free particle solution because of spontaneous symmetry breaking. Symmetry goes from lower symmetry (a vector) to higher symmetry (a scalar) when the probe is removed. This is the reverse of most symmetry breaking that is found in physics. Usually an interaction is turned on due to a potential and the symmetry is lowered and degeneracy is lifted. How is this done for a free spin?

It is postulated in the sub-quantum theory that the 4 dimensional Dirac spinor space of a spin ½ breaks into two non-hermitian components. This is the basis of the sub-quantum theory presented here.

That is, the individual particles that form the ensembles that make up the wave function do not obey the usual SU(2) symmetry—they are non-hermitian.

Now this is a radical departure from quantum mechanics, but in all cases, spins states are manifest as hermitian. However this symmetry reduction introduces additional degrees of freedom to a spin, and as symmetry breaking usually does degeneracy too.

Break here again but I will continue with part three of the talk by showing how sub-quantum particles have structure and how they lead to a new spin state and disentangle the entanglement of quantum mechanics.

Part 3: Non-hermitian states

For the third part of the talk I discuss the sub-quantum theory in more detail which depends upon non-hermitian states.

In terms of the Pauli spin matrices, these non-hermitian building blocks show two angular momenta and a phase. This is now fundamentally different from quantum mechanics. The quantity “s” is the state of one ontic particle. It does not obey quantum mechanics because it is non-hermitian. This is a definition. Unless it gives the right answers, it should be thrown out. In fact it gives the right answers and using this, as I will show, resolves all the questions raised by EPR; gives a totally different view of a free particle with spin and accounts not only for quantum mechanics, but also for the anomalies.

Let us compare the quantum hermitian state with this sub-quantum particle state. In quantum mechanics the statistical or density operator has two pure states of +1 and -1. The non-hermitian form relates to a single particle, not an ensemble. That is a major difference.

Now the statistical density operator was first introduced by John von Neumann in 1934 and for spins the form given describes a pure state which can have two components, one lying parallel to the external polarizer oriented in the direction Z and the other one anti-parallel.

Note the presence of this term which is missing in quantum mechanics. It accounts for coherence but it is very different from the coherence of quantum mechanics. This coherence is between eigenstates. However eigenstates are orthogonal and therefore there is no coherence between them from quantum theory. The situation is different for non-hermitian operators that can have non-orthogonal eigenstates.

Another difference is that quantum mechanics gives the quantum state as polarized in the laboratory Z direction. In contrast, an isolated sub-quantum particle is oriented in its own body fixed frame of reference, called the spin microframe. Every sub-quantum particle is in general oriented differently, and each spin microframe can be rotated to the laboratory frame.

I told you the sub-quantum theory is different from quantum mechanics.

There is more.

The sub-quantum spin has internal structure. Quantum mechanics does not predict any structure. It treats it as a point particle. However sub-quantum spins have two orthogonal axes of spin quantization, one determined by the z component of the Pauli spin matrix and the other by the x component. The structure is therefore two dimensional, with one magnetic moment pointing along the microframe z axis and the other along the x axis.

The last term is not angular momentum but rather a rotation operator. As such it orients the 2D structure of a spin in 3D space by the commutation relations. This is another major difference. Whereas in quantum mechanics the commutation relations lead to the Heisenberg Relations, which show dispersion, in the sub-quantum theory the non-commutation does the opposite: it orients the 2D particle exactly and specifies it completely with no dispersion, much like the vector cross product orients two vectors in 3D space.

Now I have mentioned that the sub-quantum mechanics is beyond measurement so let us go to the limit and assume that at the briefest instant of time, we can freeze a sub-quantum particle. In this limit, it looks like a 2D particle.

Finally it is assumed a magnetic moment lies along both axes of quantization. Without this structure, agreement with experiment is not possible.

Symmetry breaking leads to degeneracy. Once again this is one spin from an ensemble of many; each oriented in its own microframe. Within a microframe, each spin can be oriented in four ways. In fact these are resonance structures with the eigenvalues being identical and the wave functions differing by a sign only. These are degenerate orientations of a two dimensional spin. The integers simply define the different octants of a microframe. The integers are hidden variables.

Now these extra hidden variables cannot be seen in the presence of a probe. That is, if we take our 2D spin and place it in a magnetic field, one axis of quantization lines up and the other precesses so fast that is randomizes leading to the usual spin of quantum mechanics.

Unless sub-quantum theories predict something new, they are simply interesting exercises. In addition to the ensemble view, there are two major consequences.

The first is that a new spin state is predicted. If a spin is completely isolated, our usual notion is that it retains its spin vector property.

But not for sub-quantum particles. They are quite different. First the two axes of quantization are indistinguishable (not true in the presence of an anisotropic probe) and so superpose to give a hermitian state of root 2 greater in magnitude than usual spin ½. It lies along a vector that bisects the two dimensional spin.

This root 2 spin is a new state of matter that cannot be predicted from quantum mechanics or the Dirac equation. It is a unique sub-quantum resonance of a single spin between two internal magnetic moments. Many examples of resonance are observed in microscopic particles and this is just another. Recall earlier I mentioned that resonance and indistiguishability are two properties of the microscopic that do not occur in the macroscopic (see Blog entry 5). The fact this is a pure dispersion free state of one spin. But symmetry breaking involves degeneracy and here. This leads to a sub-quantum exchange spin in each of the four quadrants.

So the sub-quantum theory predicts that an exchange spin exists in four basically equivalent orientations. Because the four orientations the spin can take are degenerate, all we can say is that at any instant of time it is in one orientation, and resonates between them.

This picture of an isolated spin is quite different from predicted from quantum mechanics. It is as if in the absence of any interaction, a spin sort of shuts down into a resonance state of zero angular momentum.

For an isolated spin, Quantum mechanics predicts a spin is a vector magnetic moment and has two states of +1 or -1. A sub-quantum spin in the absence of all interactions sort of shuts down into a resonance state of net angular momentum of zero.

As I will now show, exactly the same sort of situation occurs for two sub-quantum particles in a singlet state

The second major consequence is that the Bell states are separable. The sum over all the terms leads to cancellation of many terms leaving the usual isotropic singlet state.

The 8 terms organize into four hermitian pairs. Each pair, being a singlet, has opposite angular momentum, and the phase gives two orientations.

First row: ++ –, second row +- -+ third row: -+ +- and forth row: — ++. Each pair has opposite angular momentum.

Each row is hermitian and a product state: not entangled. This is the singlet state of one pair of spins.

So you see what I mean when I say the singlet is like an isolated spin because it has four hermitian terms resonate between the quadrants in a state of zero angular momentum. It is not hard to imagine that combinations of more spins will lead to a similar sort of Clebsch-Gordan coupling, but I haven’t pursued that.

I write each of the four product states as single terms called bi-particles. That is each row of the last slide is written as one of the four possible hermitian states that are the biparticles.

Now it is fundamentally important to this theory that when two particles in a bound singlet state separate, they can only decompose into one of the four bi-particles. It is also assumed that one spin moves towards Alice and the other towards Bob then are only correlated by having microframes which have identical orientations relative to the laboratory frame.

That is why they are called bi-particles. Notice that this correlation is not due to entanglement. It is only due to the fact that the two spins have identical orientations and are in the same quadrants of their microframes.

Just to see this explicitly. Now simply multiply these out and collect terms, and we find that each bi-particles can be written in terms of Pauli spin vectors and reveal, as might be expected from the product of two vectors, the usual isotropic scalar part that is the quantum mechanics result.

In addition there are two vectors, pointing oppositely; and a symmetric traceless 2^nd rank tensor. These are the extra terms predicted by the sub-quantum theory. If we sum over the quadrants, the n_z and n_x, then these terms all cancel leaving only the quantum part.

This is the sub-quantum state for two spins formally entangled. From this all the correlations for EPR experiments can be calculated. In particular the coincidences agree with the data and are products with no entanglement.

The quantum result is just a constant of ¼. But that is not the case here. Each spin is filtered along a definite direction and defines a sub ensemble with specific orientation.

Summary so far:

Sub-quantum spins have 2D structure oriented in its microframe
Indistinguishable axes of quantization predict a new exchange state
Degeneracy between orientations in a microframe leads to a resonance state of net zero angular momentum
The Bell states separate into products of two 2D spins that also display resonance between 4 hermitian states called bi-particles
Upon separation, the bi-particle product state remains correlated because both spins have the same orientation

Part 4: Sub-quantum ensembles

In this part I talk about how sub-quantum ensembles are formed and answer questions concerning the filter settings for maximum correlation; resolution of the detection loophole and the limit when the sub- ensemble averages to give the quantum results .

Let’s go back to our product representation before transforming it to the laboratory frame. This product form agrees with quantum mechanics and accounts for the anomalies. Notice that it has the form that the filters at Alice and Bob form an inner product with the two axes of quantization for the two spins: one moving to Alice and the other to Bob with no entanglement. This is one pair of spins, and each pair leaves the singlet source, pair by pair, and each is filtered.

Note that the hidden variables and the spin microframes are the same for each partner of the formally entangled pair. If they are not from a common source, then the hidden variables and the orientation of the microframes would be different and they spins would not be correlated.

If we set Alice’s angle to any fixed value, then all the spins reaching Alice will define a unique ensemble that maximized the probability which, if you recall, is (theta(a)-theta)=45 degrees.

Without going through the detailed calculation here the joint probabilities from the sub-quantum theory are given by a product. One describes data collected at Bob and the other at Alice. There is no communication between them. There are no quantum channels. It is a product state. Correlations between them arise because they both come from the same singlet and therefore their microframes and hidden variables coincide.

The form in terms of angles is obtained by introducing the filter angles and transforming the spin from its microframe to the laboratory frame. Then in addition to the hidden variables n_x and n_z, there is the angle that orients a 2D spin in the laboratory. It has also been assumed that there is no component of angular momentum in the direction of linear momentum. Therefore the azimuthal angle is taken to be zero.

Now let us look at this expression. There are two cases: n_x = n_z and n_x=-n_z. The maximum probability is give by + 45 degrees and in the other by -45 degrees.

These are two distinct ensembles and, as we will see are responsible for the detection loophole

Consider the coplanar polarizers at Alice and Bob, with the polarizer angles set at angles “a”and “b”. Let us put a along the Z axis, then the two ensembles occur at +/- 45 degrees. Bob’s polarizer cannot be aligned at both positions at the same time.

Hence 50% of the particles cannot be detected. This is likely the major contribution to the detection loophole.

Choosing theta as 45 degrees gives exactly the results of quantum mechanics. That is of the many possible sub-ensembles which can be filtered, only the 45 degree sub-ensembles reproduce quantum mechanics. When theta is not 45 degrees, then the probabilities will not be maximized and anomalies are found.

Quantum mechanics appears to correspond to the sub-ensembles of a system which maximize the probability.

Recall the filter settings that maximize the violation of the CHSH form of BI have the four filter setting differ by 45 degrees, as predicted by the sub-quantum theory.

In support of this is a paper by Karl Gustafson (Noncommutative Trigonometry and , in Advances in Deterministic and Stochastic Analysis (N.Chuong, P.Ciarlet, P.Lax, D.Mumford, D.Phong, eds), World Scientific (2007), 341-360.) from the U of Boulder in which he analyzed the CHSH violations. Using non-commutative trigonometry he found that a vector of root two is responsible. It has identical properties new exchange spin discussed here. In the next entry I will summarize briefly.

Part 5: Conclusions

I will now draw some conclusions.

Due to the presence of the root two spin, the locality assumption is intact.
The sub-quantum theory presented here is local and realistic, providing an interpretation of all known coincidence experiments.
Entanglement becomes a property of quantum theory but not of Nature.
A single sub-quantum spin has 2D structure.

As I mentioned before, a fundamental difference from quantum mechanics is the sub-quantum theory must allow for coherence (interference) between eigenstates. This is not possible in the formulation of quantum mechanics because hermitian operators can only have orthogonal eigenstates.

In contrast, non-hermitian states have non-orthogonal eigenstates and hence can interfere, for example this sort of coherence between two non-orthogonal spin states gives a non-hermitian state of the type I am discussing.

Neither quantum field theory nor the Dirac equation can predict the exchange spin state. To include the sub-quantum theory, QFT need to be generalized to state operators rather than vector states. Only then can the non-hermiticity be introduced.

A local realistic sub-quantum theory accounts for the main features of the experimental data and resolves the anomalies.
Predicts a new exchange spin state and the Bell states disentangle.
More experimental data is needed to quantify this new state of spin.
Need not be concerned about the locality or detection loopholes.

Beyond?

What are some of the other consequences of this approach which completes quantum mechanics? One can only speculate and so my final comments are simply ideas that arise as interesting notions pop up along the way, and might fit. I have not delved into these, and my list is incomplete and needs you to expand it.

First, quite prosaically, the 1935 EPR paper can be exonerated and we can conclude that the objective reality of position and is resolved since now non-locality can be put into its rightful place in history like cold fusion.
Completing quantum mechanics wrt to spin has led to a number of new properties and concepts that could lead to the resolution of difficulties with modern physics. Spin is ubiquitous and occurs in many particles. It is a fundamental intrinsic property of matter and of many individual nuclear particles. Of course when spin is in the presence of a probe, or other interaction, it obeys the statistical results of quantum mechanics, but in free flight between collisions, a spin goes into its resonant state of zero angular momentum.
We have shown that the coincidence probabilities are indeed sensitive to the 2D spin structure as seen from the filter settings of 45 degrees. Could this mean we have to re-consider collisions and Feynman Diagrams? What about the Standard Model? What about other experiments, like the 0.7 anomaly noticed in Ballistic electron experiments? 0.7 is the inverse of the square root of 2. How does symmetry breaking and non-hermitian state affect its formulation? Could the existence of distinct sub-ensembles have an impact on the Dark Matter problem? What about the cosmological constant? How do we formulate QFT in terms of Hilbert-Schmidt space and what will the consequences be? Will this affect string theory?

There is another point. As enthusiastic as I am about high energy physics that require huge investments to build instruments like the Large Hadron Collider, it seems that some answers also lie at the low energy limit that can be done in a small lab with some good optical equipment. Bi-particles need much more work.

In the sub-quantum domain resonance, indistiguishability and most of all objective reality play dominant roles.

These and many more issues need to be re-considered but what is most striking is a totally different conceptual approach is needed in physics which comes under the truism:

“He does not roll dice”.

006 Anomalies in EPR data–Preamble

Bryan — Mon, 14 Jun 2010 13:33:40 +0000

Anomalies in coincidence probabilities in EPR data

Bryan Sanctuary

Department of Chemistry

McGill University

Preamble

httpvh://www.youtube.com/watch?v=n3mCauDFzvE

httpvh://www.youtube.com/watch?v=xeKfWAT-Ef4

Quantum Mechanics is incomplete

Up to now I have talked quite generally about where quantum mechanics fits into the scheme of mechanics. The underlying theme is that quantum mechanics is incomplete from a philosophical point of view; from a physical point of view; and if you believe EPR from a mathematical point of view. Physically quantum mechanics predicts most properties of matter and is the most successful theory we have of the microscopic.

However in some cases it gives nonsense results, such as the persistence of entanglement to separated particles, non-locality and these new quantum anomalies. So in these next few entries of this blog I am going to be more technical and discuss my new sub-quantum theory. The title of the talk is Anomalies in coincidence probabilities in EPR data. But first a preamble to set the stage:

I gave a short 15 minute version of this talk in Torino Italy, (May 2010) and a 30 minute talk in Torun, Poland (June 2010) , the birthplace of Nicolaus Copernicus.

Notice that the theme of the conference is “Quantum channels and quantum information – theory and application.” Now one of the consequences of the sub-quantum theory I presented at these meetings is that quantum channels do not exist. Entanglement is a property of quantum mechanics and not of Nature and that Bell’s theorem is repudiated.

All of quantum information theory rests on the validity of Bell’s Theorem

In 2009 I also attended a meeting in Toronto and at that meeting the first John Bell prize for work in quantum information was given to Nicholas Gisin from the University of Geneva. In his talk he made a profound and far reaching statement:

“The whole of quantum information theory rests upon the validity of Bell’s Theorem”

So I have a question: what happens to quantum information if Bell’s Theorem is incorrect?

Quantum channels

So what are quantum channels and what is Bell’s theorem?

In 1993 Bennett, Brassard, Crepeau, Jozsa, Peres and Wootters wrote the classic paper on teleportation. The title is:

Teleporting an Unknown Quantum State via Dual Classical and Einstein Podolsky Rosen Channels.

Now by classical channels, they mean calling on the telephone. Einstein Podolsky Rosen Channels refer to the paper on 1935 called EPR and are the quantum channels.

It is certainly my contention that experimental data cannot support the notion of quantum channels. They also cannot be supported on the basis of physical intuition. Einstein Podolsky Rosen actually ruled out such connectivity in their 1935 paper.

Here it is, “Can quantum-Mechanical Description of Physical Reality Be Considered Complete? It is worth reading a few of their points view:

“A sufficient condition for the reality of a physical quantity is the possibility of predicting it with certainty, without disturbing the system.”

And then

“Any serious consideration of a physical theory must take into account the distinction between the objective reality, which is independent of any theory, and the physical concepts with which the theory operates.” Please note “Independent of any theory”

And to emphasize that everything is local (that is no quantum or EPR channels) they state,

“If, without in any way disturbing a system, we can predict with certainty (i.e. with probability equal to unity) the value of a physical quantity, then there exists an element of physical reality corresponding to this physical quantity.”

Which is one of the most quoted parts of the paper.

Nonetheless Quantum channels are insensately conjectured to be responsible for conservation of angular momentum between a pair of separated and entangled spins. What this means is that no matter how far the entangled pair is apart, if one is flipped, the other must flop, with the connectivity between these particles given by “quantum channels”.

The quantum channels are supposed to mediate nonlocality.

Many people believe quantum mechanics itself is non-local. Here we find:

“Nonlocality is one of the most striking properties of quantum mechanics. Two distant observers, each holding half of an entangled quantum state and performing appropriate measurements, share correlations which are non-local.”

They are talking about quantum channels mediating nonlocality, but what is half a quantum state? I defy anyone to write down half an entangled state from quantum mechanics. According to David Bohm, an entangled state is an “undivided whole”.

Speed of communication

The speed that information is communicated over quantum channels has been calculated. It is fast:

”We set a lower bound for the speed of quantum information in this frame at 150 thousand times the speed of light.” We need tachyons for that.

This made it to journals like scientific American,

“Quantum weirdness wins again: Entanglement clocks in at 10,000 + times faster than light.”

What is quantum weirdness???

Books have been written to try to rationalize quantum mechanics and relativity with mixed reviews.

You often hear to statement:

“Quantum mechanics and relativity live in peaceful coexistence.”

Well it’s not true. Let us put tachyons aside and just accept that believing that connectivity between separated entangled particles means just the opposite quantum mechanics is in conflict with relativity.

There is another alternative of course. There is nothing incompatible between quantum mechanics and relativity, but rather quantum mechanics is an incomplete local theory and the long range correlations have an origin which is local.

Bell’s Theorem

Let’s turn to Bell’s theorem, which is not a mathematical theorem. Rather it is a deduction based upon the fact that quantum mechanics violates Bell’s inequalities and states

Bell’s Theorem: No physical theory of local hidden variables can ever reproduce all of the predictions of quantum mechanics.

Note that Bell’s theorem only refers to sub-quantum theories; it says nothing about quantum mechanics being a non-local theory. Let’s read the introduction:

“The paradox of EPR was advanced as an argument that quantum mechanics could not be a complete theory but should be supplemented by additional variables (sic. Hidden Variables). These additional variables were to restore to the theory causality and locality.”

I think Bell’s intentions are abundantly clear; he is talking only about hidden variables, not quantum mechanics. It also seems that John Bell disagreed with EPR and thought quantum mechanics a complete subject. In deriving his inequalities, and showing quantum mechanics violated them, he concluded (incorrectly as I will show) that the objective reality of position and momentum that EPR proved required a hidden variable theory displaying non-local correlations. Since the notion of non-locality is absurd, Bell ruled out hidden variables and therefore quantum mechanics is complete.

We came across “quantum Weirdness”. In Google it gets 121,000 hits Read a few:

“Quantum weirdness arises when a quantum system is enlarged to a macroscopic scale and then measured in a way that would violate the indeterminacy principle” I do not understand this.

“non-local behavior” (or colloquially as “quantum weirdness” or “Spooky action at a distance”) So quantum weirdness refers to non-locality.

Or Quantum magic, well I will let you read. 527,000 hits for Magic.

Quantum spookiness—more of the same—3,210,000 hits. When scientists use words like quantum weirdness, magic and spookiness to describe Nature, then you can only conclude one thing: They do not understand what they are talking about. It is that simple.

Let’s move on.

As I said, Bell’s Theorem, incorrect as it might be, only refers to sub-quantum mechanics. However many attempts have been made to try to extend Bell’s theorem to quantum mechanics. Here is one paper by Stapp: Bell’s Theorem without Hidden Variables. Read the abstract: “Experiments motivated by Bell’s theorem have led some physicists to conclude that quantum theory is nonlocal. However, the theoretical basis for such claims is…”

And he goes on to say that Bell’s theorem refers to hidden variable theories and not quantum mechanics, and then presents a proof that extends non-locality to quantum mechanics.

His proof has not lived up to scrutiny, for example Bill Unruh from UBC has convincingly argued against Stapp. Nonetheless, due to entanglement being considered a property of Nature, and in the absence of a reasonable alternate explanation; people continue to believe that Bell’s theorem should be extended to quantum mechanics making it is a non-local theory

But quantum mechanics is a local theory and so too, as we will see, is the sub-quantum theory that resolves the anomalies found in the EPR data. If I can give you such a local sub-quantum theory then it means Bell’s theorem is incorrect.

This entry is more of a preamble to set the stage for the talk. The next entry is the first part of my talk where I show that all known data including the anomalies can be obtained from a product of two spins correlated by orientation only, with no entanglement, with no quantum channels, with no magic, no weirdness and no spookiness, and definitely no tricks.

However if you wish to follow my sub-quantum theory, you will have to put aside your pre-conceived ideas of quantum mechanics. You will have to accept that non-commuting operators have simultaneous reality; the Heisenberg relations do not hold for the sub-quantum theory; a point particle of a spin ½ is not a point particle but has structure; that Bell’s theorem is wrong and that EPR is correct.

Most physicists today have been brought up with the idea that Bell is correct and that EPR are wrong. Most scientists I talk to shake their heads and tell me that they cannot understand it. It makes no sense, but the majority also believes that quantum mechanics is the most fundamental theory and we have to accept its incompleteness as a property of Nature. So this is a paradox

005b Micro and macroscopic reality (cont.)

Bryan — Tue, 16 Mar 2010 00:17:29 +0000

httpvh://www.youtube.com/watch?v=8ilWHkL9m2Y

Resonance

The second major difference is that microscopic reality displays degenerate states. One example is different states can have the same energy, and we say that the energy of these states is degenerate. This leads to resonance that also does not exist macroscopically.

Two structures can be different but have the same energy. Quantum mechanics considers that both exist simultaneously as a superposition of the two.

Let’s look at resonance a bit more. In an example is the Zeeman Effect where energy levels of are split in the presence of a magnetic field. For illustrative purposes, let us forget about electronic structure of this atom and consider these are the possible states available to electrons (although we will obey the Pauli Principle).

If we count the states in the presence of a magnetic field, in this case we have 12 distinct levels. If the magnetic field is turned off, then those twelve energy levels all have the same energy.

We say the states are 12-fold degenerate with respect to energy. When the field is on, the degeneracy is lifted and now we can distinguish the 12 states because they have a property, energy, that is different between them.

Degeneracy means we cannot distinguish one state from another on the basis of some property, in this case, energy alone.

It is like gravity. On Earth, there is one way up and depending on your position the force of gravity changes. In space, there is no up or down, and therefore all directions are same, or degenerate.

Let us suppose that there is only one electron available and which occupies one of the 12 states when the field is turned on, we know its state, say it is F=2 and m=2 . But when the magnetic field is turned off, we would not know which of the 12 possible ones it would occupy.

Therefore, in the absence of further evidence, any one of those degenerate states can exist at any instant but we cannot know which one. That is the system is in resonance between them all. In the absence of any other information, the electron on the degenerate side is equally likely to be in any one of the 12 states. When the field is on, it is distinguished by its energy and is in one state labels be, in the example by 2, 2.

At any instant, that one electron on the LHS can be in any one of those degenerate states. It cannot, however, be in all 12 states at the same time. It resonates between all 12. If these are the states of one electron only, then those states must be objectively real.

Quantum Mechanics superposes states

Of course this is not the way quantum mechanics views things. In quantum theory this is called the Superposition principle which treats the electrons as being in all the states with a certain probability. Quantum mechanics cannot distinguish those degenerate states. The reason is clear a state is a statistical ensemble, and the electrons that make up the ensemble can occupy any of the states with a certain probability.

Sub-quantum theory should resolve superposition

This gives us another hint about sub-quantum mechanics:

A sub-quantum theory should resolve, or disentangle, the superposition principle into ontic states. That is the statistical ensembles of quantum mechanics is replaced in a sub-quantum theory by individual ontic particles that make up the ensemble.

Degeneracy and resonance are common at microscopic dimensions and not restricted to energy.

Just because a sub-quantum theory is objectively real does not mean it is “classical” because indistinguishability and resonance lead to new predictions that do not exist in the macroscopic.

We have seen already how such properties account for 90% of the hydrogen molecule’s bond energy. Recall a chemical bond is completely quantum with no classical contributions whatsoever. There is nothing classical about it.

Hence, since these properties must carry over to any successful sub-quantum theory, it could predict new phenomena that can be described by neither classical nor quantum mechanics. Is there anything that cannot be described by either classical or quantum mechanics?

Something New

It seems so. I mentioned in my last entry there is one experiment where quantum fails and this is it. “Anomalies in experimental data for the EPR-Bohm experiment: Are both classical and quantum mechancs wrong?” by G. Adenier and A. Khrennikov published in 2008 on the quantum archives. A careful analysis of the data shows that no known theory explains the data.

Even so, in both the micro and the macroscopic, objective reality means that all objects possess exact values of their defining properties. However new properties exist microscopically that cannot exist macroscopically and these properties arise from indistinguishability and resonance.

Next time

Up to now I have not given many examples. Over the next few entries, I will discuss the Stern Gerlach experiment and use the objective data it gives to illustrate many of the ideas that we have come across so far.

005 Micro and macroscopic reality 1

Bryan — Tue, 16 Mar 2010 00:14:12 +0000

httpvh://www.youtube.com/watch?v=zPicA0FmkMI

Microscopic and Macroscopic reality is different

In this entry I will discuss the difference between reality at the microscopic and macroscopic levels.

Last time I talked about where quantum mechanics fits and called the domain that lies beyond measure the quantum. Let us suppose that the statistical nature of quantum mechanics can somehow be bridged, so that quantum noise can be resolved into structure by a deeper sub quantum theory.

An Objective Realist would expect a complete microscopic theory to have pure dispersion-free properties in the limit of one particle. Also causality should be restored, so we can predict the states of particles from initial conditions and the known forces.

Empiricists would worry about how to measure such a particle, but need not because, as I said, a sub-quantum theory is beyond measure. Quantum mechanics, in contrast, is a theory all about measurement.

Differences between the microscopic and macroscopic

I think we all have a really good idea of the reality around us. We know fact from fiction, and even though we might be fooled, we can usually work it out. But here is a question that is worth considering:

Is reality at the one particle level the same as in our macroscopic surroundings?

Many who believe that quantum mechanics is the most fundamental theory criticize microscopic objective reality and label such sub-quantum theories as “Classical” .

But it is well known that correlation exists between microscopic particles that cannot be explained by any classical theory. In quantum mechanics the property that describes these quantum correlations is called entanglement, about which I will come back to later. But are those critics right? Are local realistic sub-quantum theories classical?

No! Absolutely not. So be ready to consider that reality is different between the micro and macroscopic.

Quantum and Classical Mechanics differ

First off the mechanics of any sub-quantum theory will be completely different from Classical Mechanics. Here we see Professor Lewin put his life on the line by demonstrating his faith in the Conservation of Mechanical Energy. But he knew that he was safe because he knows that the pendulum cannot exceed its amplitude.

However if that were a quantum pendulum, the ball could extend beyond the classical range and hit him. This is quantum tunneling:

Consider a quantum pendulum

There is the classical turning point right at Professor Lewin’s chin which in this case is a physical barrier, like a wall. A quantum pendulum can tunnel right through his chin.

In other words, classical and quantum mechanics are quite different in many ways. It is more likely that a sub-quantum theory be closer to quantum mechanics than to classical mechanic, so there will not be too much that can be called “classical” in a sub-quantum theory.

Those who call a sub-quantum theory “classical” are incorrectly applying notions from our macroscopic surroundings to the microscopic.

Moreover reality is different between the micro and macroscopic even though both are objectively real; both are local, complete and deterministic.

Indistinguishability

Reality is different between the microscopic and macroscopic levels because of Indistinguishability and Resonance. These properties do not exist classically.

You can always find differences between any two macroscopic objects but you cannot tell one Hydrogen atom from another, or one electron from another. They are indistinguishable.

That is, indistinguishablity is a property that cannot be found in our macroscopic world.

Resonance is another property unique to the microscopic. There are forms and structures that flip between one and the other without any obstacles.

However if you want to apply a mathematical description, say by writing down the Hamiltonian in quantum mechanics to understand the hydrogen bond, we label them so we can keep track of them.

But labeling the two H atoms makes them distinguishable and if we keep the labels, we will get the wrong answer.

A hydrogen molecule bond is one of the simplest. Recall that the protons, A and B are positively charged and the electrons are negative. Since like repels like and unlikes attract, we have two repulsions (between the two protons and two electrons; and four attractions between electrons and protons. ) It is impossible for us to apply quantum mechanics to any problem without labeling the parts to distinguish them so we can apply the mathematical equations.

But labeling the two H atoms and two electrons makes them distinguishable and if we keep the labels, we will get the wrong answer.

In order to correct this, we have to make the two atoms indistinguishable in our calculation by symmetrizing the two forms. This is done frequently in quantum theory. In this case, shown schematically here, the symmetrized sum is called the exchange term in quantum chemistry.

Remarkably if we do not do symmetrize then the calculation misses 90% of the bond strength!! That is, this purely microscopic property of indistinguishable particles cannot be ignored.

This is a major difference between the macro and microscopic worlds.

In other words, indistinguishability predicts new phenomena that cannot exist macroscopically.

(this is continues in entry 005b)

004 Where quantum mechanics fits.

Bryan — Sat, 13 Mar 2010 17:59:49 +0000

httpvh://www.youtube.com/watch?v=8EbBasYGb_E

Where quantum mechanics fits.

Last time I discussed a bit about how scientists view Nature at molecular dimensions. One of the reasons scientists think that quantum mechanics is a complete theory of the microscopic is because it is capable of explaining all objective data. Well as we will see, not quite all. There is one experiment that causes trouble but otherwise with no evidence of anything deeper. How can we know if a sub-quantum domain actually exists?

Requirements of a physical theory

The least we should expect from a physical theory is that it is consistent with reality; completely explains all phenomena; and deterministically allows for events to be predicted from some initial cause. We also should expect interactions to be local.

Quantum mechanics fails in all these.

Particles are real and we have many ways of determining and confirming the structure and function of molecules—that is chemistry.

Interactions fall off with some inverse power law—so interactions are local. Near a source the intensity drops off the further you are, like the light from a distant star. This is an example of an inverse power law and all forces (well there are only four) become weaker with separation until they are negligible and can be ignored.

Evolution is deterministic. Here is an example of cause and effect. In our world where classical mechanics is applicable all processes are deterministic, but not in quantum mechanics.

We’d also expect a physical theory to describe all properties of a system accurately. Quantum fails there too.

Maybe these are not failures of quantum mechanics, maybe quantum mechanics is complete and accurately reflects the way Nature is.

So maybe reality does change and we can let philosophers argue the ontological difficulties. Maybe Nature is not deterministic, and only gives probabilities and God really does roll dice.

But that is not very satisfying as attested to by the large number of attempts to understand and interpret quantum mechanics.

Troubling issues with quantum mechanics

Right from the beginning, scientists have been troubled by these issues yet wowed by its success.

It started about the time of this famous photograph showing the participants of the 1927 Solvay conference in Brussels which was chaired by the well known grandfather of physics Hendrick Lorentz. The focus of the conference was the interpretation of the wave function and most were on the side of Niels Bohr who believed quantum mechanics a complete theory, but with Louis de Broglie and Einstein as notable exceptions. In his summary at the end of the conference, Lorentz expressed what has been echoed many times since: dissatisfaction with the rejection of determinism in quantum mechanics. Let us look at a chronological list of some of the many attempts to interpret quantum mechanics since that time

Many interpretations

Consider all these approaches.

Ensemble interpretation—Born 1926
Copenhagen—Bohr and Heisenberg 1927
Hydrodynamic—Madelung 1927
Projective measure—von Neumann 1932
Quantum Logic—Birkhoff 1936
Bohmian mechanics—Bohm 1954
Many-worlds—Everett 1957
Stochastic mechanics—Nelson 1966
Many minds—Zeh 1970
Statistical-ensemble—Ballentine 1974
Consistent histories—Griffiths 1984
Objective collapse theories—GRW 1989
Transactional—Cramer 1986
Rational—Rovelli 1994
Incomplete measurement de Dinechin 2006

All accept quantum mechanics to be a complete description of Nature except the ensemble approaches (1 and 10) and David Bohm’s Bohmian sub-quantum mechanics, 6.

Notably is the Copenhagen interpretation which today is still perhaps one of the most accepted, and first articulated by Bohr at the 1926 Como conference in Italy. It too assumes the completeness of quantum mechanics.

Quite a few interpretations require the wave function collapse upon measurement. This is also called “reduction of the wave function”. I remember when I was taking a course in quantum physics as a grad student at UBC. I was not really paying attention when suddenly I heard the professor say, “..and the wave function collapses…” He suddenly had my attention and I had a strange image of quantum mechanics falling apart. But the more I looked at it, the less sense it make. I had no answers of course, but it needled me from then on.

The Statistical-Ensemble Interpretation

There is a notable paper by Leslie Ballentine where he explains the statistical interpretation of quantum mechanics and compares it to other approaches. In that paper regarding the enormous number of papers on the theory of quantum measurement, Ballentine states,

“The reader can shorten his task greatly by ignoring all papers which try, without modifying quantum theory, to accommodate the reduction of the state vector and which also assume the state vector to describe an individual system.”

Cross out 4, 12 to 15 because they all require wave function collapse. Of the remaining interpretations of quantum mechanics, only the Statistical-Ensemble approach leaves open the door for sub-quantum theories. All the others maintain that quantum mechanics is a complete theory of the microscopic. So since we are discussing the possibilities of sub-quantum theories, let us cross them out too.

Only the statistical-ensemble interpretations, as discussed in that paper by Ballentine, allows for a sub-quantum theory to complete quantum mechanics with properties that satisfy local realism, causality and determinism. That a suitable sub-quantum theory has not been found is a human failing and nothing more.

I am not including number 6, Bohmian mechanics, because it is a sub-quantum theory rather than an interpretation of quantum mechanics. Also I am not rejecting the other interpretations just noting that they all consider quantum mechanics is complete.

Where does quantum mechanics fit?

So to what systems is quantum mechanics applied? Since we can recover classical mechanics from quantum mechanics, we could move into the cosmos, but let’s not go too far. Let us not consider the cosmos and questions of quantum gravity, black holes and dark matter etc. The cosmos is big. Cosmologists estimate the number of starts in units of sextillion.

How about our macroscopic surroundings: we know that quantum effects are manifested in many ways, but they are indirect. They are there but you can safely ignore them without hindering your ability to function normally. In fact from an empiricists point of view, we can only see microscopic effects indirectly as numbers on meters and deflections of needles.

Quantum mechanics becomes relevant when Planck’s constant becomes important. Planck’s constant is a very small number. He first discovered his constant while studying blackbody radiation in 1898. As you heat a black body, say by turning on your stove, it starts to glow and give out radiation. The intensity and colour depend upon the temperature of the body.

One of his critics, James Jeans, who tried unsuccessfully to use classical mechanics to describe BlackBody radiation and which led to the ultraviolet catastrophe, said “The real value of Planck’s constant is zero.” In classical mechanics he is right, but quantum mechanics describes phenomena where its value is non-negligible.

This is where quantum starts to be relevant.

Many people incorrectly think that Planck’s constant the smallest quantum of energy, but that is not correct. It has the units of Joule seconds which is angular momentum.

Likely the value of Planck’s constant was fixed at the time of the Big Bang and after that, along with other fundamental constants, …, our periodic table was set.

The limit of quantum mechanics

But back to the fit of quantum mechanics in Nature. Earlier I mentioned that the Heisenberg Uncertainty Relations have nothing to do with measurement, but they do put a limit on how we prepare a system for a measurement. That preparation fails unless it satisfies the Heisenberg Uncertainty Relations . If preparation is impossible, then measurement is impossible. Quantum mechanics is a theory about measurement of the microscopic and the Heisenberg Uncertainty Relations give the limit of its applicability.

Quantum Noise

Let us call the microscopic domain that lies below the Heisenberg Uncertainty Relations the quantum noise. Is it only noise : that is uncertainty, dispersion and random events? This is the sub-quantum domain.

Here I do not mean quantum noise in any experimental sense, like shot noise. Quantum noise is defined here by the statistical nature of quantum mechanics as determined by the Heisenberg Uncertainty Relations.

Sub-quantum theories are beyond measure.

This gives us a big hint. If Quantum mechanics is a theory of measurement which is limited by the Heisenberg Uncertainty Relations, then we can surmise that one of the properties of a sub-quantum theory is that is cannot be directly measured. We can ignore the measurement problem in developing a sub-quantum theory. Quantum mechanics does the job very well and even sets limits of applicability.

So what good is sub-quantum theory if it cannot be measured?

Well just as quantum effects indirectly affect our macroscopic surroundings, so a sub-quantum theory can lead to measureable effects indirectly on quantum mechanics. In other words, unless something new emerges from a sub-quantum theory, then we might as well forget it. New predictions and results are needed and these must be consistent with quantum mechanics. This is one of the difficulties with Bohmian mechanics—an intriguing sub-quantum theory, but nothing new is predicted, so it cannot be confirmed.

Summary

Here is a summary: Cosmology down to our Classical Earth, and then into the quantum world where Planck’s constant rules and finally perhaps to the elusive hidden variable sub-quantum mechanics that restores Objective Reality to Nature and restores ontological sense to science.

Of course a complete unified theory is still a holy grail of physics. Perhaps some clues lie in trying to understand if something lies below Quantum Mechanics, and if so what?

The truth about reality would be nice. So in my next entry I want to talk a bit about how objective reality at microscopic dimensions differs from that of our macroscopic surroundings.

003 Positivism, empricism

Bryan — Wed, 10 Mar 2010 16:41:36 +0000

httpvh://www.youtube.com/watch?v=6wQyMxYuR_s

Positivism, empiricism and objective reality

In my last entry I talked a bit about reality and introduced the ideas of Ontology (the philosophy of being) and Epistemology (the philosophy of knowledge). In this entry we move down to the microscopic level where things are quite different. Our intuition in the macroscopic Naïve Reality in which we live changes dramatically.

Positivism

In fact the last holdout who denied the existence of microscopic particles was perhaps the famous and influential 19th century physicist and philosopher, Ernst Mach (you have heard of Mach force and Mach number). He was a Positivist who believed that what we can know is restricted to our sensory perception alone. Therefore he did not believe in the existence of atoms and molecules.

Ernst Mach

So Mach would only accept what he can see macroscopically. This is different from Naïve Realists because Positivists do not ever think about what lies deeper.

Positivists maintain this stance because they only need a way to calculate the observed objective data without trying to understand it.

This is because Positivists abhor the metaphysical: questions that do not have a measureable answer. If they interpret, then paradoxes and difficulties can arise and a Positivist does not want to get into that game.

Ontology

Is the Microscopic world real? Are microscopic particles real?

It is difficult to find scientists today who do not believe particles are real objects. Microscopic particles do exist. Here you see iron on copper as viewed by using a scanning tunneling microscope. This technique does not see particles the same way light or electron microscopes do by use of diffraction. Rather the scanning microscope detects the electrons in atoms and molecules and makes use of the quantum phenomenon of tunneling. The changes in electric field as the probe passes over a surface are changed into images.

Scanning Tunnel Microscope of Iron and Copper

The resolution is about 0.1 nano meters (1 nanometer is 10 to the minus 9 meters), this is down to the dimensions of single particles.

All matter is composed of smaller particles. Quantum mechanics cannot directly describe one particle. Rather only the collective effects of many particles prepared in a similar way fall under the purview of quantum mechanics.

Since we use instruments to probe the microscopic, we cannot use our normal naïve perceptions to interpret what we observe.

We also need a different mechanics.

What is microscopic reality?

However there is disagreement as to how we obtain microscopic properties and describe them. Basically the question is:

Do we observe the microscopic properties of individual particles,

Do we measure the microscopic interaction between many particles and a measuring instrument?

The former view is that of an Objective Realist: objects possess real attributes that naturally exist even if they are too small or too fragile to observe.

The latter is that of an Empiricist:

Discussions of the interpretation of quantum mechanics cannot ignore the famous and important Einstein-Bohr debates. At this stage I wish to discuss the ideas that are most prevalent today rather than the rich and exciting history of quantum mechanics. I will come back to the early debates later. At this stage, let us generally consider that Einstein was a realist and Bohr was an empiricist.

Empiricism

So what do Empiricists believe? They recognize that microscopic interactions are manifested macroscopically.

These readings constitute the objective reality of measurement.

They are macroscopic real numbers, not the properties of individual particles, because they are obtained by the amplification of individual interactions of many particles within a measuring instrument.

In contrast to Positivists, Empiricists gain knowledge by experimentally testing the assumptions and hypotheses of our logical description of Nature. They want to interpret the experimental data within quantum mechanics.

Empiricists are therefore concerned about what we measure and not primarily about whether microscopic objects possess real values or not.

However empiricists accept that quantum mechanics might not be a complete description of Nature but work within its framework to resolve difficulties.

Objective Realism

Let’s leave empiricism for a while and discuss how an objective realist views Nature.

In object reality, all attributes of a system are real and dispersion free whether we measure them or not.

In our classical surroundings, this is not a problem. We figure we can measure as accurately as our instruments allow and our challenge is to build instruments to measure the exact values of the properties of a system with as little error as possible.

When we know all these attributes, the only error is in the final digits of our instrument accuracy, and this is called dispersion. We believe this can reduce by improving the instrument.

An accurately known quantity has small dispersion (or error).

In a nutshell, an Objective Realist believes that microscopic objects possess values which have no dispersion. All attributes have exact values that exist simultaneously.

This is not true of Quantum mechanics and it is impossible to describe all attributes without fundamental error arising that we cannot surmount by improving equipment. But look at this image from IBM—it is a bit fuzzy, but that is instrumental error. A single molecule can be seen and it looks real.

Heisenberg Uncertainty Principle

Of course the fundamental error in quantum theory is succinctly expressed by the Heisenberg Uncertainty Principle which puts a limit on quantum theory. I will talk more about this later but it is important to note that there is nothing in the derivation of HUR that has anything to do with measurement

All you need is two non-commuting Hermitian operators and a bit of math.

If you believe fundamentally that objects are real, then you cannot accept quantum mechanics as a complete description of nature because some attributed disrupt each other.

What to believe?

If you believe Quantum mechanics is the most fundamental theory of Nature then you have to accept that reality changes depending on how it is observed.

That is the reality we associate with the result from one measurement, say position of a particle, is different from the reality we associate with another measurement, say of the momentum of a particle.

If you believe this then you are in good company even if the company is not very large. Einstein could not accept that quantum mechanics was complete, and he sought a sub-quantum theory to understand the statistical nature of quantum mechanics—and we all know his famous quote:

“God does not play dice.”

Although many would like to believe that quantum mechanics is incomplete, after trying unsuccessfully since the late 1920’s to complete it, you can understand why Richard Feynman might have said:

“Shut up and calculate!”

Summary

Lets me summarize here:

You believe that quantum mechanics is complete, then you must accept that Nature is statistical and that reality changes depending upon how you look at it (that is performing different experiments).
If you believe that particles exist and posses values of their attributes whether or not they are known (that is you are an objective realist), then you must accept that quantum mechanics is incomplete.

You cannot have it both ways.

Next time I want to explain where quantum mechanics fits into our description of Nature.

002 How Scientists Think

Bryan — Wed, 10 Mar 2010 16:12:45 +0000

httpvh://www.youtube.com/watch?v=zHgceOCFb_Y

How Scientist Think

Although the following overview of how scientists think is quite general, in the next few entries to this blog I will be discussing primarily what is involved in acquiring data about the microscopic world and understanding how scientists think about what they measure and what those measurements mean.

Ontology

This involves trying to understand how information is obtained and how we interpret data leading us to knowledge? The first thing to confront is the question:

“What is reality?”

This is not a trivial question and one that is at the core of understanding Nature. In philosophy this is called Ontology. Ontology is the philosophy of “being” and of “reality”.

Ontology

The Greeks were the first to develop the ideas: Parmenides on existence, Plato on separating the mind from the body and Aristotle on metaphysics.

In the macroscopic world we live in reality is quite intuitive. We probe our surroundings with our senses and these are automatically interpreted by our minds as perceptions. We usually believe our perceptions, or maybe misled by them too, but for the most part we are convinced that the objects we see are real.

Normally if you doubt something is real, you simply ask a friend: “Do you see it too?” and seek confirmation. Yes the moon is really there because when you do not look at it, someone else can, and sees it in a reproducible experiment.

Moon: we all can confirm it is there.

Naive Realism

Our view of the world around us is WYSIWYG . We do not think much about preparing the object we observe: we might just pick it up. Nor do we think about how to measure it: we just look and feel it, maybe shake it, sometimes smell or taste it. We do it without much thought. We perceive and that is our reality.

This is called Naïve Realism

Although this works well in our world, for example animals function very well without any knowledge of physics, Naïve Realism does not work at the microscopic level.

Objective Reality

Objective Reality means that objects around us exist and possess exact values for their properties independently of our intervention. If, however, an observation is made, then it must be possible for others to confirm it by independent observation. You see the moon, and others see it too.

Subjective Reality

Naïve Realism does not extend to the microscopic level, does objective reality? Some say yes, most say no. Besides objective reality, there is also subjective reality.

For example, no-one can confirm that God exists because it is a matter of faith. God is real to all believers and not real to non-believers. This is not the type of reality of science. This is called Subjective reality but it plays an important role in the interpretation of objective results

These interpretations must be consistent with the objective results, and be accepted by a large number of other scientists who can agree on some things and disagree on others.

Epistemology

The subjective interpretation of objective reality is knowledge and the branch of philosophy is epistemology—how we know.

In Summary, ontology is the philosophy of the state of being and Epistemology is the philosophy of how we know.

In my next entry I will discuss some common philosophies of science and what they mean.

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005 Micro and macroscopic reality 1

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