PART 21.  WHICH PATH MARKERS IN QUANTUM INTERFERENCE EXPERIMENTS.  PART 1. THE WALBORN ET AL EXPERIMENT

The which path marker  used in the Walborn et al  experiment  used a quarter wave plate in front of each slit and these changed plane polarised light from the source into circularly polarised light. For each type of incident photon, one of the plates produced clockwise polarisation and the other produced anticlockwise polarisation.

With the plates in place the pattern produced did not seem to show clear evidence of two slit interference fringes but resembled a single slit diffraction pattern. It’s a pattern that can easily be explained using the laws of Fresnel and Arago, but this seems to have been overlooked in favour of the arguably weird explanation which refers to which path information. This assumed that because the experimental arrangement can be used to gain which path information, interference fringes could not be observed. But a flaw with this explanation is that two slit interference was sort of observed because the pattern produced was a mixture of two overlapping interference patterns which were out of phase.

Fresnel – Arago explanation

The state of polarisation leaving each wave plate was a combination of two linear orthogonal components, the ordinary (o) and the extraordinary (e). The o component from each plate had the same plane of polarisation as the e component from the other plate and so there were two sets of o and e components where the components in each set shared the same plane of polarisation. The components in each set interfered in accordance with the laws of Fresnel and Arago and this resulted in two interference patterns.  

Because of the 90⁰ phase difference between the o and e components from each of the two plates there was a 180⁰ phase difference between the two patterns, the result being that the peaks of each pattern overlapped the troughs of the other pattern. The resultant pattern resembled a single slit diffraction pattern.

In the experiment two interference patterns were observed separately by means of a linear polariser in the path of the idler photon. The idler photons with the same axis of polarisation as the polariser axis reached the idler detector. The other photons didn’t. When the axis was parallel to the axis of one of the sets of o/e components the interference pattern due to the other set of o/e components was observed. This is because the coincidence circuit enabled observation of the signal photons which were correlated with plane of polarisation of the idler photons. By rotating the polariser through 90⁰ the second interference pattern was observed and for the reasons given. The rotating polariser can be described as a pattern selector. That’s what I call it anyway.

Anyone interested in the 2002 experiment may also be interested in the 1975 more classical interference experiment carried out by Piano and Pescetti. The 2002 experiment can be considered as a variation of the 1975 experiment. It may be interesting to note that that there was no explanation of the overlapping interference patterns in either of the two papers.

If you thought this section was boring wait till you read the section referring to the experiment of Kim et al. It’s so boring it will make your teeth itch.

PART 22.  PLUG AND CHUG

Are you a member of the Plug and Chug brigade?  When faced with problems do you immediately go searching for equations? When faced with sums do you immediately reach for your calculator?

Probably everyone suffers from some degree of plugchugism but if your case is extreme there is a simple cure which boils down to the following piece of advice:

Sit down, relax and have a nice cup of tea.

PART 23.  WHO KNOWS WHAT PHOTONS ARE?

There are certain conceptual problems associated with our understanding of photons and included amongst these is the apparent weirdness that some people associate with the concept of entanglement. In order to try to resolve some of the difficulties it could be helpful to go back to basics and try to find if there are some aspects of theories that have been overlooked. A good start can be made by considering again observations that are made or can be made in various relevant experimental set ups.

Consider a simple system containing two parts which can be defined as:

1. A photon source
2. A photon detector

Using these two parts we can set up experiments to make observations and conclude, with reasonable confidence, that what can be observed, at the detector is correlated with what happens at the source. But should the conclusion be the other way round, in that what can be observed at the source is correlated with what happens at the detector? Perhaps there are some sort of two way exchanges between source and detector. But let’s forget that for the moment and imagine that the photons travel by some method or other from the source and to the detector. If they do should we assume that they have a real existence at empty places on their journey? Here an empty place can be defined as a place which is devoid of anything that interacts with photons. 

 Has anyone seen the position operators for photons?

PART 24.  IS RELATIVISTIC MASS REAL?

The relativistic mass equation is partly based on the assumption that a moving body has energy due to its mass as well as its kinetic energy.

   Energy due to mass = mc²

   Kinetic energy = mc²(γ – 1)

m = mass of the body, often referred to as the rest mass or invariant mass.

c = the speed of light

γ = the Gamma factor. This is a dimensionless quantity which depends on the speed of the body, it is equal to one when the body is at rest but increases with speed and approaches infinity as the speed approaches the speed of light.

The total energy, E, is the sum of the two separate energies:                                                                                         

                                           E = γmc²

We can divide by c²to express the equation in terms of mass, M, rather than energy

                                          M = γm

(We can still call this an energy equation but with the energy expressed in mass units, for example kg instead of energy units, for example J)

The total mass, M, is called the relativistic mass and the equation is called the relativistic mass equation. But is the concept of relativistic mass meaningful or helpful? Should it even be taught? These are questions that seem to have split the physics community into two camps. There is a tiny minority who accept the concept and a vast majority who reject the concept. One reason why the concept is not very popular is that speed and kinetic energy are relative quantities.

But what if rest mass was not constant?

PART 25.  ANOTHER SIMPLE SYSTEM

Imagine a system containing a quantum source which is known to emit one or more quantum objects, for example electrons or photons, at indeterminate times after being switched on. Let the system also contain a suitably placed detector of those objects. Now let’s introduce an experimenter with advanced practical skills who pops into the system to switch everything on and then pops out again for a cheese sandwich.

If at a later time the experimenter returns and notices that the detector had recorded the arrival of a quantum object she might conclude that an interesting event had occurred.  She might describe the emission process and the detection process but be at a loss to describe how the event proceeded during the interval between emission and detection. It seems obvious that the emitted quantum object reached the detector but how did it get there? If this question is thrown open to the wider community of quantum physicists there may be a range of responses a few examples of which are summarised below:

• There’s not enough information to answer the question.
• The object moved straight to the detector.
• The question doesn’t make sense.
• The event had two states only, emission and detection. There were no in between states.
• The object followed a path that can be classically defined.
• The object was emitted as a wave but detected as a particle.
• For quantum objects it’s meaningless to talk about paths.
• The object followed every possible path.
• There would have been a resultant fuzzy path.
• Quantum objects are not like tiny lumps of matter, they don’t have paths.
• The object moved in a superposition of all possible states
• Between emission and detection the only thing that evolved was the wave function. This collapsed into an eigenstate at the detector.
• It doesn’t matter, shut your cake hole and do the sums.

Anyone baffled by some of the answers should bear in mind that they may have been made by quantum physicists. Remember that these are the type of people who would go into a dark cellar at night without a light looking for a black cat that isn’t there. ANON

PART 26.  DEBATES IN PHYSICS

It can be very productive to have debates in physics but it’s best to listen carefully to others and be open-minded and flexible. If anyone wants to promote ideas that they consider as being relevant and possibly correct there are a few basic rules that would be helpful to follow. These include:

1. Know what the debate is about. For example if there is a debate related to the concept of mass all parties need to make it clear what they understand about that concept.

2. Know the relevant subject area including the limitations of any theories referred to. Sometimes it can be questionable trying to prove the correctness of a point by referring to a theory that has been developed on the assumption that the point is correct.

3. Know the experiments. Remember that observations are key and observations inform theories. One of the most relevant questions that can be asked is:

 Where’s the proof?

If it’s difficult to find experimental proof try to come up with suggestions about experiments that could be tried. Hopefully the experiments will be cheap and easy to carry out using sophisticated bits of equipment such as a bit of light inextensible string and a red bucket. These types of experiments stand a good chance of getting the funding needed.

Blimey it seems that I’ll need to do a bit of a rethink on this.

 PART 27.  IF THEORY PREDICTS IT CAN HAPPEN IT MAY HAPPEN

Despite the fact that the concept of relativistic mass is widely ignored it may be interesting to assume that the different ways that the equation can be interpreted are all correct. The equation can be written as follows:                                                                                                                                                                                                     

                                                                M/m = γ

Looking at the equation as written this way might make it clear that it can be interpreted as predicting that it is not necessarily just M that changes with speed, it is the ratio M/m that changes with speed. There are different ways this ratio change can be interpreted but there are two extreme interpretations.

1. m stays constant and M only changes.
2. M stays constant and m only changes.
3. Between the extremes M and m both change.

Interpretation number one is the normal interpretation, in fact in the original derivation of the equation it was implicit that m is constant. However, it could be that the interpretation that applies depends on the structure of the system. Within which events occur.

 M and m both change with fuel carrying vehicles. But can they both change with particles? It’s something to think about.

Part 28.  Bare Mass

In part 15 it was suggested that part (or possibly all) of the potential energy of a system of particles is stored within the mass content of the particles. This suggestion is backed up to some extent by quantum field theory and the concept of bare mass. According to the concept the measured mass of a particle (M) is the sum of two parts, the bare mass (Mb) plus extra mass due to the contribution of the energy of the field (Mf).

                                               M = Mb + Mf

A problem is that calculations can show that Mf is infinite. The problem can be overcome by a process called renormalisation which very roughly speaking involves mucking about with infinities. It sort of boils down to adding a negative infinity in such a way that it compensates for the positive infinity and then adding a finite number to get the wanted answer.

 Looks like a fiddle to me, but it seems to work.

PART 29.  THE HYDROGEN ATOM AND INFINITY

The hydrogen atom continues to feature in this work as does the concept of excitation. So let’s take another look at what it’s all about. Consider again a hydrogen atom in the ground state which absorbs an input of energy equal to the ionisation energy.

The ionisation energy can be described as the minimum energy needed to separate the proton and the electron. In other words it’s the energy needed to bring the proton and electron to states of rest at an infinite separation. At this separation the system would be in a state of unstable equilibrium being finely balanced between the bound and unbound states. It’s a bit like a quantum superposition state in that a slight disturbance can tip it one way or the other.

A major problem with concepts involving infinity is that they can easily lead us into a world of silliness as exemplified by Bob Newharts hilarious Infinite Number of Monkeys Sketch. We can avoid the silliness by defining infinity in terms of the relevant features of what can be measured. In this case an infinite separation can be defined as follows:

An “infinite separation” can be defined here as being a separation which is equal to or bigger than a certain minimum separation which is such that any consequences of increasing the separation further are immeasurable and or can be considered as negligible, no matter how big any separation increases may be.

In other words an infinite separation can be any value within a range which has a lower limit which may increase as more precise observations and data becomes available, but no upper limit.

Perhaps other infinities should be looked at in terms of what can currently be measured.

PART 30.  MOVING MAGNETS

There is one aspect of radio communication that has been known of since the pioneering days but which may be worthy of further investigation. To see what this is it’s helpful to go back to basics. We start by carrying out an experiment which is quite easy to do. In fact it’s so easy that there are some theoreticians who might be able to do it. But extensive training will be needed.

                 THE INCREDIBLE SHAKING A MAGNET EXPERIMENT

Apparatus

1. Magnet.

Method

Shake the magnet.

And clear away the apparatus at the end of the experiment.

The shaking magnet acts as a sort of transmitter and as a result there will be parts of the surroundings which act as receivers, for example certain lumps of metal and bits of circuits within which currents are induced.  Another type of basic transmitter can be made by using some wire fed by an alternating current such that the wire acts as a sort of aerial. Again, currents will be induced in receivers.  These induction effects are well known and often come under the heading of electromagnetic induction. This covers things such as generators and transformers as well as some of the basic principles of radio.

Receivers always react to the presence of transmitters no matter how basic or sophisticated the circuits are. But something that is often glossed over is that it is a two way process and transmitters react to the presence of receivers. One way by which this mutual interaction occurs can be expressed by Faraday’s law and in particular by the negative sign used in the equation. The sign is an expression of Lenz’s law which can be considered as an expression of the conservation of energy. The law states that that the induced currents flow in directions which oppose the changes producing them. In other words the changes produced at a receiver result in a sort of feedback to the transmitter which itself undergoes changes. Expressing it differently we can say that transmitters communicate to receivers and receivers communicate back to transmitters. Of course there’s nothing new about this and such two way effects are well known and exploited, but mainly within near field regions.

What is relevant is that there can be non negligible feedback effects which are not necessarily confined to near field regions only but which can extend into far fields. For example in a system containing a transmitter and a receiver there will be correlated currents in both circuits and these currents will result in there being changes to the field in which the circuits reside along with changing magnetic forces on the circuits. In other words each circuit feels the presence of the other circuit.

Results such as those described above challenge the sometimes implied assumption that the radiation characteristics of transmitter systems can be independent of the characteristic and locations of every single surrounding receiver no matter how sophisticated or simple some of these may be. This assumption is questionable because if radio transmitters react to the presence of receivers it could imply that transmitters systems and all other electromagnetic wave sources radiate in relation to the surroundings and not independently of them. But do they?

“That’s a rather tenuous implication old chap” remarked Carruthers.                                                                                                      “Shut your gob innit” replied the old geezer.    

Part 31.  ACCELERATED CHARGES

When a charge accelerates there are correlated changes in what may be described as its field and by analysing the changes it’s predicted that an accelerated charge emits electromagnetic radiation. Formulae for the radiation emitted have been derived, most notably by Larmor, and by Lienard and Weichert. But there is a problem with derivations that consider single accelerating charges only because they are not thorough enough. This is mainly because too little attention is paid to the environment within which the charge moves. Any changing fields are not due to the single charge only but are due to all of the interacting charges and other interacting parts which make up the field system within which the accelerating charge is just one part.

The concept of there being systems containing single accelerating charges is questionable, but charges can accelerate if they are a part of an interacting system of charges. The simplest system to analyse will contain at least one other thing which is charged and the other thing, whatever it is, may also accelerate, for example to conserve momentum. Any changes of fields accompany all interacting parts and the total radiation changes can be attributed to changes in the system and not changes in just single parts of the system. Also, it should be recognised that radiation detectors be they photographic emulsions, retinas, bolometers, aerial systems, GM tubes or anything else all involve charge interactions and so can be considered as being parts of the field.

“Oy, old geezer, does a charge which accelerates due to it sitting in a gravitational field radiate” enquired Carruthers?

“Don’t be daft, to radiate it must be accelerating due to being a component part of an electromagnetic field” replied the old geezer whilst writing his notes on the equivalence principle?

PART 32. QUANTUM SUPERPOSITIONS

One of the most common words that crops up when searching for information about quantum physics is Schrodinger, it refers to dear old Erwin Schrodinger and in particular to his very famous equations. Another common word that crops up is cat which refers to cats, vicious hunters and killers ………. beautiful cuddly furry cats. Used separately the words are fine but put them together and we come up with the dreaded:

                                  SCHRODINGERS CAT!

For now it can be said that the weird concept of the cat going into superposition is unfounded because:

• The concept of superposition states as often described does not conform to common sense and general knowledge.
• The theory predicts that superposition states happen but only in systems that are isolated. The requirement of isolation, even if it could be partly achieved, restricts what observations can be made.
• Physics is based on what we can observe and observations that can be made, before and after any attempted isolation experiment, give no evidence that the superposition states happen during the isolation period.

Apart from everything else nothing in the box is isolated. From the atoms perspective there’s the internal surfaces of the box, a cat and all the paraphernalia needed to construct the killing device.

We will come back to the above and also look at other silly stuff like something being here and there at the same time.

I’ve got a cat called Tiddles. Tiddles tiddled in my cornflakes.

PART 33. THE CONCEPT OF LIGHT MOVING THROUGH SPACE

Probably, most people like to think of light as being something that’s always real, for example something that can leave a source and travel through the surroundings to wherever it goes. But what is light? Is it waves or could it be particles? Or should we think of light in other ways such as in terms of electromagnetic fields or quantum fields?

A contender for a possible best answer is that it doesn’t matter what light is. When we think of light in terms of waves or particle or anything else we are using a model and for practical work we can choose models that are most suitable for the task in hand. For example, when working on geometrical optics the model that light travels as rays and spreads as wave fronts is useful. When calculating resolving power we would use the model that light travels as waves. Models and theories have their own domains of usefulness and applicability.

Things can be different when it comes to theoretical physics and when we try to get a deeper understanding of what’s going on. Theoreticians should not only be aware of the different models of light but should also have a greater awareness of the limitations of those models and of any other models they use.

One simple photon model is that after emission from a source each photon travels at the speed of light until it enters a place  where there is something to interact with, for example the eye or a particle that participates in a scattering event or an atom that absorbs the photon and then emits a copy of that photon. It’s a model that may seem to make sense, but it has a limitation:

Photons cannot have any interactions at empty places. They can interact only at places that are suitably occupied.

 Any attempt at setting up a photon interaction at an empty place requires that something suitable be at that place thereby rendering it non empty. Catch twenty two crops up again.

The limitation applies to all models of light and raises the possibility that light does not have a real existence at empty places. Whether this is true or not is open to question but can usually be ignored. But if we want to be really fussy what shouldn’t be ignored is the supposition that light has properties at empty places. We will come back to this and consider the concept of light having properties.

Is light real in empty places? We could ask a similar question about atomic particles. But it’s all philosophy and metaphysics isn’t it? I can’t even spell those long words.

34. WHAT HAPPENS WHEN WE ARE NOT LOOKING?

In some respects it doesn’t matter what happens we’re not looking because our perception of the world is based on what happens when we are looking. It is based on what we are aware of and what we can observe. Have a look and see for yourself.

Can you see it? It’s over there next to the things that have always been there.

PART 35.  QUANTUM WEIRDNESS AND OBSERVATIONS

Many accounts of quantum theory, particularly those in the popular non specialist media, describe some rather weird events. Just a few of them are summarised below:

• A particle can be in two different places at the same time.
• Photons can instantly influence each other even when they are millions of light years apart.
• A neutron and its spin can separate and move in different directions.

A problem is that physics is based on observations and a majority (if not all) of the weird events that have been predicted over the years cannot be observed in enough detail to absolutely confirm that the weirdness really does happen. For example we cannot clearly observe a particle being in two places at the same time and nor can we clearly observe a photon being in a state of superposition. If we can’t observe the weird events why should we assume they happen?

After reading Alice in Wonderland and demolishing several G and Ts, the old geezer reported seeing a neutron looking for something or other whilst its spin was hiding in a tree and taking the piss.

PART 36.        CONSIDER OBSERVATIONS MORE CAREFULLY

It’s widely assumed that the act of observing an event always affects that event but with that assumption it can be taken as implicit that events happen without being observed. And of course they do just one reason being that it can be very counterproductive to think otherwise, particularly from a practical applications point of view. Arguably, some of the best examples of observations affecting events are to do with quantum superposition states. It’s still fairly widely accepted that such states can exist without being observed and it’s also widely accepted that attempts to observe those states are likely to fail because the attempts will knock the events out of superposition before the observation can be made.

It may seem that one can’t win in such catch twenty two situations but it should be realised that the act of trying to observe an assumed event becomes an integral part of the event. The system being studied is much bigger than is often appreciated and includes the observer and the observational equipment as well as all of the other stuff. In other words we are not detached from observed events, we are parts of them. Ideally any observational methods will have minimal effects but that’s not always the case. In fact any attempt to observe an assumed quantum superposition state can become a major part of the event.

Imagine an extremely tiny pendulum type thingy which is vibrating, with a very small amplitude and a very high frequency between extreme points A and B. If we were able to observe the vibration we might be able to see that the pendulum spends most of its time at  A and B the reason being that the pendulum spends most of its time at those extremes where it moves slowest and momentarily stops. There should be nothing surprising about the observations but somebody might state that they show the pendulum can be at different places, A and B, at the same time. What a rascal that somebody is. Was it you? Whoops, it might have been me!

37. THE BORN RULE

Please use the space below to write your own notes on the Born Rule

PART 38.  ARE SOME PHOTONS MAXIMALLY SPEEDED UP ELECTRONS?

Consider again the relativistic equation as described in part 15 of this work:

                                                     M/m = ϒ

Now consider the interpretation that there might be situations where for a particle M stays constant but m varies with speed. The equation shows that if m reduces to zero, the speed, v, increases to the speed of light c.  Looking at it in a slightly different way, which is usually the preferred way we can write the following equation:

                                                   M²c² – M²v² = m²c²

Again it can be seen that if m reduces to zero v increases to c.

It’s often assumed that the relativistic equation prevents stuff from reaching the speed of light but the equations do the opposite and can be interpreted as predicting that stuff can reach the speed of light. This possibility has always been inherent in the equations but it seems it hasn’t been given the full attention it deserves. Perhaps it’s because a mechanism by which m vanishes to zero hasn’t been fully appreciated.

But are there examples in the real world where this actually happens? The answer is yes, it happens during matter-antimatter annihilation events. Consider a relatively common type of annihilation event involving an electron and a positron. At one instant we can have two particles both with mass and energy and at a certain instant later the two particles can seem to have morphed into two photons both with energy but no mass. In other words there has been an event where the rest masses of the particles reduced to zero. Although quantum electrodynamics theory may give a brilliant description of the event it’s possible that the theory can be tweaked a little and even more detail added. For example the conversion to photons may start earlier in the event than currently realised. Also, certain insights about the matter antimatter imbalance may be revealed.

 Quantum electrodynamics! What’s that? The title alone makes it sound complicated.

PART 39. IMAGINING AN EVENT WHERE AN ELECTRON ACCELERATES TO THE SPEED OF LIGHT.

Imagine an event where an electron starts from rest and moves with increasing speed as a result of its rest mass reducing with speed. At the start of the event the De Broglie wavelength of the electron will be infinite but as the speed increases from zero the De Broglie wavelength and the mass get smaller as the kinetic energy and momentum get bigger. If this trend continues a point will be reached where the mass reduces to zero this being when the speed becomes equal to the speed of light. The overall result would be that an electron annihilation event has occurred resulting in the creation of a gamma ray photon of energy approximately equal to 0.5 Mev. 

There are loads of problems with this thought experiment just one being that there will be no conservation of charge or momentum. However, some of the features used to describe the event can possibly be incorporated, advantageously, into the quantum mechanical description of the event. We will come back to it.

“Adding classical concepts to quantum mechanical descriptions serves no useful purpose at all” said Carruthers with his nose in the air.

PART 40. ALPHA DECAY

A summarised and very fudged and simplified classical description of alpha decay would have it that alpha particles can be fairly stable structures within certain nuclei and that that they can reach positions towards the edges of the nuclei where the electrical forces of repulsion can sometimes overcome the strong forces of attraction. The result is that each particle goes flying off with a relatively high energy in one direction whilst its daughter nucleus recoils with a much lower energy in the opposite direction.

Quantum mechanics gives a more detailed description of the decay process in terms of quantum tunnelling, a concept that might be mentioned later in this work. All might seem to be in order but in the early days of radioactivity research there was a problem with the explanation of alpha particle tracks. According to the quantum theory of the day alpha particles should not move in straight line paths due to the relevant wave functions being spherical. But it seems that alpha particles are naughty and they do move in straight line paths regardless of the sources, be they macroscopic such the button structures incorporating Americium 241 or microscopic such as Radium 222 atoms.

Early evidence of the paths came from observations in cloud chambers which contain gas and a saturated vapour. When an alpha particle travels through a cloud chamber it ionises atoms at different points along its path and the ions produced act as nuclei for the vapour to condense upon. The result is that the path taken by the particle is revealed as a series of liquid drops which, when the dots are joined together, resembles a straight line.

In the late 1920s Neville Mott solved the apparent paradox by using quantum mechanics to carry out a detailed analysis of how alpha particles should move. In a nutshell he found that when a more detailed analysis is carried out by taking into account other contents of the system the particles should move in paths which have very high probabilities of being straight. Clever stuff and strong evidence that quantum mechanics as well as classical mechanics can predict classical like paths.

But even without Motts explanation the straight line paths are what we might expect from the correspondence principle and from observations of other paths including those of the type described earlier in this work. It was pointed out that the separation between interacting parts is a key factor linking the quantum and classical realms with quantum effects being more dominant within tiny separations. For example, the alpha particle decay process is best described in terms of quantum mechanics but as the separation between a particle and its daughter nucleus moves into larger non microscopic values the event becomes more classical in nature.  If now the particle (or daughter nucleus) moves close enough to something which it interacts with, for example an atom that gets ionised, the event(s) becomes more quantum like in nature.

If the closeness of approach is restricted for example due to the available energy of collision  not being large enough to cause ionisation or excitation, an elastic collision can occur the observations of which can be explained in terms of classical theory. A rather nice example of this is the nearly right angled fork observed when an alpha particle collides elastically with a helium atom.

By searching online it can appear that Motts work and the experimental investigation of particle tracks have been rather neglected over the years.