ODDS AND ENDS FROM THE WORLD OF PHYSICS 

 This work is a mixture of odds and ends, from different areas of physics and is presented as a series of simple accounts most of which are further developed as the work progresses. The work goes back to basics and there is an emphasis on observations that are made or can be made. It attempts to describe certain physical phenomena in a way that is simple and intuitive.

 PART 1. SIMPLIFYING ASSUMPTIONS 

 When analysing events and developing theories it's impossible to take everything into account and so it becomes necessary to make simplifying assumptions. In most cases events are analysed as taking place in isolated systems where the surroundings are ignored due to them being considered as having negligible effects on the system being studied. Other assumptions depend on the events being analysed.

 A SIMPLE EVENT?

 Imagine an electron in a vacuum accelerating towards a lump of metal which has a very large positive charge. The system can be considered as being made of three main parts, the electron the charged lump of metal and the field. The simplifying assumptions made may normally include the following:

1. The charge of the electron is so small that it has a negligible effect on the field of the metal.
2. The mass of the metal is so large that its motion is negligible compared to the motion of the electron.

The assumptions ignore the field of the electron but consider its motion and ignore the motion of the metal but consider its field. There's something a bit doubly lopsided about it and although sometimes good approximate answers can be gained by making simplifying assumptions it can be instructive to think a bit more deeply about events and take more care when making assumptions.

It will be shown that for events involving interacting parts the ratio of the masses of the parts is more significant than is currently appreciated. 

 PART 2. ELECTROMAGNETIC INDUCTION 

 To give a simple demonstration of electromagnetic induction we could use a source of magnetism, for example a bar magnet and a suitable conductor, for example a coil of wire connected to a galvanometer. We need to put energy into the system so that the wire experiences a changing field and this can be done by moving the coil only or moving the magnet only or moving both.

It's often assumed that the induced electricity depends only on the relative motion, for example the changing currents induced by moving the magnet only can be duplicated by moving the coil only. This assumption is difficult to justify experimentally because the motional symmetry that exists in an imaginary system of coil and magnet only does not exist in a real system which would have interacting surroundings.

 In a real system electricity would be induced at other places where there are suitable conductors and not at the coil only. Such places could include metals, and certain parts of instrumentation used to make the measurements. This is just one example of a situation where it can be difficult to justify the concept of an isolated system.

Extra thought Some observations on electromagnetic induction are well known but some of the consequences of these seem to have been overlooked despite the fact that they give clues about the nature of the propagation of electromagnetic waves. We will come back to this. 

PART 3. THOUGHT EXPERIMENTS IN GENERAL 

Thought experiments can be useful if they can be extended and applied to real world experiments where it would be possible to make the relevant observations. One of the most famous thought experiments which doesn't adequately meet these criteria is the over hyped Schrodinger's cat experiment:

Erwin Schrodinger imagined an isolated system containing a cat and a radioactive atom which is linked to a killing device. If the atom decays the killing device gets switched on and kills the cat. That's a nasty situation.

 But some people believe that the atom can reach a quantum superposition state which has been described as being decayed and not decayed at the same time. It has been suggested that the result of this would be that the killing device would be switched on and off at the same time and the cat would be dead and alive at the same time. That's a weird situation.

There's another belief that superposition states can happen and be maintained but only if there are negligible interactions with the surroundings. Because of this the superposition states cannot be observed because any attempts to make the observations will knock the system out of superposition before the observations can be made. That's a catch twenty two situation.

Of course the weirdness can't happen and common sense alone should be enough to tell us that. Schrodinger knew it and was trying to prove it with his thought experiment. But are there any real world experiments which display weird quantum superposition states? We will take a brief look at a few of them.

Extra thought Carrying out some thought experiments can be described as the act of applying the laws of physics to imaginary systems that don't obey the laws of physics.

 PART 4. BASIC CONCEPTS

 Mass length and time are just three of the basic concepts used in physics and it seems to be fairly widely accepted that these concepts are well understood and clearly defined. But are they? What for example is the definition of mass? At one level we might define mass in terms of amount of matter. Or perhaps we could define it in terms of inertia. Such definitions are rather vague, despite the fact that by accepting them it might seem easy to get an intuitive feeling of what mass is.

In order to be more rigorous we might try to define mass in terms of other concepts such as force and acceleration. Perhaps we should try to define it in terms of the energy something has when it has zero momentum, or refer to it in terms of quantum mechanical operators. Doing any of these would usually require definitions of other concepts and it can become a chicken and egg situation with definitions going round in circles. To add to the difficulties there are different labels attached to the concept of mass, such as komar mass, inertial mass, gravitational mass and invariant mass. Plus there is relativistic mass, a concept which is taken to be obsolete by what seems to be a majority of the physics theorist community.

One thing we can do with a high degree of clarity is to define a unit of mass. The Kilogramme is a widely used unit and for many years had been defined with reference to a certain lump of metal which is stored in Paris. Also, it can seem that we have the expertise to accurately measure some masses. For example the electron mass can currently be measured to twelve decimal places.

But the question remains .... Is there a really good definition of mass, not a definition of a unit of mass but a definition of mass itself? Perhaps some ideas and a good working definition can be found in philosophy. Without a good definition things can get a little bit tricky. An example of this is related to the debates about the pros and cons of relativistic mass. Not everyone rejects the concept of relativistic mass and there are some people still in favour of it. But how can there be a constructive and meaningful debate about something without a good definition and a precise knowledge of what that something actually is?

 Come to think of it it's probably a good idea to look again at definitions of other concepts we use.

PART 5. WHAT IS A HYDROGEN ATOM ? 

 Can a system of a very widely separated electron and proton, both of which are momentarily at rest, be described as a hydrogen atom? 

 One way by which a system such as that described above is formed is when the hydrogen atom in its ground state receives an input of energy equal to the ionisation energy. The energy input, along with the internal kinetic energy of the atom, is converted to an increase in potential energy with the particles separating to positions of rest. It's a system which in a sort of state of unstable equilibrium at a border between a bound state and an unbound state and is often referred to as an ionised hydrogen atom.

A tendency of the ionised atom is to return to the ground state and when this happens the ionisation energy is radiated back to the surroundings. This tendency reduces if the particles are not at rest and become unbound and free of each other. It's not usual to refer to the completely unbound system as an atom. It's all a bit more involved than has been described here and we will come back to it because it has implications to other areas of physics, including to the concept of particle masses.

Before leaving this section imagine an electron finely balanced, in a state of unstable equilibrium, mid way between two very widely separated protons. Can the electron be considered as being part of an ionised hydrogen atom with both protons at the same time? Perhaps it can be thought of as a sort of quantum superposition. And can the just ionised atom itself be described as being in a superposition state? Just saying.

 PART 6. THE ANNOYING (particularly to many theoretical physicists) WAVE PARTICLE DUALITY

 Many physicists, particularly theorists, consider wave particle duality to be an outmoded concept and don't bother with it. But there are other physicists, particularly some experimentalists and some physicists who participate in science popularisation, who seem to pursue the subject. It seems that the concept of duality as understood by some theorists is different to that as understood by some experimentalists and some physics popularisers.

Duality is regularly mentioned in reports of quantum interference experiments, those involving De Broglie matter waves as well as those involving photons. And many of the experiments have gained a bit of a reputation for being difficult to understand and weird when compared to classical interference experiments. But should quantum interference experiments be considered as less weird if the observations made can be predicted from a knowledge of classical interference experiments?

What we know from classical interference in a nutshell.

Provided all the necessary conditions are met interference can be produced with any number of slits or sources. Diffraction is always evident for example as an intensity modulating envelope of interference fringes.

 Consider the classic double slit experiment being set up in a symmetrical way so that light has access to the detector via both slits equally. By doing this we would observe a pattern of highly visible interference fringes. If access to the detector via one of the slits is increasingly disturbed, for example by reducing the width of the slit to zero, regions of constructive interference become less intense and regions of destructive interference become more intense as the double slit pattern morphs into the single slit pattern of the undisturbed slit. In other words the visibility of the double slit pattern reduces as the visibility of the single slit pattern increases.

It can be said that the classical two slit experiment has an inherent "which path marker" because the pattern produced gives some evidence about the path taken by the light. For example a high visibility pattern of one of the slits gives an indication that light had greater undisturbed access to the detector via that slit.

 Quantum Interference

Quantum double slit experiments use very low intensity, usually what is described as one photon at a time, light sources. As can be predicted from a knowledge of classical experiments, a pattern of interference fringes is detected but one which builds up relatively slowly and bit by bit across the image planes. As an explanation of these results some people have suggested that photons somehow interfere with themselves. It can seem that people who make that assumption are accepting some aspects of the classical explanation of interference.

It's widely assumed that high visibility interference fringes cannot be observed if the apparatus has a certain type of "which path marker" which can determine with certainty the slit which each photon passes through. What is often promoted as being weird is that the marker doesn't need to be used and the fact that it is part of the apparatus is enough to destroy interference fringes. One reads weird comments such as: How does a photon know that we can know what slit it passes through?

 It's all a bit daft really because the results of which path marker experiments can be predicted using a knowledge of classical physics experiments. We shall look at two well known types both of which use entangled photons with correlated orthogonal polarisations.

Something to ponder: At what level of reducing illumination does a classical interference experiment become a quantum interference experiment. Perhaps it would be better to consider quantum experiments as low intensity classical experiments...and vice versa. 

 PART 7. POTENTIAL ENERGY ( a reminder of some difficulties of the concept)

 Consider again a system containing an electron separated from a positively charged metal plate. The system has potential energy and as with all other systems that have potential energy we cannot calculate an absolute value of what that potential energy may possibly be at any particular separation. Although we can calculate by how much the potential energy changes when the separation changes. 

To help with calculations we often make two arbitrary choices, one regarding separation and the second regarding a value of potential energy at the chosen separation. The most widely accepted and probably the most logical and useful choices are infinity for separation and zero for potential energy. Using the above choices we would say that when the electron and metal plate are separated by infinity the potential energy of the system is zero and as the separation reduces the potential energy becomes more and more negative. That may sound strange to anybody coming across it for the first time particularly when it's realised that for attracting objects the potential energy is a maximum at an infinite separation and at lesser separations the potential energy has positive values. Dealing with differences in energy rather than absolute values takes a bit of getting used to.

 But could it be that potential energy actually does have absolute values and moreover can it be described as having locations? In any ensuing debate a good start could be made by referring to energy sources such as a litre of petrol or a chocolate bar. We can describe, for example, that the energy of the chocolate bar is located within the chocolate itself. We can pin the energy down further by referring to the mass and kinetic energy of the particles in the chocolate and the potential energy of the fields in the chocolate.

Can we pin it down further still and say, with some confidence, that whereas each particle has kinetic energy due to its movement it also has an absolute value of potential energy due to its location? In other words is the potential energy in a system somehow shared between the interacting parts? In a two particle system one particle might have some of the potential energy and the second particle might have the rest of the potential energy. It's a bit more involved than just that and it's not a new idea. We shall return to it.

But don't knock it until you've read through it.

PART 8. EVERYTHING IS MADE OF FIELDS

Many physicists who have knowledge of quantum field theory will tell us that the fundamental building blocks of everything are not particles but fields. There are different fields associated with different particles and so there is an electron field, an up quark field a Higgs field and so on. One hand wavy way to describe particles is to call them discrete excitations of their underlying fields, for example an electron is a discrete excitation of the electron field.

 If it's starting to seem a bit odd it might seem even odder when told that each field is assumed to exist throughout the whole of space. What! Isn't physics sort of nice? Odd perhaps, weird perhaps but often hard for sure. This topic is hard so it's time to take a little break from it and come back to basics. We will look at the first field that many people are introduced to. We will look at the magnetic field.

 And it will be very interesting. But perhaps not. 

PART 9. ALL ELECTRONS ARE IDENTICAL? 

People who claim that all electrons are identical have what might seem to be convincing evidence to back up that belief. And much of that evidence, such as the measured value of the electron mass is freely available for everyone to see. Just search the NIST website and look the data up. Doing so will reveal that the current uncertainties of the measurements are so extremely small that any variations in properties allowed by the uncertainties are also extremely small. Negligibly small perhaps.

However, it should be realised that the data is very limited and applies only for those systems within which the measurements are made, for example within Penning traps. It could be that properties such as electron mass are environment dependant in that the mass of each electron depends on the structure of the environment in which the electron exists and the instantaneous location of the electron within that environment. If there are any variations in electron properties they could start to become appreciable within extremely small particle separations or regions of extremely high fields. In other words the measured properties can be different at places where there are very few reliable measurements available as of yet. So all electrons may be identical but only when they are in identical places. Keep watching this space, you might observe an electron or two.

A little bird once told me that at any one time there are approximately 10 to power 8 electrons in the universe. I wonder how many electrons have been inside Penning traps.

 PART 10. THE MAGNETIC FIELD 

Many of us are introduced to the concept of fields at a young age when we use detectors such as iron filings to plot magnetic field lines. The results of such experiments and more sophisticated experiments can lead to the assumption that the magnet sets up a field and the field exists in all of the surroundings. Extending this it can be assumed a that all fields exist everywhere. The assumptions needs clarifying:

 Consider a place in the surroundings of a magnet which is empty in that there are no iron filings or anything else that interacts with the magnet. Because there is nothing that can be detected at the empty place it might seem reasonable to assume that the magnetic field does not exist at that place and does not exist at all other places that are empty. But is the assumption a good one, is it true that magnetic fields and all other fields for that matter, do not exist at empty places? To reiterate, in the context of this work an empty place, is not necessarily literally empty, it is a place devoid of anything that can be considered as part of the field in that it interacts with other parts of the field.

Some advocates of quantum field theory might claim that there are no empty places and that the whole of space is occupied with fields. There's nothing deeply questionable about the claims if fields are mathematical constructs only, but some people might further claim that fields are real, and have substance and there truly are no places that are empty, temporarily or otherwise. So where is the experimental proof to give credence to the claims? Or indeed to give credence to any counter claims.

To kick off any debate that might ensue a few comments based on observations are given:

1. Fields have observable effects only at locations where there are interacting parts.

2. There is no observable field at all unless there are at least two interacting parts.

3. Fields are mutual things and the resultant field is such that it represents every interacting part.

4. If an interacting part changes its location the field changes at all locations where there are interacting parts.

 In summary the effects of fields are felt by the interacting parts only whether these parts be microscopic, such as electrons or macroscopic such as charged metal plates. These parts of the fields are real and have substance. 

 PART 11. WHICH PATH MARKERS IN QUANTUM INTERFERENCE PART 1.
 (Any readers who may be interested in this page are advised to familiarise themselves with the 2002 experiment of Walborn et al and with quarter wave plates.)

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 interference fringes but resembled a single slit diffraction pattern. It's a pattern that can be explained easily from the laws of Fresnel and Arago, but this seems to have been overlooked in favour of the arguably more weird explanation which refers to which path information. This assumes that because the experimental arrangement can be used to gain which path information, interference cannot be observed. But a flaw with this explanation is that interference is 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 90 degrees phase difference between the o and e components from each of the two plates there is 180 degrees phase difference between the two patterns, the result being that the peaks of each pattern overlap the troughs of the other pattern and the resultant pattern resembled a single slit diffraction pattern.

The two interference patterns could be observed separately by means of a linear polariser in the path the idler photon. The idler photons with the same axis of polarisation as the polariser axis reach the idler detector. The other photons don't. When the axis is 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 enables 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 a what I call it anyway.

 Readers 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 12. 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 cure which boils down to the following simple piece of advice:

STOP AND THINK. And a nice cup of tea helps.

 PART 13. IS RELATIVISTIC MASS REAL? 

As far as relativistic mass is concerned the physics theorist community seems to be split into two camps, those who accept the concept, who seem to be in a tiny minority and those who reject the concept. Both camps calculate the same values for the total energy and the kinetic energy of a moving particle but differ in how they interpret the change of kinetic energy.

 The total energy of a moving body expressed in mass units, for example kg, is given by the relativistic equation:

                                         M = Gm 

 In the equation m is the measured mass of the particle and G is the dimensionless gamma factor which increases from one for a body at rest and approaches infinity as the speed approaches the speed of light. M can be expressed as the sum of two parts Gm - m and m

1. Gm - m = kinetic energy of particle.
2. m = energy due to the mass of the particle. 

The difference between the two camps is that the acceptors of relativistic mass believe that the increasing kinetic energy of an accelerating particle is displayed as an increasing mass of the particle. They believe that m is constant but only when the particle is at rest. For that reason they usually refer to m as the rest mass.

The rejectors believe that m is independent of speed and always constant. For that reason they usually refer to m as the invariant mass or just simply the mass.

 And so the two camps go their own ways. 

PART 14. DEBATES IN PHYSICS

It can be very productive to have debates in physics but one needs to listen carefully to others and be open minded and flexible. If anyone wants to promote ideas that they consider to be 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 on 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. 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. Yes it happens.

3. Know the experiments. Remember that observations are key and It's observations that inform theories and not the other way round. 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. Such experiments stand a good chance of getting the funding needed. 

 PART 15. IF THEORY PREDICTS IT CAN HAPPEN IT MAY HAPPEN

 The relativistic equation can be written in the following way that may be unfamiliar to some people: 

                                                             M/m = G

Looking at the equation as written this way might make it clear that it can predict 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 can change can be interpreted but there are two extreme interpretations.

1. m stays constant and M only changes. This is the normal interpretation. It happens but only approximately so.

2. M stays constant and m only changes. This can and does happen but is relatively rare.

3. Between the extremes both M and m change. This is what happens in the majority of events the change of m being so extremely small that for most problems it can be considered as negligible.

 It can be shown that In systems where M/m tends to infinity the first interpretation above is approached and in systems where M/m approaches one the second extreme interpretation is approached.

 M and m both change with fuel carrying vehicles. But can they really both change with particles Keep watching this space.

 PART 16. WHO KNOWS WHAT LIGHT IS? 

There are certain conceptual problems associated with our understanding of light and included amongst these is the apparent weirdness some people associate with the concept of entanglement. In order to try to resolve some of the difficulties we should go back to basics and try to find if there are some aspects of theories that have been overlooked. As a start consider a system containing two main parts which we can define as:

1. A light source.

 2. A light detector

Using these two parts we can make observations and conclude, with reasonable confidence, that what is observed at the detector is correlated with what happens at the source. Taking it further we may imagine that light somehow travels from the source and to the detector.

To imagine is good but should we let our imaginations allow us to assume with 100% confidence that if light really does travel it has a real existence in any empty places on its journey? In this instance an empty place is defined as a place which is devoid of anything that interacts with light. We will keep an eye on this and come back to it.

 Does anyone know where the position operators for photons are kept? They're kept with the photons you say. So where are photons kept?

 PART 17. SHAKING A MAGNET

 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 so easy to do that even I can do it:

 THE INCREDIBLE SHAKING A MAGNET EXPERIMENT 

Apparatus

1. Magnet.

Method 

1. Shake the magnet.

Please 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 wire fed by an alternating current such that the wire acts as an 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 can be 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, in turn, is 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 the 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 effects are well known and exploited, but mainly within near field regions. What is relevant is that non negligible feedback effects are not necessarily confined to near field regions only but extend into far fields. 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 magnetic 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 and both will tend to react accordingly.

 Results such as those described above challenge the often implied assumption that the radiation characteristics of transmitter systems can be independent of the characteristic and locations of all surrounding receivers. This assumption is questionable because if radio transmitters react to the presence of receivers it could imply that transmitters 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 18. ACCELERATED CHARGES

When a charge moves there are correlated changes in the fields associated with the charge and by analysing the changes it's predicted that accelerated charges emit electromagnetic radiation. Formulae for the radiation emitted have been derived, most notably by Larmor, Lienard and Weichert. But there is a problem because derivations that consider single accelerating charges only, are not necessarily thorough enough. This is mainly because the environment within which the charge exists changes as the charge changes its location, for example in many real systems where radiation is emitted, the charge moves through considerable changes of electric field strength. Of course this is known but these changes can be difficult to factor effectively into the theory of a single accelerating charge.

The concept of a single accelerating charge is questionable, but a charge can accelerate if it's part of an interacting system of charges. The simplest system will contain at least one other thing which is charged and the other thing, whatever it is, can also accelerate, for example to conserve momentum. Any changes of fields accompany all interacting parts and the total radiation emitted can be attributed to changes in the system and not changes in just one part of the system. We will come back to this topic and take a brief look at some well known real examples where radiation is emitted from simple systems of interacting charges.

"Oy Carruthers, does a charge sitting in a gravitational field radiate" enquired The old geezer? "Don't be daft, how can it radiate if it's not accelerating due to being part of an electric field" replied Carruthers?

 PART 19. 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 equation. 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 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 achieved, stops adequate observations of superposition states from being made.

• Physics is based on what we can observe and observations that can be made, before and after any attempted isolation, give no evidence that the superposition states happen during the isolation period. We will come back to this and 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 20. THE CONCEPT OF LIGHT MOVING THROUGH SPACE

 Most people like to think of light as being something that's 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?

One 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 tasks 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 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 an awareness of the limitations of those models and of any other models they use. A simple and basic photon model, in summary, 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 scatters the photon or an atom that absorbs the photon and then emits a copy of that photon. It's a model that seems to make sense but it has a major limitation:

Photons cannot have any interactions at empty spaces

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 from a physics perspective can usually be ignored. What shouldn't be ignored is that light doesn't have an observable existence at empty places and this puts a question mark over the assumption 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? That's philosophy and metaphysics isn't it? I can't even spell those long words.

PART 21. 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 adequately observed. For example we cannot clearly observe a particle being in two places at the same time. Nor can we cannot observe a photon being in a state of superposition. If we can't observe the weird events why should we assume they can happen?

We will come back to this and amongst other things look at more macroscopic events.

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 22. ACCELERATING CHARGE EVENTS

Here we will consider events in systems containing two charges, an electron and a second charge which is positive. The nature of the events depends to a large extent on the ratio of the masses of the charges. The ratio can be written as:
                                        
                                                                    R = Ms/Me

Ms = mass of second charge, Me = Mass of electron.

 By referring to R we can define the whole range of systems:

1. At one extreme of the range there is a perfectly asymmetrical system where R equals infinity. This system cannot be achieved exactly but can be approached by using a macroscopic structure as the second charge.

2. At the opposite extreme there is a perfectly symmetrical system where R equals one. This system can be achieved exactly if the second charge is a positron.

3. Systems between these extremes can be defined as intermediate systems. A good example of an intermediate system is one where the second charge is a proton.

We will consider an event in each of the three systems where the charges approach each other from rest in a vacuum. The events will be analysed from a perspective such that the momentum of the system remains equal to zero during the approach.

 But first it's time for some community singing.

 PART 23. System 1. THE NEAR PERFECT ASYMMETRICAL SYSTEM

Here we consider the approach and impact of an electron and a macroscopic positively charged object. During the approach it's assumed that there is a conversion of potential energy to kinetic energy the result being that the charges move together with increasing accelerations. Impact of the charges results in the emission of photons, for example bremmstrahlung or radiation that is characteristic of the target atoms.

The radiation is usually attributed to interactions between the electron and the target atoms, an assumption being that the energy lost during certain interactions is converted to radiant energy. That's the simplified theory in a nutshell but even in its simplified form it conforms well to experimental observations, particularly from certain X-ray tubes. A very relevant observation is that for an accelerating voltage V, the frequency of each maximum energy photon emitted is given by: eV = hf This result is usually attributed to those electrons which lose all of their gained kinetic energy as a result of a single interaction.

 But certain questions arise and briefly, these include:

1. since the second charge, or parts of it, also undergoes kinetic energy losses do these losses also result in radiation?

2. Do the accelerating particles radiate during their approach and before impact?

 Hooray, it's time to blow ones nose and have a scratch. The passing of wind will be delayed until bath time. 

 PART 24. System 2. THE HYDROGEN ATOM AS AN INTERMEDIATE SYSTEM

Here we consider an electron and a proton moving to lower energy levels of the hydrogen atom from an initial ionised state. During each energy level transition potential energy is lost and this results in the particles gaining kinetic energy and energy being converted to radiant energy which is lost to the surrounding as a photon. The event is probably best described by quantum theory which amongst other things describes changes of particle separations in terms of probability distributions, for example in the ground state the most probable separation is equal to the Bohr radius.

There are features common to all transitions but we will concentrate on the most energetic transition where the particles skip intermediate levels and move straight to the ground state. One result of this is that all of the ionisation energy is radiated as a single photon. Certain questions come to mind such as:

When during the event is the photon radiated?

 To answer the question it's helpful to consider approach events in reverse namely ionisation and excitation events. One known event is that the ground state atom can get ionised as a result of receiving an input of energy equal to the ionisation energy. This suggests that the particles separate because they gain more kinetic energy and this is converted to potential energy as the separation proceeds. This gives further credence to the assumption that during the approach back to the ground state the reverse energy changes occur and there is a conversion of potential energy to kinetic energy, half of which is retained at the ground state and the other half of which is converted to the radiant energy of the escaping photon.

If during each transition both particles accelerate it might be expected that both particles would radiate a photon. However present evidence seems to show that only one photon is emitted for all de excitation transitions and that the energy of the photon emitted in each case is equal to the total energy lost. More convincing evidence of this comes from observations of positronium, for example each Lyman-alpha transition results in a single photon of energy equal to the energy difference between the relevant orbitals.

 The observations therefore seem to show that the observed radiation is due to energy losses in the system of two charges. It seems that the electron, on its own, does not radiate to the surroundings. And nor does the proton. But do they radiate separately and if not why not? It could be that each particle does radiate but the radiation remains within the system. Perhaps the particles radiate to each other.

We will come back to and consider it in more detail before looking at system 3 -the symmetrical system

PART 25. ARE SOME PHOTONS MAXIMALLY SPEEDED UP ELECTRONS?

Consider again the relativistic equation as described in part 15 of this work: M/m = G. Now consider the interpretation that there might be situations where 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 we can write the equation as follows:

 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 here it is shown that the equation does the opposite and predicts that stuff can reach the speed of light. Of course 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 may reduce hasn't been fully appreciated. But are there examples in the real world where this actually happens? The answer is a sort of 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 particle both with mass and kinetic energy and at a certain instant later the two particles can seem to have morphed into two photons each with energy but no mass. Although quantum electrodynamics theory gives a good description of the event it's possible that the theory can be tweaked a little and some more detail added. For example the conversion to photons may start at the instant the particles begin their approach. Also, certain insights about the matter antimatter imbalance may be revealed.

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

PART 26. The 1999 QUANTUM ERASER EXPERIMENT OF KIM ET AL

Firstly it's helpful to reiterate what is known from classical double slit interference experiments:

 • Light having access to the detecting plane from one slit only builds up the diffraction pattern due to that slit. With two slits there are two diffraction patterns.

 • Light having access to the detecting plane symmetrically via both slits builds up a high visibility interference pattern.

• Deviations from symmetry result in a reduced visibility of interference and an increased visibility of diffraction.

From observations such as those above we can predict what sort of results should be obtained in the 1999 experiment: In the experiment laser light was split into two diffracting beams by a double slit which was in contact with a slice of nonlinear crystal. Entangled photons were the light sources for the experiment and these were generated when atoms within the two illuminated regions of the crystal got excited by the incident laser light.

 The entangled photons emerging from the sources were divided into two sets by sending one of each pair in one direction and the other in a different direction. One set was called the signal photons and the second set called the idler photons. The signal photons, passed through a convex lens and continued building up a pattern in a similar way as is done in one photon at a time experiments. The developing pattern was sampled with a detector which was scanned along the image plane of the lens.
Predictions

1. The overall developing pattern should be a mixture of separate developing patterns as described in the bullet points.

 2. Because the width of each illuminated region was comparable to the width of its illuminating slit we would expect that each single source pattern would have similarities to the diffraction pattern as would be obtained from the slit on its own.

3. Because the widths and separation of the illuminated regions were comparable to the widths and separation of the slits we would expect that any interference pattern due to photons emerging from both illuminated regions would have similarities to the interference pattern as would be produced by the two slits only.

 4. The experimental arrangement lacked in symmetry when compared to a carefully set up double slit experiment two reasons being that:

a. The locations where the photons were generated were randomised within the illuminated regions. 

b. The directions of most emitted photons were different to the directions of the photons that excited the parent atoms. Because of the lack of symmetry the developing patterns should be of poor visibility

5. The mixture of interference and diffraction patterns should continue to develop regardless of what becomes of the idler photons.

But the idler photons weren't being lazy. They were used as part of a pattern selector arrangement that could be used to observe different developing sub patterns in the mixture.

How the patterns were viewed and the results reported

 Each idler photon was directed to one of four different detectors. Coincidence circuits connected the signal detector to each of the four idler detectors and with this arrangement the experimenters detected the signal patterns correlated with each set of idler photons separately.

One of the idler detectors detected photons which came from one of the sources only. As should be expected the pattern revealed by the corresponding signal photons resembled a single slit diffraction pattern.

 A second idler detector detected photons from the second source only and a similar pattern should have been revealed with, perhaps, a slight lateral displacement from the other pattern. There was insufficient data to confirm this because only one of the two patterns was shown in the report.

A third detector detected photons which came from both sources which were brought in line and superimposed by an interferometer arrangement. As should be expected an interference pattern was reported. The fringes were of very poor visibility revealing the high lack of symmetry in the experiment.

A fourth detector also detected light from both sources and a similar interference pattern was observed but this was out of phase with the first pattern. The difference was due to the photons from one of the slits undergoing a phase change of pi due to being reflected from the surface of a beam splitter.

 PART 27. LIGHT STARTS FROM SOMEWHERE AND GOES TO SOMEWHERE

It's reasonable to say that all photons, whether they be in the visible region of the electromagnetic spectrum, or any other region, have a source, in other words they start from somewhere. It's also reasonable to say that all photons go to somewhere where there is some sort of interaction. At some destinations a photon might add its energy content to whatever happens to be at the destination.

 It might be argued that some photons don't necessarily go to somewhere, for example the sun seems to radiate in all directions regardless of what surrounds it. And some of the radiated photons may continue moving for ever through empty space. That might be described as energy escaping from the universe because the photons would forever evade detection.


How sad that would be. Or is it sad? And does it really happen?


PART 28. THE HYDROGEN ATOM REVISITED

It was earlier suggested that a widely separated proton and electron which are momentarily at rest could be described as an ionised hydrogen atom. The suggestion needs clarifying and in particular there is a need to clarify what is meant by "widely separated".

An answer based on Coulomb's law could be that the separation needs to be infinite. But dealing with infinities can often lead to silliness. Here we can avoid the silliness by defining what is meant by "infinity" as it applies to this work. In general the meaning of infinity depends on the context in which it's used and upon the relevant data and observations which are available. For this work an infinite separation can be defined as follows:

 An infinite separation is any separation which is equal to or bigger than a certain minimum separation which is such that any increases of potential energy due to further increases of separation are immeasurable and or can be considered as negligible, no matter how big the 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 become available, but no upper limit. The lower limit is microscopically small.

 And this leads logically to part 29. Well I think so anyway.

PART 29. IS A GROUND STATE HYDROGEN ATOM LIGHTER THAN A SYSTEM OF A SEPARATED PROTON AND ELECTRON? 

A quick search shows that the above question and variations of it has proved to be fairly popular and has been discussed in several places on the internet. It's a question worth thinking about here: A common answer refers to the event where a proton and an electron come together to form the ground state hydrogen atom, one result being that the ionisation energy of the atom is radiated to the surroundings. The energy changes are expressed by the following equation:

                            MP + ME = Mg + ∆M .................................................... (1) 

MP = Energy due to mass of proton, ME = Energy due to mass of electron, Mg = total energy content of ground state atom, ∆M = ionisation energy.

Using data from reliable sources such as NIST we can show that, within the limits set by experimental uncertainties, the equation seems to be correct. This result would be expected if Mg is calculated by plugging measured values of MP, ME and ∆M, all of which are measured to fairly high precision, into the equation. However we shall assume that the value of Mg so obtained is the actual value and is, or in principle may prove to be, in close enough agreement to values obtained from other methods of measuring Mg. In other words we will assume that the equation is correct.

There's something that seems to be missing from the equation and to see what this is we need to consider the event in more detail and in particular deduce what type of system structure, as quantified by the left side of the equation, could evolve to reach the outcome of the event, as quantified by the right side of the equation. The obvious structure is the one produced when the above event happens in reverse, in other words it's the structure produced when the ground state atom receives an input of energy equal to the ionisation energy. I shall refer to this structure as the ionised hydrogen atom.

We can now rephrase the question as follows:

Is a ground state hydrogen atom lighter than an ionised hydrogen atom?

 Of course the answer is yes but we need to consider the energy content of the ionised atom in more detail. The atom has a structure, albeit possibly only temporary, where the particles are stationary and separated by infinity. With this structure the potential energy has the maximum possible value. Yet the left side of the equation doesn't seem to include this energy. Or does it?

Before proceeding it should be pointed out that the equation, as it stands, is what we may write when using the convention that the potential energy for an infinite separation is given the value of zero. A limitation of all such conventions is that they are not able to account for actual values of potential energy, only differences of potential energy. However, if equation one is correct it would account for actual values as well as differences.

 From the analysis above we can conclude that if the equation is correct the total energy of the ionised atom, Mi, is given by:

                                                    Mi = MP + ME 

Since the total energy includes potential energy we can further conclude the potential energy is contained within MP + ME, in other words the potential energy is contained within the mass content of the particles. It's all more involved than has been described here particularly when we take into account potential to kinetic energy changes and the photons that carry the mass exchanges between the particles. We will come back to it.

Well would you believe it I said to me with a quizzical look on my fizzog!

 IS QUANTUM WEIRDNESS REALLY WEIRD?

Should we accept reported quantum weirdness as really being weird and something we need to get used to, or should we try to make some sense of it? Consider the superposition state where it has been stated that a particle can be moving to the right whilst it's moving to the left. To get clarification about this we could ask suitable questions such as those below:

• Does moving to the right mean the particle is moving to the right only and in no other direction?

• Does moving to the left mean the particle is moving to the left only and in no other direction?

 If the questions are answered with a yes it confirms that the statement is a description of an impossible situation. If the questions are answered with a no then further clarification is needed to explain what exactly is meant by moving to the right and moving to the left. Whatever answers are given, questions of the type above and if necessary more probing questions, reveal that descriptions of quantum superposition states as given in certain publications. are descriptions of concurrent different states which are mutually exclusive and therefore impossible.

Perhaps the descriptions lack the necessary detail for them to make sense. This puts a question mark over the existence of certain quantum superposition states. Perhaps they have not been reported very accurately in certain versions of the scientific media. Perhaps they are not real. Perhaps they are real but not properly defined and understood. Who knows? But crucially, it should be remembered that observations during any assumed superposition periods are necessarily limited and give very little empirical evidence to justify the assumption that superposition states really do occur...or not.

 One option is to accept the weirdness and put up with it on the assumption that nature is not required to make sense. But perhaps nature is not required to not make sense. 

                                                        Part 31. Bare mass

In quantum field theory there is something called bare mass and depending on the particle and what version of the theory is used bare mass can have a value which might be plus or minus infinity. Oh dear.

In the electroweak interaction theory involving the Higgs boson every particle has a bare mass of zero and the measured mass of a particle (M) is related to the bare mass (Mo) as given by the equation below:
                                                    M = Mo + dm

dm is the mass increase of the particle owing to its interaction with the medium or field.

 The equation, if correct, implies that the mass of a particle can vary between zero and M, its actual value depending on the geometry and structure of its surroundings. This variability is one of the things being promoted in this work but by using physics which is more classical than quantum. Let's try and see in more detail how the concept of a variable mass relates to an event involving a hydrogen atom.

 See you later. I'm off to the Penning traps to bring back a spare proton and electron.

                                                 Part 32. Properties of Light 

Some observations may be interpreted as light having certain properties which are independent of the system within which the observations are made. Possible examples common to all models of light are that light can travel through empty space and the speed of light is constant.

 Other observations can be better interpreted as displaying properties of the system within which observations are made. For example, experiments using a light and a mirror do not reveal properties of light on its own or the mirror on its own but reveal properties of the system within which light and the mirror are parts. Observations of other interactions involving light, including those involving refraction, interference and polarisation can also be best described as displaying properties of the system.

The fact that light doesn't necessarily have properties independent of the system should be obvious but often isn't given the attention it deserves. An assumption sometimes made is that certain properties are not revealed until the moment of detection. To assume that those properties exist before that moment, for example to assume that light has properties whilst in transit, is an assumption which cannot yet be justified by observations. In our models of light, however, it's envisaged that light does have properties.

 Models can be very useful but they are not necessarily good descriptions of what really happens. And they have other limitations. Consider now the seemingly perennial discussion topic known as wave particle duality. When reading reports on duality we are likely to read statements similar to the one below:

There are systems within which light displays the properties of waves and systems within which light displays the properties of particles. 

 Such statements can lead to conceptual difficulties because of the implication that it is light that has those properties whereas what is observed is due to properties of the system of which light is a part.
The statement could be better expressed as follows:

 There are systems within which light can be modelled as having the properties of waves and systems within which light can be modelled as having the properties of particles. 

This statement expresses a duality, not in the properties of light but in models of light. In summary the properties referred to in duality are best described as properties of the system and there is no duality of any independent properties of light. It should be of no surprise, that different types of observations can be made in different types of systems. Let's see how this applies to entanglement and Mr Bell.

 Part 33. Dynamics of Hydrogen Atom Excitation Events 

We will consider in a little bit more detail the dynamics of the event where a ground state hydrogen atom receives an input of energy equal to the ionisation energy, this resulting in the proton and electron both gaining kinetic energy and separating to a state which can be described as an ionised hydrogen atom.

All detailed descriptions of the event, whether they be using quantum physics or anything else, should agree on the following:

 1. The separation between the particles does not happen instantaneously.

2. The separating particles lose speed and kinetic energy.

3. Momentum is conserved.

4. Most of the initial kinetic energy is gained by the electron.

5. The kinetic energy losses are converted to potential energy.

Because the particles decelerate we might expect them to convert their kinetic energy to radiant energy. However, there is no evidence of radiation in the surroundings. So where does it go to? An obvious answer is that the radiation remains within the system. Bearing in mind what has been written previously a likely mechanism is that each particle radiates its kinetic energy losses to the opposite particle where the energy is absorbed. The absorbed energy results in the increasing potential energy of the system.

For this and other asymmetrical systems the energy exchanges are not equal and during the separation part of the event the electron is a net radiator of energy and the proton a net absorber. If the particles subsequently return to the ground state the reverse happens with each particle gaining its increasing kinetic energy as a result of receiving the radiated potential energy losses of the opposite particle. During this part of the event the proton will be a net radiator and the electron a net absorber.

A back of an envelope calculation shows that in all two particle systems both particles display the same fractional change of potential energy. Energy is exchanged with the surroundings but only during excitation or de excitation parts of the event.

Summarising the above we can say that the energy of a system, both potential and kinetic, is contained within the energy content of the particles that make up that system and the energy content of any radiation which is exchanged between the particles.

 So now it's time to revisit an earlier part of this work. Ain't it?


Part 34. Is Relativistic Mass Real? Part 13 Revisited 

The total energy of a moving body expressed in mass units, for example kg, is given by the relativistic equation:

                                               M = Gm 

In the equation m is the measured mass of the particle and γ is the dimensionless gamma factor.

 M can be expressed as the sum of two parts m and γm - m

1. γm - m = kinetic energy of the particle.

2. m = energy due to the mass of the particle.

 Above was a recap of part 13. Good wasn't it? No! All right then let's move on.

In the light of earlier work we can now be more specific and describe m not necessarily as the measured mass of the particle but as the instantaneous mass it has due to its location in its particular environment. We can also describe m as being the potential energy of the particle. If this is a good description we can say that the potential energy of the ionised hydrogen is MP + ME and when the particles move to the ground state of the hydrogen atom the potential energy and therefore the total mass of the particles reduces by 2∆M.

Questions that may arise include the following.

 1. What should we take the mass of a particle to be?

 For many purposes we can take the mass of a particle to be the mass it has when separated by infinity from other particles it interacts with. To a good approximation this is the currently measured mass.

2. Is the maximum change of potential energy for the hydrogen atom equal to 2∆M? 

It's probably best to describe 2∆M as the maximum (indirectly) observable change of potential energy because during transitions between the ionised state and the ground state there is a measurable energy exchange of ∆M, between the atom and the surroundings. But the real maximum change of potential energy can be very much bigger.

 3. How?

Quantum theory shows that for each energy level there is a range of possible particle separations This allows particle separations to reach values very much smaller than the Bohr radius. Also, theory along with observations seems to show that the total energy, potential plus kinetic, within each energy level is constant. From this one can imagine that within each energy level region the particles can move around exchanging potential and kinetic energy.

Doing a sort of zitterbewegung dance perhaps


                                                 Part 35. Entanglement

 Tests carried out to investigate Bell's theory disprove hidden variable theories of the type which assume that photons travel through space with predetermined properties. A problem is that those type of theories are based on shaky foundations in that they don't take into account the limitations of the models they imply or refer to and in particular they don't take into account the fact that those properties are best described as properties of the system and not properties of light only.

It should be of no surprise, therefore, that Bob and Alice get the results that they do.

 Quick get Bob and Alice on the blower