It will be shown although the results from quantum eraser experiments may seem to be mysterious they are no more mysterious than the results from classical two slit experiments. ........................................................................................................................

Part 1. Classical Observations

In the classical two slit experiment we can make various observations including the following:

1. If light has access to the screen through one slit only a diffraction pattern will be observed

2. The diffraction patterns due to each slit separately are centred at different locations.

3. If light has unhindered access through both slits equally an interference pattern will be observed. The pattern will contain alternate bright and dark fringes modulated by a diffraction envelope.

4. If an interference pattern is observed and changes are made such that the access through one slit is disrupted and reduced we would observe a reduction in the visibility of the interference pattern, for example the regions of destructive interference will become brighter and the regions of constructive interference will become less bright. If the disruption is total the only thing remaining would be the diffraction pattern due to the undisrupted slit.

4. If the intensity of the incident light is reduced a corresponding reduction in the intensity of the observed pattern will be reduced.

Similar results to those above will be observed for very low intensity illuminations including those which can be described as “one photon at a time” illuminations. In some low illumination

 Introduction to Quantum Erasers

 We shall consider two different quantum eraser experiments. Both experiments used coincidence counting methods and entangled photons generated from a BBO crystal illuminated by a laser. The resulting illumination was very low.

The experiments also used “which way detectors”. With these detectors it’s possible to obtain “which way information” in other words to observe through which slit each photon passes. It’s assumed that if it’s possible to obtain which way information it’s impossible to observe interference. That might seem to be weird.

But are quantum eraser experiments really weird? In this paper it will be shown they are no weirder than classical experiments. In fact the results obtained from quantum eraser experiments can be explained in terms of classical physics.

The first experiment was published in 2000 and the second experiment published in 2002. Readers are advised to familiarise themselves with the details of these experiments before reading the notes that follow.

 The 2002 experiment

In this experiment one from each pair of entangled photons, the signal photon, was directed towards a double slit. A detector behind the double slit was used to make observations of the pattern produced by the arrival of the signal photons. The second photon of each entangled pair, the idler photon, was sent to a second detector. The two detectors were linked by means of a coincidence counter.  

 The observations made can be explained in terms of classical physics:

Observation 1. Photons were allowed undisrupted access through the two slits and an interference pattern was revealed. This should be expected since two parallel coherent linear polarised waves can interfere.

The patterns produced by the horizontally polarised waves and the vertically polarised waves were in phase and they combined to give the resultant pattern.

 Observation 2. Quarter wave plates were used one in front of each slit. The plates were arranged so that the two sets of waves emerged from the slits in orthogonal states of circular polarisation. Because of the arrangement used the ordinary waves from the first slit had the same plane of polarisation as the extraordinary waves from the second slit and therefore the two sets of waves interfered. In a similar way the ordinary waves from the second slit interfered with the extraordinary waves from the first slit.

Because of the phase differences between the two sets of waves the resultant interference patterns were 180 degrees out of phase and there was overlap between the regions of constructive and destructive interference. The resultant pattern which was observed resembled a single slit diffraction pattern.

 Observation 3. When a polariser was placed between the idler and the second detector and with its axis parallel to an axis of one of the plates, one of the interference patterns was clearly observed. When the polariser was rotated through ninety degrees so that its axis became parallel to the corresponding axis on the second plate, the second interference pattern was clearly observed.

This result should be expected because the plane of polarisation of the signal photons was correlated with the plane of polarisation of the polariser. When the polariser axis was parallel to an axis of one of the quarter wave plates, one of the sets of o and e signal waves passed through the slits with minimum reduction of amplitude whilst the other set had maximum reduction of amplitude. When the polariser was rotated the pattern changed from one to the other due to the changes of amplitude of both sets of o and e waves. For a rotation of 90 degrees the set of waves that previously had minimum reduction of amplitude now had maximum reduction of amplitude and vice versa.

Quantum theory gives different explanations for observations 2 and 3:

It was assumed that the placement of the quarter wave plates enabled the possibility of gaining which way information and therefore interference was not observed. The subsequent placement of the polariser erased the possibility of gaining which way information and therefore interference was observed.

The 2002 experiment can be considered as a variation of earlier experiments and in particular an experiment carried out by Piano and Pescetti in the 1970s. The earlier experiment was more classical in construction. It used a screen and the illumination was high. The polariser was placed between the double slit and the screen.

The observations made in the 1970s experiment were explained in terms of the generalised laws of interference according to Fresnel and Arago. The relevant laws can be summarised as follows:

Two linear waves in orthogonal states of elliptical (and therefore circular) polarisation cannot interfere unless bought into the same plane.

The experimenters seemed to confirm these laws because when they used the quarter wave plates they did not observe any two slit interference patterns but when they used the polariser they did. All relevant observations made were basically the same in both experiments.

  

IN FAVOUR OF THE MASS VARIATION EQUATION

IN FAVOUR OF THE MASS VARIATION EQUATION

Introduction It is generally assumed that there are two contributions to the energy of a moving particle:

1. The energy (Emp) due to the mass m of the particle itself..... Emp = mc2
2. The kinetic energy (Eke) of the particle..................................Eke = mc2 (L- 1)

The total energy E is therefore given by....................................  E=mc2L
                                    
(m is the mass of the particle and is often called the rest mass, c is the speed of light and L is the Lorentz(gamma)factor. L increases with speed and approaches infinity as the speed approaches the speed of light.)

This paper will examine the equation and the widely held assumption that the rest mass of a fundamental particle remains constant. It will be shown that there is evidence that suggests otherwise. The paper will also consider the mechanisms by which potential energy contributes to the energy of interacting particles. The analysis is simple and obvious and leads to new insights including giving some clarification to the concept of antimatter.

PART 1.

 A common assumption is that microscopic particles, for example electrons, have a mass that remains constant.

1.Where is the evidence to back up this assumption?

An interesting place to start would be to look at the metrological data. When we do so we find that the mass of the electron is currently measured to ten decimal places. The uncertainty is indicated by the last two digits which are highlighted by the use of brackets.

                   Electron mass =9.109 382 91(40) times 10 -31Kg

2. Does the data prove that the rest mass is a constant?

Surprisingly the answer is no. The reason is that the data has very limited applicability. It applies only for those types of locations and systems within which the measurements have been made and where any possible variability may seem to be negligible. It will be shown that there are other locations and systems within which the rest mass can vary appreciably the best example being when particle separations reduce to microscopically small values.

 3. Does the equation predict rest mass variability?

The equation has always predicted variability as can be seen by looking at it:

                                                            E/m = Lc2

If no assumptions are made about the constancy or otherwise of rest mass we see that it’s not necessarily just E that changes with speed, it’s the ratio E/m that changes with speed. There are two extreme ways of interpreting this change:

                           1. E changes and m stays constant.
                           2. E stays constant and m changes.
                           3. Between the extremes a third interpretation is that both E and m change.

(Interpretation one is usually accepted but interpretations two and three are usually ignored)

 4. Are there known events where rest mass changes? 

Yes, for example with fuel carrying vehicles. The mass of the fuel can be counted as being part of the rest mass of the vehicle. When fuel is burnt and the vehicle accelerates some of the rest mass is converted to kinetic energy.

4. Vehicles are macroscopic, are there any known rest mass changes for microscopic objects?

Consider events such as the approach of an electron and positron. During such events rest mass changes completely. It reduces to zero when the particles annihilate. But we need to consider the question:

 CAN REST MASS HAVE VALUES OTHER THAN ITS CURRENTLY MEASURED VALUE?

5. But annihilation events are explained extremely well by quantum electrodynamics. 

Agreed, but even the most successful theories can be tweaked.

6. Can particles move in a way which is analogous to the movement of fuel carrying vehicles?

Imagine they could. If so we could have an electron which accelerates due to its rest mass being converted to kinetic energy. It could reach the speed of light if its rest mass reduces to zero.

7. Such an event can’t happen. For one thing it wouldn’t conserve momentum.

 That’s correct and shows that we cannot consider the electron in isolation. Interesting things are revealed when we consider the whole system. ..............................................................................................................................................................

 PART 2

 Below is an important question which seems to have been given little or no attention.

 AT WHAT PLACES DO WE FIND POTENTIAL ENERGY?

 1. Why is it an important question? It doesn’t make sense. Or is it a trick question?

 Well other forms of energy can be pinned down roughly to some sort of location. Consider a moving electron where there is a change between potential energy and kinetic energy. We sort of know where the kinetic energy is, it’s part of the energy of the electron. But where is the potential energy?

 2. Easy. The potential energy is in the electric field............ plus there’s a tiny bit in the gravitational field.

Okay so let me rephrase the question.

                                     WHERE IS THE FIELD?

Let’s just concentrate on the electric field for now.

3. Easy again. The field is in the surrounding space. For every point in that space we can calculate things such as the magnitude of the force that would act on a charged particle when placed at that point.

Yes, but what exactly is at those points when they are empty? By “empty”, I mean when there is nothing there at all or when there is nothing there which has a mutual interaction with the electron. By the way you started to describe a classical field. It can be a useful mathematical construct but it adds to the sometimes mistaken impression that there is something in empty spaces. There is nothing in empty spaces.

4. If that’s true then where is potential energy?

 Well if it’s not in empty spaces it must be in occupied spaces. To be more precise it’s stored as rest mass in the electron and in those parts of the rest of the system that the electron interacts with. For most systems the electron stores just a tiny fraction of the potential energy.

5. Where did you get that idea from? It seems silly but I will think about it. 

And while you’re doing so I’ll summarise some relevant properties about fields.

 a. A field has an observable effect only at locations where there are interacting parts.
 b. There is no observable field at all unless there are at least two interacting parts.
c. A field is a mutual thing and the presence of every interacting part is instrumental in creating the observable field at its location and at other locations where there are interacting parts.
 d. If an interacting part changes its location the field changes also and at all places where there are interacting parts.

 It should be stressed that no field is predominantly due to just one or more parts of the system. It’s due to all parts no matter how small or insignificant some of those parts may seem to be.

 6. Let me get this right. Are you claiming that all of the energy, potential as well as kinetic, is carried in the interacting parts of the system?

 Basically yes, but it’s a bit more involved. I see that you’re not convinced.

7. Convince me then.

I’ll try. Consider a two particle event involving an electron and a something else which is positively charged. I’ll call that “something else” the second particle. For the time being I will not specify what the second particle is.

8. I’m with you so far.

Now consider the particles separating and slowing down because of the attraction between them. Each particle would be losing kinetic energy and these losses would be balanced by the system gaining potential energy. Let the momentum be zero and let all the surrounding parts have negligible effects on the event.

9. Ho hum, as usual there are simplifying assumptions. 

Stop moaning I’m showing you the principle here. Anyway, kinetic energy leaves each particle and goes elsewhere. How do you think the energy moves away from the particles?

10. You seem to be suggesting that energy is something that can be transferred from particles by travelling through space....................perhaps it’s carried away by photons. 

 Let’s assume that’s right. If so where do the photons go? Remember that photons display their presence only at suitably occupied places where there is some sort of interaction.

 11. I guess the photons must go somewhere. If not they would move away forever. Some may describe that as energy escaping from the universe. 

 I agree they must go somewhere. But where do they go?

12. Could it be that each particle radiates its kinetic energy losses to the opposite particle? That’s what you want me to say isn’t it?

 I just want you to say what you think. If the particles did radiate to each other each particle would gain the kinetic energy losses of the opposite particle, the result being that the rest mass of each particle would increase.

13 Again that’s silly but I’ll go along with it for now. Okay, what would happen if the particles reached a momentary maximum separation and then started to approach?

 As you know there will be a conversion of potential of potential energy back to kinetic energy. Each particle would gain its increasing kinetic energy as a result of receiving the radiated rest mass losses of the opposite particle. 14. But if photons are involved they must make up part of the energy content Yes, it could be said that photons are the agents which carry the energy exchanges between the interacting particles. Perhaps each particle experiences some sort of fluctuations as photons are emitted and absorbed the changes becoming more smoothly continuous for wider particle separations. Also, if photons have a real existence in the interconnecting space then whilst in that space each photon would carry part of the overall energy and momentum.

 14. Are you sure that photons transfer energy between the particles? 

Let’s think about it. When we describe photons and their movement we are using a model. The model is informed by everyday observations and by observations from different areas of study such as geometrical optics. A preferred model, in summary, is that after they are emitted photons travel in approximately straight lines until they encounter something to interact with, for example the eye or a dust particle that scatters the photons or an atom that absorbs the energy of a photon and then emits a copy of the original photon. It is a model that seems to make sense and it is a useful model. But like other models it has the following major limitation:

PHOTONS OR ELECTROMAGNETIC WAVES OR FIELDS CANNOT HAVE ANY INTERACTIONS AT EMPTY LOCATIONS. THEY INTERACT ONLY AT LOCATIONS THAT ARE SUITABLY OCCUPIED.

 There are no observable interactions at any empty places between the suitably occupied locations no matter how close those locations may be. In the two particle event, therefore, all interactions occur at the locations of the particles themselves. If a photon is absorbed at a particle it will lose its energy to that particle. Similarly if a photon leaves a particle energy will be lost from that particle.

15. Would they be real or virtual photons? 

Go with any models that conform to the observations. The idea of virtual photons as being force carriers for the electric force works pretty well so it would be interesting to see how well it works in the situation which has been described here. I like to think of photon exchange in different ways including the interaction of the particles by means of the electromagnetic field.

16. I can’t believe any of this.

That’s fine but just look at the evidence that’s been presented so far and the evidence that’s to follow. I hope to see you again.
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PART 3.

 1. I’m back and I need a reminder of where we were with the electron event. Also I think I need some more details. 

 Let me summarise what is being proposed by referring to the two particle event. For the time being consider the two particles only and ignore the surroundings.

• When the particles separate both of them lose kinetic energy.

• The kinetic energy loss of each particle is converted to potential energy by being transferred to the rest mass of the opposite particle

• From momentum considerations the smaller the mass of the particle the greater the amount of kinetic energy it loses and the smaller the amount of potential energy it gains. A rough calculation shows that each particle displays approximately the same fractional rest mass change.

• When the particles approach each one gains its kinetic energy as a result of receiving the reducing rest mass content of the opposite particle.

• In conclusion we can say that the change of potential energy with separation is displayed as a change in the rest masses of the interacting particles.

 2. Can the energy transfer be explained in terms of the electromagnetic field as you suggested? 

That’s one way I like to think of it. Each particle feels the presence of the opposite particle because of the force of attraction between them. This can be described it in terms of the field which is mutual to both of them. Remember that the field can have no interactions at empty spaces and so in a closed two particle system the field exists entirely at the locations of the particles themselves. Remember also that, crudely speaking, photons can be described as being disturbances in the field. Because the particles interact by means of the field you can’t have energy changes in one of the particles without having correlated changes in the other particle. The two particles are somehow linked. I find it as being somewhat analogous to entanglement.

3. What happens with repelling particle, for example when two electrons approach?

The potential energy and total rest mass increases as the separation decreases.

 4. Where does gravity come into your analysis?

 In general the force of gravity between the particles can be considered as negligible compared to the electrical force. However the nature of the forces may be different in as yet untested regions such as extremely small particle separations?

5. Stop speculating.

I will do if you stop moaning.

 6. Earlier you did not specify what the second particle is. Why?

I’ll do it now. But first a reminder about the mass variation equation where it was pointed out that there are two extreme ways of interpreting the ratio (E/m) change.

 EXTREME INTERPRETATION 1.      m STAYS CONSTANT AND E CHANGES

 EXTREME INTERPRETATION 2.       E STAYS CONSTANT AND m CHANGES

 Something that is most relevant to these extreme interpretations is the structure of the system in which the electron moves. There can be an infinite number of different structures but there two extreme types of relevance.

 a. THE PERFECTLY ASYMMETRICAL STRUCTURE

 With this structure the second particle would be infinitely more massive than the electron. Such a structure cannot be achieved exactly but it can be approached. An electron interacting with a positively charged lump of metal would be a good example of a near perfect asymmetrical structure. It is only in the theoretical perfectly asymmetrical structure that extreme interpretation number one applies, with m remaining constant.

b. THE PERFECTLY SYMMETRICAL STRUCTURE

With this structure both particle would have the same mass. If the first particle is an electron the second particle would be a positron. It is only in this extreme structure that interpretation number two apples with E staying constant. The majority of structures would lie somewhere between these extremes and in such structures both E and m would change. If the second particle is macroscopic the structure would be close to being perfectly asymmetrical and changes in m could be considered as negligible.

 In summary we can say that:

 As E/m tends to infinity changes in m tend to zero and as E/m tends to one, changes in E tend to zero. 

Anyway I’m tired now so let’s pick this up tomorrow.

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PART 4

1. I’ve had a peek at your mathematical analysis and I think it needs to be carried out more rigorously.

Do it then.

2. I might. Anyway, apart from having a positron as the second particle how can you move towards a symmetrical structure?

Use other microscopic particles.

 3. What particles? If we stick with an electron the next smallest thing to a positron I can think of would be a proton. 

Yes and when we consider an electron proton event we would be considering the hydrogen one atom. If the particles are separated from the ground state to infinity the fractional rest mass change of each particle is about three parts in ten to the eight.

 4. Where did you get those numbers from? 

I’ll show you later.

 5. The standard uncertainty for the electron rest mass is about 4.4 parts in ten to the eight. That means that as far as hydrogen or more asymmetrical structures are concerned, we cannot as yet measure your imagined rest mass changes, even using Penning traps or whatever it is that’s used.

Probably the biggest problem is trying to measure the rest mass of each particle at places where it changes most, which is within extremely small particle separations. However we can and do measure some rest mass changes by measuring things such as excitation energy and ionisation energy.

 6. Please explain

Well, for a start the combined rest mass of the separated proton and electron is greater than the mass of the hydrogen atom in its ground state and by an amount equal to the mass equivalent of the ionisation energy.

7. As I explained in a previous discussion that’s wrong. The ionisation energy is negative and so the mass of the hydrogen atom is equal to the proton mass plus the electron mass minus the mass equivalent of the ionisation energy. There is no need for a change of rest mass. 

There is a need. Imagine a widely separated proton and electron accelerating towards each other from an initial state of rest. As the ground state separation is reached the loss of potential energy and gain of kinetic energy in mass units is approximately equal to 4.8 times 10-35 Kg. This is twice the ionisation energy of hydrogen. When the particles fall into the ground state configuration of the hydrogen atom half of this energy is lost from the system due to the other half being radiated away to the surroundings in the form of a photon. 

If now the atom in its ground state gets an energy input of 13.6 eV then this along with the kinetic energy of the particles can completely separate the particles to a momentary state of rest. Whatever way you look at it the combined rest mass of the particles changes with separation. By the way I think your misunderstanding of potential energy goes back to the convention that the potential energy at infinity is taken to be zero. Saying that the potential energy is negative simply means that the potential energy decreases with separation.

 8. Are you seriously suggesting that measurements of things such as ionisation energy provide proof that rest mass is variable? 

Yes and don’t forget excitation energies. Any mechanism involving a change of separation results in a change of potential energy and therefore a change of rest mass. And by the way, it’s already accepted in many quarters that rest mass can change. It’s just that the fuller consequences of this have not been developed yet. We are making a start on it here.

9. What about other atoms? 

Same sort of thing, but of course different things have different energy levels. And there’s the evidence of binding energy as well.

10. Tell me something about binding energy?

Take the helium 4 nucleus as an example. To completely separate the four nucleons requires an energy input of approximately 28 MeV. This results in the combined rest mass of the nucleons increasing by 28 MeV.

11. This is so confusing. Consider any particle, for example the electron. What should we take its mass to be? We know its value in the locations where the measurements have been made and depending on the structure of other locations we can calculate its value.

Basically we can use Coulombs law. Remember that except for very small particle separations the variability is extremely small, usually negligible in fact.

12. So why bother?

We bother because we should. Evidence suggests that the rest mass of a particle depends on where it is in relation to other particles it interacts with. In other words rest mass depends on the structure of the frame and the location of the particles within it. We shouldn’t just ignore that.

13. I’m trying to get a clearer picture in my mind of an electron and proton approaching due to the attraction between them.

 Do you see each particle gaining its kinetic energy as a result of gaining the rest mass losses of the other particle?

14. What I mainly see is that the approach can be momentarily interrupted as the particles jump through different energy levels. At each jump a photon will be released.

What’s the difficulty with that?

15. You didn’t factor things like quantum effects into your analysis.

I was considering those parts of the approach when there are energy exchanges between the two particles only. When there are quantum jumps some energy is exchanged with the surroundings and existing theories explain those events rather well.

16. But the mechanism you’re proposing surely contradicts those existing theories. 

Who said it does? If there is anything to the mechanism proposed here it should be possible to incorporate it into existing theories and perhaps improve them. I’m dying for a cuppa. Put the kettle on please.

 17. No you do it.

Let me tell you something before I do. Your comment about particles jumping between energy levels is very relevant to this discussion. I know I just glossed over it but I will come back to it and explain its relevance in greater detail.

18. So you should. Let me put the kettle on.

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PART 5

1. Can I change the subject? There’s something that’s been bothering me since the start of this.

What’s that?

2. You do not use the mass variation equation.

Well the equation in its original format has fallen out of favour with many physicists because, for example, it can imply that it is the total mass that increases with speed and not the kinetic energy.

 3. But it’s also assumed that the rest mass is constant and you’re suggesting otherwise. If you’re right mass does in fact change with speed. That’s rather ironic.

 What’s even more ironic is that in asymmetrical structures the larger mass particle undergoes a mass increase when it slows down and a mass decrease when it speeds up.

4. How did Einstein describe the movement of the larger particle?

 I don’t know what he did in his later work but in his original paper he described the electron moving in a field. If there is a field there must be something else in addition to the electron that creates that field. That “something else” is equivalent to what I referred to as the second particle and a second particle is needed, for example to conserve momentum.

 He also ignored any radiation emitted and justified that by assuming that the electron was being “slowly accelerated”. I’m fairly confident that it was implied that his “second particle” would have been something like a macroscopic structure and so therefore he was analysing the electron event in a near perfect asymmetrical structure.

5. That’s fair enough, he made simplifying assumptions. It could mean, however, that the equation he derived and perhaps any modern equivalent of it does not necessarily apply in those system structures where the simplifying assumptions do not apply? For example it could become increasingly in error as systems tend towards a symmetrical structure.

I suppose that’s a possibility so I suggest you look into it. You could start by looking at other derivations of the equation. In the meantime I’m going to continue assuming that the equation works reasonably well in all structures.

6. You do that. I’m going to the library.

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PART 6

 Have you found anything?

1. Not yet. It’s all well and good you coming up with this stuff but where’s the proof that rest mass is not a constant?

Good question but where’s the proof that rest mass is a constant? I would say that the body of evidence we have so far leans more to the possibility that rest mass changes.

2. But we want more than just that. Where else should we start looking? 

I’ll make a list. • Examine experimental evidence that’s already available, for example from annihilation events and emission and absorption spectra. Look for fine details which perhaps are not explained well enough by existing knowledge. • Consider the two particle approach more critically. As a starter you might want to try and imagine how the event proceeds.

3. Sorry but let me interrupt you there. I can get a sort of crude picture in my mind of particles or even waves approaching each other but I can’t help wondering how realistic that picture is.

I don’t think it matters too much if it’s realistic or not. It all comes back to your previous comment when you referred to particles jumping between energy levels. It’s only with imagined events like that that we get some experimental evidence of the imagined two article approach event. • Most likely they are particles with non zero size. • They can display wave properties such as diffraction. That raises the possibility that they move like waves. • The above possibility is strengthened when you look at the success of the Schrodinger wave equation. I think you’ve said enough for now but what’s your point?

 4. It’s a question. How do you measure the separation of waves or of particles which are very close together? 

Perhaps you could measure the distance between the centres of the two particles. Just kidding