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Summary. This paper presents two novel models, The Toolbag Exclusion Principle and the Invisibility Conundrum to describe the quantum behaviour of macroscopic objects in the real world, with reference to the properties of the common screwdriver.

The possibility that quantum phenomena may apply to events in the macroscopic world was first proposed by Schrödinger, who left it famously unresolved. This paper describes an experimental system in which quantum uncertainties can be studied under the conditions of the ‘real world’.  

Consider two points, A and B. A is defined as ‘the workshop’ and B as ‘the job’ or ‘ the site’. There is also a third point, C, but in general no-one knows where it is, although there is always someone who knows where it was, but we will come on to that later. There are also three characters who could be called Schrödinger, Mrs Schrödinger and Schrödinger’s mistress (ref 1), but we will not call them that here, only point out that one or other of them may, or may not, exist.

The experimental procedure is called ‘ the job’ and it is located at point B, but the mystery is, who started it, or why it is being done at all, as it turns out that Mrs S didn’t want it done and Mr S was reluctant to do it. Mrs S is often heard to say that it would have been better to ‘get the man in’, but naturally this does not go down well with Mr S, although his motivation is only partially understandable. However, the point is that ‘the job’ is underway and there is some sense in which it will be finished eventually and in order to achieve this an object called the toolbox, but usually better described as the toolbag, will often move from point A to point B and back, possibly stopping at point C, although the reasons for this remain obscure.

Here the nature of the toolbox must be examined in some detail, because this is where the action, or more commonly inaction, lies. The first point to be established is that it is only a concept. Some would describe it as a wave equation that can collapse to reveal its solid contents, here known as ‘the tools’. There are clearly cases where it can be termed as de-localised and the contents may, or may not, be distributed, but in some sense are entangled such that their movement in space and time are correlated with the movements of Mr S. The equations describing this are so complex that they remain unsolved and that is why they are always written to resemble ancient Greek letters that can never be precisely named. This has to be accepted, that is, the fact that it can never be understood has to be accepted, and whether that can be accepted or not depends on the capacity of the observer for abstraction. Neither Mr S, nor Mrs S has this, but they might have had it if they could have achieved what is called ‘agreement’, but here there is inevitable confusion. Whilst the contents of their observations may be identical, the sign attached to these observations may be positive or negative, and the rule is that no two closely linked observers can attach the same sign to their conclusions.

Mr S’s mistress, known here as Miss/Mrs X, would,  if she existed, certainly have known a thing or two about entanglement, but because nobody can decide whether or not X is the known or the unknown, this remains unhelpful, especially because Mrs S would both believe everything she had to say and disbelieve it at the same time.

At this stage it is necessary to make a brief digression to discuss the Theory of Causality which explains that when something goes wrong, it must be somebody’s fault. A deeper analysis suggests that it is intricately bound up with the fact that nothing can travel faster than light, thereby irreversibly undermining the excuse, “ It couldn’t have been me, I wasn’t there at the time”. Nevertheless there is a fundamental problem here; something can appear to travel faster than light provided that that light is not switched on, and, for example, in times like this a screwdriver can fail to locate the screw-head and do irreparable damage and, once more, provide a dramatic and regrettable illustration of the irreversibility of the arrow of time.  

Scientists aware of this problem have made great steps to solve it. The approach has been to design an electrical screwdriver which also has a light pointing in the direction of ‘the job’ with both the light and the rotating action being activated by a switch. However a feature called ‘Parity’ has proved to present an insurmountable problem. Because a single switch controls both functions, the light only illuminates the job in time to see ‘the damage’ being done. but not in time to prevent it. Providing a solution to this problem has baffled some of the finest brains of the engineering community.

The fact that causality is preserved because information cannot travel faster than light has been derived from a study of the symmetries of nature and reveals another deep structure. Whilst someone is always responsible when things go wrong, the  same person cannot be held responsible if they go right.

Armed with all of these facts we can now go forward with a discussion of the nature of time and how it happens that the time perceived by Mrs S and that perceived by Mr S are quite different, and how this difference is subject to intense perturbation in the presence of ‘the job’. Basically time is divided into units, often called seconds, as in the expression, ‘It’ll only take a second’ often presumed to be the time required to travel between A and B. In fact there is another symmetry of nature involved because for every A-B there is an unavoidable B-A and these packets of time, often referred to as -∆t, which have the capacity to summate extremely rapidly, frequently take a great deal of explanation, indeed most of them can never be explained away for the simple reason that the explanation is of a class called ‘unbelievable’ although the underlying cause is highly recognisable and passes the major test for any scientific observation, that it is exquisitely repeatable, provided that only one observer is present at the scene.

To return to the contents of the toolbag, the one positive conclusion we can make is that they do exist, but this is where the root of the problem lies and once again it can be best illustrated by consideration of the class of objects known as ‘screwdrivers’. Archeology has not so far revealed whether or not the screw came before a related object, now termed ‘the screwdriver’ and the reasons for this reverberate down to the present time, but will not be discussed here. The screw itself has two parts, the screw-head and the threaded part. In its robust form, the screw-head was shaped like a bolt head, but more commonly it had a single groove, enabling the screwdriver to grip or slip, whichever came first. In order to provide a more reproducible response, a second groove was added at right angles to the first and this required a new type of screwdriver, the cross-head model. This has resulted in an abundance of screwdrivers of both types, but of many different sizes, becoming potential, or even actual, occupants of toolbags and workshops, in preparation to meet and engage with screws of all types and sizes. A further development has resulted in the appearance of the interchangeable bit, again of all types and sizes, for use with an electrical or manual driver. The well-equipped workshop or toolbag will certainly have, at many stages in its existence, well-ordered rows of both sorts, but this is where the paradox arises. Because the toolbag is necessarily smaller than the workshop, a selection has to be made before setting out from A to B. It is somewhere in this process that the phenomenon of uncertainty sets in and gives rise to what is universally known as ‘The Toolbag Exclusion Principle’(TEP).

The paradox, mentioned above, is that uncertainty is nothing more than the evil twin of certainty. If the worker (here Mr S) is quite certain that the screws at point B are exclusively of the straight groove type and fills the toolbag accordingly, he will find on arrival at B that they have all changed to become the cross-head type. Should he, on the other hand, have started at point B and taken part of ‘the job’ to point A, he will find that no matter which type of screw is present, the only screwdrivers or bits present at point A are of the opposite type. On returning to point B he will find that the congruous screwdrivers are not there either, and will conclude that they must have migrated to point C.  Unfortunately he no longer has any precise information about the location of point C, but decides that he will save time by looking for it and not ask the one person who, for reasons he will never grasp, is certain to have known where it is (was).  Eventually he leaves the movable part of ‘the job’ at point B and returns to point A only to find that the items he had concluded were at point C had mysteriously returned.  

It is now that Mr S realises that within the space-time continuum of the toolbag, objects exist as a superposition of two states, a high energy state capable of doing work and a low energy resting state that is not, and that when the waveform of the toolbag collapses, it ceases to be a closed system and in the macroscopic environment of ’the job’, thermodynamic imperatives dictate that no work will be done.  The ‘tools’ must then adopt their resting, or ground, state and transfer energy to Mr S causing him to make the futile class of translations, B-A followed by A-B. It is now that he discovers that the translation A-C is of the type known as ‘forbidden’ He senses that Mrs S will, however, make the translation C-A or C-B and radiate a certain amount of energy whilst doing so, but will not have the slightest interest in any hypothesis he might present to explain the position. Of course he would like to discuss the situation with Miss/Mrs X, but the problem of her existence remains unresolved. However the greater the value of -∆t, the more Mrs S becomes convinced that she, or something like her, must exist. However, in contemplating this, Mr S asked himself a key question “does it always have to be like this?” and the answer, “sometimes it doesn’t” produced the first glimmer of understanding.

He now realised that the tools could only adopt high or low energy states in the presence of an external field and this lead directly to the concept of the ‘unsuspected exception field’ or USE field and its remarkable properties. To explain his accumulated results, such a field must have two possible states, the ‘full’, or F state and the ‘low’ or L state. Here F would correspond with the high energy state and L with the lower energy state of the tools. At first sight it seemed that these energy levels might be expressed by F=1 and L=0, but further analysis showed that L has the most unusual property of tending to zero, but never reaching it, and it is for this reason that it is now called the ‘less’ state.

This property of the USE field is as remarkable in its way as the fact that the neutron is less stable than the proton. Thus, just as the sun did not immediately burn out in a blaze of glory, the old view that there is nothing new underneath it is also untenable. Because L must retain a low, but non-zero, value then it is not possible to say either ‘Everything that can be done has been done already! or, Nothing will ever be done!’ And, in consequence, generations of individuals can continue to look forward to pottering around into protracted old age.

He is about to break the good news of this discovery to Mrs S, but decides that she will see it as a very weak excuse. Besides he has already lost the overwhelming confidence that accompanied this realisation. Later he has the warm and comfortable feeling that Miss/Mrs X would understand him completely, but a sudden fleeting view of further implications of his theory shows the less stimulating picture of a man ‘ hoist by his own petard’.

The general consensus is that the Toolbag Exclusion Principle has its roots in the Invisibility Conundrum (IC), namely that tools of any kind become invisible either just after you finish using them, or, in more unfortunate cases, just before. Whether or not these phenomenon are independent, it is clear that they hybridise to maximise the value of -∆t. Nevertheless both the TEP and the IC require that ‘the worker’ functions in isolation. It was here that Mrs S, whose reasoning so far had been of the class known as ‘faultless’, made her only factual error, assuring Mr S the that the TEP could not take place in any other workshop in the known world.

  The Invisibility Conundrum, on the other hand, has not been fully discussed because Mr S remains under the illusion that this is a problem he will be able to fix, as, to use his own words, “It won’t happen again.” The consequence is that Mrs S never finds out about it and any chance of sorting it out remains extremely remote.

As for Miss/Mrs X, all that can be said here is that Mr and Mrs S each hoped (h) and feared (f) that she did/did not, exist, but another universal exclusion principle dictated that four so-called force-carriers, which took the forms:-

 (h,f), (-h,f), (h,-f) and (-h,-f)

exchange continuously between them and, although not intuitively obvious in the macroscopic world, resolved into an attraction that increased continuously with the distance of separation.  

Meanwhile Miss/Mrs X, would, had she been visible, be seen to be looking at the world with a strange blend of eagerness and indifference, in front of her a shallow dish that may, or may not, once have contained cream.

References.

1) Why does E=MC2?  Cox and Forshaw. De Capo Press  2009.

Schrödinger’s Kit