These apparent mandalas are actually 'photographs' of electron  probability clouds within atoms.




Electrons passing through this apparatus, in so far as we are able to fathom the matter, do not take route h and do not take route s and do not take both of these routes and do not take neither of these routes; and the trouble is that those four possibilities are simply all of the logical possibilities…[i]

- David Z Albert (twentieth century physicist)

It’s character is neither existent, nor non-existent,
Nor both existent and non-existent, nor neither.
Centrists should know true reality
That is free from these four possibilities.[ii]

 - Bhavaviveka (1st century Madhyamika)

The structural similarity between the two opening quotes, which are separated by nineteen hundred years and a few continents, is evident.  The first quote, which comes from the quantum physicist's David Z. Albert's excellent book Quantum Mechanics And Experience, concerns the behaviour of electrons in a split beam experiment within which they seemingly travel on one of two routes (h or s) depending upon whether they are transmitted or diverted by a beam splitter.  A schematic illustration of the hypothetical experiment that Albert is referring to is shown in fig 1.  Electrons are fed, one at a time, into a contraption which divides them up depending on an attribute called ‘hardness’; hard electrons are diverted to the left and thus emerge out of the top opening in the diagram, soft electrons travel straight through as shown.  The hard electrons ostensibly travel on route h whilst soft are supposed to travel along route s.  The split beam is reunited at the ‘black box’ and emerges along path ‘h and s’.



Fig 1

The experiment will be described presently; for the moment we merely need to take note of the conclusion that David Z Albert reaches after a thorough analysis of the results.  The electrons cannot be said to travel on either one of the paths, nor on both, nor on neither, a conclusion that quite clearly has severe implications for our understanding of the type of 'existence' which is exhibited by the electrons. 

The second observation was made the 2nd-3rd century Madhyamika philosopher Bhavaviveka who, we can be fairly certain, had no knowledge of electrons and split beam experiments.  In his observation Bhavaviveka describes the innermost character of reality is best described as being neither existent nor non-existent nor both nor neither.   According to the Madhyamaka this existential paradox, the tetralemma of the extremes, lies at the heart of reality and, remarkably, the electrons in Albert’s experiment certainly seem to confirm this view.

In Albert’s exposition the attributes he gives to electrons are fictional – hardness (hard or soft) and colour (black or white).  The description of the experiment, however, does precisely describe the situation exemplified by actual experiments which have been performed on many occasions; the actual attributes of electrons usually employed in these experiments are aspects of electron ‘spin’.[iii]  The following discussion, which recapitulates Albert’s exposition, will follow his terminology for convenience. 

The theoretical experiment described by Albert requires the use of a ‘hardness’ box and a ‘color’ box.  The ‘hardness’ box is able to split electrons up according to whether they are ‘hard’ or ‘soft.’  Hard electrons emerge from the top opening and soft along the horizontal.  In a similar fashion the color box sends ‘black’ electrons out the top opening and ‘white’ electrons along the horizontal.

Fig 2

The first experiment involves three successive boxes, a colour box followed by a hardness box and then another colour box.




                                                                                       Fig 3

                              Percentages are of the original number of electrons entering the first colour box.


The experiment is performed with a large number of electrons that are sent into the first colour box one at a time.  The results are surprising.  The first colour box sorts out electrons into black, which are ejected out of the line of fire as shown, and white, which continue on to the next box which is a hardness box; all of the electrons that enter this hardness box should be white.  This hardness box should sort the incoming white electrons into hard and soft as shown, so the electrons emerging from the right hand opening of the hardness box should be white and soft.  It follows that all these electrons, being all white, should pass straight through the final colour box.  However this is not what happens; when the experiment is performed half of the remaining white electrons (12.5% of the original number sent into the first colour box) mysteriously turn into black electrons.  It seems that the attributes of the electrons are not intrinsic to the electrons but, rather, the electrons adopt attributes in order to fit a pattern.

This is an extremely surprising situation and in order to emphasise just how surprising this quantum behaviour is Jeffrey Santinover, in his book The Quantum Brain, gives the following analogy:


As babies are born at a local hospital, the girls are brought through one door into a pink room, the boys through another door into a completely separate blue room.  But when the babies are brought out of the pink room, or out of the blue room, through doors at the other end, they once again must be sorted into boys and girls.[iv]

It seems as if the characteristics of quantum entities such as electrons, protons, neutrons, photons, and the experiment can be performed with any of these, are not fixed.  Instead it appears that characteristics are adopted in order to fit into a pattern of quantum behaviour, and this leads to some very strange results.

  The next experiment discussed by Albert is that briefly discussed at the beginning of the chapter which is shown in diagram fig 1.  Electrons are fed into the hardness box that sends ‘hard’ electrons out along route h and soft electrons out along route s.  Hard and soft electrons meet at the black box which sends both out along route h and s without altering the hardness or softness of the electrons.  Electrons are fed into the hardness box one at a time.  The hardness box has the effect of randomising the colour so that white electrons emerge 50% black and 50% white and black electrons also emerge 50% black and 50% white.  We check that soft electrons emerge as soft electrons and hard electrons as hard and then perform some experiments.

1)      Send white electrons into the hardness box.  Fifty percent of these will be hard and take route h, and the other 50% will be soft and take route s.  So the result, as expected, is that 50% hard and 50% soft emerge along h and s.

2)      Send hard electrons into the hardness box.  The hardness box randomises the colour of the electrons so 50% are white and 50% black.  All the electrons take route h and the result is, as expected, 50% white and 50% black emerge along h and s. 

3)      Send soft electrons into the hardness box and the result is, as expected, 50% white and 50% black emerge along h and s. Furthermore we know that these electrons have travelled along route s.

4)      Now we send white electrons into the hardness box and measure the color at h and s.  We expect that 50% of the electrons will be hard and so travel route h and 50% are soft so take route s.    Now consider the 50% of hard electrons on route h; we have already done the experiment 2) which tells us that 50% of these (25% of the total) will emerge black and the remainder white.  And, similarly according to experiment 3) 50% of the soft electrons (25% of the total) will be black and the remainder white.  So overall we expect to get 50% white and 50% black along h and s.  What actually happens, however, is that we get 100% white along h and s.

In other words the last experiment contradicts experiments two and three.  The next stage is to introduce a sliding screen which can block electrons along one of the paths, (s) for instance.



                                                                              Fig 4


Now we have seen that when the wall is out we get 100% white along h and s (experiment 4), 50% of the electrons having travelled route s and 50% route h.  So we would naturally expect that when we slide the wall in to block the electrons on route s that all of the electrons (50% of the original number) along h and s will still be white, having travelled along h.  But we know that the hardness box changes the colour of the electrons so that 50% are white 50% black; and what we actually get is 50% white (25% of original number) and 50% black.  Albert comments on this remarkable situation:


Now we’re in real trouble.  Consider an electron which passes through our apparatus when the wall is out.   Consider the possibilities as to which route that electron could have taken.  Can it have taken h?  Apparently not, because electrons which take h are known to have the property that their color statistics are fifty-fifty, whereas an electron passing through our device with the wall out is known to have the property of being white at h and s!  Can it have taken s, then?  No, for the same reasons.  Can it somehow have taken both routes?  Well, suppose that when a certain electron is in the midst of passing through this apparatus, we stop the experiment and look where it is.  It turns out that half the time we find it on h, and half the time we find it on s.   We never find two electrons in there, or two halves of a single split electron, one on each route, or anything like that.  There isn’t any sense in which the electron seems to be taking both routes.  Can it have taken neither route?  Certainly not.  If we wall up both routes, nothing gets through at all.[v]


It is clear, then, that there is a fundamental indeterminism regarding the characteristics, or attributes, of quantum entities.  As Albert says:

It’s that any electron’s even having any definite color apparently entails that it’s neither hard nor soft nor both nor neither, and that any electron’s even having any definite hardness apparently entails that it’s neither black nor white  nor both nor neither.[vi]

So, Albert says, if an electron has a definite hardness then it will be in a superposition of being white or black.  And this state of being in a superposition means that it is neither black nor white nor both nor neither.  In other words the condition of being neither this nor that nor both nor neither can be identified with the state of being in a superposition:


So, it follows that a white electron can’t be a hard one, or a soft one, or (somehow) both, or neither.  To say that an electron is white must be just the same as to say that it’s in a superposition of being hard and soft.[vii]

And, furthermore and crucially, Albert is completely adamant that:


… it isn’t at all a matter of our being unable to simultaneously know what the color and the hardness of a certain electron is (that is: it isn’t a matter of ignorance).  It’s deeper than that.[viii]

In other words when an electron is forced to adopt a definite hardness its color becomes superpositioned in reality, and vice versa.

In the last chapter we saw that the feature of being in a superposition is the fundamental nature of the wavefunction, and the wavefunction is the fundamental quantum nature of unobserved reality.  It must follow therefore that, from the quantum perspective, the fundamental characteristic of reality when it is not manifested to consciousness, which is the same as the fundamental wavefunction which underlies the manifestation of reality is that, as Bhavaviveka so clearly describes it:


It’s character is neither existent, nor non-existent,
Nor both existent and non-existent, nor neither.

The way that this tetralemma of the extremes of existence, which the Madhyamaka considers to be the hallmark of emptiness, emerges within Albert’s experimental setup is that if an electron is forced into existence as having a definite colour, then it is also necessarily forced into the superpositioned state of the tetralemma of the extremes of existence with regard to its hardness.  Conversely if an electron is forced into existence as having a definite hardness then it is also necessarily forced into the superpositioned state of the tetralemma of the extremes of existence with regard to its colour. 

It might now be thought, well at least these electrons are only half superpositioned, so to speak; we can make a definite white, or black, one, as it were; we just have the problem that this process will send its characteristic of hardness into the superpositioned condition of hovering between extremes of existence.  Or, on the other hand, we can grab a definite hard, or soft, one and send its characteristic of colour into the superpositioned realm of the tetralemma.  However, if we are speaking in terms of knowledge of the ultimate nature of the electrons, this will not do.  Any ultimate knowledge of the nature of these electrons, or anything for that matter, presupposes knowledge of the way that they are within themselves as it were.  And it is quite clear that prior to any interaction with the experimental setup both characteristics, hardness and colour, must be considered to be in the realm of the tetralemma of the extremes of existence; which is the same as saying that they reside in the realm of emptiness.

It is extremely important that the reader comprehends the significance of the analysis thus far.  In chapter one we saw that the perennial criticism of the kind of analysis which has been undertaken here is that it merely indicates a random coincidental similarity of language which has no serious significance.  However, the precision and clarity of the mapping, or correspondence, between the two domains which has been demonstrated with regard to Albert’s analysis of the implications of a fundamental quantum experiment and the Madhyamika analysis and description of the inner nature of reality is far too conspicuous for any such critique to be seriously entertained.

According to the Madhyamaka the tetralemma of the extremes of existence constitutes, insofar as one can say anything with precision regarding ultimate reality, the innermost nature of ultimate reality.  Furthermore this tetralemma of the extremes of existence also describes, insofar as it may be described, emptiness, which is also a term denoting the nature of the fundamental ground of reality:


Since they [phenomena] neither exist by themselves nor by any intrinsic character,

Since they do not abide as their own entities,

And since they do not exist as they are apprehended,

He [the Buddha] presented their lack of nature.[ix]

‘Lack of nature’, of course, is another term for emptiness.  The fact that the electrons which take part in Albert’s experiment, and any other quantum experiment, do not have an ‘intrinsic character’ has certainly turned out to be correct.  Furthermore they cannot ‘abide as their own entities’ because they alter their characteristics in dependence on the overall pattern of manifestation.  Thus these electrons, as they exist at their most fundamental level, quite dramatically exemplify the characteristics of emptiness, insofar as, of course, one of the characteristics of emptiness is to lack definite intrinsic characteristics.  And this situation clearly threatens to undermine any grip on the reality of the nature of independent entities and their characteristics:

A thing without a characteristic does not exist anywhere.

If a thing without a characteristic does not exist,

What do characteristics characterise? [x]

It might be said that the fundamental characteristic of these electrons is a profound lack of definite characterisation which would mean, of course, that emptiness was a fundamental characteristic of these electrons.

The configuration of the tetralemma of the extremes of existence, which has the basic form:


Neither existent,

Nor non-existent,

Nor both existent and non-existent,

Nor neither existent and non-existent,


is fundamental to the Madhyamika analysis of reality.  The Madhyamaka insists that this configuration, the configuration of emptiness, lies at the heart of reality, and quite obviously, the issue of exactly what is meant by ‘reality’ is thrown into question by such seemingly paradoxical assertions.  But whilst the paradoxical nature of this tetralemma might be thought, by the thoughtless, to be a mere product of Eastern inscrutability, its precise adumbration of the paradoxes of quantum theory can only give us pause for perhaps deeper thought on the matter.

[i] David Z. Albert, 1994, Quantum Mechanics And Experience, p11.

[ii] Karl Brunnhölzl, 2004, Centre of the Sunlight Sky p84.

[iii] QM&E p33.

[iv] Jeffrey Santinover, 2001, The Quantum Brain p141 - Santinover uses an experiment with reflected and transmitted photons from a series of half-silvered mirrors in his exposition.

[v] QM&E p11

[vi] QM&E p11

[vii] QM&E p15

[viii] QM&E p15

[ix] Karl Brunnhölzl, 2007, Straight from the Heart p34

[x] Nagarjuna's Fundamental Verses on the Middle Way (Mulamadhyamakakarika).