ELECTRONS HOVERING BETWEEN EXISTENCE AND NON-EXISTENCE:
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
- David Z Albert (twentieth
It’s character is neither
existent, nor non-existent,
Nor both existent and
non-existent, nor neither.
Centrists should know true
That is free from these four
- Bhavaviveka (1st
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’.
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
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
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
The first experiment involves three successive boxes, a colour box
followed by a hardness box and then another colour box.
Percentages are of the original number of electrons entering the first
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
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
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.
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
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
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:
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
[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.
[ix] Karl Brunnhölzl, 2007, Straight from the Heart
[x] Nagarjuna's Fundamental Verses on the Middle Way (Mulamadhyamakakarika).