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Found Phys (2014) 44:557–575
DOI 10.1007/s10701-013-9770-0
On the Gravitization of Quantum Mechanics 1:
Quantum State Reduction
Roger Penrose
Received: 7 September 2013 / Accepted: 3 December 2013 / Published online: 11 January 2014
© The Author(s) 2014. This article is published with open access at Springerlink.com
Abstract This paper argues that the case for “gravitizing” quantum theory is at least
as strong as that for quantizing gravity. Accordingly, the principles of general relativity
must influence, and actually change, the very formalism of quantum mechanics. Most
particularly, an “Einsteinian”, rather than a “Newtonian” treatment of the gravitational
field should be adopted, in a quantum system, in order that the principle of equivalence
be fully respected. This leads to an expectation that quantum superpositions of states
involving a significant mass displacement should have a finite lifetime, in accordance
with a proposal previously put forward by Diósi and the author.
Keywords Quantum theory ·Linear superposition ·Measurement ·Gravitation ·
Principle of equivalence ·Diósi-Penrose state reduction
The title of this article (and of its companion, [16]) contains the phrase “gravitization
of quantum Mechanics” in contrast to the more usual “quantization of gravity”. This
reversal of wording is deliberate, of course, indicating my concern with the bringing
of quantum theory more in line with the principles of Einstein’s general relativity,
rather than attempting to make Einstein’s theory—or any more amenable theory of
gravity—into line with those of quantum mechanics (or quantum field theory).
Why am I phrasing things this way around rather than attempting to move for-
ward within that more familiar grand programme of “quantization of gravity”? I think
that people tend to regard the great twentieth century revolution of quantum theory,
as a more fundamental scheme of things than gravitational theory. Indeed, quantum
mechanics, strange as its basic principles seem to be, has no evidence against it from
accepted experiment or observation, and people tend to argue that this theory is so well
R. Penrose (B)
Mathematical Institute, Oxford, UK
e-mail: penroad@wadh.ox.ac.uk
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established now that one must try to bring the whole of physics within its compass. Yet,
that other great twentieth century revolution, namely the general theory of relativity,is
also a fundamental scheme of things which, strange as its basic principles seem to be,
also has no confirmed experiments or observations that tell against it—provided that
we comply with Einstein’s introduction of a cosmological constant , in 1917, which
now appears to be needed to explain the very large-scale behavior of cosmology. So
why give quantum theory pride of place in this proposed union?
It is true that there are far more phenomena, on a human scale, which are found to
require quantum mechanics for their explanations, than are those that require general
relativity for their explanations—far, far more. Also, I think it is felt that since quantum
mechanics normally refers to very small things, and general relativity to very big
things—and we tend to think of big things as being made up of small things—then the
theory of the small things, i.e. quantum mechanics, must be the more fundamental.
However I think that this is misleading. Moreover, there is another issue that I regard
as far more important than this issue of size, namely that of the consistency of the
theory.
We know of the problems of the infinities that so frequently tend to arise in the
quantum theory of fields, and much work is geared to trying to eliminate or, at least,
deal with these infinities in a consistent and appropriate way. But, of course, general
relativity also has its infinities, these arising inevitably in the gravitational collapse to
a black hole, or perhaps of an entire universe. These are serious issues, representing
potential mathematical inconsistencies in the global applicability of each theory. These
are issues that certainly do need attending to, and it is often argued that the infinities of
one theory might be alleviated if the principles of the other theory can be appropriately
brought to bear on them.
But quantum mechanics also has another basic inconsistency, which applies to the
very basis of its founding principles. This is usually referred to as the “measurement
problem”, though I tend to prefer Tony Leggett’s terminology: the “measurement
paradox”. We can think of this as a fundamental conflict between two of the very
foundational principles of quantum mechanics, namely linearity and measurement.
Let us have a look at these issues, starting with linearity, which is an essential part of the
unitary evolution Uof the quantum state-vector. In Fig. 1, we envisage a high-energy
photon aimed at some brown object, which ejects various other objects as soon as the
photon hits it. In Fig. 2, a mirror is inserted in the path of the photon, and the reflected
photon hits a green object instead, which ejects a quite different family of objects
when hit by the photon. In Fig. 3, the mirror is replaced by a beam-splitter (effectively
a half-silvered mirror) which splits the photon state into a quantum superposition of
the two considered earlier, so that its state now becomes a superposition of being
transmitted, and aimed at the brown object, and of being reflected, and aimed at the
green object. Quantum linearity demands that the two superposed photon states, as
they emerge from the beam splitter each individually maintains the evolution that it
would have achieved in the absence of the other. If quantum linearity holds universally,
then the results of the photon impacts (for a photon of high energy) could be perfectly
evidently macroscopic events.
This issue was clearly appreciated by Schrödinger, as he illustrated the problem
with his famous “cat” thought experiment. In his version he considered a decay of
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Fig. 1 Top Single direct photon hits brown object emitting many particles. Middle Direct photon kills cat.
Bottom Killed cat with environment, sad observer, sad thoughts
a radio-active atom, but it will fit in better with what I have to say if I employ a
beam-splitter instead. In Fig. 1, the brown object is replaced by a murderous device
(photon detector connected to a gun) which kills a cat. In Fig. 2, a mirror is inserted
between the photon source and the device, so the cat survives. But in Fig. 3, the mirror
is replaced by a beam-splitter so, according to quantum linearity (as demanded by U),
the resulting quantum state is one involving a superposition of a dead and a live cat!
Sometimes people object to this direct kind of description of a quantum U-evolution,
pointing out that I do not appear to have taken into consideration the complicated
environment that must be entangled with the detector and the cat, etc.—since in the
“environmental decoherence” description of quantum measurement, this environmen-
tal involvement is all-important, the unobserved degrees of freedom in the air mole-
cules, for example, having to be averaged out in our quantum descriptions. Other
objections come from the fact that no “observer” has been brought into the picture, it
being frequently argued that it is by bringing in an observer’s consciously perceived
alternatives—necessarily of one clear outcome or another—that finally breaks the
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Fig. 2 Top Photon reflected, hits green object emitting different particles. Middle Photon reflected, cat
lives. Bottom Live cat, environment, happy observer, happy thoughts
chain of continuing superpositions. In Fig. 1, I have indicated the environment, with
some dots to represent air molecules, in the situation described previously in Fig. 1.
I have also included a human observer. The observer’s conscious perception of the
dead cat is depicted in a “thought bubble”, but whether or not such a thing can be
represented as part of the quantum state is not important here, because one can see
from the observer’s unhappy expression that the cat’s demise has been consciously
perceived. In Fig. 2, I have done the same, but with the mirror inserted, so that the cat
remains alive, accompanied by a different environment, represented by some slightly
differently placed dots. Now the observer consciously perceives the cat to be alive (as
indicated in the thought bubble), and this is made evident from the now happy expres-
sion on the observer’s face. None of this appears to affect the situation arising when
the mirror is replaced by a beam splitter, as depicted in Fig. 3. The environment is now
a superposition of these two possibilities, and the observer’s facial expression is now
a superposition of a smile and a frown, as the outward expression of the superposed
conscious perception of a dead and live cat.
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Fig. 3 Top Beam-split photon produces both sets of particles in superposition. Middle Beam-split photon
creates Schrödinger’s cat. Bottom Schrödinger’s cat with superposed environment, observer, and thoughts
Of course, some might object that conscious perceptions are not like this, and our
normal streams of consciousness do not involve us in perceiving such gross superpo-
sitions. Of course they do not, in our actual experiences, but I see no contradiction in
this kind of conscious perception, and we need to explain why they do not occur. The
U-evolution of the standard quantum formalism, with its implied linearity, provides,
in itself, no explanation for this remarkable but utterly familiar fact.
To get the right answer for the un-superposed nature of the perceived macroscopic
world, we need to wheel in the other part of quantum formalism, namely the reduction
Rof the quantum state, according to which the state is taken as “jumping”, probabilis-
tically, to an eigenstate of some quantum operator that is taken to represent the action
of quantum measurement. If we don’t bring in Rthen we just don’t get a description
of the physical world that we all perceive. Strictly speaking, Ris simply inconsistent
with U. Whereas Uis a continuous and deterministic evolution, Ris (normally) dis-
continuous and probabilistic. Moreover, any measuring apparatus is itself constructed
from the same kind of “stuff” that constitutes all the quantum systems that are under
examination, being built from quantum particles, quantum fields and quantum forces.
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Fig. 4 Clash between basic QM and GR principles
So why do we not use Uto describe its action in the course of performing a measure-
ment?
Of course there are innumerable different ways that quantum physicists and philoso-
phers try patch up this inconsistency, normally taking Uto represent an underlying
truth of Nature and regarding Ras coming about somehow as an approximation, or
as an “interpretation” of how the quantum state is supposed to be viewed in relation
to physical reality. I do not propose to enter into a discussion of any of these alterna-
tive viewpoints, but I merely present my own view, which is to regard Uitself as an
approximation to some yet-undiscovered non-linear theory. That theory would have
to yield Ras another approximation to a reality, describing how quantum measuring
devices actually evolve in a way that subtly deviates from the action of U.
Again, there are numerous different approaches to such “realistic” evolutions, and I
shall restrict attention to my own point of view [11–13], which is closely similar to one
put forward, rather earlier (but motivated by somewhat different considerations), by
Diósi [3,4], namely to regard gravitation as being the key to the issue of how standard
quantum theory is to be modified. Other rather different gravitational proposals have
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Fig. 5 Schrödinger’s lump; proposal for superposition decay
been proposed by [5–8,17]. My own approach to this is to take the principles of general
relativity as having a defining role in how quantum mechanics is to be modified. Some
of the relevant issues, relating to the idea that gravity should be involved in this
modification of quantum mechanics are listed in Fig. 4.
In Fig. 5, I have schematically depicted a more inanimate version of the Shrodinger
cat (which had been illustrated previously in Fig. 3). Instead of the cat I have placed a
simple massive (spherical) lump of material, which is moved to the right if the detector
receives a photon but remains in its original location if that photon is deflected away
from the detector, this photon having been fired from the laser on the left of the
picture, and where there is to be a beam-splitter placed between the laser and the
detector, all as before. The scheme that Diósi and I have proposed is concerned with a
superposition between two states, each of which—had it been on its own—would have
to be a stationary state. This superposition is to be taken as being unstable (owing to
some non-linear effects coming from the putative unknown “gravitization” of standard
quantum mechanics), with a lifetime τ, of the order of
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Fig. 6 Schrödinger’s lump gives space-time bifurcation
τ≈¯
h/EG
where the quantity EGis taken as some fundamental uncertainty in the energy of the
superposed state see [12], and the above formula is taken to be an expression of the
Heisenberg time-energy uncertainty relation (in analogy with the formula relating the
lifetime of a radioactive nucleus to its mass/energy uncertainty).
The quantity EGis the gravitational self-energy of the difference between the mass
(expectation) distributions of the two stationary states in superposition. (If the two
states merely differ from one another by a rigid translation, then we can calculate EG
as the gravitational interaction energy, namely the energy it would cost to separate
two copies of the lump, initially considered to be coincident and then moved to their
separated locations in the superposition.) The calculation of EGis carried out entirely
within the framework of Newtonian mechanics, as we are considering the masses
involved as being rather small and moved very slowly, so that general-relativistic
corrections can be ignored.
Nevertheless, we are to consider that regarding EGas an energy uncertainty comes
from considerations of general-relativistic principles. In Fig. 6, I have schematically
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Fig. 7 Space-time bifurcation and one branch dies
illustrated the two space-times involved, being taken as more-or-less identical until
the lump locations begin to separate. When the separation becomes significant, in an
appropriate quantum-gravity sense, then one branch dies off and the other survives
(Fig. 7). The time-scale for this to happen (according to the τ≈¯
h/EGformula) is
estimated as being a measure of the amount of space-time difference (shown shaded
in Fig. 8) in the regions where the two space-times in superposition differ from one
another by an amount of order unity when measured in Planck units (i.e. taking c=¯
h=
G=1). Thus the instability that results in just one of the space-time branches surviving
sets in at the kind of scale when the space-time difference is of order unity. This
measure of space-time difference is calculated according to the standard symplectic
measure that can be estimated by considerations of linearized gravitational theory see
[11].
Another, rather more rigorous, way of obtaining the τ≈¯
h/EGestimate is to
appeal to the principle of equivalence see [15] which is the basic foundational prin-
ciple of general relativity. Let us first imagine a table-top quantum experiment being
performed, and we wish to calculate the wavefunction of the quantum system under
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Fig. 8 Decay after Planck-scale difference geometry measure
consideration, so that Schrödinger’s equation can then be used to calculate the time-
evolution of this state. In this particular case, we are interested in taking the Earth’s
gravitational field into consideration. We may envisage two different procedures for
doing this (illustrated in Fig. 9). The first (with the green coordinates) would be the
conventional quantum physicist’s approach, where we simply include a term in the
quantum Hamiltonian representing the Newtonian potential of the gravitational field,
where we are just treating the gravitational field as providing an “ordinary force” in
the same way that we would for any other force (such as an electric or magnetic force).
This procedure gives us what I shall call the Newtonian wavefunction ψ(written in
green in Fig. 9). The second procedure is more in the spirit of Einstein’s general
relativity, where we imagine doing our quantum mechanics in a freely falling frame
(purple coordinates), and in this frame there is no gravitational field, the accelerated
fall cancelling it out, and our Einsteinian wavefunction (written in purple in Fig. 9),
described in terms of these free-fall coordinates, evolves according to a Schrödinger
equation whose quantum Hamiltonian has no term representing the gravitational field.
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Fig. 9 Principle of equivalence leads to phase difference
We would expect these two quantum evolutions to agree with one another—and,
indeed a famous experiment performed in 1975, by Colella, Overhauser and Werner
did confirm that Einstein’s principle of equivalence is indeed respected by quantum
mechanics in this respect. In fact, a direct calculation shows that the Newtonian and
Einsteinian wavefunctions are related to each other simply by one being a phase
multiple of the other. This multiple is explicitly shown in Fig. 9(outlined with a yellow
broken line), 3/4 of the way down the picture for the dynamics of a single particle,
and at the bottom of the picture for the dynamics of a system of many particles.
Now, surely, this shows that standard quantum mechanics is perfectly consistent
with Einstein’s equivalence principle, since an overall phase multiplier for the wave-
function ought not to affect the interpretation in terms of probabilities, when a mea-
surement (R) is performed on the system. However, there is an additional subtlety
here, because if we examine this particular phase factor we see that it contains a term
in t3in the exponent (with coefficient proportional the square g2of the gravitational
acceleration vector −→
g)where t(=T) is the time in both coordinate systems. Because of
this non-linear dependence of the phase factor on t, we find that the notion of positive
frequency differs in the two viewpoints (Newtonian and Einsteinian). Accordingly, the
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two different reference systems, the Newtonian one and the Einsteinian one, refer to
two different quantum field theory vacua.
The fact that physics in an accelerating frame is described by a different vacuum
from that in an unaccelerated one is familiar in relativity, where according to what is
called the “Unruh effect” [2,18] the accelerated vacuum is a thermal vacuum with a
temperature ¯
hg/2πck.(kbeing Boltzmann’s constant, etc.). Here, we are considering
the Galilean limit c→∞, so we see that the temperature goes to zero. Nevertheless,
the accelerated vacuum remains different from the unaccelerated one even in this limit,
although in this limiting case the accelerated vacuum is not a thermal one, but the phase
discrepancy between the Newtonian and Einsteinian wavefunctions agrees with that
shown in Fig. 9(confirmed in a private communication from B. S. Kay).
Although, strictly speaking, the notion of alternative vacua is a feature of quantum
field theory, rather than of the “Galilean” non-relativistic quantum mechanics that
is under consideration here, the issue has direct relevance to the latter also. Standard
quantum mechanics indeed requires that energies remain positive (i.e. that frequencies
remain positive). This is not normally a problem, because the quantum dynamics
governed by a positive-definite Hamiltonian will preserve this condition. But in the
situation arising here we appear to be forced into the prospect of its violation unless
the vacua are kept separate, the presence of the t3term coming about through the
adoption of the Einsteinian perspective with regrd to the gravitational field.
In the particular experimental situation just considered, where the gravitational field
is external and given, this difference in vacua is of no particular concern, since we
can use one or the other description consistently without any discrepancy between
the two choices of vacuum, as regards the results of measurement. But when the
gravitational field itself becomes involved in a quantum superposition, the issue is
more serious. In Fig. 10 I have illustrated this kind of situation, where a massive
sphere is placed in a quantum linear superposition of two separate locations. We are to
consider how quantum mechanics is to be used to treat this situation in accordance with
the (preferred) Einsteinian viewpoint. The problem now is that in order to describe this
superposition of gravitational fields, according to this viewpoint, we are confronted
with the problem of superposing states that relate to two different vacua.
Strictly speaking this is illegal, according to the rules of quantum field theory, as
the two states that are proposed to be under superposition belong to different Hilbert
spaces. The general problem that arises would be that when we try to form an inner
product between a state described in relation to one vacuum with a state described in
relation to a different vacuum, we tend to get a divergence which violates the very rules
that Hilbert spaces are supposed to satisfy (that inner products should be finite num-
bers), and for which the probability interpretation (Born rule) now makes nonsense.
Nevertheless, we might take the view that such things come about merely because
some mathematical idealization has been made (such as is the case for momentum
states, for example, which are, strictly, not Hilbert space members) and that if full
details of the situation are properly encoded, then such divergences would not occur.
But how are we to deal with this when the very Hilbert spaces are diiferent, so that
superpositions cannot actually be performed? An analogous situation might come from
some mathematical treatments of, for example, a superconductor, where one might
consider the superconducting state to be described in relation to a vacuum different
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Fig. 10 Displaced mass: illegal superposition of different vacua
from the standard one. Of course, if an actual physical superconductor were in a quan-
tum state belonging to a Hilbert space with a different vacuum from that of the Hilbert
space describing the system before the superconducting state were set up, then there
would be no way to build a superconductor, since transitions from one Hilbert space
to another, each with a different vacuum, would be “against the rules” of standard
quntum field theory.
In the case of our superposed states of displaced massive spheres, we must imag-
ine that the “illegality” in performing the superposition between states from different
Hilbert states would take some time (≈τ) to make itself manifest in the physics. It
has been hard, so far, to see how to make this completely unambiguous, but it seems
that one can make a preliminary estimate by applying the Heisenberg time-energy
uncertainty principle, rather in the way that this is done for a radioactive nucleus.
For such a nucleus, there is a (mass-energy) uncertainty that is in reciprocal relation
to its lifetime. Here the argument is similar (the converse of this), where we pro-
pose to estimate a superposition’s lifetime from a fundamental energy uncertainty
that it necessarily possesses by virtue of the clash between the general-relativistic and
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quantum principles that are being invoked in relation to the description of stationary
gravitational fields in quantum linear superposition. We can try to estimate the error
that is involved in trying to form a stationary state out of the superposition of loca-
tions, where we take the view that the divergences involved in the superposition will
come about from the coefficient of t3in the “discrepancy” phase factor that we see in
Fig. 10, namely
(M/3¯
h)(
−→
g2−−→
g1)2.
If we take the integral of this expression over space, at one moment of the time t(=T),
as a measure of this error, then we obtain the quantity EGdescribed earlier (the grav-
itational self-energy of the difference between the two mass distributions involved.
(See [12] for this derivation and for an alternative motivation for this energy uncer-
tainty.) When EGis substituted into Heisenberg’s time-energy uncertainty formula,
we get the aforementioned estimate of the lifetime of such a superposed state, before
it spontaneously decays into one alternative or the other.
One point should be made clear about this proposal [3,4,11,12], namely that all R
processes of state-reduction are to be the result of actions of this gravitational proposal.
In a deliberate measurement by means of a conventional quantum detector, Rwould
be triggered by some movement of mass within the detector, sufficient to reduce the
state within a very small period of time ∼τ. In other situations, where there is no
deliberate measurement of the quantum system, but some considerable entanglement
with an extended random environment, the major mass displacement would likely
come about from the mass displacement of material within that environment, so when
the environment state collapses to one or the other so does that of the quantum system
itself, because the two parts, being entangled, both reduce together. This makes contact
with the point of view whereby Ris deemed to occur via environmental decoherence,
but now we have a clear ontology of an objectively real reduction of the quantum state,
and we do not have to appeal to some vague concept of the environmental degrees of
freedom being, in some sense, “unobservable”.
In order to get an impression of the role of EGwe can first think of the case of
a solid spherical ball of radius a, made from some uniform massive material of total
mass m, where the ball is in a superposition of two locations, differing by a distance
b. See Fig, 11. We use a Newtonian calculation to work out the value of EG, obtaining
the expression depicted in the figure. The only point of particular relevance here, in
this expression, is the fact that for a displacement successively from coincidence to
contact of the two instance of the sphere, the value of EGis already nearly 2/3 of the
value it would reach for a displacement all the way out to infinity. Thus, for a uniformly
solid body like this, we do not gain much by considering displacements in which the
two instances of the body are moved apart by a distance of more than roughly its own
diameter.
Of course, ordinary material is not really uniform in mass distribution, like this,
but consists of huge numbers of nuclei where most of the mass is concentrated, where
we might try to consider that the actual mass distribution is distributed among precise
point-like locations of the quarks and electrons—marked in brown, in the middle of
Fig. 12. However, when we then try to calculate EGby considering a very slightly
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Fig. 11 Newtonian self-energy for displaced uniform balls
shifted mass distribution, taking the difference between the two (the mass difference
distiribution indicated by the brown–green difference shown in Fig. 13), then we get
an infinite answer if the mass distributions are actually taken as the delta functions
representing these point-particle locations. Such an infinite answer for EGwould give
azero decay time, in other words an instantaneous reduction of any superposed state
of actual material—and we would have no quantum mechanics!
Clearly this is not the correct answer, and indeed the procedure has not been carried
out correctly, because (as noted earlier) the procedure of calculating EGapplies only
when each of the two states in superposition is actually stationary. A state involv-
ing delta function mass distributions like this would not be stationary, according to
Schrödinger’s equation, since the delta-function mass distributions would instantly
spread out from these locations. What we need to do is first to solve the stationary
Schrödinger equation for the material in our object. Even this would lead to a nonsense,
however, if carried out strictly, for an actual stationary state, since such a state would
have to be spread out over the entire universe, and we would now get the opposite
problem of obtaining a zero answer for EG.
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Fig. 12 Different models of mass concentration
What one tends to do, in practice, when considering the wavefunction of a stationary
state is to factor out the mass centre, regarding the wavefunction to be concerned with
distances relative to the mass centre. This procedure is a little artificial, and one can
adopt the more systematic procedure of modifying the Schrödinger equation in the
form of the self-coupled “Schrödinger-Newton equation”, for a wavefunction ψ, which
incorporates an additional term in the Hamiltonian, that is given by the gravitational
potential due to the expectation value of the mass distribution in ψitself see [10,13].
The “Newton” term prevents the stationary solutions from being infinitely spread out.
In situations of relevance here, to a reasonable enough approximation, this amounts to
the aforementioned procedure of factoring out the mass centre, and then just solving the
Schrödinger equation. This saves us from having to solve the non-linear Schrödinger-
Newton equation in detail in order to calculate EG. On the other hand, incorporating
the Schrödinger-Newton equation has another theoretical importance in also providing
the possible stable stationary states to which a quantum superposition can reduce by
the operation of R.
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Fig. 13 Different models of displaced mass concentrations
It might be presumed, since we are looking at space-time differences whose mea-
sure is of the order of the extremely tiny Planck scale, that nothing of observable
consequence would be likely to come from considertions of this kind. Indeed, experi-
ments aimed at testing the influences of quantum mechanics on space-time structure—
the presumed consequences of “quantum gravity” in the usual interpretation of that
term—would be enormously far from what can be achieved by current technology.
However, we are here concerned with the role of gravitational principles on the struc-
ture of quantum mechanics, not the other way about, where the experimental situation
is very different. One way of looking at this issue is to realize that the scales at
which quantum mechanics is expected to influence space-time structure would indeed
be the absurdly tiny Planck length (¯
hG/c3)1/2≈1.6×10−35m and Planck time
(¯
hG/c3)1/2≈5.4×10−44s, these being so very tiny, compared with ordinary scales,
because they involve dividing a very small quantity by a very large one. However, the
quantity of relevance to our considerations of the “gravitization of quantum mechan-
ics” under consideration here is τ≈¯
h/EG,which is one very small quantity divided
by another very small quantity (since EGis scaled by the gravitational constant), which
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Fig. 14 Bouwmeester experiment (schematic)
need be neither very small nor very large. Accordingly, one must examine the quanti-
ties involved in any proposed experiment very carefully, to see whether the time scale
τturns out to be one that comes within the scope of the experiment being envisaged.
In Fig. 14, I have sketched the rough idea see [9] underlying an experiment that has
been under development by Dirk Bouwmeester and colleagues, at the Universities of
Leiden (Netherlands) and California (Santa Barbara, CA, USA), for several years now,
where a tiny cubical mirror (∼10−5m in dimension) is to be put into a superposition of
two different locations, differing from one another by about the diameter of an atomic
nucleus. This is to be achieved by multiple impacts (∼106of them) by a single photon,
which has been beam-split into a quantum superposition of two alternative routes, in
only one of which the photon hits the tiny mirror. This mirror is to be maintained in
its superposed state for seconds or perhaps up to minutes which, depending on the
details, might be a sufficient time τfor the decay of the superposition to take place
(according to the aforementioned state-reduction proposal). This spontaneous state
reduction could be tested by subsequently reversing the photon routes, and observing
whether there is consequent lack of phase coherence between the two branches of the
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Found Phys (2014) 44:557–575 575
beam-split photon, such breaking of phase coherence leading to the possible activation
of the detector at the top of the picture. Clearly there are enormous difficulties in
eliminating unwanted possibilities of decoherence, etc., but there appears to be a
reasonable prospect of a result from experiments of this kind within the next decade.
Open Access This article is distributed under the terms of the Creative Commons Attribution License
which permits any use, distribution, and reproduction in any medium, provided the original author(s) and
the source are credited.
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