### Physics

Author: A.C. Elitzur, S. Dolev

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\begin{document}

\title*{

Quantum Phenomena within a New
Theory of Time

}

\author{Avshalom C.
Elitzur\inst{1} \and Shahar Dolev\inst{2}}

\institute{Unit of
Interdisciplinary Studies, \\

Bar Ilan University, Ramat-Gan,
Israel \\

\texttt{avshalom.elitzur@weizmann.ac.il}

\vspace{4mm}

\and Edelstein Center for the
History and Philosophy of Science, \\

Hebrerw University, Jerusalem,
Israel \\

\texttt{shahardo@cc.huji.ac.il}}

\maketitle

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{\em A few discontents in
present-day physics' account of time are pointed out, and a few novel
quantum-mechanical results are described. Based on these, an outline for a new
interpretation of QM is proposed, based on the assumption that spacetime itself
is subject to incessant evolution.}

\vspace{4mm}

In a few crucial passages in the
history of physics, seemingly-unrelated riddles turned out to merely reflect
different facets of the same phenomenon. Such, we submit, may be the lot of the
quantum oddities on the one hand, and the elusive nature of time on the other.

Our path to this hypothesis went
through puzzling over several physical issues, which we shall first recount in
the following chapters before describing our findings and proposing our theory.
Chapter \ref{ch:time-pecu} briefly introduces the two old enigmata of time's
apparent transience and asymmetry. Chapters
\ref{ch:indeterminism}-\ref{ch:asym-rime} point out a simple argument for an
intrinsic time arrow. Chapter \ref{ch:adv-action} briefly introduces the
Advanced Action interpretations of QM and their implications. Chapters
\ref{ch:inconsistent}-\ref{ch:q-liar} describe some novel experiments that seem
to indicate that the wave function evolves in a way that defies ordinary
notions of space and time. Chapter \ref{ch:hypothesis} proposes an interpretation of these findings, which in
chapters \ref{ch:outline} we broaden to a sketchy outline of a new theory of
spacetime.

\section {Two Peculiarities of
Time: Transience and Directionality}

\label{ch:time-pecu}

Ordinary experience notoriously
clashes with physical theory with respect to time. We keep feeling that time
``goes by," that there is a special ``Now" moving from past to
future, and that future events are born anew out of the present. These
characteristics of reality are referred to as ``Becoming." Yet theoretical
physics dismisses this so-natural impression as mere illusion, and for good
reasons. Time is the {\em parameter} of all motion and change; ascribing motion
or change to time itself is bound to run into absurdities. For example, if time
flows, or if the ``Now" moves, how fast is this motion? To apply such
terms to time would entail a higher time parameter, which would in turn
necessitate a yet higher time and so on {\em ad
infinitum}. The vast literature on this issues (see e.g.
\cite{Isham96,Atmanspacher97} and references therein) makes it clear why the
overwhelming majority of physicists have avoided this line of thinking
altogether, opting instead for the simple and self-consistent ``tenseless"
account, which has culminated in relativity theory. Time, by this account,
constitutes the fourth dimension, alongside with the three spatial ones, of
spacetime. All events -- past, present and future -- coexist along time, just
as different sites coexist along space.

It should be stressed that this
``Block Universe" picture is not just an interpretation of relativity
theory but an integral part of it,\footnote{Even Einstein himself \cite[p.
151]{Zeh89} has regarded the absence of the moving Now in his theory as ``a
matter of painful but inevitable resignation.''} for even familiar relativistic
effects such as length contraction entail it. Consider the following exercise,
which may be regarded as the spatial analogue of the ``twin paradox." A
spaceship of length $L_0$ passes at near-{\it c} velocity through a space
tunnel of the same length. From the tunnel's reference frame, the spaceship's
length is contracted to

\beq

L=L_0\sqrt{1-\frac{v^2}{c^2}}

\eeq

due to its motion, hence there
is a certain time interval during which the tunnel's two gates can be briefly
shut while the entire spaceship travels within the tunnel.

From the spaceship's reference
frame, however, it is the tunnel that contracts, hence at no time can the
entire spaceship reside within it, let alone with the two gates shut!

\begin{figure}[h]

\centering

\includegraphics[scale=0.41]{graphics/rest.eps}

\caption{Different relativistic
reference frames give different accounts: (a) the spaceship and the tunnel are
of equal length when in relative rest; (b,c) conflicting accounts arise due to
the spaceship's and the tunnel's relative motion.}

\label{fig:rest}

\vspace{30pt}

\includegraphics[scale=0.41]{graphics/frames.eps}

\caption{From what seems to be
an objective four-dimensional set of events, the spaceship's reference frame
picks $(x_1, t_1)$ and $(x_2, t_3)$ as simultaneous, while for the tunnel
$(x_1, t_3)$, $(x_2, t_1)$ are simultaneous.}

\label{fig:frames}

\end{figure}

The two conflicting accounts are
compatible only because the two events -- {\it i}) the entering of the
spacecraft's rear through the tunnel's entrance, followed by the entrance
gate's shutting, and {\it ii}) the emergence of the spacecraft's front from
tunnel's exit, following the exit gate's opening -- occur in opposite time
sequences for the two reference frames (Figs.~\ref{fig:rest},
\ref{fig:frames}). In the relativistic framework, then, the only objective
elements are the two {\em world-lines} of the spacecraft and the tunnel,
extending from past to future, while the ``now" plane is observer
dependent.\footnote{Notice that even the familiar temporal ``twin
paradox," when resolved within special relativity without appeal to acceleration, is achieved by employing
different ``now" planes for the two observers \cite{Bohm65}.} This
``tenseless" picture is even more pronounced in general relativity, where
the reciprocal effects of mass and spacetime on one another presuppose the
objective existence of a 4-D spacetime. Time's geometric aspect is pronounced
even more strongly in several exotic solutions of relativity that allow
spacetime tunnels and closed timelike loops. Relativity, then, allies with
basic logic in dismissing time's passage.

Similarly dismissive is
mainstream physics towards the other distinctive property of time, namely, its
apparent {\em directionality}. In this respect too, time radically differs from
the spatial dimensions: There is no universal ``south" or
``up"\footnote{True, weak interactions do not conserve parity, therefore
mirror images of the same physical process are not always equally probable.
Nevertheless, there are still no absolute directions of space.}. Not so with
time, as ``past" and ``future" strongly differ everywhere in the
universe, due to the second law of thermodynamics. Most physicists, however,
belittle this directionality by pointing out that physical law itself is
$T$-invariant. Hence, as nearly all microscopic interactions are time-symmetric,\footnote{Only ``nearly all.'' The $CP$
violation exhibited by weak interactions entails, by $CPT$ invariance, a basic
$T$ violation too. ``It is hard to believe," says Penrose \cite[p.
583]{Penrose79}, ``that Nature is not, so to speak, `trying to tell us
something' through the results of this delicate and beautiful experiment."
Hear, hear!} the second law is often denied the status of a real law.
Irreversibility, so goes the argument, occurs only in {\em ensembles} of
particles, hence it may merely reflect the universe's initial state, which, for
some reason, happened to be highly ordered. One could equally conceive of a
universe whose initial state was totally disordered but which, by the same
$T$-invariant laws, gradually becomes {\em
ordered} in time.\footnote{In fact, due to the ergodicity of physical laws, a
universe with any initial condition, given a long enough period of time, will
reach both entropy increasing and entropy decreasing phases. But the huge
amount of astronomical and other scientific observations are all compatible
with the proposition that the universe was created some thirteen billion years
ago, a period much too short for the spontaneous occurrence of
entropy-decreasing phases.}

It is a very impressive feature
of mainstream physics' position that these two negative assertions -- {\em i})
dismissing time's passage as illusion and {\em ii}) dismissing time's arrow as
an artifact of the initial conditions -- neatly accord with one another. If the
universe is a four-dimensional collection of equally-existent events, with no
privileged ``Now," then both readings of its history are equally valid.
Entropy increases {\em as well as decreases} with time, depending on whether
the observer chooses to read the universe's history forwards or backwards!
Whether one likes this account or not, it is admittedly coherent and paradox-free.

Yet, a few dissenting voices are
heard, most notably Davies \cite{Davies74}, and for convincing reasons too. To
believe that even {\em future} events, including all actions what we may decide
to take, ``already" exist in time, just as other places exist in space, is
very awkward. True, intuition has often proved deficient by modern physics, but
it should not be dismissed off-hand. Our immediate perception of time might be
directly sensing an inherent feature of it that has not yet found its place in
the formalism. Even relativity theory indicates that time differs from the
spatial dimensions in some yet-unclear way: It bears the imaginary sign. Why,
in Minkowski's equation

\beq

\Delta s^2=\Delta x^2 + \Delta
y^2 + \Delta z^2 - \Delta t^2 ,

\eeq

is $t$ assigned the minus sign?
Relativity simply {\em presupposes} rather than explains this difference
between $t$ and its three counterparts.\footnote{The question may be better put
this way: Why can world-lines extend only in a timelike, never a spacelike
fashion? The answer would be that the speed of light must never be exceeded,
but as Sudarshan \cite{Bilaniuk62} has shown, relativity does not forbid the
existence of tachyons, whose world-lines would be spacelike. Why, then, are
such entities never observed?}

But if the conventional
dismissal of time's directionality is congruent with the dismissal of its
transience, wouldn't a loophole in the former challenge the latter? Such a
possible loophole is discussed next.

\section {Indeterminism Entails
an Intrinsic Time-Asymmetry}

\label{ch:indeterminism}

\begin{figure}[tb]

\centering

\includegraphics[scale=0.85]{graphics/fig1a.eps}

\caption{A computer simulation
of an entropy increasing process, with the initial and final states (right) and
the entire process using a spacetime diagram (left). One billiard ball hits a
group of ordered balls at rest, dispersing them all over the table. After
repeated collisions between the balls, the energy and momentum of the first
ball is nearly equally divided between all the balls.}

\label{fig:sim.inc}

\end{figure}

\begin{figure}[tb]

\centering

\includegraphics[scale=0.85]{graphics/fig1b.eps}

\caption{The time-reversed
process. All the momenta of the balls are reversed at {\it $t_{350}$}.
Eventually, the initial ordered formation is re-formed, as at {\it $t_{0}$},
ejecting back the ball that has initiated the original process.}

\label{fig:sim.dec}

\end{figure}

It is embarrassing to observe
how rarely the vast literature on time's arrow (See, e.g.,
\cite{Price96,Albert00}) refers to the closely related issue of determinism.
Are the basic interactions between particles truly random, or is information
always preserved at some smaller level? This issue is crucial, as it
straightforwardly bears on the origins of irreversibility. We shall point out
this bearing first, and in the next chapter discuss determinism itself.

Recall again the conventional
approach: The second law is not a real law but a mere fact -- albeit
ill-understood -- about the beginning of the universe. ``What needs to be
explained is the low-entropy past, not the high-entropy future -- why entropy
goes down towards the past, not why it goes up towards the future'' \cite[p.
262]{Price96}. One could, so goes the argument, conceive of a closed system,
such as the entire universe, where the initial conditions lead to increasing
{\em order}. All that such an evolution takes is that the system's particles
would be pre-arranged with the appropriate precise correlations that would
ensure their later convergence into increasingly ordered states.

There is, however, a crucial
difference between the normal, entropy increasing evolution, and the
time-reversed, order increasing one. {\em The latter, not the former, requires
an infinitely precise pre-arrangement of all the system's elementary
particles}. Consequently, when setting a system to evolve into a lower entropy
state, and given sufficiently many interactions between the system's
constituents, any failure of a state to precisely determine the consecutive
state will ruin the increase of order. Boltzmann's entropy measure,

\beq

S=k \ln W,

\eeq

is based on the trivial
arithmetic fact that there are countless non-special microscopic arrangements
that make disordered states, while very few, special arrangements make ordered
ones. So, if nearly every initial arrangement will eventually give rise to
entropy increase, then any interference following such an initial state is very
unlikely to alter this destiny. Not so for the few initial arrangements that
lead to order increase: They can give rise to eventual order only if nothing
interferes with their later evolution.

Fig.~\ref{fig:sim.inc} shows the
results of a computer simulation of an ensemble of billiards balls. In the
initial state, the balls are ordered and all the momentum is concentrated in a
single ball that hits them. The consequent evolution of the system takes it to
a higher entropy state, where the balls are scattered and the momentum is
evenly distributed amongst them. Fig.~\ref{fig:sim.dec} shows the development
of a very unique initial state, which looks disordered but its consequent
evolution takes it to an ordered state. So far so good. Now we introduced a
small random disturbance into the progression of the two systems. Allowing the
entropy-increasing system to evolve (Fig.~\ref{fig:sim.inc.interrupted}), the
disturbance causes only an insignificant shift in its
destiny, from one high-entropy configuration to another, practically
indistinguishable one. Not so with the time-reversed process
(Fig.~\ref{fig:sim.dec.interrupted}): The slightest variation in the position
or momentum of a single particle creates a disturbance in the system's
evolution that -- given sufficiently many interactions between the particles --
further increases as the system evolves. Consequently, entropy increases in the
time-reversed system too.\footnote{The ergodicity argument can be raised here
too: In an indeterministic but ergodic system, given long enough time, the
system will display both entropy increase and decrease. One might therefore
argue that the universe's relatively ordered state at present is due to a mere fluctuation, within which all our scientific
observations just happen to comply with a systematic physical theory. No need
to bother to refute such a possibility as, by the laws of probability, it is
susceptible to a powerful {\em reduction ad absurdum} into solipsism: It is
much more probable that it is only the reader's brain state, rather than the
entire universe or even a part of it, is the result of such a unique
fluctuation.}

\begin{figure}[tb]

\centering

\includegraphics{graphics/fig2a.eps}

\caption{The same simulation as
in Fig.~\ref{fig:sim.inc}, with a slight disturbance in the trajectory of one
ball (marked by the small circle). Entropy increase seems to be
indistinguishable from that of Fig.~\ref{fig:sim.inc}. }

\label{fig:sim.inc.interrupted}

\end{figure}

\begin{figure}[tb]

\centering

\includegraphics{graphics/fig2b.eps}

\caption{The same computer
simulation as in Fig.~\ref{fig:sim.dec}, with a similar disturbance. Here, the
return to the ordered initial state fails. }

\label{fig:sim.dec.interrupted}

\end{figure}

The relevance of this
observation to the origins of irreversibility is immediate \cite{Elitzur99a}:
Had physics been able to prove that determinism does not always hold -- that
some interactions are genuinely probabilistic -- it would follow that entropy
{\em always} increases, regardless of the system's initial
conditions.\footnote{For many years, Hawking has been claiming that unitarity
is lost during black hole evaporation. At the same time he has been maintaining
that the thermodynamic asymmetry is only due to the universe's initial
condition. We have pointed out the contradiction between these two assertions
\cite{Elitzur99b}. Interestingly, Hawking recently recanted his unitarity loss
hypthesis \cite{Hawking04}.} An intrinsic
time arrow would then emerge in {\em any} closed system under {\em whatever}
initial conditions, congruent with the time arrow of the entire universe, of
which closed systems are supposed to be shielded.

\section {``Hidden-Variable
Theories" are ``Forever-Hidden-Variable Theories"}

In other words, if God plays
dice, irreversibility is inherent to nearly any process. But {\em does} he? QM
is the natural place to look for an answer.

QM's bearing on the issue can be
summarized with three observations: {\em i}) The Schr\"odinger equation is
deterministic and works perfectly well for the pre-measured state. {\em ii}) It
fails miserably once the state is measured, observed or interacts in any other
way with the environment, whereby superposition gives its place to one out of
the many equally-possible states. {\em iii}) This new, ``collapsed'' state is
not known to be causally determined by the pure state that preceded the
instance of measurement. For example, when the spin superposition

\beq

\Psi = \ket{\uparrow} +
\ket{\downarrow}

\label{eq:superposition}

\eeq

gives its way, upon measurement,
to either \ket{\uparrow} or \ket{\downarrow}, nothing in the original state is
known to have determined the outcome. Indeterminism, therefore, seems to sneak
in during this transition.

The uncertainty principle
further stresses this causal void in the pre-measurement state. Intuitively, a
tradeoff like

\beq

\Delta x\Delta p \geq \hbar/4\pi

\eeq

which assigns a constant degree
of uncertainty to the measurement of certain pairs of variables, suggests that
there is a certain {\em ontological} indeterminacy, rather than mere {\em
epistemological} ignorance, to many physical variables. Indeed, the double-slit
experiment -- the best visual demonstration of this position-momentum tradeoff
-- shows that, when the photon/electron wave function passes through the
partition, the position is not merely unknown but, genuinely, ``smeared'' over
space, enabling it to gauge both slits at the same time. Momentum, in turn, is
similarly ``smeared'' when the position is accurately measured.

Ironically, it was the
discoverer of the uncertainty principle that seemed not to have fully grasped
its profoundness. The conceptual device known as ``Heisenberg's
Microscope" \cite{Heisenberg27} turned out to be insufficient for
explaining the true nature of the uncertainty. It only showed that the measurement's
influence prevents accurately measuring the particle's position and momentum at
the same time. To see that there is more to quantum uncertainty, consider the
EPR-Bell experiment \cite{Bell64}. This setup seems to indicate that the
variables are not only unknown but {\em do not exist} before measurement. The
symmetry under rotation of the singlet state

\beq

\Psi =
\frac{1}{\sqrt2}(\ket{\uparrow}_1\ket{\downarrow}_2 -
\ket{\downarrow}_1\ket{\uparrow}_2)

\label{eq:singlet}

\eeq

implies that the two particles
lack definite spin values, not only in the $z$ direction but in all other
directions as well. And indeed the experimental violations of Bell's inequality
showed that the two particles' spins could not have have been fixed prior to
the measurement. The simplest conclusion, therefore, is that, if
Eq.~(\ref{eq:singlet}) does not give any preference for either the ``spin-up''
or ``spin-down'' outcomes, then such a preference simply does not exist. Each
particle's spin is probably determined {\em de novo} at the instant of
measurement, thereby forcing the opposite direction on the other particle.

Determinism, however, proved to
be too precious to be given up by all physicists. A survey of the
interpretations of QM \cite{Elitzur95} shows that about half of the
interpretations preserve determinism in some form of hidden variables or
parallel universes, which supplement the superposition of Eqs.
(\ref{eq:superposition}, \ref{eq:singlet}) with some additional variables.
These variables are believed to non-locally determine the results of
measurements performed on the particles. Even radical new models, such as
'tHooft's (this volume) and Smolin's (this volume), go to great length to
preserve determinacy by assuming hidden variables of one kind or another.

But can these models be
scientifically proved? We have a serious concern that research on this issue
might go astray for many years, claiming numerous years of futile labor, in
search of something that may, {\em a priori}, be undetectable. Consider again
the above EPR-Bell proof against local realism. While it has lead several
authors to abandon the idea of hidden variables altogether, many others
(including Bell himself) kept envisioning {\em nonlocal} hidden variables
instead. What these models basically assume is that the two particles leave the
source not superposed but with some pre-existing values of the hidden variables
which carry on a common context for both particles' spins. Then, upon
measurement of one particle, this shared context affects the result of the
measurement performed far away on the other particle. Now, to the extent that
these models are fully deterministic, they assume that even this change of the
spin, brought about by the measurement, obeys causal laws. But here a simple
question aught to be raised: Can such hidden variables ever be observed? A
simple analysis can show that, {\em if quantum nonlocality is not buffered by
indeterminacy, relativity must be empirically violated}.

This conclusion is quite
straightforward, yet its bearings have seldom been explored. Elitzur
\cite{Elitzur92a} has pointed out that the three basic no-no's of theoretical
physics -- {\em i}) the quantum-mechanical impossibility of predicting a
measurement's outcome, {\em ii}) the relativistic prohibition on superluminal
velocities, and {\em iii}) the thermodynamic unlikelihood of a closed system's
entropy to decrease -- intriguingly preserve one another, such that violation
of one principle leads to violations of the two others.

The argument, however, was
qualitative, failing to give a rigorous proof. Yet an indirect support for it
came from a work that has made an opposite claim. Valentini
\cite{Valentini02a,Valentini02b} boldly suggested that the relativistic
impossibility of superluminal velocities is merely due to entropy increase at
the quantum level which has ``scrambled" the quantum hidden variables,
making them akin to ``noise." He went on to suggest that if a technique is
developed to distill a handful of particles in a low-entropy state, these
particles could be used, for example, to instantaneously transmit information
through the singlet state. The relativistic upper limit of $c$ was thus
rendered ``fact-like" rather than ``law-like," just like the second
law of thermodynamics. This is a far-reaching hypothesis, with the added merit
of being testable. For our purpose it should be noted that it reaffirms that,
once quantum nonlocality is not buffered by indeterminacy, violations of
relativity are bound to occur.

We, however, believe that the
laws of relativity -- so simple, coherent, and, well, so beautiful -- reflect
something very profound about physical reality rather than being only a
consequence of noise. Similarly for quantum uncertainty: It is more likely to
be conveying some fundamental aspect of causality than to be merely reflecting
a technical limit of measurement. Indeed, the Bekenstein-Hawking
\cite{Bekenstein74,Hawking74,Hawking75} and the Unruh \cite{Unruh76} effects
seem to indicate that QM, relativity and thermodynamics are related in some
yet-unfathomed ways. Most likely, therefore, the next revolution in physics
will be a theory that will incorporate relativity and QM as important
ingredients.

So, although there is no clear
resolution at present to the issue of (in)determinism, our conclusion stands:
{\em For any future theory in which relativity theory will be an integral
ingredient, hidden variables must remain forever unobservable}. This places
these entities in a position that is much more problematic than that of the
ether. A physical theory based on entities, the detection of which is {\em
forbidden} by the theory itself, belongs rather to the realm of
religion.\footnote{In order to better assess the theoretical impasse involved
with hidden variables within a relativistic theory, consider the status of
quarks in particle physics. Quarks too cannot be directly observed, due to
their confinement. Yet particle physics has pointed out several predictions
that follow from the existence of quarks and are unaccountable in any theory
that does {\em not} make this assumption. These predictions have so far been
verified. No such a falsifiable prediction is proposed by the hidden variable
theories.}

\section {An Interim Conclusion:
Time is Intrinsically Asymmetric}

\label{ch:asym-rime}

To summarize the issue of time
asymmetry, the evidence we can point at is admittedly circumstantial, but seems
fairly compelling. It is reasonable to say that:

\begin{enumerate}

\item QM implies an
indeterminacy in any interaction in which a quantum system interacts with the
environment.

\item To the extent that this
indeterminacy is only apparent and deeper hidden variables underlie it, then,
by relativity theory, these variables must never be detected.

\item A theory based on {\em
absolute} unobservables is unscientific. Indeterminism, therefore, is a
simpler, hence perhaps ontologically better description of Nature.

\item But if any
measurement-like interaction is truly indeterminate, then an intrinsic time
asymmetry, independent of initial conditions, must be inherent to any process
in which such an interaction of a quantum system with the environment is
present.

\end{enumerate}

This argument for time asymmetry
reopens the issue of time transience. If determinism does not hold, then
mainstream physics can no longer boast the consistency between denying time
transience and dismissing time asymmetry, pointed out at the end of section
\ref{ch:time-pecu}. In a universe not strictly governed by determinism, one
reading of the universe's history -- initial order gradually giving way to
increasing entropy -- is perfectly reasonable, while the time-reversed account
-- high entropy gradually converging into order -- is absurd or even
solipsistic. In other words, in the absence of a proof for determinism, we have
no reason to believe that the future ``already" exists, causally
determining the universe's present and past. The person-in-the-street picture
of Becoming, in which the future is ontologically inexistent, to be genuinely
created anew, regains credibility.

We shall next offer some new
quantum-mechanical evidence in favor of this apparently-\naive view.

\section {The Advanced Action
Hypothesis}

\label{ch:adv-action}

It is again to QM that we turn
in search for new insights into the nature of time. Aharonov (\cite{ABL64} and
this volume) and later Cramer \cite{Cramer86} proposed two very appealing
interpretation of QM (``the two vector formalism" and ``the transactional
interpretation," respectively) that, for the purpose of the present
discussion, can be taken as one model, henceforth dubbed ``the Advanced Action
(AA) hypothesis." The adjective ``Advanced'' is {\em i}) in compliance
with physicists' caprice convention that refers to retroactive action as ``advanced"
and to normal action as ``retarded," and {\em ii}) to disclose our
personal bias in favor of this idea. The noun ``hypothesis" further
conveys the hope that this interpretation may eventually yield testable
predictions.

According to the AA, any quantum
interaction is brought about not by one wave function but by the combined
effect of two (or even more) waves, going back and forth in time. The initial
wave goes from the source to the future absorber(s), such as measuring device,
observer, etc. (one or more), while the reciprocal, ``advanced", waves(s)
return to the source backwards in time.

\begin{figure}[tb]

\centering

\includegraphics[scale=0.75]{graphics/zigzag.eps}

\caption{AA in EPR experiment:
After the emission of the particles at the EPR source (1), a measurement occurs
at one of the detectors (2). The effect of the measurement then returns back to
the EPR source along the past world-line of the particle (3) from there it
follows the other particle's world-line to inform it of the change in the state
(4). }

\label{fig:zigzag}

\end{figure}

The famous EPR experiment
provides a quick demonstration of AA's elegance: The measurement of one
particle affects not only that particle's state at the moment of measurement
but also all its previous states -- indeed its entire world-line right down to
the source -- and then zigzags back to
the other particle up to the present (Fig.~\ref{fig:zigzag}). Cramer
\cite{Cramer86} has systematically applied the AA for explaining a vast range
of quantum-mechanical peculiarities (see \cite{Kastner04} for a recent
perspective, and also \cite{Elitzur90} for some novel information-theoretic
advantages of this model).

As revolutionary as AA is,
however, Cramer \cite{Cramer86} stresses that his interpretation of QM is just
that, namely, an interpretation, not a theory, and hence yields just the same
predictions as the quantum formalism itself. He furthermore endorses the
standard Block Universe picture of time. It is within a ``static"
(Cramer's term) four-dimensional spacetime that the mutual ``transactions"
between past and future events take place.

In contrast, Aharonov, while not
proposing predictions that differ from those of quantum theory, still derives
from AA predictions that would probably have never been predicted within
another theoretical framework. He is even more unorthodox in his approach to
the nature of time, stating -- although so far only in personal communication
-- that his interpretation entails a true dynamics of spacetime itself. Every
instant in time within a quantum process, he believes, is visited twice: First
by the forward propagating wave function and then by the complimentary one.

It is here that we would like to
go a step further. In the next chapters we propose two experiments whose
predicted results, as obliged by QM and inspired by AA, strongly clash with
ordinary notions of space and time. On the basis of these experiments, we shall
follow Aharonov's vision of AA within a theory that ascribes genuine dynamics
to spacetime itself.

\section{When one Quantum Object
Measures another: Inconsistent Quantum Histories}

\label{ch:inconsistent}

\begin{figure}

\begin{center}

\includegraphics[scale=0.6]{graphics/ifm.eps}

\caption{Interaction Free
Measurement. $BS_1$ and $BS_2$ are beam splitters. In the absence of the
obstructing bomb, there will be constructive interference at path c (detector
clicks) and destructive interference on path d (no click).}

\label{fig:ifm}

\end{center}

\end{figure}

The oddities of QM, whether in
the form of real experiments or conceptual paradoxes, are many and famous, such
as the ``double-slit,'' the ``delayed-choice,'' the EPR and
Schr\"odinger's cat. They are paradoxical in that they point out
inconsistencies between QM and classical physics, especially relativity. In
this chapter and the next we present a new family of thought
experiments\footnote{In what follows we shall not bother to distinguish between
gedanken and real experiments. QM is so rigorous that no one expects a gedanken
experiment not to give the predicted result when performed in reality. And
indeed, most of QM's gedanken experiments have by now been successfully
performed.} that are paradoxical in a deeper sense: They derive from QM an
evolution that seems to be inconsistent with itself.

One origin of these experiments
may be found in Elitzur and Vaidman's \cite{EV93} Interaction Free Measurement
(IFM) (Fig.~\ref{fig:ifm}). Using a Mach Zehnder Interferometer (MZI) with an
object placed along its $v$ path, EV pointed out that, in 25\% of the cases, a
single photon traversing the MZI may end up in detector D, indicating that it
has been affected by the object on its $v$ path, yet, by the photon's very
arrival to BS2, it must have taken the opposite, $u$ path, otherwise it would
have been absorbed by the object. To make things more dramatic, EV took, as the
blocking object, a supersensitive bomb that can be detonated by a single
photon. Is it possible to know whether the bomb is good without detonating it?
Their device allowed saving 50\% of the bombs tested this way, a figure later
brought close to 100\% by a significant improvement proposed by Kwiat \etal
\cite{Kwiat95b}, who also carried out the experiment.

The essence of the EV device's
novelty lies in an exchange of roles: The quantum object, rather than being the
{\em subject} of measurement, becomes the measuring apparatus itself, whereas
the macroscopic detector (or super-sensitive bomb in the original version) is
the object to be measured. In their paper \cite{EV93}, EV mentioned the
possibility of an IFM in which both objects, the measuring and the measured,
are quantum objects, in which case even more intriguing effects can appear.

\begin{figure}

\begin{center}

\includegraphics[scale=0.6]{graphics/hardyifm.eps}

\caption{Mutual IFM, where the
``bomb'' is also quantum-mechanical.}

\label{fig:hardyifm}

\end{center}

\end{figure}

This proposition was taken up in
a few seminal papers by Hardy \cite{Hardy92a,Hardy93b,Hardy94}. In one paper,
the bomb was replaced by another superposed atom. Fig.~\ref{fig:hardyifm} gives
a short description of this experiment. A photon traverses an MZI. On one arm
of the MZI there is a spin $^1\!/_2$ atom prepared in a spin state $\ket{X+}$
(that is, $\sigma_x=+1$), and split by a non-uniform magnetic field $M$ into
its two $Z$ components. A box is then carefully split into two halves, each
containing either the $\ket{Z+}$ or the $\ket{Z-}$ part, while preserving their
superposition state. In other words, if the atom's spin in the Z direction is
``up'' it resides in one box and if it is ``down'' it is in the other. The
boxes are transparent for the photon but opaque for the atoms. The atom's $Z+$
box is positioned across the photon's $v$ path in such a way that the photon
can pass through the box and interact with the atom inside it in 100\%
efficiency. Then a photon is sent into the apparatus. This way, the photon and
the atom, so to speak, measure each other's position.

In 25\% of the cases, this
mutual measurement will be completed, with the result that the photon took the
$v$ path and the atom turned out to be in the intersecting box on that $v$ arm,
hence it absorbed the photon and went into an excited state. Let us discard
these cases. In another 50\% cases, a photon will end up in detector $C$. This
group gives no conclusive results, so let us ignore it too.

It is the remaining 25\% cases
that are the most curious. The photon ends up in detector $D$, indicating that
its $v$ path has been blocked and that it must have taken the $u$ path, but
this measurement has also ``collapsed'' the atom on the $v$ path. In other
words, the atom must always be found in the intersecting box.

Notice that this loss of the
atom's superposition is a real physical effect: Prior to the photon's passage,
the atom's two boxes could be reunited, and the atom's spin state $\ket{X+}$
could be measured and shown to be intact (This is quite analogous to the
interference effect). Not so after the photon has traversed the MZI! The atom's
position in the intersecting box is now certain and its $X$ spin consequently
becomes random. And yet, despite this physical effect exerted on the atom, the
photon, which is supposed to have caused this effect, seems to have taken the
opposite, $u$ arm!

Stimulated by this result of
Hardy, we began devising other setups in which several particles ``measure''
one another before the macroscopic detector completes the measurement. The
result is a few experiments in which the history they yield seems to be inconsistent.

\begin{figure}

\begin{center}

\includegraphics[scale=0.6]{graphics/threeMZI.eps}

\vspace{0.3cm}

\caption{One photon MZI with
several interacting atoms.}

\label{fig:atemp}

\end{center}

\end{figure}

In one experiment
\cite{Dolev00}, we have replaced Hardy's superposed atom on path $v$ by a row
of such atoms (Fig.~\ref{fig:atemp}). The result predicted by QM is that only
{\em one} out of the atoms, {\em not necessarily the first}, will lose its
superposition, while all the others will remain intact. In other words, all
atoms on path $v$ except one will preserve their $x$ spin when reunited.

Did one of the atoms in the row
block the photon's way on path $v$? No, because if one places an opaque object
at the end of the atoms row (object $B$ in Fig.~\ref{fig:atemp}), and no atom
has absorbed the photon, {\em all} atoms will remain superposed! It seems that
something must, after all, have passed through the row.

How can the photon's wave
function affect only one out of many atoms positioned in a row along its path,
leaving the others apparently intact, and yet complete its way through the row
to the BS? Naturally, any answer to this question is bound to be controversial,
as the Copenhagen, Guide Wave, Many Worlds and other interpretations would
propose different explanations. One lesson, however, is likely to be accepted
by the majority of physicists: {\em Measurement affects not only the system's
present state but its entire history.}\footnote{One of us (AE) owes this
insight to a student's question about Schr\"odinger's cat. She argued
that, if the box is opened after sufficiently many hours, it should be possible
to know whether the cat has been dead or alive during the preceding hours. If
it has been alive, it would soil the box and leave scratches on its walls,
whereas if it has been dead, it would show signs of decomposition. Here too,
the measurement at the moment of opening the box must select not only the cat's
state at the moment of opening the box but its {\em entire history} within the
box. \label{ftnt:insight}} It is the final click at $d$ that seals the process.
This, in fact, is the lesson derived from Wheeler's delayed choice experiment
\cite{Wheeler78}. Wheeler himself chose to interpret it by strict adherence to
the Copenhagen interpretation (``No phenomenon is a phenomenon until it is an
observed phenomenon''). But perhaps it is time we do not shy away from an
ontological conclusion, namely, that a measurement at the end of a quantum
process genuinely affects the process's history, in both directions of
time.

\section{The Quantum Liar
Paradox}

\label{ch:q-liar}

\begin{figure}

\centering

\includegraphics[scale=0.8]{graphics/RPE.eps}

\caption{Entangling two distant
atoms that have never interacted.}

\label{fig:entangle}

\end{figure}

If measurement can sometimes
``rewrite'' the history of a quantum processes, some traces of this
``rewriting'' may be found in the form of odd inconsistencies within the
resulting history. In terms of footnote \ref{ftnt:insight} above, a scenario is
possible which is analogous to a Schr\"odinger cat found to be long dead
alongside with scratches and droppings within the box that indicate that it has
been alive all that time.

Consider two atoms in the
$\ket{X+}$ state, each separated according to its $Z$ spin into two boxes as in
the previous chapter (Fig.~\ref{fig:entangle}). Two coherent laser beams are
directed towards an equidistant beam-splitter (BS), behind which there are two
detectors. Each beam crosses one of either atom's two boxes. The laser sources
are of sufficiently low intensity such that, on average, only one photon is
emitted during a given time interval $t$. When the atoms are not present, the
two laser sources are set to constructively interfere on branch $c$ and destructively
on $d$. This coherency can last for a period of time $\tau \gg t$. Notice the
oddity of the situation: A single photon is detected at $C$, yet, by QM, the
very uncertainty about its origin makes it interfere constructively, as if it
has originated from the two sources!

Now consider the case in which
the two atoms are present and detectors $D$ click. We know that one of the
beams was blocked (thereby spoiling the destructive interference). That means
that one of the atoms ``collapsed" into the intersecting box, while the
other, into the non-intersecting one, but we don't know which atom
``collapsed" into which box. Again, this uncertainty suffices to entangle
the two atoms into an EPR state \cite{Elitzur02}:

\beq

\ket{\Psi} = \ket{Z+}_1\ket{Z-}_2
- \ket{Z-}_1\ket{Z+}_2

\eeq

This experiment may be regarded
as a time reversed EPR, as the two atoms do not share a common event in the
past but, so to speak, in their future. It will be therefore be referred to as
RPE henceforth.

But the experiment's most
intriguing feature emerges once we employ the famous tool for proving a
nonlocal influence between entangled particles, namely, Bell's inequality. Let
us first recall the gist of Bell's nonlocality proof for the ordinary EPR
experiment \cite{Bell64}. Let a pair of EPR particles be created with their
total spin being zero. Let the two particles travel to two equidistant
measuring instruments. Now consider three spin directions, $x$, $y$, and $z$.
On each particle out of the pair, a measurement of one out of these directions
should be performed, at random. Let many pairs be measured this way, such that
all possible combinations of $x$, $y$, and $z$ measurements are eventually
performed. Then let the incidence of correlations and anti-correlations be
counted. By quantum mechanics, all same-spin pair measurements will yield 100\%
correlations, while all different-spin pair measurements will yield non
correlated results (half correlated, and half non-correlated). And indeed, this
is the result obtained by numerous experiments to this day \cite[to name a
few]{Aspect82,Aspect86,Tittel98,Rowe01}. By Bell's proof, such a unique
combination of correlations and anti-correlations cannot have been
pre-established. Conclusion: {\em The spin direction (up or down) of each
particle is determined by the choice of spin angle ($x$, $y$, or $z$) measured
on the other spacelike separated particle, no matter how distant.}

This is the familiar EPR-Bell.
Let us now apply this method to the RPE. Recall that each atom has been split
according to its spin in the $z$ direction. Therefore, to perform the $z$
measurement, one has to simply open the two boxes and check where the atom is.
To perform $x$ and $y$ spin measurements, one has to re-unite the two boxes
under the inverse magnetic field, and then measure the atom's spin in the
desired direction. Having randomly performed all nine possible pairs of
measurements on the pairs, many times, and using Bell's theorem, one can prove
that the two atoms affect one another instantaneously, as in the ordinary EPR,
with the difference that they share an event not in the past but in the future.

However, a puzzling situation
now emerges \cite{Elitzur03}. In 44\% (\ie, $4 \over 9$) of the cases (assuming
random choices of measurement directions), one of the atoms will be subjected
to a $z$ measurement -- namely, checking in which box it resides. Suppose,
then, that the first atom was found in the intersecting box. This seems to
imply that {\it no photon has ever crossed that path, which is obstructed by
the atom}. But then, by Bell's proof, the other atom is still affected
nonlocally by the measurement of the first atom. But then again, if no photon
has interacted with the first atom, the two atoms share no causal connection,
in either past or future!

\begin{figure}

\centering

\includegraphics[scale=0.80]{graphics/RPE-collapsed.eps}

\caption{Entangling two atoms.}

\label{fig:RPE-co}

\end{figure}

The same puzzle appears in the
cases in which the atom is found in the non-intersecting box. In this case, we
have a 100\% certainty that the other atom is in the intersecting box, meaning,
again, that no photon could have taken the other path. But here again, whether
we subject the other atom to the ``which box'' measurement or to an $x$ or $y$
measurement, Bell-inequality violations will occur, indicating that the result
was affected by the measurement performed on the first atom
(Fig.~\ref{fig:RPE-co}).

Put otherwise, {\em the very
fact that one atom is positioned in a place that seems to preclude its
interaction with the other atom is affected by that other atom.} This is
logically equivalent to the statement ``this sentence has never been written.''
We are unaware of any other quantum mechanical experiment that demonstrates
such inconsistency.\footnote{It is possible to make this experiment even more
striking by entangling two excited atoms, out of which only one can emit a
photon within a given time interval. The atoms thus become entangled with
respect to their excited/non-excited state. A bell-type inequality can be
formulated for this case by using measurements that are orthogonal to the
excited/non-excited state. Here too, the measurement of one atom may show it to
be excited, thereby making it appear as if it has never emitted a photon, and
thus could never become entangled with the other atom. And yet, by Bell's
inequality, this result must also be affected by the other atom's measurement.
We are currently elaborating such an experimental scheme.}

\section {A Speculation: The
Quantum Interaction Involves ``Rewriting'' of the Evolution in Spacetime}

\label{ch:hypothesis}

To be sure, the existing
interpretations of QM will claim that they have no difficulty in explaining the
above results. Yet, our search for a model that will be, at the same time,
realistic, parsimonious, and, if possible, elegant, has led us to propose an
interpretation of our own. We aspire to deal with the oddities of QM not by
abandoning objective reality, but by working within a realistic framework that
forces one to propose new hypotheses that may later be subjected to empirical
test. We also seek to integrate relativity's four-dimensional spacetime with
the somewhat opposite hints suggested by QM that genuine change, not static
geometry, is reality's most basic property.

General relativity has taught us
that spacetime is a real entity, namely, a four-dimensional array of
world-lines with their corresponding curvatures. Within this geometric picture,
the transactional interpretations reviewed in chapter \ref{ch:adv-action} fit
in very naturally, as they require interactions between earlier and later
events. Where we break new ground is in proposing that this spacetime is not
the changeless Minkowski array. Perhaps, rather, spacetime itself is subject to
evolution. True, ascribing evolution to spacetime itself runs the risk
mentioned at chapter \ref{ch:time-pecu}, namely, invoking an infinity of
higher- and higher-order times. We shall face this concern in the next chapter.

If this is so, if spacetime
itself evolves, then experiments yielding apparently inconsistent histories, as
those described above, may warrant an account like ``first a retarded
interaction brings about history $t_1x_1, t_2x_2,...$, and then an advanced
interaction transforms this history into $t_1x'_1, t_2x'_2,...$." Consider
the above quantum liar paradox: Perhaps there was first a forward moving
evolution by which the two atoms sent virtual photons towards the BS. Then the
detection of one photon retroactively entangled the two atoms backwards in the
past. Finally, the measurement of one atom, which found it to be in the
intersecting box, obliterated all traces of its interaction with the rest of
the experimental setup. These reiterations of the process occurred by repeated spacetime
zigzags \ala Aharonov and Cramer, but in some real, higher time dimension, over
spacetime itself. The remaining inconsistencies, such as an atom blocking the
path of a photon which must nevertheless have traversed this path, might be the
traces of this ``revision." Such a model may also be better capable of
explaining a few other surprising results discovered lately by similar methods
\cite{Aharonov90,Aharonov95}.

\section {An Outline of the
Spacetime Dynamics Theory}

\label{ch:outline}

Our study was motivated by two
phenomena that, on the one hand, have no trace in physical law, and, on the
other hand, seem to constantly proclaim their presence.

\begin{enumerate}

\item Time, unlike space, seems
to be flowing. However, accepting this phenomenon as a true property of time
entails several logical and physical difficulties, such as an endless series of
time parameters. Therefore, it has been often dismissed in favor of the
simpler, self-consistent Block Universe picture.

\item The fact that we never
observe the superposed states of the microscopic world in our macroscopic
world, seems to imply a collapse of the wave function. However, accepting this
collapse entails conflicts with relativity theory as well as with $T$
invariance. Therefore, many interpretations avoided it.

\end{enumerate}

And yet, we have pointed out
several indications that these two dismissals are inadequate -- that there is
more to time than just a dimension, and that the wave function does undergo a
unique change upon interacting with the macroscopic world. Moreover, the
alleged collapse affects not only the particle's state at the moment of
observation but, sometimes, its earlier history as well, suggesting that a
whole segment of spacetime is subject to subtle evolution.

Perhaps, then, the two phenomena
-- time's passage and wave-function collapse -- are not only real but the
latter is the very manifestation of the former? A wave function, after all, is
a sum of many equally possible outcomes, while the measurement brings about the
realization of one out of them, the others vanishing. Isn't this the very
difference between future and past? Isn't collapse elusive because it creates
the elusive ``Now"? Indeed de Broglie (Quoted in \cite{Feuer74}) paid tribute
to Bergson as a philosophical ancestor of QM. Had Bergson had a chance to study
QM, de Broglie mused, he would learn that Nature hesitates at any instant
between several choices, and he would reiterate what he has said in his {\em
The Creative Mind}: ``Time is nothing but this hesitation.''

Here, then, is the unfavored
hypothesis of Becoming again, now with a cosmological twist. Suppose that there
is indeed a ``Now" front, on the one side of which there are past events,
adding up as the ``Now" progresses, while on its other side there are {\em
no} events, and hence - by Mach - {\em not even spacetime}. Spacetime thus
``grows" into the future as history unfolds. Time's asymmetry would
therefore be naturally anchored in this alleged progress of the ``Now''.

Notice that by ascribing to the
``Now" the very creation of spacetime itself, we do away with all the
logical difficulties which have so far beset the ``moving Now" hypothesis
(see chapter \ref{ch:time-pecu}). Our hypothesis is merely an extension of the
Big Bang model, taking advantage of the latter's logical rigor: If the Big Bang
has created not only matter and energy but also spacetime itself, then no one
needs to worry about ``What happened before the Big Bang?'' or ``What lies
outside spacetime?'' Similarly for our hypothesis, the Now does not move on
some pre-existing dimension but rater creates that dimension. This is not
``movement'' in the ordinary sense, so no endless series of time parameters is
entailed by it.

Now let this Becoming be made
quantum mechanical. What role does the wave function play in this creation of
new events? The dynamically evolving spacetime allows a radical possibility.
Rather than conceiving of some empty spacetime within which the wave function
evolves, the reverse may me the case: {\em The wave function evolves outside
the ``Now," i.e., outside of spacetime, and its ``collapse,'' due to the
interaction with other wave functions, creates not only the events but also the
spacetime within which they are located in relation to one another.} The
quantum interaction's famous peculiarities -- nonlocality, the coexistence of
mutually exclusive states, backward causation and the inconsistent histories
presented in the previous chapters, thus become more natural.

Can the reciprocal effects of
spacetime and matter -- the celebrated fruit of general relativity -- thus
possibly gain a quantum mechanical explanation? Perhaps it is the wave
function, we submit, that is more primitive than spacetime, and the spacetime
connecting two events is the product of their interacting wave functions. We
shall close with a more audacious consequence of this hypothesis for quantum
field theory. Perhaps the wave function of a force-carrying boson, such as a
graviton or a photon, which, by our hypothesis, creates also the spacetime
within which the final interaction is completed, determines the spatiotemporal
distance between the events. In other words, ``attraction'' and ``repulsion''
may be the consequences of the specific spacetime metric created by the
interacting wave functions.

Whether this sketchy proposal
will eventually mature into a viable theory of spacetime dynamics, can be
decided only by the future, be it the fixed Minkowskian or the open Bergsonian
one. We can only plead that the questions raised and odd phenomena pointed out
in the preceding pages call for radically new ways of thinking about quantum
and spacetime.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\bibliographystyle{unsrt}

\begin{thebibliography}{10}

\bibitem{Isham96}

C.~J. Isham and J.~C.
Polkinghorne.

\newblock The debate over the
block universe.

\newblock In R.~Russell,
N.~Murphy, and C.~J. Isham, editors, {\em Quantum

Cosmology and the Laws of Nature}, pages 139--147. University of Notre
Dame

Press, Notre Dame, IN, 1996.

\bibitem{Atmanspacher97}

H.~Atmanspacher and E.~Ruhnau,
editors.

\newblock {\em Time,
Temporality, Now}.

\newblock Springer, Berlin,
1997.

\bibitem{Zeh89}

H.~D. Zeh.

\newblock {\em The Physical
Basis of the Direction of Time}.

\newblock Springer, Berlin,
1989.

\bibitem{Bohm65}

D.~Bohm.

\newblock {\em The Special
Theory of Relativity}.

\newblock Routledge, London,
1965, 1996.

\bibitem{Penrose79}

R.~Penrose.

\newblock Singularities and
time-asymmetry.

\newblock In S.~W. Hawking and
W.~Israel, editors, {\em General relativity: An

Einstein Centenary Survey}, page 581. Cambridge University Press,
Cambridge,

1979.

\bibitem{Davies74}

P.~C.~W. Davies.

\newblock {\em The physics of
time asymmetry}.

\newblock Surrey University
Press, London, 1974.

\bibitem{Bilaniuk62}

O.~M. Bilaniuk, V.~K. Deshpande,
and E.~G.~C. Sudarshan.

\newblock ``Meta'' relativity.

\newblock {\em Am. J. Phys.},
30:718--723, 1962.

\bibitem{Price96}

H.~Price.

\newblock {\em Time's Arrow and
Archimedes' Point}.

\newblock Oxford University
Press, Oxford, 1996.

\bibitem{Albert00}

D.~Z. Albert.

\newblock {\em Time and Chance}.

\newblock Harvard University
Press, Cambridge, MA., 2000.

\bibitem{Elitzur99a}

A.~C. Elitzur and S.~Dolev.

\newblock Black hole evaporation
entails an objective passage of time.

\newblock {\em Found. Phys.
Lett.}, 12:309--323, 1999.

\bibitem{Elitzur99b}

A.~C. Elitzur and S.~Dolev.

\newblock Black hole uncertainty
entails an intrinsic time arrow.

\newblock {\em Phys. Lett. A},
251:89--94, 1999.

\bibitem{Hawking04}

S.~Hawking.

\newblock The information
paradox for black holes.

\newblock In {\em 17th
International Conference on General Relativity and

Gravitation (to be published)}. 2004.

\bibitem{Heisenberg27}

W.~Heisenberg.

\newblock {\"U}ber den
anschaulichen inhalt der quantentheoretischen kinematik

und mechanik.

\newblock {\em Z. Phys.},
43:172--198, 1927.

\newblock translated as ``The
Physical content of quantum kinematics and

mechanics'' in \cite{Wheeler83}, pages 62-84.

\bibitem{Bell64}

J.~S. Bell.

\newblock On the einstein
podolsky rosen paradox.

\newblock {\em Physics},
1:195--780, 1964.

\bibitem{Elitzur95}

A.~C. Elitzur.

\newblock Anything beyond the
uncertainty? reflections on the interpretations

of quantum mechanics.

\newblock A manuscript, 1995.

\bibitem{Elitzur92a}

A.~C. Elitzur.

\newblock Locality and
indeterminism preserve the second law.

\newblock {\em Phys. Lett. A},
167:335--340, 1992.

\bibitem{Valentini02a}

A.~Valentini.

\newblock Signal-locality in
hidden-variables theories.

\newblock {\em Phys. Lett. A},
297:273--278, 2002.

\bibitem{Valentini02b}

A.~Valentini.

\newblock Subquantum information
and computation.

\newblock {\em Pramana J.
Phys.}, 59:269--277, 2002.

\bibitem{Bekenstein74}

J.~D. Bekenstein.

\newblock Generalized second law
of thermodynamics in black hole physics.

\newblock {\em Phys. Rev. D},
9:3292, 1974.

\bibitem{Hawking74}

S.~W. Hawking.

\newblock Black hole explosions.

\newblock {\em Nature}, 248:30,
1974.

\bibitem{Hawking75}

S.~W. Hawking.

\newblock Particle creation by
black holes.

\newblock {\em Commun. Math.
Phys.}, 49:199, 1975.

\bibitem{Unruh76}

W.~G. Unruh.

\newblock Notes on black-hole
evaporation.

\newblock {\em Phys. Rev. D},
14:870--892, 1976.

\bibitem{ABL64}

Y.~Aharonov, P.~G. Bergman, and
J.~L. Lebowitz.

\newblock Time symmetry in the
quantum process of measurement.

\newblock {\em Phys. Rev.},
134:1410--1416, 1964.

\bibitem{Cramer86}

J.~G. Cramer.

\newblock The transactional
interpretation of quantum mechanics.

\newblock {\em Rev. Mod. Phys.},
58:647--688, 1986.

\bibitem{Kastner04}

R.~Kastner.

\newblock Cramer's transactional
interpretation and causal loop problems.

\newblock 2004.

\bibitem{Elitzur90}

A.~C. Elitzur.

\newblock On some neglected
thermodynamic peculiarities of quantum

non-locality.

\newblock {\em Found. Phys.
Lett.}, 3:525--541, 1990.

\bibitem{EV93}

A.~C. Elitzur and L.~Vaidman.

\newblock Quantum mechanical
interaction-free measurements.

\newblock {\em Found. of Phys.},
23:987--997, 1993.

\bibitem{Kwiat95b}

P.~Kwiat, H.~Weinfurter,
T.~Herzog, A.~Zeilinger, and M.~A. Kasevich.

\newblock Interaction-free
measurement.

\newblock {\em Phys. Rev.
Lett.}, 74:4763--4766, 1995.

\bibitem{Hardy92a}

L.~Hardy.

\newblock On the existence of
empty waves in quantum theory.

\newblock {\em Phys. Lett. A},
167:11--16, 1992.

\bibitem{Hardy93b}

L.~Hardy.

\newblock Nonlocality for two
particles without inequalities for almost all

entangled states.

\newblock {\em Phys. Rev.
Lett.}, 71:1665--1668, 1993.

\bibitem{Hardy94}

L.~Hardy.

\newblock Nonlocality of a
single photon revisited.

\newblock {\em Phys. Rev.
Lett.}, 73:2279--2283, 1994.

\bibitem{Dolev00}

S.~Dolev and A.~C. Elitzur.

\newblock Non-sequential
behavior of the wave function.

\newblock quant-ph/0012091,
2000.

\bibitem{Wheeler78}

J.~A. Wheeler.

\newblock The ``past'' and the
``delayed-choice'' double-slit experiment.

\newblock In A.~R. Marrow,
editor, {\em Mathematical Foundations of Quantum

Theory}, pages 9--48. Academic Press, New York, 1978.

\bibitem{Elitzur02}

A.~C. Elitzur, S.~Dolev, and
A.~Zeilinger.

\newblock Time-reversed EPR and
the choice of histories in quantum mechanics.

\newblock In {\em Proceedings of
XXII Solvay Conference in Physics, Special

Issue, Quantum Computers and Computing}, pages 452--461. World
Scientific,

London, 2002.

\bibitem{Aspect82}

A.~Aspect, J.~Dalibard, and
G.~Roger.

\newblock Experimental test of
Bell's inequalities using time- varying

analyzers.

\newblock {\em Phys. Rev.
Lett.}, 49:1804--1807, 1982.

\bibitem{Aspect86}

A.~Aspect and P.~Grangier.

\newblock Experiments on Einstein-Podolsky-Rosen-type
correlations with pairs

of visible photons.

\newblock In R.~Penrose and
C.~J. Isham, editors, {\em Quantum Concepts in

Space and Time}, pages 1--15. Oxford University Press, Oxford, 1986.

\bibitem{Tittel98}

W.~Tittel, H.~Brendel,
J.~Zbinden, and N.~Gisin.

\newblock Violation of Bell
inequalities by photons more than 10 km apart.

\newblock {\em Phys. Rev.
Lett.}, 81:3563--3566, 1998.

\bibitem{Rowe01}

M.~A. Rowe, D.~Kielpinski,
V.~Meyer, C.~A. Sackett, W.~M. Itano, C.~Monroe, and

D.~J. Wineland.

\newblock Experimental violation
of a Bell's inequality with efficient

detection.

\newblock {\em Nature},
409:791--794, 2001.

\bibitem{Elitzur03}

A.~C. Elitzur and S.~Dolev.

\newblock Is there more to t?
why time's description in modern physics is still

incomplete.

\newblock In R.~Buccheri,
M.~Saniga, and W.~M. Stuckey, editors, {\em The

Nature of Time: Geometry, Physics and Perception. NATO Science Series,
II:

Mathematics, Physics and Chemistry}, pages 297--306. Kluwer Academic,
New

York, 2003.

\bibitem{Aharonov90}

Y.~Aharonov and L.~Vaidman.

\newblock Properties of a
quantum system during the time interval between two

measurements.

\newblock {\em Phys. Rev. A},
41:11--20, 1990.

\bibitem{Aharonov95}

D.~Rohrlich, Y.~Aharonov,
S.~Popescu, and L.~Vaidman.

\newblock Negative kinetic
energy between past and future state vectors.

\newblock {\em Ann. N. Y. Acad.
Sci.}, 755:394--404, 1995.

\bibitem{Feuer74}

L.~S. Feuer.

\newblock {\em Einstein and the
generation of science}.

\newblock Basic Books, New York,
1974.

\bibitem{Wheeler83}

J.~A. Wheeler and W.~H. Zurek,
editors.

\newblock {\em Quantum Theory
and Measurement}.

\newblock Princeton University
Press, Princeton, 1983.

\end{thebibliography}

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