### Physics

Author: A.C. Elitzur, S. Dolev

Avshalom C. **ELITZUR**

**Quantum-Mechanical
and Thermodynamic clues in search of a deeper concept of Time. **The concept of time has
undergone a major revolution in special and general relativity, but at the same
time it became alienated from our ordinary experience. We
experience events differently in time and in space. In space, we can observe
sequences of events in whatever order, e.g., from left to right or *vice versa*, whereas in time we
experience them only from past to future. In space, we can remain at the same
place, whereas in time we seem to “move” from one moment to the next.
Relativity, however, has undermined this account of time. In the
Einstein-Minkowski spacetime, all events – past, present and future – have the
same degree of existence, time’s passage being a mere illusion. In this lecture
I bring evidence from two different realms of physics that indicate that the
present account of time in physics is insufficient. From the viewpoint of
quantum mechanics, we have shown (Elitzur, Dolev & Zeilinger, 2001) that the famous EPR
experiment can be turned upside down in time. That is, two particles can
manifest non-local influence not only if they share a common origin in the past
but also if they are about to interact in the *future*. In another thought-experiment (Dolev & Elitzur, 2001),
we have shown that a wave function that interacts with a row of atoms sometimes
seems to interact only with the middle atom, while leaving the others
unaffected. These and other results indicate that, at least at the quantum
level, time remains very poorly understood. Another work of ours (Elitzur &
Dolev, 1999) proves that, if a single genuinely random event occurs in a closed
system, then, *regardless of that system’s
initial conditions*, an arrow of time is bound to emerge in it, and this
arrow accords with that of the rest of the universe, from which the closed
system is supposed to be shielded. Hence, if Hawking’s information-erasure
hypothesis is correct, time’s arrow is intrinsic, much in accord with
Prigogine’s unorthodox claim. Based on these surprising results, I propose a
tentative model of time that tries to integrate the insights of relativity on
the one hand, and everyday conscious experience on the other hand, into a more
comprehensive scheme.

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\begin{document}

\begin{opening}

\title{IS THERE MORE TO T?}

\subtitle{Why Time's Description in Modern Physics is Still
Incomplete}

\author{A. C. ELITZUR}

\author{S. DOLEV}

\institute{The Program for History and Philosophy of
Science\\

Bar-Ilan
University, 52900 Ramat-Gan, Israel}

\runningtitle{IS THERE MORE TO T?}

\runningauthor{ELITZUR and DOLEV}

\end{opening}

\small

**\section{Introduction: The Stalemate and the Proposed
Research Plan}**

\label{sec:time}

The problem associated with time's nature is well known. It
stems from two aspects of time that cannot be reconciled:

1) Time sharply differs from space in that in space, you can
either move or stay put, and if you move you can do it in either direction. Not
so with time: You cannot remain at the same moment, neither return to earlier
moments. Time seems, then, to constantly move.

2) The last sentence in nonsensical. Time cannot move
neither can anything move in time, as the very notion of movement (passage,
flow, etc.) entails time. Just ask ``what is the speed of time’s movement?” and
the absurdity of the statement will become apparent. You can, of course, assume
another time parameter of a higher order, but that will necessitate a yet
higher time dimension and so on {\it ad infinitum}.

Mainstream
physics has chosen to deal with this problem by simply dismissing time's
passage altogether as illusory. In the Minkowski 4-dimensional
spacetime, all events –- past, present and future –- coexist along time just as
all milestones coexist along a road.
Only a few heretic theories sought to incorporate time's transitory aspect
within a new theory (see \cite{Elitzur99b} for a brief review). Frustratingly, however, the debate never
became genuinely scientific. All physical observations are equally consistent
with a Block Universe (``all events coexist along time") and with the
hypothesis of Becoming (``events are created anew one after another"). In
the absence of a decisive experimental test, both views remain in the realm of
philosophy.

In this article we discuss some works of ours that provide
clues about some more profound aspects of time. We use Hawking's
information-erasure hypothesis to counter his own claim that time's arrow
depends only on initial conditions (section \ref{sec:HAWK}). Next, we present
an intriguing experiment supporting the orthodox view that time is symmetric at
the quantum level (section \ref{sec:RPE}). Then, however (sections \ref{sec:
atemporal}-\ref{sec: inconsistent}), we propose quantum-mechanical experiments
that yield inconsistent histories, suggesting that not only events but also
entire histories might be governed by a more fundamental dynamics. Finally, we
indulge in a speculation of our own (section \ref{sec:spec}). Because of space
limits, our report is somewhat telegraphic, but references are given to the
extended works, published in other journals with full mathematical details and
relevant references.

**\section{Whence Time's Arrow?}**

\label{sec:HAWK}

This problem is also familiar. The basic laws of physics are
time-symmetric, as well as all basic interactions. And yet, our macroscopic
world is clearly time-asymmetric, in compliance with the Second Law of
Thermodynamics. How can numerous time-symmetric interactions give rise together
to one overall time-asymmetry? Two answers are available:

\begin{enumerate}

\item {\it It's all a matter of initial conditions.} The
universe's initial conditions, \ie, the big bang, are highly ordered, allowing
entropy only to increase. One could conceive of the opposite case, namely, a
universe whose big bang is seemingly disordered, but with such a perfect
correlation between all particles that entropy will eventually decrease. In
fact, if one dismisses time's passage, then our universe is just such a
universe. If the universe's beginning and end coexist along time, then one can
read its history in either direction of time!

\item {\it Perhaps the basic interactions are not completely
time symmetric after all.} Perhaps there is a very slight asymmetry in every
basic interaction, unobservable by present-day means but underlying the
macroscopic asymmetry that emerges from innumerable microscopic interactions.

\end{enumerate}

Clearly, (1) is the mainstream view as expressed by Hawking,
while (2) is a hypothesis endorsed only by Penrose and a very few authors (for
the controversy, see \cite{Hawking96}). Intriguingly, Hawking himself, in
respect to another issue, holds a famous heresy without noticing that it
clashes with his conservative account of time's arrow. We refer to his claim
that black hole evaporation involves a complete erasure of the information of
all the objects that have earlier fallen into the black hole \cite{Hawking96}.
We do not consider ourselves competent to voice an opinion in this old debate.
We only wish to point out that ``information-loss" is synonymous with
``indeterminism." But then, {\it for any closed system that contains an
indeterministic event, that system's entropy can only increase, regardless of
its initial conditions, in accordance with the time arrow of the rest of the
universe.}

We have demonstrated this argument(\cite{Elitzur99b,Elitzur99c,Elitzur99})
by the means of a computer simulation of an entropy increasing process: On a
billiard table, one ball is set to hit a group of ordered balls at rest,
dispersing them around. After repeated collisions between the balls, the energy
and momentum of the first ball is nearly equally divided between the balls.
Although this state looks random, the correlations between the balls are
strict: Reversing their momenta will time-reverse the scattering, resulting in
a convergence back into the initial ordered state, ejecting back the first ball
with the entire kinetic energy content of the system.

Obviously, this time-symmetry strictly necessitates perfect
determinism. But what if determinism fails, say, if one ball's position is not
a direct consequence of its previous state? We tried that by slightly
disturbing the trajectory of one ball during the simulation. The entropy increasing
process seemed to be the same, resulting in a similarly disordered state.
However, when we applied the same disturbance to the time-reversed process, the
return to the ordered initial state failed.

In short: Entropy increasing processes do not require any
special initial correlations, while entropy decreasing processes do -- they are
extremely sensitive to any disturbance. This difference is so well-known to be
a truism, but its straightforward bearing on time’s arrow has not been noticed
yet: {\it If physics ever proves that determinism does not always hold -- that
some processes contain a truly random element -- it would follow that entropy
always increases regardless of the system's initial conditions.} An intrinsic
time-arrow must then emerge in any system, even in a closed one, independent of
the initial conditions but congruent with the time arrow of the entire universe
outside, from which that system is supposed to be shielded. If Hawking's
information-loss conjecture turns out to be correct, its bearing on time's
nature (and hence, on the nature of spacetime) would be much more far-reaching
than his otherwise-orthodox viewpoint allows.

**\section{Is Time symmetric at the Quantum Level?}**

\label{sec:RPE}

\begin{figure}

\begin{center}

\includegraphics[scale=0.55]{RPE.eps}

\caption{Entangling two atoms by a future interaction (a
single photon emitted by two sources). C and D denote constructive and
destructive interference.}

\label{fig:RPE}

\end{center}

\end{figure}

Despite the apparent time-asymmetry associated with any
measurement, the formalism of quantum theory is time symmetric. Recently, we
have proposed an experiment that takes this time-symmetry to the extreme.

The famous EPR experiment (\cite {EPR35}) involves two
distant particles, emitted from the same atom. By spin conservation, they have
opposite spins. On the other hand, by the formalism of QM, these spins are
undecided until they are measured. Hence, measuring one of them must instantly
determine the spin of the other, in apparent defiance of special relativity.
Indeed, a celebrated theorem by Bell (\cite {Bell64}) proves that the
correlations between the spins could not have been determined earlier than the
very moment of measurement.

Consider now another quantum effect, namely, the
interference of light coming from different sources \cite{Paul86}. Though not
as famous as the EPR, this effect is no less astonishing: When the radiation
involved is sufficiently weak, then even the detection of a single particle can
display interference pattern, as if one and the same particle ``has
originated'' from two distant sources!

How about inbreeding the two forms of magic (Figure
\ref{fig:RPE})? Let two atoms be placed on the two possible routes of the two
``half photon”s. Let each atom be superposed in two boxes (\eg, by taking a
spin 1/2 atom and splitting it according to it’s $z$ spin). The boxes are
transparent for the photon but opaque for the atoms.

In 50\% of the cases, one of the atoms will ``choose"
(or ``collapse”) to reside in the box that intersects the path that the photon
``has chosen" too. These cases will result in photon’s scattering and will
be discarded. In 25\% of the cases, however, one of the atoms will
``choose" to reside in the box that intersects one of the photon's
possible paths, but the photon itself will ``choose" the other path. Here,
the photon's interference will be disrupted, since one of its paths has been
blocked by one of the atoms. On the other hand, the fact that the photon has
arrived to the detector means that the other path was not blocked, \ie, that
the other atom ``chose" not to intersect the other path. But {\it which}
path? {\it Which} atom? Recall, now, that this is quantum mechanics, hence the
ignorance about the atom is not merely epistemological but ontological. In
other words, the very uncertainty about the positions of the atoms -- \ie, the
question which atom lies in the intersecting box and which lies in the
non-intersecting one -- suffices to physically entangle them in a full EPR
state:

\beq

\Psi = {1 \over \sqrt 2}(\ket{Z_1^-} \ket{Z_2^+} - \ket{
Z_1^+} \ket{ Z_2^-})

\eeq

Which means that tests of Bell's inequality performed on the
two atoms will reveal, just as the EPR, that the spin value of each atom
depends on the choice of spin direction measured on the other atom, no matter
how distant. The novelty in the present setting is that, unlike the ordinary
EPR, where the two particles have interacted earlier, here the only common
event lies in their {\it future}, namely, the detection of the single photon
that might have visited either one of them.

The heavy use of anthropomorphic and counterintuitive
notions such as a photon ``choosing" to ``have originated" from a certain
source might sound suspicious to readers accustomed to a more prudent language.
The findings, however, are no less striking when described in strictly
technical terms (\cite{Elitzur02}).

This inversion of the EPR setting brings to mind some
ingenious ``transactional" interpretations of QM (\eg, Aharonov
\cite{Yakir90,Yakir95}, Costa de Beauregard \cite{Costa87}, and Cramer
\cite{Cramer86}), that proposed that each quantum interaction is the result of
two interactions, one going forwards in time and the other backwards,
complementing one another so as to produce the observed quantum peculiarities.
Thus, the EPR experiment is explained as an interaction extending along a spacetime
zigzag between the two particles through the common past. It seems that our
inverse EPR is particularly amenable to such an interpretation. It is the later
detection of the photon that entangles the two atoms, even though their
interactions with the photon have occurred earlier. Further variations of this
experiment \cite{Elitzur02}
also add to it Wheeler’s ``delayed choice" (\cite{Wheeler78})
element, with the difference that, in our setting, the effect on the past
leaves physically detectable traces.

**\section{Does the Wave Function Move Consequentially?}**

\label{sec:atemporal}

Quantum-mechanical objects, then, seem to ``experience’’
spacetime in a unique way. This is strongly demonstrated in an intriguing
experiment by Hardy \cite{Hardy92a,Hardy93},
in which a single photon traverses a Mach-Zender Interferometer (MZI)
while an atom is superposed in two semi-transparent boxes, as in section
\ref{sec:RPE}. Here too, one of which is positioned across one of the photon’s
routes. If the photon ends up showing that the interference within the MZI was
disrupted, it means that a) the atom must have been in the intersecting box in
order to disrupt the interference, yet b) the photon must have taken the {\it
other} route, otherwise it would have been scattered by the atom! The
intriguing thing is that, although the photon has taken one path, the state of
the atom positioned on the other path has been changed in a physically
measurable way, although a very subtle one: It has lost its initial
superposition and assumed a definite state.

\begin{figure}

\centering

\includegraphics[scale=0.55]{atemp.eps}

\caption{Non sequential interaction: i) the photon ends up
in D, indicating that one of the superposed atoms is in the intersecting box,
ii) the middle atom is found to be in the intersecting box, iii) all the other
atoms return to their superposition (\eg, manifesting full interference), as if
noting has ever interacted with them.}

\label{fig:atemp}

\end{figure}

Hardy argued that this experiment supports the ``guide
wave" interpretation of quantum mechanics: It is the half wave plus
particles that went through the left arm, while the other empty half wave went
through the right arm and ``collapsed" the atom.

This argument challenged us \cite{Dolev00} to modify the device
in a way that may enable one to empirically distinguish between the ``guide
wave" and the ordinary ``collapse" interpretation. In the latter
interpretation, the wave function is evenly split, then goes through both MZI
arms, and then, upon encountering a measuring object, vanishes from one arm and
becomes fully materialized in the other. In order to test both interpretations
against each other, we have simply replaced the one atom in Hardy’s version
with a few (say, three) atoms (Fig. \ref{fig:atemp}). This, we hoped, will
enable us to trace the photon’s subtle action along space. True, the guide wave
interpretation is often formulated in a way that yields the same experimental
predictions as ordinary quantum theory, but we still felt that the results
might strain one of the two ontologies so as to favor the other.

Much to our surprise, the results supported neither interpretation
but demonstrated an even more intriguing effect. As in Hardy’s version, here
too, if the photon indicates that interference was disrupted, then, with 100\%
certainty, {\it one} of the atoms has ``collapsed" into the intersecting
box. However, it can be {\it any} of the N atoms, not necessarily the first.
Worse, once we have measured one of the atoms and found it in the intersecting
box, all the other atoms return to their original, undisrupted, superposition
state. Consequently, if we do not measure these atoms’ positions but reunite
the boxes and perform an ``interference" measurement, these atoms will
{\it always} exhibit full interference, as if no photon has ever interacted
with them!

This result severely offends ordinary spatio-temporal
notions. If one assumes that the photon's wave function has interacted with the
particular atom we've measured so as to ruin its interference, how come that
all the other atoms in the row, positioned before and after that particular
atom, seem to have never been affected?

**\section{Does Measurement Always Give Consistent
Histories?}**

\label{sec:inconsistent}

Another offence to the ordinary temporal notions comes from
our above inverse EPR experiment (section \ref{sec:RPE}). At first sight, that
setup seems to add support to the claim that quantum mechanical interactions
are transactions between earlier and later events, thereby lending support to a
static view of spacetime (see section \ref{sec:time}). However, a variation of
that experiment gives a result that hardly accords with the conventional account.

Let us first recall the essence of Bell’s nonlocality proof
(\cite {Bell64}) for the EPR experiment. Consider three spin directions, $x$,
$y$, and $z$. On each pair of EPR particles, one out of these directions should
be measured at random on each particle. Let many pairs be measured this way,
such that all possible pairs of $x$, $y$, and $z$ measurements are performed.
Then let the incidence of correlations and anti-correlations be counted. If
quantum mechanics is correct, all same-spin pairs will yield correlations,
while all different-spin pairs will yield 50\% correlations. And indeed, this
is the result obtained by numerous experiments to this day. By Bell’s proof,
such a result could not have been pre-established. Hence, an instantaneous
influence between the particles must take place at the moment of measurement.

Let us now apply this method to our inverted EPR. Each
atom’s position, namely, whether it resides in one box or the other,
constitutes a spin measurement in the $z$ directions (as it has been split
according to its spin in this direction). To perform the $z$ measurement, then,
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, and using Bell’s theorem, one can prove that the two atoms affect
one another instantaneously, with the difference that they share an event not
in the past, as in the ordinary EPR, but in the future.

However, a bizarre situation now emerges. In 44\% (\ie, $4 \over
9$) of the cases (assuming random choice of measurement directions), one of the
atoms will be subjected to $z$ measurement -- namely, checking in which box it
resides -- while the other atom will be subjected to $x$ or $y$ -- namely,
reuniting its two boxes and then measuring another spin direction. Suppose,
then, that the first atom was found in the intersecting box. This means that
{\it no photon has ever crossed that path, since the atom obstructs it}. 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 (remember that we post-selected out all cases of scattering),
the two atoms share no causal connection, in either past of future!

Like the wave function's inconsequential behavior in section
\ref{sec:atemporal}, this experiment yields a history that is not consistent:
One atom indicates that the photon has taken only one path, while the other
atom's state proves that both atoms have been visited by the same photon.

**\section{A Speculation}**

\label{sec:spec}

What alternative picture of time might eventually emerge
from these cracks in the prevailing paradigm? Fully aware of this question’s
pretentiousness, we risk a speculation.

First, concerning Hawking’s information-loss conjecture, we
reiterate that, if this conjecture turns out to be correct, its bearing on the
present picture of time would be devastating. Time’s asymmetry would turn out
to be inherent to all physical processes, rather than an artifact of boundary
conditions. Perhaps this conclusion might be less surprising for one who keeps
in mind the still unexplained CP violation exhibited by neutral kaons, which,
by CPT invariance, entails a fundamental violation of T. Consequently, if a
subtle time-asymmetry is inherent to physical interactions themselves, the
orthodox picture of time as a mere dimension loses much of its conviction.

Our next comment concerns the apparently inconsistent
histories implied by the experiments in sections \ref{sec:atemporal} and
\ref{sec:inconsistent}. Earlier (section \ref{sec:RPE}) we have mentioned the
``transactional" interpretations (\cite{Cramer86,Costa87}, that, by
invoking retarded-plus-advanced actions, offer a simple and elegant explanation
for many spatial and temporal peculiarities manifested by QM. However, these
interpretations adhere to the ``Block Universe” view and deny any dynamics to
spacetime itself. Is it possible to have a transactional model that allows some
dynamics to occur in spacetime itself?

We envisage such a model, although at present it is highly
tentative. From general relativity, we take the concept of spacetime as a real
physical thing, namely, a four-dimensional manifold of world lines with their
corresponding spacetime curvatures. Within this geometric picture, the
transactional interpretations fit in very naturally. Where we break new ground
is in proposing that this spacetime is not the changeless Minkowski manifold.
Perhaps it, too, is subject to some subtle dynamics. In other words, perhaps changes
affect not only events but also {\it entire histories}. Admittedly, ascribing
evolution to spacetime itself runs the risk mentioned at section
\ref{sec:time}, namely, invoking an infinity of higher- and higher-order times.
But this problem alone should not make one seek refuge back in orthodoxy. Other
lines of reasoning (\eg, \cite{Davies95, Saniga02}) have similarly found the
present picture of spacetime insufficient. Even Einstein himself (\cite{Zeh89,
p. 151}) has regarded the absence of the moving Now in his theory as ``a matter
of painful and inevitable resignation.’’

If this is so, if spacetime itself evolves, then, time’s
asymmetry will be anchored in that evolution (\ie, the alleged progress of the
``Now’’). Also, quantum mechanical experiments yielding apparently inconsistent
histories, as those described above, would give rise to 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 $t_1x’_1, t_2x’_2,...$.”

Such a model will be better capable of explaining quantum
peculiarities of the kind described above, as well as a few other surprising
results discovered lately by similar techniques (\cite{Yakir90,Yakir95}). But
then, it will be nothing short of a new theory of spacetime.

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