Physics
Author: A.C. Elitzur, S. Dolev
The Inexhaustible Source of
Insights Revealed by every Photon
Avshalom C. Elitzur and Shahar Doleva aPhilosophy
Department, Haifa University, Israel
“Mehr licht!” (“More light!”) G¨othe, on his deathbed
ABSTRACT
We present several quantum mechanical experiments involving
photons that strain the notions of space, time and causality. One for these
experiments gives rise to the “quantum liar paradox,” where Nature seems to
contradict herself within a single experiment. In the last section we propose
an outline for a theory that aspires to integrate GR and QM. In this outline,
i) “Becoming,” the creation of every instant anew from nothingness, is real.
ii) Forcecarrying particles, such as photons, do not merely mediate the
interaction by propagating in some preexisting, empty spacetime; rather, they
are the very progenitors of the spacetime segment within which the interaction
takes place.
Keywords: Interactionfree measurement; EPR; Quantum entanglement;
Quantum liar paradox; Spacetime
1. INTRODUCTION
Ever since Newton waged his ferocious wars against Huygens and the
wave theory proponents, light kept being the delight as well as the nightmare
of theorists and experimentalists alike. While theoretical advance has been
slow during the last few decades, several experiments have been proposed that
keep oﬀering
intriguing clues for any future theory. Accordingly, this paper presents a few
simple experiments that we believe show that a photon is a much more elusive
and odd entity than most physicists are willing to believe. The ﬁrst of these
experiments has already been carried out, the others still being
gedankenexperiment, which we hope will pose challenges to experimentalist to
carry out too. The last experiment gives rise to the Quantum Liar Paradox. With
all due modesty we argue that this paradox is more acute than all the
traditional quantum paradoxes such as EPR or Schr?dinger’s cat. This is because
the conﬂict it reveals is not only between quantum and classical mechanics or
relativity theory. Rather, Nature seems to logically contradict herself within
a single experiment. Finally, in the last section we shall take the liberty of
speculating how the photon will look like within the long waitedfor Uniﬁed
Field Theory, in which quantum mechanics and relativity theory will be merged.
2. GETTING AWAY WITH SUPERSENSITIVEBOMB TESTING
1Consider a supersensitive bomb with which even the slightest
interaction possible leads to its explosion. Can one detect the bomb’s presence
at a certain location without destroying it? Elitzur and Vaidmanposed this
question with a new answer in the positive. Their solution was based on the
device known as MachZehnder Interferometer (MZI), shown in Fig. 1. A single
photon impinges on the ﬁrst beam splitter, the transmission coeﬃcient of which is 50%. The transmitted and reﬂected
parts of the photon wave are then reﬂected by the two solid mirrors and then
reunited by a second beam splitter with the same transmission coeﬃcient. Two detectors are positioned to detect
the photon after it passes through the second beam splitter. The positions of
the beam splitters and the mirrors are arranged in such a way that (due to
destructive and constructive interference) the photon is never detected by
detector D, but always by C.
In order to test the bomb, let it
be placed on one of the MZI’s routes (v) and let a single photon pass through
the system. Three outcomes of this trial are now possible:
Contact info: Avshalom C.
Elitzur: avshalom.elitzur@weizmann.ac.il Shahar Dolev: shahar do@huji.ac.il
Figure 1. Interaction Free Measurement. BS1
and BS2
• The bomb explodes, • Detector Cclicks, • Detector Dclicks.
2
3
4
3. HYBRIDIZING IFM WITH EPR
5
are beam splitters. In the absence of the
obstructing bomb, there will be constructive interference at path c (the
detector C will click) and destructive interference on path d (detector D never
clicks).
If detector Dclicks (the probability for which being 1/4 ), the
goal is achieved: we know that interference has been disturbed, ergo, the bomb
is inside the interferometer. Yet, it did not explode.
The problem can be formulated in
an even more intriguing way: Can one test whether the supersensitive bomb is
“good” (better say: “bad”) without bringing about its explosion? Again, all one
should do is to place the bomb on one of the MZI’s routes such that, if the
photon passes on that route, the bomb’s sensitive part can be triggered by
absorbing only some of the photon’s energy. Here too, the bomb constitutes a
“which way” detector: Just as its explosion would indicates that the photon
took the bomb’s route, its silence indicates that it took the other route. And
again, interference is destroyed by the bomb’s mere nonexplosion, indicating
that the bomb is explosive.
Since the EV paper, numerous
works, experimental and theoretical, have elaborated it and expanded its scope.
Zeilinger et. al.reﬁned it so as to save nearly 100% of the bombs. Other
applications of IFM range from quantum computationto imaging.
Apart from its technological applications, IFM is extremely eﬃcient for experiments that aim to give better
understanding of the nature f the wavefunction. One such an experiment has
been proposed by usfor studying the EPR eﬀect. Consider a particle split not only to two parts, as in the
ordinaryMZI, but to 100. Then measure one of the wavefunction’s parts. In most
cases, no detection would occur. This is a weak IFM that changes the
wavefunction only slightly. Rather than the abrupt transition from
superposition to position, the likelihood of the particle to be in a certain
state has increased or decreased. This is partial measurement. Next consider an
EPR pair whose particles undergo partial measurements. Here, some intriguing eﬀects occur:
1. Partial measurement on one particle yields a partial nonlocal eﬀect on the other particle; 2. The other
particle can then undergo another partial measurement and exert its own slight
eﬀect back
on
the ﬁrst. 3.
Partialmeasurementcan be totally timereversed, returning the wavefunctionto
its originalsuperposition,
giving rise to a new kind
of quantum erasure.
Figure 2. Mutual IFM, where the
“bomb” is also quantummechanical.
4. This erasure nonlocally erases the previous partial nonlocal eﬀect on the distant particle. 5. This way, the
particles may keep “talking” to one another for a long time, unlike the
ordinary EPR in
which they become disentangled after one measurement.
This method, and the ones describebelow, havethis featurein
common. Quantummeasurementis illunderstood and abrupt. If one makes it
gradual, some novel features of the measuring process emerge.
4. MAKING IFM MUTUAL: SUPERPOSED PARTICLES MEASURE ON ANOTHER
1Next we
study more advance variants. To understand their intriguing nature, recall that
the uniqueness of IFM lies in an exchange of roles: The quantum object, rather
than being the subject of measurement, becomes the measuring apparatus itself,
whereas the macroscopic detector is the object to be measured. In their
original paper,6,7Elitzur and Vaidman mentioned the possibility of an IFM in which
both objects, the measuring one as well as the one being measured, are single
particles, in which case even more intriguing eﬀects can appear. This proposition was taken up in a seminal work
by Hardy.He considered an EV device (Fig. 2) similar to that described in
Section 2, but with a more delicate “bomb,” henceforth named a “Hardy atom.”
+
This atom’s state is as follows. Let a spin
−
1 2
+atom be prepared in an “up” spinxstate (x
) and then split by a
nonuniform magnetic ﬁeld Minto its zcomponents. The two components are
carefully put into two boxes Zand Zwhile keeping their superposition state:
Ψ = γ · 1√ 2(iZ+
+Z−). (1)
The boxes are transparent for the photon but opaque for the atom.
Now let the atom’s Z−box be positioned across the photon’s vpath in such a way that the
photon can pass through the box and interact with the atom inside in a 100% eﬃciency.
Next let the photon be transmitted by BS1:
Ψ = 1√ 2(iu +v )· 1√ 2(iZ+ +Z−). (2)
−Discarding
all these cases of the photon’s absorption by the atom (25% of the experiments)
removes the term v Z , leaving: Ψ =1 2· (− uZ+ +iuZ− +ivZ+). (3)
Next, reunite the photon by BS2:
v
u
BS2−→ 1√ 2
BS2−→ 1√ 2
· (d +ic) (4)
· (d − ic), (5)
so that Ψ =
i √23
· [c · (iZ+ +2Z−)− d Z+]. (6)
After the photon reaches one of the detectors, the atom’s Zboxes
are joined and a reverse magnetic ﬁeld − M is applied to bring it to its ﬁnal
state F. Measuring F’s xspin gives:
Ψ = 14 · d · (− iX+ +X− )
+ 14 · c · (− 3X+ +iX−). (7)
−In 1/16 (6.25%) of the cases, the photon hits detector D, while
the atom is found in a ﬁnal spin state of X rather than its initial state X+ . In
every such a case, both particles performed IFM on one another; they both
destroyed each other’s interference. Nevertheless, the photon has not been
absorbed by the atom, so no interaction seems to have taken place.
Hardy’s analysis stressed a striking
aspect of this result: The atom can be regarded as EV’s “bomb” as long as it is
in superposition, and its interaction with the photon can end up with one out
of three consequences:
• The atom absorbs the photon – this is analogous to the explosion
in EV’s original device. • The atom remains superposed – this is analogous to
the noexplosion outcome. • The atom does not absorb the photon but looses its
superposition – a third possibility that does not existwith the classical bomb
and amounts to a delicate form of explosion.
+Hence, when the last case occurs, it appears that the photon has
traversed the uarm of the MZI, while still aﬀecting the atom on the other arm by forcing it to assume (as
measurement will indeed reveal) a Zspin!
5. STRAINING SEQUENTIALITY
8Hardy argued that this result supports the guidewave
interpretation of QM. His reasoning was that the photon
tooktheuarmoftheMZIwhileitsaccompanyingemptywavetookthevarmandbroketheatom’ssuperposition.
However, Cliftonand Pagonis910argued that the result is no less
consistent with the “collapse” interpretation. Griﬃths,11employing the “consistent
histories” interpretation, argued that the result indicates that the particle
might havetaken the varm as well, and Dewdny et. al.12reachedthe
same conclusion using Bohmian mechanics. Rather than taking a side in this
debate, we pointed outa more peculiar case for which all the above
interpretations seem to be insuﬃcient.
Consider the setup in Fig. 3. Here too, one photon traverses the MZI, but now
it interacts with, say, three Hardy atoms rather than one. Formally:
Ψ = γX+ 1 X+ 2X+ 3. (8)
After the photon’s passage
through BS1
and the atoms splitting into their zspins:
Ψ = 14 · (iu +v )· (iZ+ 1 +Z+ 2) ·(iZ
+Z2)· (iZ+ 31 +Z3 ). (9)
u
g
BS 1
v
D
BS 2c d
B
C
Z
1
+
Z
2
+
Z3+
Z
1

Z
2

Z3
Figure 3. One photon MZI with several interacting atoms. Here too,
introducing the blocking object B will prevent the predicted result.
As in the previous experiment, we discard all the cases (44%) in
which absorption occurred:
Ψ = 14 · [− vZ1Z2Z+ 1 (10) +u(+iZZ+ 2Z33 +iZ+ 1Z2Z+ 3+ 1 +Z Z2 Z3 +iZ1 Z+ 2 Z+ 31 +Z Z+ 2 Z3 +Z1Z2Z+ 31 − iZZ2Z3 − Z+ 1 Z+ 2 Z+ 3)]. Now let us pass the photon
through BS2and select the cases in which it has lost its
interference, hitting detector D:
Ψ = 14 √2 · d
·(iZ+ 1Z+ 2Z+ 3 +Z+ 1Z+ 2Z+ 1 +ZZ2Z+ 3 − iZ+ 1Z23Z1 +Z Z+ 2Z+ 3 − iZ1Z+ 2Z31 − iZZ2Z+ 33). (11)
Measuring the 3 Hardy atoms’ spins now will yield, with a uniform
probability, all possible results, except the case where all the atoms are
found in their Zii boxes, which will never occur. This is only logical, since if the
atoms were all in their Z boxes, the photon would not have been obstructed,
and the interference would have remained intact.
Next, reuniting the atoms’
Zboxes and measuring their xspin will yield all possible combinations of X+
and X−
in uniform probability, except the case of all three atoms
measuring X+
8,9
+
+ 2 (57% of
the cases):
Ψ = 14 √2 ·d · (− iZ1 +Z+ 1+ 2) ·Z ·
(iZ+ 3 +Z3). (12)
which has a higher probability.
That is also natural, as these atoms are supposed to have interacted either
with the guide wave, or with the real particle itself, or with the uncollapsed
wave function, depending on one’s favorite interpretation.
Let us, however, return to
the intermediate stage prior to the uniting of the Zboxes (as per Eq. (11)). We
know that at least one atom must be in the Z box to account for the loss of
the photon’s interference. Let us, then, measure atom 2’s spin, and proceed
only if it is found to be Z
Atom 2
Z
Z
+2
2
2
BS 2
Detectors D
X+ F2M M
c d
C
u
g
BS 1
v
Z
+1
Z
X+ F1Atom 1M M11
Figure 4. Entangling two atoms that never interact.
Now unite the zboxes of atoms 1 and 3 and apply the reverse
magnetic ﬁeld − M:
Ψ = 12 √2 · d · X+ 1 · Z+ 2 · X+ 3 . (13)
Surprisingly, atoms 1 and 3 will
always exhibit their original spin undisturbed, just as if no photon has
interacted with them. In other words, only one atom is aﬀected by the photon in the way pointed out by
Hardy, but that atom does not have to be the ﬁrst one, nor the last; it can be
any one out of any number of atoms. The other atoms,
whosewavefunctionsintersectthe MZI armbefore orafter that particularatom,
remain unaﬀected.
thAny attempt to reconstruct a comprehensible account from these
correlations gives a highly inconsistent scenario. For, if it is the
measurement of the second atom that have cancelled the photon’s vterm, then,
for the photon to reach that atom, it must have ﬁrst passed through the ﬁrst
atom, and, later, through the third as well. If one tries to visualize this
result, then a single photon’s wave function seems to “skip” a few atoms that
it encounters, then disturb the matom, and then again leave all next atoms
undisturbed. Ordinary concepts of motion, which sometimes remain implicit
within prevailing interpretations, are inadequate to explain this behavior.
6. EPR EFFECTS BETWEEN PARTICLES THAT NEVER INTERACTED IN THE PAST
Another elegant experiment by Hardy6brings
together nearly all the famous quantum experiments, such as the doubleslit,
the delayed choice, EPR and IFM – all in one simple setup (Fig. 4).
Let again a single photon
traverse a MZI. Now let two Hardy atoms be prepared as in Section 4, each atom
superposed in two boxes that are transparent for the photon but opaque for the
atom. Then let the two atoms be positioned on the MZI’s two arms such that atom
1’s Z+ 1box lies across the photon’s vpath and 2’s Zbox is positioned
across the photon’s upath. On both arms, the photon can pass through the box
and interact with the atom inside in 100% eﬃciency. Now let the photon be transmitted by BS: Ψ =1 √23(iu +v
)· (iz+ 1+z+ 2+z21) ·(iz12). (14)
Figure 5. Entangling two atoms.
Once the photon was
allowed to interact with the atoms, we discard the cases in which absorption
occurred (50%), to get:
Ψ =
1 √
2
1z+ 2(15) +ivz+v z). Now, let photon parts uand vpass through BS2:1z2
− uz1z+ 2
( − iuz+ 1z+ 2
3
v
u
BS2−→ 1√ 2
BS2−→ 1√ 2
· (d +ic) (16)
· (c +id), (17)
1z+dz+ 21z2− 2cz1z2
thereby hitting detector
D, we get: Ψ =
+ 2
+z1z2
giving Ψ =
1 4
( d z+ 1z+ 2
1 4d(z+ 1z
(18) − icz). If we now postselect only the experiments in which
the photon was surely disrupted on one of its two paths,
). (19) Consequently, the atoms,
which nevermet in the past, become entangled in an EPRlikerelation. In other
words,
they would violate Bell’s
inequality. Unlike the ordinary EPR, where the two particles have interacted
earlier or emerged from the same source, here the only common event in the two
atoms’ past is the single photon that has “visited” both of them.
7. EPR UPSIDE DOWN
6Hardy’s
abovementioned experiment
inspired us to propose a simpler versionthat constitutes an
inverse EPR. Let two coherentphoton beams be emitted from two distant sourcesas
in Fig. 5. Let the sources be of suﬃciently low intensity such that, on average,one photon is emitted
during a giventime interval. Let the beams be directed towards an equidistant
BS. Again, two detectors are positioned next to the BS:
13
γv
= p1u= p1v= 1√ 2
+q0+q0uv
), (22)
+z+ 2
A1
ψA2
= 1√ 2
1
2
+z+ 1
), (23)
φγu
(iz
, (20) φ, (21) ψ(iz
where 1 denotes a photon state (with probability p2), 0
denotes a state of no photon (with probability q22+q2), p≪ 1, and p= 1. Since the two sources’
radiation is of equal wavelength, a static interference pattern will be
manifested by
diﬀerent
detection probabilities in each detector. Adjusting the lengths of the photons’
paths vand uwill modify these probabilities, allowing a state where one
detector, D, is always silent due to destructive interference, while all the
clicks occur at the other detector, C, due to constructive interference.
Notice that each single photon
obeys these detection probabilities only if both paths uand v, coming from the
two distant sources, are open. We shall also presume that the time during which
the two sources remain coherent is long enough compared to the experiment’s
duration, hence we can assume the above phase relation to be ﬁxed.
Next, let two Hardy atoms
be placed on the two possible paths such that atom 1’s Z+ 1box lies
across the photon’s upath and 2’s Z2box is positioned across
the photon’s vpath. After the photon was allowed to interact with the atoms, we
discard the cases in which absorption occurred (50%), getting
Ψ = 1√ 23(− ivz+ 1z+ 2
− v z1z+ 2
(24)
+iuz
1z+ 2
+uz1z2).
We now postselect only
the cases in which a single photon reached detector D, which means that one of
its paths was surely disrupted:
Ψ = 14 d(z+ 1z+ 2
+z1z2
z+ 1z+ 2
+z1z2.
), (25) thereby entangling
the two atoms into a fullblown EPR state:
In other words, tests of Bell’s
inequality performed on the two atoms will show the same violations observed in
the EPR case, indicating that the spin value of each atom depends on the choice
of spin direction measured on the other atom, no matter how distant.
Unlike the ordinary EPR generation,
where the two particles have interacted earlier, here the only common event
lies in the particles’ future.
One might argue that the atoms
are measured only after the photon’s interference, hence the entangling event
still resides in the measurements’ past. However, all three events, namely, the
photon’s interference and the two atoms’ measurements, can be performed in a
spacelike separation, hence the entangling event may be seen as residing in the
measurements’ either past or future.
8. NATURE CAUGHT CONTRADICTING HERSELF
Acloserinspection ofthe abovementionedinverseEPRrevealssomething
truly remarkable. Beyondthe apparent timereversal lies a paradox that in a way
is even more acute than the wellknown EPR or Schr¨odinger’s cat paradoxes. It
stems not from a conﬂict between QM and classical physics or between relativity
theory; rather, it seems to defy logic itself.
The idea underlying the
experiment is very simple: In order to prove nonlocality, one has to test for
Bell’s inequality by repeatedly subjecting each pair of entangled particles to
one out of three random measurements. Then, the overall statistics indicates
that the result of each particle’s measurement was determined by the choice of
the measurement performed on its counterpart. A paradox inevitably ensues when
one of the three measurements amounts to the question “Are you nonlocally aﬀected by the other particle?”
Let us, then, recall the
gist of Bell’s nonlocality proof14for the ordinary EPR experiment.
A series of EPR particles is created, thereby having identical polarizations.
Now consider three spin directions, x, y, and z. On each pair of particles, a
measurement of one out of these directions should be performed, at random, on
each
Figure 6. Entangling two atoms.
particle. Let many pairs be measured this way, such that all
possible pairs of x, y, and zmeasurements are performed. Then let the incidence
of correlations and anticorrelations be counted. By quantum mechanics, all
samespin pairs will yield correlations, while all diﬀerentspin pairs will yield 50%50%
correlations and anticorrelation. Indeed, this is the result obtained by
numerous experiments to this day. By Bell’s proof, no such result could have
been preestablished in any localrealist way. Hence, 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 particle, no matter how distant.
Let us apply this method
to the abovementioned timereversed EPR. Each Hardy atom’s position, namely,
whether it resides in one box or the other, constitutes a spin measurement in
the zdirections (as it has been split according to its spin in this direction).
To perform the zmeasurement, then, one has to simply open the two boxes and
check where the atom is. To perform xand yspin measurements, one has to
reunite 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 nonlocally, just as in the ordinary Bell’s test.
A puzzling situation now emerges. In 44% (i.e. ,
The situation boils down
to:
4 9
) of the cases (assuming random
choice of measurement directions), one of the atoms will be subjected to a
zmeasurement – namely, checking in which box it resides. Suppose, then, that
the ﬁrst atom was found in the intersecting box. This seems to imply that no
photon has ever crossed that path, since it is obstructed by the atom. Indeed,
as the atom remains in the ground state, we know that it did not absorb any
photon. 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!
The same puzzle appears when the
atom is found in the nonintersecting 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, if we do not perform
the whichbox measurement (even though we are certain of its result) and
subject the other atom to an xor ymeasurement, Bellinequality violations will
occur, indicating that the result was aﬀected by the measurement performed on the ﬁrst atom (Fig. 6).
1. One atom is positioned in the intersecting box. 2. It has not absorbed
any photon. 3. Still, the fact that the other atom’s spin is aﬀected by this atom’s position means that
something has
traveled the path blocked
by the ﬁrst atom. To prove that, let another object be placed after the ﬁrst
atom on the virtual photon’s path. No nonlocal correlations will show up.
Thus, 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.
9. THE QUANTUM LIAR PARADOX SIMPLIFIED
An even simpler versionof the aboveexperiment can be devised. This
time let us consider 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/ground state. Here too, the measurement of one atom may show it
to be excited, implying that it has never emitted a photon and thus could never
become entangled was the other atom. But here again, by Bell’s Inequality, this
result must be eﬀected by
the other, supposedly nonentangled atom! All one has to do to make such a
clearcut experiment possible, is to chose another variable that is orthogonal
to the ground/excited state and then randomly employ the two measurements on a
series of atom pairs. This gedankenexperiment, just like all the others
described above, is technically feasible and we urge experimentalists to carry
it out.
10. WHAT, THEN, IS A PHOTON?
It is only natural to try to make some sense of the above
experiments. Of course, the formers’ validity does not depend on our favorite
interpretation. They pose a challenge to any interpretation of QM.
Let us bear in mind that the
photon is so strange because it belongs to three of physics’ most notorious
crime families. It is, at the same time,
1. a quantum object, like electrons, neutrons and atoms, hence its
motion is governed by the wavefunction, an odd entity that deﬁes ordinary
notions of space and time;
2. a relativistic object, like gravitons, whose velocity is
invariant, appearing the same for any observer; and 3. a forcecarrying
particle, like gravitons, gluons and W and Z bosons, whose interchanges between
bodies
alter, in yet unknown ways, their
relative motions. Most likely, an explanation for all these peculiarities
amounts to no less than the long soughtfor uniﬁed ﬁeld
theory, not a modest task. Is there any point trying? Well, is
there any point trying to say what is a photon without trying? Let’s aim high!
15We believe that solving the photon’s riddle requires physics to
face another, longneglected question, that of the very nature of time.
Mainstream physics denies any objective reality to time’s “passage,” viewing it
as an illusion. Our model’sbasic assumption is just the opposite: Time “ﬂows”
in a way that makes spacetime, together with its events and worldlines, “grow”
in the future direction.
Once spacetime itself is granted
evolution, then all the wavefunction’s peculiarities may be looked at in an
entirely new way: Perhaps the wavefunction is more fundamental than spacetime.
Rather than proceeding as an extended wave within an empty spacetime and then
“collapsing” to a localized particle, perhaps wavefunction collapse gives rise
not only to the particle’s position within spacetime but to the entire
spacetime region associated with it.
Ifthewavefunctionismorefundamentalthanspacetime,soshouldbetheinteractionbetweenwavefunctions.
When two particles interact with one another, being in their privileged “now,”
reside on the very “edge” of spacetime. Beyond this “edge” lies the ultimate
nothing, that is, not even spacetime, just as the BigBang model portrays the
“outside” of the universe.
The wavefunctions interact,
then, “outside” spacetime, and this interaction gives rise not only to the
particle’s future relative locations. The quantum interaction creates the
entire new spacetime region within which the particles interact. Whether they
will be closer to one another (attraction) or further (repulsion), is thus
determined by their prespace interaction.
This speculation oﬀers novel ways to think about interactions
and the very notions of motions and forces. Can it fruit into a precise and
testable theory? We hope to be able to answer this question in the aﬃrmative one day. About one thing we are sure:
Enough with the prevailing straightjacket approach of “Shut up and calculate!”
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