TI (Transactional Interpretation)
and TSVF (Time Symmetric Vector
Formalism): A comparison
and some remarks about free will
Ruth E. Kastner
Trinity College Cambridge 2014
Part 1: Overview of TI, its newer
version PTI, and comparison with TSVF
First remark: PTI is a realist theory that proposes a
novel ontology not based on beables or ‘elements of
reality,’ where such beables/elements are determinate
but unknown values of observables
Instead: quantum objects are taken as physically real
possibilities not contained in spacetime, but which can
give rise to spacetime events.
Overview of TI
• Based on the Wheeler/Feynman and Davies direct-action theories,
in which the basic field propagation is time-symmetric and the
response of the absorber plays a crucial role.
• in TI, the usual quantum state, emanating from an emitter, is called
an ‘offer wave’ (OW): |Y>
• the absorber’s response to the offer wave is a negative energy
(advanced) solution, called a ‘confirmation wave’ (CW): <F|
• the interaction of OW and CW is like a ‘handshake’ that occurs
outside spacetime (in my version, Possibilist TI) . In general, one OW
generates several CW responses. Each of these sets up an incipient
(possible) transaction.
• One of these is actualized, whereupon a real transfer of energy
occurs from emitter to ‘winning’ absorber in spacetime. The set of
incipient transactions is the physical basis for von Neumann’s
‘process 1’ or measurement transition (pure state to mixed state);
collapse is the transition from mixed state to a single outcome.
Offer and Confirmation Waves
•
•
•
According to the time-symmetric
theory, any emission of a retarded
offer wave (OW) is accompanied by
an advanced wave. This is the timesymmetric propagator in Davies
relativistic theory—each field is half
strength.
absorbers are stimulated to
respond with their own timesymmetric field, exactly out of
phase with the offer wave: any
confirmation wave (CW) is
accompanied by a corresponding
retarded wave
the advanced wave from the
emitter and the retarded wave
from the absorber are cancelled
while the field between emitter
and absorber are reinforced to full
strength
Courtesy of John G. Cramer (1986)
Completed transaction
The ‘transacted’ wave has a dual
role:
(1)superposition of retarded field
and advanced field adds to an
effective full strength real
retarded field: ½( e-iwt + eiwt) =
cos( wt)
(2)the product of the amplitudes of
the two components, Y*Y,
provides a natural physical
explanation for the Born Rule.
Courtesy of John G. Cramer (1986)
Example of several absorber responses: a MachZehnder interferometer:
An OW |s> from the source encounters
two possible absorbers C and D.
The component absorbed by C is
<c|s>|c> and the component absorbed
by D is <d|s>|d>. Each absorption
results in the advanced CW <s|c><c|
and <s|d><d|, respectively (response of
the absorber to the emitter).
Thus the interaction of offer and
confirmation for a particular absorber is
represented by a weighted projection
operator, e.g.:
<c|s><s|c>|c><c|= |<c|s>|2 |c><c|,

from which we can just read off the Born S
Rule, as well as gain a physical referent
for the ubiquitous projection operators.
C
D
Von Neumann’s “process 1”
• The preceding account leads to a weighted set of ‘competing’
potential transactions, each of which is called an ‘incipient
transaction’
• Each incipient transaction is represented by a projection
operator multiplied by the relevant squared amplitude (the
Born Rule), so this weighted set of incipient transactions is just
von Neumann’s “Process 1,” or heretofore mysterious
measurement transition.
• thus, it is the responses from absorbers x to the initial pure
state |s> that gives the mixed state:
| 𝑠 𝑥 |2 |𝑥 𝑥|
𝑥
Not all of these ‘incipient transactions’ can be actualized…..
What decides which transaction is actualized?
The measurement basis is
specified by what
absorbers are available
(‘Process 1’);
but what ‘causes’ a
particular transaction
|x>< x| out of the
weighted set
2
𝑥 | 𝑠 𝑥 |𝑥 𝑥| ?
Proposal (‘Possibilist TI’ or PTI):
QM suggests that nature has a
deeper kind of spontaneous
symmetry breaking characterizing
the transition from the potential
to the actual; an analog of
spontaneous symmetry breaking:
Weighted SSB.
This is an opening for volition at
some level (Nature? Individual
agents? Both?)
References on PTI
• Kastner (2012) The Transactional Interpretation of
Quantum Mechanics: The Reality of Possibility. Cambridge
University Press
• Kastner (2012) “The Possibilist Transactional
Interpretation and Relativity”, Foundations of Physics: Vol
42, Issue 8, Page 1094-1113
[http://arxiv.org/abs/1204.5227]
• Kastner (2010) “The Quantum Liar Experiment in
Cramer's Transactional Interpretation ,” SHPMP: Vol 41,
Issue 2, May 2010, 86-92 ) [arXiv:0906.1626]
The first two references (cf.
http://arxiv.org/abs/1204.5227) provide an account for the
micro/macro divide, and the emergence of classicality, in
terms of the likelihood of the emission of offers and
confirmations and resulting actualized transactions. These
considerations involve the relativistic level.
Concerning the emergence of classicality, I recently
observed that ‘Quantum Darwinism’ in an Everettian
approach, i.e., ‘decoherence’ and ‘einselection’ in a
unitary-only dynamics, does not work as advertised:
Kastner (2014) 'Einselection' of Pointer Observables: The
New H-Theorem? Forthcoming in SHPMP, arXiv:1406.4126
Now, the comparison between
PTI and TSVF
Areas of commonality
1. Both TI and TSVF involve ‘something more’ beyond the onestate formulation of QM
2. Both TI and TSVF make use of advanced states, although in
different ways
3. TI and TSVF are both empirically equivalent to standard
QM.* The founders of TSVF have said: “…Does it mean that the
TSVF has different predictions than the standard quantum approach?
No, the two formalisms describe the same theory with the same
predictions.” (Aharonov and Vaidman, “The Two-State Vector Formalism:An Updated
Review,” www.tau.ac.il/~yakir/yahp/yh165.pdf
#3 is why I object to claims that various experiments allegedly support TSVF as
opposed to standard QM: that is not possible, since they both yield exactly the same
observable predictions. (Argument from simplicity is unreliable; specifics given later if
time allows.) Note that I don’t claim that any particular experiment (at the
nonrelativistic level*) corroborates TI, since all such experiments also corroborate
standard QM. What I do claim is that TI provides a better explanation for certain
peculiarities of the formalism (e.g. Born Rule), as well as the physical nature of
‘measurement’ and collapse. It does so by providing physical referents for crucial but
ad hoc formal machinery in the theory (e.g. Born Rule, V.N. ‘Process 1’.)
*There is a possible deviation between PTI and standard QED at the relativistic level
(see Kastner 2013, arXiv:1312.4007 )
Another commonality that, on further
reflection, is actually just PTI with itself….
TI in its possibilist form (PTI) agrees with A. Elitzur that the past is
‘empty’ pending a measurement result; measurements bring
about certain aspects of the past. However, arguably this picture
is not consistent with the TSVF, since it treats an emitted
quantum as existing for some time without a post-selection
measurement; i.e., as a single forward-directed state (offer wave
in TI). That is the only way that the past could ever be ‘empty.’
But in TSVF, quanta are always described by TSV, not by single
states. This is indicated by E.C. and L.V.’s references to ‘future
measurements’ as existing and having influences on the present
and past. Therefore, by assumption in TSVF, the past can never
be ‘empty.’ Perhaps what A.E. has in mind is really the
transactional picture and not TSVF?
Areas of divergence
1.
In TI the advanced state is a separate entity, the ‘confirmation wave’ : <F|
2.
In PTI, both offers and confirmations are pre-spacetime entities.* It is only an
actualized transaction that establishes spacetime events. In contrast, TSVF
takes two-state vectors as spacetime entities (see also below).
3.
Two-state vectors are essentially offer wave components, i.e., the different
components of the OW reaching different absorbers; so they are not the
whole story according to the transactional picture
4.
TI gives a straightforward account of the Born Rule, while TSVF must assume
it.
5.
PTI involves pre-spacetime, sub-empirical retrocausation only, while TSVF
asserts that retrocausation occurs within spacetime
6.
In PTI there is a growing universe, whereas TSVF implies a block universe: all
future measurements must be assumed to exist as events in spacetime in
order to define the basic quantum states, which always include postselection.
*So are microscopic emitters and absorbers such as individual atoms.
7. It is inconsistent with the relevant direct-action theories (such as
Wheeler-Feynman (1945, 1949) and Davies (1971, 1972)) to combine the
retarded state |y> and advanced state <f| into a single hybrid entity, <f||y>.
The advanced and retarded solutions are fundamentally distinct entities,
even though they can and do interact and function to produce phenomena
Isn’t the transactional interpretation ‘retrocausal’?
Only at the sub-empirical, pre-spacetime level.
.
•
In possibilist TI (PTI), offers and confirmations bring about spacetime events
from a pre-spacetime domain of possibilities. Thus any ‘retrocausality’ in PTI
is not a causal influence within spacetime. Rather, it is part of the process by
which ST events are created. (cf. Kastner 2012, Chapter 8)
• PTI therefore does not have explicit retrocausal effects within spacetime, nor
does it imply a block world picture.
Part 2: Free Will
Basic definitions
• Compatibilism: free will is compatible with
determinism (and/or a block world)
• Incompatibilism: free will is incompatible with
determinism; also incompatible with
indeterministic block world
• Agent-causal libertarianism: a form of
incompatibilism asserting that we do have
free will; agents are the irreducible causes of
their willed actions
Ginet’s formulation of incompatibilism:
‘Consequence Argument’ (1966)
• “No one has power over the facts of the past and the laws of
nature.
• No one has power over the fact that the facts of the past and
the laws of nature entail every fact of the future (i.e.,
determinism is true).
• Therefore, no one has power over the facts of the future.”
Thus, Ginet’s argument acts as a refutation of compatibilism.
If in addition the future is already determinate (as in a block
world picture), no one has power over the facts of the past,
present, and future, regardless of laws. Being ignorant of
choices we are fated (and thus compelled) to make is not
equivalent to having free will.
another way to look at it
• the spirit behind the preceding principle is that if the laws
governing events require those events given certain
conditions not dependent on the agent, and those conditions
are met, then the agent is not the free cause of those events.
• In this sense, a block world picture rules out free will, because
it specifies laws and conditions, all of which obtain without
any input from an agent participating in the events. This
applies also to an indeterministic block world; in such a world,
all events already exist without any input, external to those
events, from the agent .
• (Possible exception: agents are seen as bringing about the
spacetime events from outside spacetime—an account would
be needed)
None of the dominoes has any say in its behavior (simple
determinism); if in the future each is already fallen, doubly so.
None of them needs to be consulted on whether it will fall or not.
Incompatibilist libertarian
• Argues that events are neither deterministic
nor fated, and that we do have free will
permitted by this fundamental indeterminism.
• Various demands for an adequate libertarian
account – a few preliminary comments about
that
• Various objections to this view; I’ll focus on a
specific one that is arguably the most
important
the ‘common thesis’ contra
libertarianism
• The idea that libertarians are necessarily
committed to anomic or ‘lawless’ human
action, i.e. that human choices are not subject
to any law
• This is certainly questionable; e.g.: Balaguer
2010, Kane 1996, and O'Connor 2000. Clarke
2003, chaps. 8-10 also takes libertarianism to
be compatible with comprehensive natural
laws.
In this context, some libertarians have attempted to
give an account of free choice in terms of reasons for
the choice….
• Many accounts of free will implicitly assume Principle
of Sufficient Reason (PSR). These kinds of
considerations often lead to difficulties (e.g. the
‘problem of luck, which replaces volition with ‘luck’
without justification)
• The characterization of libertarianism as requiring
‘anomic’ or ‘lawless’ action (e.g. Pereboom 2005) is an
implicit adoption of PSR: it effectively equates basic
indeterminism with ‘lawlessness’
• However: PSR not at all required for a free choice. In
fact, it is a key element of free choice that an agent
need not have any reason--or even desire-- for the
choice, but makes it out of pure volition.
Example of a free choice lacking
a sufficient reason: Buridan’s Ass
Would a donkey starve to
death because he has no
specific reason to choose
one bundle of hay over
another? Probably not. A
political cartoon (ca. 1900)
satirizing U.S. Congress’
inability to choose
between a canal through
Panama or Nicaragua, by
reference to Buridan’s Ass.
[Wiki Open Source; public domain]
Volition…
• The ability and power to make a completely arbitrary
choice. [Example: The arbitrary and capricious choice
of the evil Centauri Emperor Cartagia on ‘Babylon 5’]
• No reason, desire, or asymmetrical cause of any kind
required for that choice.
• Well-known example in physics: spontaneous
symmetry breaking--the actualization of one of a set of
equally legitimate solutions, where there is no reason
at all to prefer the one selected. This phenomenon is
certainly not ‘anomic,’ even if it is underdetermined.
Objection to free will even if the world
is indeterministic
Pereboom (2013): “…it might be that if we were undetermined agent
causes – if we as substances had the power to cause decisions without
being causally determined to cause them – we would then have…free
will. But although our being undetermined agent causes has not been
ruled out as a coherent possibility, it is not credible given our best
physical theories.“ He is referring to Sider’s argument: (Sider 2005:
“agent causation [is] a slave to quantum mechanical probabilities")
Specifically: if a class of choices is governed by quantum statistical
laws, this places a constraint on free choices that some have taken as
ruling out free will. The argument: it would take a ‘miracle’ for all the
freely chosen actions, out of a class of actions, to conform to the
statistical constraints.
A counterargument…
• Clarke (2010): argues that an agent can freely
choose even under a probabilistic constraint;
there is no inconsistency
• In what follows, we develop his argument
further. To do so, we need to journey to…
The Land of the
Quantum Dominoes
The God of the Quantum Dominoes
I decree that whenever one of
my Subjects is struck, he has
a free choice of whether to fall
or not. However, each has a
50% chance of falling, and
they must collectively
demonstrate that by a
frequency of 50%. Therefore,
if all my Subjects are struck,
only half of them should fall.
the paradox…
• if each domino has a free choice of whether to
fall, doesn’t this imply that they could all fall if
they so chose, thus violating the God’s
decree? I.e., isn’t the God’s decree selfrefuting? (This is Sider’s objection.)
• on the other hand, if each just happened to
freely choose so as to conform to the
collective statistics, wouldn’t that be a
miracle?
Not if the dominoes’ volitional choices are
subject to quantum influences—’steering’
Nominally, each domino has an objectively indeterminate 50%
chance, and therefore a free choice, of whether to fall or not.
Suppose ‘Yes’ means it chooses to fall and ‘No’ means it chooses
not to fall. We could model the state of each by the
superposition
|Y> = (1/√2) [|Y> + |N>],
where the choice options instantiate a physically well-defined
‘computational basis’
Model them by a collective quantum state. Toy example: 3
dominoes
3-domino state
(Y=falls; N=does not fall)
|Y> = (1/2√2) {|YYY> + |YYN> + |YNY> + |YNN>
+ |NYY> |NYN> + |NNY> + |NNN>}
Suppose the first two dominoes make their choices.* The third domino
is ‘steered’ more toward one choice than another, based on the
choices of his fellows. This constrains the exercise of his will, but does
not eliminate it.
Significantly: who said that exercise of the will need be effortless? In
fact, it usually takes an ‘effort of will’ to carry out certain morally
correct actions (such as taking back the library book that you insisted
you had returned 10 years ago, but just found in your basement). Thus,
exercising free will under contrary pressures is certainly an empirically
valid experience.
*This need not imply a preferred frame. QM constraints apply atemporally in TI (see
Kastner 2012, Chapter 5)
Specifically,
|Y> = (1/2√2) {|YYY> + |YYN> + |YNY> + |YNN>
+ |NYY> |NYN> + |NNY> + |NNN>}
Probability that 3rd domino will choose to fall:
applicable states are 1,3,5,7.
If the 1st and the 2nd domino choose to fall, the 3rd has only a
25% chance (term #1). But if at least one of the others chooses
not to fall (terms #3,#5, and #7), 3rd has a 75% chance of falling.
Thus, 3rd is steered away from falling based on choices of the
others to fall. It is still perfectly possible for 3rd to choose to fall;
however, it requires a ‘stronger effort of will’. In this way, the
decree of the God of the QM Dominoes is satisfied.
Conclusion
QM constraints are no obstacle to free will, but they can be
seen as influencing the likelihood of an agent’s making a
particular choice, in effect requiring different amounts of
effort required to make various choices.
The influence can be seen as a collective effect arising from an
‘entanglement’ of wills of individual agents. Reminiscent of
Jung’s ‘collective unconscious’? Or Aboriginal ‘Dreamtime’?
“Dreamtime is a place beyond time and space……” and
“[Aboriginals] believe that every person essentially exists
eternally in the Dreaming. This eternal part existed before the
life of the individual begins, and continues to exist when the
life of the individual ends.” [http://www.crystalinks.com/dreamtime.html]
Recap: PTI explains the Born Rule and measurement
process, including the physical basis for Von Neumann’s
“Process 1,” the transition from a pure to mixed state.
• PTI involves a limited and subtle form of subempirical retrocausation
• In that sense, it has overlap with A. Elitzur’s notion of
‘filling in the empty past’
• However it lacks the tension of the TSVF which
invokes explicit retrocausality while implying a block
world ontology.
• PTI has room for a robust form of free will, whereas
TSVF does not.
• PTI is based on well-developed time-symmetric field
theories, while TSVF deviates from those theories in
an ad hoc way.
Available down the street at the CUP
bookstore…
Kastner (2012)
The Transactional
Interpretation of
Quantum Mechanics:
The Reality of Possibility
supplemental material & references
• for reference specifics, contact the author via
transactionalinterpretation.org
remarks on weak values and
retrocausality in a block world
•
As Silberstein, Stuckey et al have pointed out, a block world certainly has
relations between events, but it is acausal in a dynamical sense. If all events
already exist in spacetime, nothing within spacetime is required to bring them
about. Causality is superfluous in this picture. (One could still consider
creation of events from beyond spacetime, as in Sorkin’s causal set approach
allowing for the creation of events from a pre-spacetime ontology)
•
Two-state vector formalism implies a block world, since all future
measurements must be assumed to exist in order to define the states. So
there is tension between the idea that we can have well-defined, spacetime
two-state vectors and that they also involve causation, in either direction.
•
In any case, weak values in themselves, as elements of the standard QM
formalism (basically matrix elements or two-time transition amplitudes), have
nothing to say about the ontology of the world or causal flow. In particular,
they do not imply retrocausation within spacetime. To see this, consider the
parable of…
Weak SHOE Values and
the DRUNKEN Shoe Factory
Alice owns a shoe factory. On Thursday night, her workers party too hard, and the
shoes they make on Friday have a high rate of defects. In contrast, on Sunday night
the workers are all in a state of repentance and abstention, and their performance
on Monday is exemplary.
Bob owns a retail shoe store and is one of Alice’s customers. When receiving
shipments of shoes (preselection state |A>), he sorts them into two piles, one for
‘ready to sell’ (|S>) and another for ‘return due to defects’ (|D>) . The observable in
question is the day of the week each shoe was made. Compare the (unnormalized)
weak values of Monday and Friday for the “two-state vector “ <D||A> :
<D|M|A> << <D|F|A>
Weak SHOE Values and
the DRUNKEN Shoe Factory
Alice owns a shoe factory. On Thursday night, her workers party too hard, and the
shoes they make on Friday have a high rate of defects. In contrast, on Sunday night
the workers are (of course) all in a state of repentance and abstention, and their
craftsmanship on Monday is exemplary.
Bob owns a retail shoe store and is one of Alice’s customers. When receiving
shipments of shoes (preselection state |A>), he sorts them into two piles, one for
‘ready to sell’ (<S|) and another for ‘return due to defects’ (<D|) . The observable in
question is the day of the week each shoe was made. Compare the (unnormalized)
weak values of Monday and Friday for the “two-state vector “ <D||A> :
<D|M|A> << <D|F|A>
Do we conclude that Bob’s selection of a defective shoe retrocausally influences that
shoe to have been more likely made on a Friday? No. This is no different from
ordinary statistical inference, i.e., a defective shoe is simply more likely to have been
made on a Friday. In standard QM terms, the states |F> and |D> have a large
overlap, whereas the states |M> and |D> are almost orthogonal.
Thus, causation is underdetermined
in the context of ‘weak values’:
The expression <D|M|A> << <D|F|A>
in this example simply reflects the fact that most of the defective shoes are
coming from the Friday production. The post-selection sorts the process into
different ensembles, each with its own characteristics; but retrocausation is
neither implied, nor necessary, nor the most natural explanation of the
phenomena. It is entirely superfluous. There is nothing about quantum
entities (as opposed to classical objects like shoes) that escapes these
conclusions; they can apply also to electrons in a Stern-Gerlach apparatus.
Weak values are simply normalized transition amplitudes, and as such do not
themselves imply anything about the direction of causal influences, or even
whether there are any causal influences. For example, in an explicitly acausal
block world such as that proposed by Silberstein & Stuckey, these sorts of
statistical correlations would express only acausal relations; there need be no
explicit causal flow even in the future direction!
Nevertheless: the directionality of causation is of course an interesting and
highly nontrivial question, and PTI does have things to say about that (see
Kastner 2012 and Kastner (forthcoming): Understanding Our Unseen Reality:
Resolving Quantum Riddles, Imperial College Press).
Further consideration—weak pointer measurement
and system post-selection could be spacelike
separated
• Model system/apparatus as an EPR pair:
there is a frame in which post-selection
occurs before weak pointer measurement
(pointer could be a poorly localized
photon)
• In this case, the system’s post-selection
can be viewed as steering the pointer in
the forward time direction
Conclusions re retrocausation in a
weak values context
• Retrocausation is a metaphysical assumption not implied or
required by the QM formalism or by weak values
• Of course, it’s not ruled out by the formalism either, but the
construction of a ‘two-state vector’ and attendant calculations
of weak values (which do not require a two-state vector for
their construction in any case) does not constitute an
argument that retrocausality obtains, or even that it is a
better way to understand what’s going on.
• What about the ‘argument from simplicity’?
Argument from simplicity favors retrocausal effects even from Bob’s
straightforwardly classical, future-directed shoe selection process. Thus, the
argument may well be overrated.
It is certainly simpler for Bob to assume that his selection of each shoe as
either defective or not retrocausally influences on which day it was crafted:
|A> →
|F><F| ← <D|, or
|A> →
|M><M| ← <S|
As opposed to the less simple account:
|S>
|D>
M><M| →
|
|A>
→
|F><F|
→
|D>
|S>
But we know that the latter accurately describes what happened in this case : the
projection of Monday-crafted shoes on the state |D> is very small, while the
projection of Friday-crafted shoes on the state |D> is very large.
"Make everything as simple as possible, but not simpler.“
- Albert Einstein
argument from simplicity can amount to a logical fallacy:
specifically, correlation demonstrates causation
Simplest explanation for data: pirates cause global warming? Or global warming
causes pirates? Which is it? Both? Or are there other things going on here, and should
we take them into account for a more accurate--even if less simple--story?
[http://en.wikipedia.org/wiki/Flying_Spaghetti_Monster#mediaviewer/File:PiratesVsTemp%28en
%29.svg]
3-box experiment demystified
Weak measurement of box C for given pre- and post-selection is
a projection of the pointer onto an x value when it is in the state
-1/3 |sort of yes> + 2/3 |sort of no>,
where ‘sort of yes’ and ‘sort of no’ states are not orthogonal, i.e.
<x|sort of yes> ~ exp[(x-1)2/D]
(x=1 corresponds to a definite ‘yes’ and D >> 1)
<x|sort of no> ~ exp[(x)2/D] (x=0 corresponds to a definite
‘no’)
Avg. value of pointer reading turns out to be -1. This does not
necessarily translate to any property of the system such as
negative mass or momentum. Measurements of the apparatus in
a strange superposition are not measurements of the system.
Rather, the apparatus is steered to an exotic state through the
given pre- and post-selection states of the system, which confer
on it the necessary phase relationships to attain strange x values.
superposed weak pointer state with
mean value x = -1