## 1. History



The philosophical debate about backward causation is relatively new.
Only little consideration of the problem can be found in the
philosophical literature before Michael Dummett and Anthony Flew
initiated their discussion in the mid 1950s. The reason for this is
twofold. No empirical phenomena seem to demand a notion of backward
causation for our understanding of them. And for a long time it was
thought that such a notion involved either a contradiction in terms or
a conceptual impossibility. David Hume's definition of the cause
as the one of two events that happens before the other thus rules out
that the cause can happen after its effect. Moreover, according to
Kant's idea of synthetic *a priori* truth the claim that
the cause temporally precedes its effect was considered to state such
a truth. In 1954 Michael Dummett and Anthony Flew had a discussion
about whether an effect can precede its cause. Dummett defended the
idea whereas Flew argued that it involved contradictions in terms.



Two years later, Max Black (1956) presented an argument against
backward causation, which became known as the bilking argument, and
later attempts to meet the argument seemed to generate all kinds of
paradoxes. Imagine \(B\) to be earlier than \(A\), and let \(B\) be
the alleged effect of \(A\). Thus, we assume that \(A\) causes \(B\),
even though \(A\) is later than \(B\). The idea behind the bilking
argument is that whenever \(B\) has occurred, it is possible, in
principle, to intervene in the course of events and prohibit \(A\)
from occurring. But if this is the case, \(A\) cannot be the cause of
\(B\); hence, we cannot have backward causation. Since then
philosophers have debated the effectiveness of the bilking argument in
particular and, in general, the validity and the soundness of the
concept of backward causation.



In the 1960s and 1970s, physicists began to discuss the possibilities
of particles travelling with a speed greater than light, the so-called
tachyons, and as a consequence a similar debate about paradoxes
involving backward causation arose among them. In case superluminal
particles, like tachyons, exist and could be used to generate signals,
it seemed possible to communicate with the past because tachyons going
forward in time with respect to one set of reference frames would
always be seen as travelling backwards in time from another set of
reference frames.



Now and then physicists and philosophers also invoke backward
causation in order to explain some experimental and theoretical
results within quantum mechanics. For instance, this might be in
connection with understanding quantum entanglement after several
experiments have proven the violation of Bell's inequalities.


## 2. Philosophy



A general notion of backward causation raises two sets of questions:
those concerning conceptual problems and those that relate to
empirical or physical matters. Among the first sets of questions that
require a satisfactory answer are the following:


### 2.1 Time and Backward Causation



*Can metaphysics provide a notion of time that allows that the
effect precede its cause?* Answering this question, one may argue,
on the one hand, as Maudlin (2002, p. 184) does, that in case we allow
backward and forward causation to be parts of our description of the
world, the "metaphysical picture of the past generating the future
must be abandoned, and along with it the mathematical tractability of
local theories." On the other hand, one may argue, as Evans (2015)
among others does, that backward causation is not "precluded by the
known structure of reality." Indeed, Evans's claim presupposes that
the future is ontologically on par with the past and that basic
physical laws are time symmetric such that the influence of a physical
process may under certain special conditions reach backwards in
time.



A proper notion of backward causation requires that the future is just
as real as the present and the past. It is common among metaphysicians
to distinguish between three different views on time. The first is
*presentism*. This view claims that only events that exist now
really exist. Past or future events do not exist. Past events have
ceased to exist, whereas future events are yet to become real. So only
statements about the present or related to the present have a definite
truth value. The second view is *possibilism* according to
which both past and present events exist, but future events are still
only possible or non-existing. This view is sometimes called *the
growing block universe*. As a consequence, the view holds that
only statements about past and present events have a definite
truth-value, but statements about the future are either probably true
or may completely lack any truth-value. Finally, the third view is
called *eternalism*, also named *the block universe*.
This position maintains that every past, present and future event
*tenselessly* exists at a certain time and that statements
about these events therefore have a definite truth-value at every
other time.



Usually, presentism and the growing block universe are associated with
the dynamic view of becoming. The transient now plays an ontological
role as the ever changing time in which things become real or perhaps,
if you are a presentist, cease to exist. One reason to prefer the
growing block universe from presentism may be the analysis of forward
causation. In order for a present event to be caused by a past event,
the past event must exist. Nothing, which does not exist in the past,
can cause something that presently exists. By the same token, if the
backward causation is a conceptual possibility, something must exist
in the future in order for it to cause something in the present.



Thus, backward causation demands eternalism or a static account of
time in the sense that there is no objective becoming, no coming into
being such that future events exist on the par with present and past
events. It means that the future is real, the future does not merely
consist of unrealised possibilities or even nothing at all. Ordinarily
we may think of the past as a nothing that once was a something. But
when asked what makes sentences about the past true or false, we would
probably also say that it is the facts of the past that make present
sentences about the past either true or false. The fact that I went to
the cinema yesterday makes it true today when I say that I went to the
cinema yesterday. This view is a realist one with respect to the past.
If backward causation is to be conceptually possible, it forces us to
be realists with respect to the future. The future must contain facts,
events with certain properties, and these facts can make sentences
about the past/future true or false. Such a realist account is
provided by static and tenseless theories of time. Eternalism is such
a theory and holds that the participation of time into the past, the
present and the future depends on the perspective we human beings put
on the world. The attribution of pastness, presentness and futureness
to events is determined by what we take to exist at times earlier than
and times later than the time of our experience. (For further
discussion, see the entry on 
 being and becoming in modern physics.)


### 2.2 Affecting the Past?



*Does backward causation mean that a future cause is changing
something in the past?* Talking about forward causation we think
of the cause as the event that produces its effect or brings it about.
It is not part of our notion of forward causation that the cause
changes anything in the future. A cause determines what the effect
will be. Regardless of whether one is an advocate for presentism, the
growing block universe, or eternalism, one never considers the cause
as an event that will make the future different from what it will
be. Indeed, without the forward-directed cause the future would have
been different from what it is going to be.



Even most protagonists consider it an unwarranted consequence that the
notion of backward causation, if consistent, involves the idea that
the future is able to change the past. Their answer has therefore
usually been that if we have the power to bring something about in the
past, what came about really already existed when the past was
present. We have to make a distinction between changing the past so it
becomes different from what it was and influencing the past so it
becomes what it was. A coherent notion of backward causation only
requires that the future is able to have an influence on what happens
in the past. Nonetheless, we can say, quite parallel to forward
causation, that the past would have been different if the
backward-directed cause had not made the past as it turned out to
be.


### 2.3 Distinguishing Cause from Effect



*Can the cause be distinguished from its effect so that the
distinction does not depend on a temporal ordering of the events*?
For a long time the distinction between cause and effect was their
temporal order. This view goes at least back to Hume who claimed,
"We may define a cause to be an object followed by another, and
where all the objects, similar to the first, are followed by objects
similar to the second," which is to say that "[...]
if the first object had not been, the second never had existed"
(Hume, [1748] 2007, 56). Although Hume did not explicitly say so, the
expression "followed by" has always been read as
"temporally followed by" and not "causally followed
by". So the adherents of this definition have usually tried to
give an account of causation in which the cause and the effect are
seen as temporal regularities between types of events. But we can also
see that Hume himself added a counterfactual statement about causation
which cannot be derived from his temporal definition. Apparently, he
noticed that if we have a cause and an effect, there exists a
relationship between them that is not given by the temporal order.



What is required for backward causation to be possible is some account
of the direction of causation which does not rely on the direction of
time. Various alternative proposals refer to counterfactuals,
probabilities, agency, manipulation and intervention, common cause or
causal forks. Among these it seems that only a Humean notion of
causation explicitly makes a temporal identification of the cause and
the effect. But there are also problems with some of the other
accounts.



For example, it is quite common to follow David Lewis and define
causation in terms of counterfactuals (Lewis, 1973). Assume event
\(c\) causes event \(e\), then we have a situation in which both \(c\)
and \(e\) occur, and in which the counterfactual statement "If \(c\)
had not occurred, then \(e\) would not have occurred" is true. Thus, in
Lewis's view, \(e\) is causally dependent on \(c\) if, and only if,
\(e\) is counterfactually dependent on \(c\). According to the
traditional theory, formulated by Lewis and Stalnaker, any
counterfactual statement is true if the consequent is true in the
closest possible world to the actual world in which the antecedent is
true. Apparently, Lewis' definition delivers a non-temporal
causal asymmetry, since the effect \(e\) is counterfactually dependent
on the cause \(c\).



As we saw above, Hume also believed that causal statements entail
counterfactuals, but the question is whether causal statements are
definable in terms of counterfactuals. Here is an objection against
such an attempt: Consider the following example. Because of severe
frost during the night, ice covers the lake this morning. So, given
the circumstances, if it had not been severe frost, there would not
have been any ice on the lake. However, in these circumstances, the
frost as the cause of the ice seems to be not only causally necessary
for the ice, but the frost also seems to be causally sufficient for
the ice cover. In other words, given the actual circumstances, it
seems correct to say that the frost is causally sufficient as well as
necessary for the ice. If we are going to represent causally
sufficiency in terms of a counterfactual statement, we might then say
that, given the actual circumstances, if no ice had covered the lake
this morning, there would not have been a severe frost during the
night. But if one accepts this objection, it shows that causal
statements cannot be defined in terms of counterfactuals because such
a definition does not give us the wanted asymmetry between cause and
effect since each is counterfactually dependent on the other.



Sometimes this problem is called the *Problem of
Effects*. According to this problem, the effect does not
distinguish itself other than temporally from the cause because both
the cause and the effect are counterfactually dependent on each
other. Over the years several attempts have provided solutions to this
problem. Lewis himself proposed some criteria consisting of a
hierarchy of possible worlds such that a world in which \(c\) occurs
but \(e\) does not occur is closer to the actual world than a world in
which \(c\) does not occur due to the absence of \(e\). But a number
of philosophers have challenged the aptness of these criteria, among
others Bennett (1974); Faye (1989); Horwich (1993); Baker (2003); Choi
(2007); Wasserman (2015), and Seli (2020).



However, and more importantly in the present context, is that
Stalnaker-Lewis' theory of counterfactuals has difficulties with
backtracking counterfactuals and backward causation because if \(c\)
occurs later than \(e\), the proposed method of truth evaluation
assumes that \(e\) occurs in the relevant possible worlds in which
\(c\) does not occur. In general, the assessment of a counterfactual
conditional is carried out by assuming that the possible world must be
identical with the actual world up to \(c\). Therefore, it is
stipulated that the closest possible world is one in which everything
happens just as in the actual world up to the time of \(c\)'s
occurrence, which means, given \(e\) occurs before \(c\), that the
possible world will include the occurrence of \(e\). But then it is
necessarily true that there is never a possible world closer to the
actual world which includes \(c\) but not \(e\). This creates a
problem because we consider any causal connection between \(c\) and
\(e\) as contingent. Rather we would expect that if we face a case of
backward causation where both a present event \(c\) and a past
event\(e\) occur, the following counterfactual would be true: "If
\(c\) had not occurred, then \(e\) would not have occurred." The truth
evaluation of this counterfactual, if it were to represent backward
causation, would require that the closest world without \(c\) is also
one without \(e\). Nevertheless, the traditional theory does not allow
such an evaluation.



How else can causality be specified so that the order of the
cause-effect relationship is not time-dependent? Several possibilities
seem open for such an account. Here we shall just mentioned some. One
could hold that the cause makes the effect more probable in the
circumstances; one could argue that causation can be understood in
terms of manipulation and intervention; one could argue that we can
specify causation in terms of transmission of information or conserved
physical quantities. Or, finally, one could argue that causality is a
primitive notion that may imply, or be used to explain, regularities,
counterfactuals, probabilities, transmission of signals, or
manipulation and intervention, but it cannot be completely analyzed in
any of these terms. If we take into consideration that higher animals
show a sense of causation, it may be a good indication that the origin
of this notion goes back in history and that it stems from the
cognitive evolution of grasping in which ways one's environment is
stable and in which ways one's behavior can interact and change the
environment.



This observation may come close to Lewis much later analysis of
causation as influence (Lewis, 2000). Thus, it is through our ability
to influence our environment that we improve our ability to manipulate
and intervene in the cause of events and through which we receive
knowledge of causal relationships and the causal order of this
relationship (Faye, 1989; Woodward, 2003). However, such an
understanding of causation is already rather complex, building on our
capacity of foreseeing the effect of our own actions, on our capacity
of foreseeing the effects of others' actions, on our understanding the
cause of others actions, and on our understanding the cause of
physical events (Gardenfors, 2006, p. 41).


### 2.4 The Bilking Argument



*Can the bilking argument be challenged in such a way that the mere
possibility of intervention does not generate any serious
paradoxes?* The bilking argument is due to Max Black (1956) who
assumed the following scenario. Suppose Houdini makes a prediction
about the outcome of, say, a coin about to be flipped \(B\) before
someone actually does the flipping \(A\). We may also assume that in
the past Houdini rarely failed in his predictions. In this case we
might be tempted to say that the Houdini's answer is caused by
the later flipping. But, as Black argued, after Houdini's
prediction of \(B\), we can always intervene such that the coin is not
flipped or arranged opposite to Houdini's prediction. The
implication is that \(A\) seems both to be the cause and not to be the
cause of \(B\). Black also argued that if \(A\) is the cause of \(B\),
then the causal antecedents of \(A\) are independent of \(B\). Hence,
if we cannot, after \(B\) has occurred, prevent \(A\) from happening,
then \(A\) cannot be said to be causally independent of \(B\). But
since it is in human power to intervene with respect to \(A\), Black
concluded that \(A\) cannot be the cause of \(B\)


 Since manipulation and intervention is so central for
our knowledge of causal relations, the image of our capability of
intervening in the course of backward causation, after the alleged
effect has occurred, seems to violate the whole idea that the notion
of backward causation is coherent. However, the force of the bilking
argument can, it seems, be weakened in various ways.



First, one may hold that it is not a problem for our notion of
backward causation that we can in principle intervene in the course of
the events. Usually, we find out whether two events are causally
connected trough manipulation and intervention. In case we can produce
one event \(Q\) by bringing about another \(P\), or we can obstruct
one event \(Q\) by preventing another \(P\), we think that \(P\) is
the cause of (\(Q\). Likewise, we believe that if \(P\) causes \(Q\)
in the relevant circumstances, we may be able to prevent \(Q\) from
happening if we intervene in the causal order after \(P\) occurs by
changing some of these circumstances, which make \(P\) causing \(Q\).
Should \(Q\) occurs in spite of this intervention, there must under
the new circumstances be another event \(X\) rather than \(P\) that
causes \(Q\).



Now, the bilking argument holds that backward causation is impossible
because we can always intervene after we have observe that the alleged
effect occurs and obstruct the alleged cause from occurring. Since
nothing prohibits us from doing this whenever we want, it demonstrates
that backward causation does not take place. Indeed, if we actually
intervene and prevent \(A\) after \(B\) has occurred, then of course a
particular later \(A\) (which does not exist) cannot be the cause of a
particular earlier \(B\) (which exists). But in all those cases where
nobody actually intervenes, events of the same type as \(A\) may be
the cause of events of the same type as \(B\). This situation is not
different from what may happen in some cases of forward causation.
Assume that \(P\) causes \(Q\) in the relevant circumstances. We may
still prevent a particular \(P\) from happening, but at the same time
a particular \(Q\) may nevertheless occur because in the given
circumstances it is caused by another event than \(P\).



Second, if a later event \(A\) really causes an earlier one \(B\),
then it would be impossible to intervene into the cause of the event
after \(B\) has happened and therefore impossible to prevent \(A\)
from happening. If someone tries, she will by all means fail. It may
intuitively sound strange as long as we think of backward causation as
consisting of something we can control directly by our everyday
actions. But if backward causation is a notion that is applicable only
to processes that human beings are unable to control in any
foreseeable way the notion would not provoke our intuitions so
much.



But even if we would have full control of backward causal processes
and able to intervene in their cause of events, we may not, in such
cases where we actually intervene, exclude backward causation from
taking place. Assume someone tosses a coin a minute after the magician
Houdini has predicted whether it would be heads or tails. Furthermore,
assume that Houdini's predictions are highly correlated with the
outcomes of the tossed coin. Presumably, no such high correlation
would exist unless we were facing a case of backward causation.
However, it turns out that the construction of a correlation may
behave differently depending on whether we consider Houdini's
predictions to be purely physical events or to have a semantic
content.



In an example like the one mentioned it is reasonable to think that we
discover the correlation between Houdini's predictions and the
subsequent outcomes of the tossed coin by comparing the semantic
content of the predictions with one of the two iconic sides of the
coin that define the semantic content. The side facing up determines
whether the prediction is true or not. First, in order to establish a
causal correlation between the content of the predictions and the
outcome of the tosses we would look for a high percentage of correct
statements made by Houdini. This is an epistemically necessary
condition for establishing a causal correlation. Second, there cannot
ontologically be a causal correlation between the semantic content of
Houdini's prediction and the (reading of) outcome of the head or tail if no flipping of the coin takes place. His predictions would not
carry any truth-value and we would think of them as pure guesses.
Hence, when someone attempts to bilk this experiment, he or she will
either arrange the outcome opposite to the content of Houdini's
prediction or abstain from flipping the coin.



However, one might suggest that a possible reply to Black's
bilking argument is to say that both tossing the coin and preventing
the toss may backwardly cause Houdini's behavior. That the
preclusion of the coin from being tossed may be a cause of
Houdini's response has also been proposed by Brian Garrett
(2020). But he argues, in contrast to the scenarios described below,
that the lack of flipping the coin may be the direct cause of the
Houdini's earlier prediction (because of backward causal preemption)
and not only the cause of an earlier lack of prediction. Thus, it
seems at least consistent to argue that both the toss and the
prevention could cause Houdini's earlier behavior regardless of
whether this behavior is a prediction or the lack of a prediction, but
only as long as we consider both actions to be physical
events. Indeed, if we solely consider Houdini's prediction
(regardless of its semantic content) or his lack of prediction as
purely physical events and do the same with the actions "tossing
the coin" and "preventing tossing the coin," we may
have a high correlation of these physical events.



Thus, it seems that we have three scenarios in which we can observe
backward causation even though in two of them one may attempt to bilk
the cause after the alleged effect has occurred.



Scenario 1: The experimenter asks Houdini to predict the outcome of a
tossed coin a minute later. It turns out that there is a high positive
correlation between Houdini's answers and the actual heads or
tails.



Scenario 2: The experimenter now asks Houdini to make his predictions,
but arranges the coin such that it shows heads or tails opposite to
Houdini's pronouncements. In this case, there will be a negative correlation between the semantic content of his answers and the
outcome of the tosses. (Indeed, you could also arrange the outcome so
there would be no correlation at all.) But one could still argue that
the very fact that Houdini did not abstain from responding was because
the physical act of handling the coin automatically prompted him to
produce an answer. One will observe a high positive correlation
between Houdini making physical pronouncements and the physical
handlings of the coin, although there exists a negative or no
correlation between the semantic content of his answers and the
outcomes in the form of heads and tails.



Scenario 3: The experimenter asks Houdini to make his predictions.
However, he abstains in situations where someone subsequently prevents
the coin from flipping, but in situations where no one intervenes;
there is a high correlation between his predictions and the outcomes.
In those cases where someone prevents the coin from being flipped, and
Houdini therefore abstains from saying anything, there cannot be any
correlation between the truth-value of Houdini's answers (since
he does not produce any). However, there still seems to be a high
correlation between his behaviors (i.e. the physical lack of responses)
and the subsequent prevention of any outcome.



For those reasons one may argue that the bilking argument is not as
powerful as Max Black might have thought.


### 2.5 Free will



*Does backward caution imply fatalism?* An often advanced
objection against backward causation is that if eternalism and
backward causation are possible, then the future is already
determined. And if it is already determined now what the future is
going to be, then it does not matter what an agent will do, since
everything in the future is set and done. An agent cannot do other
than what the future is determined to be. Although this argument seems
very appealing, it may not hold for a closer scrutiny.



Being an eternalist one may distinguish between a *determined*
future and a *determinate* future. Also this pair of concepts
have different names in the literature. Sometimes *determinism*
is called *physical determinism*, *causal determinism*
or *nomological determinism*, whereas *determinateness*
is named *logical determinism*, *temporal determinism*,
or *block determinism*. A future event is determined now if and
only if a present event is causally or nomologically sufficient for it
to happen. In contrast, a future event is determinate with respect to
the present if and only if this event occurs *tenselessly* at a
future time. Thus, eternalists will say that an agent still has a
choice to make tomorrow about whether or not she will go and see her
parents, because no present event causally determined her choice
tomorrow. Her choice is nevertheless determinate, and therefore it is
true today what she will do tomorrow.



The discussion of free will has a long history and the overwhelming
parts of this discussion has been dedicated to the problem that if the
world is completely governed by deterministic laws, does it then make
sense to talk about free will? Indeed, the outcome of this discussion
very much depends on how we understand the notion of free will.
Usually the concept of free will connects to whether or not a human
agent could have done otherwise. Some philosophers, the
compatibilists, believe that as long a human agent is not subject to
any external or internal forces, that individual is free to do
whatever he or she wants. But then the compatibilists have to dismiss
some part of the following *argument of consequence*.


1. We cannot change the past.
2. We cannot change the laws of nature.
3. Hence, we cannot change either the past or the laws of nature
(by 1 and 2).
4. If determinism is true, then our present actions are necessary
consequences of the past and the laws of nature.
5. Hence, if determinism is true, then we can do nothing now to
change the fact that our present actions are necessary consequences of
the past and the laws of nature (by 4).
6. Hence, if determinism is true, then we cannot change that our
current actions occur (by 3 and 5).
7. Hence, if determinism is true, then we have no power to do things
differently than what we do (by 6).
8. Free will requires a power to do things differently.
9. Hence, if determinism is true, then we do not have free will (by 7
and 8).



The non-compatibilist will argue that we have free will in the sense
that we could have done otherwise. Hence determinism cannot be
true.



Indeed, the compatibilist will accept (1), because even an advocate of
backward causation does not claim that the past can be changed.
Moreover, the compatibilist does not have to accept backward
causation. Most likely the compatibilist will not challenge the
non-compatibilist by saying that we may be able to influence the past.
It is much more likely that the compatibilist will object to the
argument either by saying that not all laws of nature are
deterministic or by saying that the brain operates based on
*ceteris paribus* laws including a clause of the absence of
external and internal forces. For the compatibilist this suffices to
say that the agent could have done otherwise. In other words, the
compatibilist's objection would usually not concern the
determinateness of the past.



As we can see, the above argument of consequence combines
determinateness of the past and determinism of laws. Whatever the
compatibilist would object in order to reject the argument of
consequence, the argument cannot be used *mutatis mutandis* to
argue against eternalism or the block universe, because in contrast to
the discussion of free will and the past that focuses on determinism,
the discussion of free will and the future focuses on determinateness.
For even if indeterminism is true, i.e. if some processes of nature
are indeterministic, one could still argue in favor of the block
universe as some of its advocates pointed out long time ago (See
Grunbaum, 1967, 28-35). Therefore, the argument against backward
causation based on free will has to be different from the one posed
against traditional fatalism. It has to look something like this:


1. If backward causation is possible, then the future has to be
determinate.
2. If the future is determinate, it is now the case that a wanted
action occurs at a later time *t* or it is now the case that it
does not occur at this later time *t*(by 1).
3. If it is now the case that a wanted action occurs at a later time
*t* or it is now the case that it does not occur at this later
time *t*, I cannot perform a wanted action that does not occur
at this later time *t*.
4. Hence if I cannot form a wanted action at a later time *t*,
then I cannot be free to do otherwise (2 and 3).
5. Now, assuming that the future is determinate.
6. Hence, I am not free to do otherwise (by 4 and 5).
7. Hence, I have no free will.
8. However, I know from experience that I could have done
otherwise.
9. Hence, the future is not determinate.
10. Hence, backward causation is not possible.



A common criticism has been that if the agent's actions tomorrow
are determinate, and it is therefore true today that the agent, say,
will visit her parents, then the agent cannot do anything other than
visit her parents. However, this conclusion seems to be a *non
sequitur*. In order to reach such a conclusion, one must tacitly
assume that the agent's action causally determines the outcome
of her choice, whereas the argument were believed to show that
backward causation violates the notion of free will.



In contrast, the eternalist could argue that the reason why it is true
today that an agent will visit her parents tomorrow is because the
agent makes a decision that causally determines her visit before she
goes to see them. If the agent makes the opposite decision tomorrow,
it will be true today that she will not visit her parents. Whatever
she chooses tomorrow, it will be her decision which makes it true
today that she is going to see her parents. The outcome of her
decision tomorrow is *determinate* not because the present
truth value fixes her decision but because her future outcome fixes
the present truth value. (Nor is it the case that the outcome of her
decision causally determines her previous decision.) Thus, the
eternalist may argue that even though the future is determinate, it
does not exclude people from having free will. If people have free
will, the argument goes, the fact that the outcome of their future
decision is determinate with respect to the past does not affect their
ability to choose freely.


## 3. Paradoxes



Of all the philosophical problems to which backward causation (and
time travel) gives rise, the paradoxes are those that have generated
the most heat in both physics and philosophy because, if they are
valid, they exclude backward causation from being both metaphysically
and logically possible. The paradoxes can grossly be divided into
three kinds: (1) Bootstrap paradoxes involve a causal or information
loop; (2) Consistency paradoxes involve generating a possible
inconsistency; and (3)Newcomb's paradox seems to foreclose free
will. So if backward causation (and time travel) should be logically
possible, one has to show that the paradoxes can be resolved and that
therefore arguments based on them are invalid.


### 3.1 The Bootstrap Paradoxes



The bootstrap paradoxes arise in cases where you have a causal chain
consisting of particular events in which \(a\) causes \(b, b\) causes
\(c\), and \(c\) causes \(a\). The problem here is that the occurrence
of \(a\) presupposes the occurrence of \(c\); in other words, the
cause presupposes its effect. But how can something be required of
what itself requires? Indeed this seems paradoxical. Some philosophers
therefore think that this makes the idea of causal loops incoherent.
Hugh Mellor even believes that 



> 
> 
> the possibility of causal loops can be excluded *a priori*, and
> so therefore can the closed timelike paths entailed by closed time,
> backward time-travel and all kinds of backward causation. (1991: 191).
> 
> 
> 
> 



His proof goes like this. Take four chains of events. Each of them
consists of three particular events \(a, b\), and \(c\), all different
tokens of the same kind of events \(A, B\) and \(C\). We then
construct the chain such that


1. \(b \Rightarrow c \Rightarrow a\)
2. \({\sim}b \Rightarrow{\sim}c \Rightarrow{\sim}a\)
3. \(b \Rightarrow c \Rightarrow{\sim}a\)
4. \({\sim}b \Rightarrow{\sim}c \Rightarrow a\)



The first two sequences may be called G-chains and the other two
H-chains. Moreover, Mellor assumes that all tokens of \(A, B\) and
\(C\) are distributed among the four chains so that the number of
chains is exactly the same, namely one fourth of the sequences. Mellor
then defines a causal relation between two singular events \(a\) and
\(b\) in terms of a situation \(k\) which makes \(b\) more likely to
occur given \(a\) than without \(a\), i.e., \(\rP(b\mid a) \gt
\rP(b\mid {\sim}a)\). But we can see that the number of chains in
which \(b\) is combined with \(a\) is equal to the number of chains in
which \(b\) is not combined with \(a\). In fact we have that
\(\rP(b\mid a) =\) \(\rP({\sim}b\mid {\sim}a) =\) \(\rP(b\mid {\sim}a)
=\) \(\rP({\sim}b\mid a)\). From this it follows that a particular
\(b\)'s chance in \(k\) cannot increase with respect to \(a\)
compared to its chance without \(a\). Hence \(a\) cannot affect \(b\),
and therefore causal loops are impossible.



Some philosophers have not found this argument very convincing. Faye
(1994) has pointed to the following problematic issues. First, Mellor
measures the probability of singular events (propensities) instead of
the probability of certain kinds of events. Second, he does not
differentiate between circumstances in which a \(B\) is followed by an
\(A\) and those in which a \(B\) is not followed by an \(A\). The
argument is valid only if it can be proved, and not be stipulated,
that (1) and (3) happen surrounded by the same facts. Many people
would say that in a world of (1) must be different from a world of (3)
in some other important respects than merely containing \(a\) or
\({\sim}a\), especially since Mellor claims that the argument is valid
for deterministic situations as well. Third, the equal distribution of
the various chains seems quite selective. In Mellor's G&H
world, in which the number of the four chains is equal, and therefore
in which the probabilities are equal, there cannot be any causal
relationship between the individual \(b\) and the individual \(a\) due
to the fact that the occurrence of \(a\) or \({\sim}a\) happens under
exactly the same circumstances given \(b\). Finally, fourth, it seems
appropriate to claim that any negative argument, like Mellor's,
should be able to show that what holds true of one world can be proved
to hold true of every other world similar in all relevant respects,
but in which G-chains and H-chains are not equally distributed.



It is clear that any world which contains G-chains rather than
H-chains does not show the same inconsistency as Mellor's
G&H-world does. If it can be proved that causal loops in such
worlds are consistent with the adopted definition, then causal loops
are possible. In other words, if we set up a consistent model in which
\(A\) increases the probability of \(B\), and \(B\) increases the
probability of \(A\), we have then proven that causal loops are
possible and that Mellor's argument is invalid. The claim is
therefore that both


1. \(\rP(A\mid B) \gt \rP(A\mid {\sim}B)\)
2. \(\rP(B\mid A) \gt \rP(B\mid {\sim}A),\)



can be shown to be true with respect to a world containing \(A\)s and
\(B\)s. Assume the following probabilities, which hold for the
distributions among \(A, {\sim}A, B\), and \({\sim}B\), are



\[\begin{align}
\rP(A \amp B) &= 0.7 \\
\rP(A \amp{\sim}B) &= 0.1 \\
\rP({\sim}A \amp B) &= 0.1 \\
\rP({\sim}A \amp{\sim}B) &= 0.1.
\end{align}\]


On the basis of the definition of the conditional probability, we
get

 

\[\begin{align}
\rP(A\mid B) = \frac{\rP(A \amp B)}{\rP(B)} &= 7/8 \\
\rP(A\mid {\sim}B) = \frac{\rP(A \amp{\sim}B)}{\rP({\sim}B)} &= 1/2 \\
\rP(B\mid A) = \frac{\rP(A \amp B)}{\rP(A)} &= 7/8; \\
\rP(B\mid {\sim}A) = \frac{\rP({\sim}A \amp B)}{\rP({\sim}A)} &= 1/2. 
\end{align}\]


Thus (i) and (ii) are both true with respect to the stated world;
hence we have proven, according to Mellor's own definition of
causality, that it is consistent to talk about causal loops. Mellor
has not been able to establish any satisfying *a priori*
argument against causal loops or backwards causation.



Moreover, even if one assumes that Mellor were correct in ruling out
causal loops *a priori*, he may be wrong in holding that this
impossibility entails the impossibility of time travel as well as
backward causation. Mellor's argument presupposes that it is the
same kind of processes obeying the same kind of macroscopic physical
laws which enters into both the forward and backward part of the
causal loop. This assumption may hold for time travel but not for
backward causation.


### 3.2 The Consistency Paradoxes



The consistency paradoxes arise when you, for instance, try to kill
your younger self by a backward causal process but evidently have to
fail. The reason why you must fail is quite obvious. Your younger self
belongs to the past and therefore, since you cannot change the past,
you cannot commit retro-suicide. This answer tacitly assumes that
resurrection is impossible. You may, of course, kill your younger self
in the past without changing the past if you have come alive again
later on. This is not what is paradoxical. What is paradoxical is the
fact that you are assumed to be able to kill your younger self in the
sense that you are well-equipped to make these kinds of
retro-killings, you may even be targeting your younger self, but you
must always miss. The same holds, indeed, for all those people who
stay alive into the present. You cannot retro-kill somebody yesterday
who is alive today. There must be certain constraints which prohibit
you from making retro-suicide or retro-killing, and these constraints
may be very local, changing from case to case, or they may be
universal in nature depending on some physical laws. So, on the one
hand, the assumption is that it physically possible for you to kill
somebody in the past; but, on the other hand, it is physically
impossible for you to do what is physically possible. This is the
paradox.



A way out of the paradox was suggested by David Lewis (1976) who
argued that the ability of killing somebody should be understood as a
possibility compossible with the relevant fact. As an opera singer,
for example, you are able to sing operas, since you have the physical
capacity and training to do so, but because of a temporary loss of
voice, you cannot hum a single tune. What you can do relative to one
set of facts, is something you cannot do relative to another set of
facts. This contextual solution explains why you are able to
retro-kill your younger self, given the fact that your gun is in
proper working-order, you have a good aim at your target, and no one
forces you to abstain from taking action. But it also explains why you
are unable to retro-kill anybody who is alive today because you cannot
change the past. The consistency paradox exists only in virtue of an
equivocation of a context-sensitive 'can', and if we
notice that, we see that the paradox vanishes like dew before the
sun.



Some may reply that we are still talking about different abilities. In
contrast to the case in which the opera singer sometimes cannot sing,
your attempt to carry out retro-suicide inevitably fails. The opera
singer is able to sing operas because he has shown it before and can
demonstrate it again, but the attempted retro-killer has not proved
and can never prove his ability. Therefore you are never in a
situation where you can kill your younger self. If we accept this
objection, we may reformulate the solution by saying that the
contextual solution explains why you should be able to retro-kill your
younger self under the appropriate circumstances. But, again, how can
we talk about the ability to make retro-suicide relative to certain
facts at all, if there are no possible worlds in which you carry out
your deed. It seems reasonable to say that you have the ability to do
something if there is a possible world in which you carry out this
action. This is true of the opera singer. He can sing operas because
he does it in a possible world in which he has not lost his voice. But
you cannot make retro-suicide because there is no possible world in
which you kill your younger self. You are unable, even in principle,
to do so.



In sum, the consistency paradox is no paradox as long as you do not
insist on changing the past. You are unable to change the past, and
therefore you are unable to retro-kill anybody who is alive when you
try to kill them. The paradox seems to arise only because you wrongly
believe that you are able to do something you are unable to do.



Now if there is no paradox on the conceptual level, what then is it
that makes retro-suicide physically impossible? It could be either
local facts or global facts. Local facts that could constrain your
action of retro-killing are many. Your hand was shaking while firing
your gun, you got a fly in your eye, you were disturbed by a cat, you
just fainted, etc. These constraining facts seem reasonable by
themselves; they could have happened independently of your overall
capacity of killing somebody in the past, but also in the actual
situation interact with your ability and turn the action into an
unsuccessful event. The problem is merely that such an explanation
looks suspicious. It is a general fact that we cannot retro-kill
anybody who is alive after the time the death purportedly took place.
Likewise it is a general fact, assuming that backward causation (or
time travel) is physically possible, that we can retro-kill anybody
who is not alive after the time the purported death took place. But
the explanation of a general fact requires an appeal to a general fact
or a law of nature. Thus a reference to a singular contingent fact to
explain why you never succeed in killing your younger self seems not
to fulfil the requirement of being an explanation.



The problem may be better understood in following way: each time you
try to retro-kill somebody who is not alive after the time the
purported effect of killing took place, your assassination may still
fail because of your hand was shaking, etc. Such particular facts
explain why you actually missed the target which you in principle were
able to hit. But to say that you are in principle able to perform
retro-killing means that there are laws of nature that normally allow
you to perform such an action in the appropriate circumstances.
Similarly, each time you try to retro-kill somebody who is alive after
the purported death took place, you may fail for one reason or
another. But you must always fail to retro-kill somebody who is alive
after you did your action, i.e., you are in principle unable to
retro-kill such a person. In those cases it is physically impossible
for you to kill, say, your younger self. It seems, therefore, that
there should be some laws of nature, working on either a local level
or a global level, which violate such an action and makes it
physically impossible.



A possible solution may be found in a recent result which shows that
the most basic features of quantum mechanics may ensure that we could
never alter the past, even if it should be possible to interact with
the past. The two physicists, Daniel Greenberger and Karl Svozil (2005
in
 Other Internet Resources),
 imagine some form of quantum mechanical feedback by introducing
figurative beam splitters which are unitary, i.e., the splitters allow
the feedback loop to be reversed because they have the same number of
entry ports and exit ports. From quantum mechanics we know that an
object may behave like a wave and that some unitary operator describes
the propagation of a physical system. The system is represented by a
wave function, also referred to as a path, and the time evolution of
the system is calculated as a sum over all possible paths from the
initial state to the final state. This calculation is usually
restricted to the forward direction of time. Now, if we think of some
of the paths as unfolding backwards in time, Greenberger and Svozil
are able to prove that either the forward and the backward component
paths of the loop cancel out, or that the propagator, which
establishes the feedback in time, "wipes out the alternative
possible futures, thus guaranteeing the future that has already
happened". Thus, if you could aim at something in the past, the
laws of nature prohibit you to act in ways that are in conflict with
what makes the future what it is (what it already turned out to be).
The authors' conclusion is that if you go back in time or effect
"the past quantum mechanically, you would only see those
alternatives consistent with the world you left behind you".


### 3.3 The Newcomb Paradox



This thought experiment involves a player playing a game against a
fortune teller. In this game there are two boxes of which the player
may select one or both. One of the two boxes is transparent,
let's call it \(A\), the other is opaque, call it \(B\). Before
the player makes her choice the fortune teller, based on her
prediction of the player's choice, puts a certain amount of
money in one or both boxes. When the player makes her choice, the
following information is available to her: 1) Up to now the fortune
teller has been able to predict the future with absolute certainty and
has foreseen what other players have chosen. Moreover: 2) sometimes
the fortune teller puts 1,000,000 dollars in box \(B\), but only if
the player selects box \(B\) and does not take both boxes, whereas she
puts 1,000 dollars in box \(A\), regardless of whether the player
chooses box \(A\) or both boxes. So when the player has to choose
between the two boxes, it is already determined whether box \(B\)
contains 1,000,000 or nothing. If the fortune teller is correct in her
prediction, the player will get 1,000,000 dollars, only if she selects
box \(B\); however, if the player wants to earn 1,001,000 dollars and
selects both boxes, she will miss most of the fortune and only receive
1,000 dollars, which she can already see in box \(A\).



This puzzle was originally proposed by William Newcomb but never
published. After its first publication by Robert Nozick (1969) it was
much discussed within decision theory. But it has also been debated in
the context of backward causation, because it gives a nice
illustration of some of the philosophical problems that arise in
relation to backward causation. In this debate it has been used to
demonstrate various claims: that backward causation is impossible or
that it implies fatalism or determinism. The earliest discussion of
some of the consequences for backward causation and free will can be
found in George Schlesinger (1974) and in an exchange between Don
Locke (1978, 1979) and Andre Gallois (1979). Here Schlesinger
argued that there are good arguments for taking both boxes, \(A\) and
\(B\), and equally good arguments for taking only box B, whereas Locke
held that backward causation is irrelevant and the player ought to
take both boxes. However, Gallois believed that Locke's
arguments for taking both boxes are misconceived.



Two opposite arguments for what the player should decide can be given.
Assuming the player has a free will it seems rational to say that the
fortune teller cannot in principle predict what the player is going to
do. When the player makes her choice, it is already determinate
whether box \(B\) contains 1,000,000 dollars or nothing. Therefore her
choice cannot be affected by the fortune teller's prediction,
and she would be better off by selecting both boxes, hoping that there
already is 1,000,000 dollars in box \(B\). The other argument
maintains that based on previous experience--which tells us that
the fortune teller has always been correct about her
predictions--it would be most rational of the player to take only
\(B\). From here philosophers have disagreed about the strength of the
argument. One could insist that fortune teller can predict the
player's choice only based on relevant knowledge of that
person's past or present behavior or state of mind
(compatibilism). Alternatively one could argue that the fortune teller
could have such a perfect knowledge only from information about the
player's choice in the future.



Nevertheless, it has been argued that the Newcomb paradox demonstrates
that backward causation is impossible. George Schlesinger (1980:75
ff.), for instance, imagines a perfect judge who is allowed to check
the two boxes after the fortune teller has placed the money in the
boxes, but before the player has made her choice. It is clear that if
the perfect judge then informs the player about the content of the two
boxes, we have a case where the fortune teller's prediction
causes the player to select both boxes as she is informed about the
1,000,000 dollars in box \(B\). Indeed this would be a clear example
of Black's case of bilking. But Schlesinger also argues that the
same holds true, if the perfect judge merely knows it without
informing the player. However, it is difficult to understand why this
should be the conclusion. If we assume that the player has a free will
and that the fortune teller is able to predict the result of the
player's choice, it seems most rational for the player to learn
from experience and opt for box \(B\) only rather than being greedy
and take both boxes. As long as the perfect judge is silent, his
knowledge about the content of the two boxes seems not to be able to
influence the player's decision. Nor does the player's
possible knowledge of the existence of a perfect judge seem to have
any effect on her decision, because this information does not add
anything to the information she already has; namely, that the fortune
teller has placed the money in the boxes before she makes her decision
and that the fortune teller has never failed to predict the outcome in
advance.



Another problem is that the paradox seems to indicate that backward
causation implies fatalism and determinism. If backward causation is
possible we cannot have a free will. If the result of the
player's action can be predicted, because it is already true
today what the player will choose tomorrow, she cannot be free to
pick. If the fortune teller already knows that the player will choose
both boxes, this has to be true, and the player cannot do otherwise.
And if the fortune teller already knows that the player will select
only box \(B\), this has to be true, and the player cannot but do it.
However, this argument seems to be misguided.



The intuitive strength of the argument stems from the general
assumption that backward causation presupposes an ontologically closed
future--a metaphysical position about time usually named
*eternalism*. Hence it is not an argument only against backward
causation but against eternalism as well. Suppose it is now already
true or false what is going to happen tomorrow; then there must be
some future truth-makers that determine that it is now already true or
false what is going to happen. The consequence seems to be that what
the player is going to do tomorrow is already determined today; hence
the player cannot do otherwise tomorrow than what is true today.
Therefore the player cannot have a free choice, and it seems futile of
her to make any decision. 



However, it can be maintained that the player still has her free
choice. Nothing around the fortune teller causes the player to make a
particular decision. The player is as free as she would be with no
prediction. What the fortune teller is able to predict is the result
of the player's choice. The choice itself may nevertheless be
free. Moreover, unless one replaces forward causation with backward
causation, one cannot argue that it is the outcome of the
player's choice that causes her decision. The statement about
the outcome of her decision is true, according to the fortune teller,
because of the particular decision the player makes; a statement about
the player's decision is not true because of the outcome of her
decision. Consequently, even with respect to the fortune teller, the
player's decision may be regarded as free in the sense that
nothing in its past nor in its future determines what the decision
actually becomes. The reason why the fortune teller is able to make
her prediction could be that the player's choice instigates an
information channel backwards in time.



Philosophers who reject eternalism may not leave the discussion here.
They could argue that it may very well be the case that the
player's choice is neither causally determined by past events
nor by future events. Yet, eternalism implies that the player's
decision is ontologically determinate before it is made, since it is
true today what she will decide tomorrow. Therefore she is not as free
as she would be if the future is ontologically open, i.e., it is not
yet ontologically determinate what the future is going to be,
including the player's choice. The eternalist may attempt to
rebut these critics by arguing that as long as the player's
decision is not causally determined, it is free in any possible sense.



## 4. Physics



The notion of backward causation raises a very different set of
questions that need to be answered before a physically adequate notion
has been developed.


1. *What, if anything, would in physical terms characterize
backward causation?*



One has to remember that causality as such is an everyday notion that
has no natural application in physics. How we could physically
identify backward causal processes depends very much on which feature
we take our ordinary notion of causation to apply to a physical
process. In physics we may be tempted to associate it with different
physical notions of processes. Four suggestions have been put forward:
(a) the causal link can be identified with the transference of energy;
(b) it can be identified with the conservation of physical quantities
like charge, linear and angular momentum; (c) it can be identified
with interaction of forces; or (d) it can be identified with the
microscopic notion of interaction. It appears with respect to all four
suggestions, however, that the involved descriptions are invariant
under the time reversal operation.



The most fundamental laws of nature are time reversal invariant in the
sense that our physical theories allow description of the fundamental
reactions and processes in terms of the time reversed order. Such
processes are said to be reversible in time. Maxwell's theory of
electromagnetism, for instance, admits two kinds of mathematical
solutions for the equations describing the radiation of energy in an
electromagnetic field. One is called the *retarded* solution
where radiation appears as outgoing concentric waves, the other is
named the *advanced* solution according to which radiation
appears as incoming concentric waves.   Apparently the advanced
solution describes the temporal inverse phenomena of the retarded
solution so that these two solutions are usually regarded as the time
reverse solution of the other. Nevertheless, retarded waves, like the
increase of entropy in quasi-closed systems, appear to be *de
facto* irreversible although they are described in terms of time
invariant laws. Nature seems to prefer certain processes rather than
their temporally inversed counterparts in spite of the fact that the
laws of nature do not show such a preference. Light, radiation and
ripples on a pond always spread outwards from their source rather than
inwards just like entropy of a quasi-closed system is always moving
from lower to higher states.


### 4.1 The Wheeler-Feynman Absorber Theory



Why do we not see any advanced waves in nature? Wheeler and Feynman
(1945) came up with an answer. If we assume, they said, that radiation
from an isolated accelerated charged particle is equally retarded and
advanced, that is half retarded and half advanced to be exact, we can
explain why it appears to be fully retarded in terms of the influence
distant absorbers make on the source. The absorber consists of charged
material that reacts with the source field by radiating with half
retarded and half advanced waves. It is this half advanced field of
the charged particles of the absorber which is added to the half
retarded field of the source. The advanced waves of the absorber
interfere constructively with the retarded waves of the source,
whereas the same waves cancel out the advanced waves of the source in
a destructive interference. Thus one of the consequences of Wheeler
and Feynman Absorber Theory is the idea that emitters are
intrinsically symmetric, another is that there is no intrinsic
difference between so-called emitters and so-called absorbers. In
other words, if this theory is true we have to conclude that radiation
from a source is a time symmetric process but the presence of an
absorber makes it asymmetric.



The Wheeler-Feynman theory takes for granted that outgoing, expanding
waves are identical with retarded radiation and incoming, contracting
waves with advanced radiation. But is such identification without any
problems? Not quite. An example with retarded and advanced emitters
illustrates clearly why. Think of a stone being thrown directly into
the middle of a circular pond. The ripples move outwards from the
point where the stone hits the water (the source) in a coherent,
organized wave front and eventually reach the edges (the absorber).
Moreover, the source acts earlier than the absorber.  What will
the inverse process look like? It depends on how we understand such a
process, whether or not we consider a case that includes a reversed
source and a reversed absorber. (A) If they are included, the edges of
the pond will now act as the source and the converging waves will
eventually reach the middle of the pond. We may create something like
this if we dropped a big ring horizontally into the pond. Inside the
ring the waves would move inwards in an organized wave front towards
the centre.   In this case the source (the drop of the ring)
would still act earlier than the absorber (the ripples meeting at the
middle of the pond from all sides). (B) But if our understanding of
the inverse process does not include an exchange of the source with
the absorber and *vice versa*, then the ripples reach the edges
of the pond (the absorber) earlier than the stone plunges into the
water (the source). This is definitely not a state of affairs we could
bring about. Furthermore, if we were to observe such a process, the
ripples would seem to move inwards as contracting waves. The problem
is that both kinds of inverse processes would seem to appear to us as
organized incoming waves but one would be a case of retarded radiation
and the other of advanced radiation.



This may not be the only problematic assumption of the Wheeler and
Feynman theory. Huw Price (1996) has singled out other problems. Among
them is the question of how we may experience the difference between
retarded and advanced waves. When Wheeler and Feynman attributed to
the source a field of half retarded and half advanced waves, they
assumed that the field actually consists of retarded as well as an
advanced component. Price objects, however, that there is no
measurable difference between the two kinds of waves, and we cannot
justify such a distinction by an appeal to the nature of the source
because both emitters and absorbers can be associated with retarded as
well as advanced waves. Instead he believes that these components are
fictitious and that Wheeler and Feynman's formalism merely offer
two different descriptions of the same wave. The problem of the
asymmetry, as he sees it, has nothing to do with the fact that
transmitters are associated with outgoing radiation rather than
incoming radiation but that transmitters are centered on organized
outgoing wave fronts whereas receivers are not centered on similar
organized incoming wave fronts.


### 4.2 Tachyons



When the discussion of tachyons began to appear in physics in the
1960s, it was soon noticed that such particles according to some
frames of reference were associated with negative energies going
backwards in time. To understand how, consider the trajectory of the
same tachyon in relation of three different reference frames, \(S,
S^\*\), and \(S^{\*\*}\) in the Minkowski-space. Now assume that \(A\)
is, in relation to \(S\), the emission of a tachyon at \(t\_{1}\) and
\(B\) is the absorption of the tachyon at \(t\_{2}\). According to an
observer in \(S, A\) will be earlier than \(B\) and the tachyon will
carry positive energy forward in time. Nevertheless it is always
possible to select a reference frame \(S^\*\) in relation to which an
observer will see \(A\) happen simultaneously with \(B\) and yet
another reference frame \(S^{\*\*}\) in relation to which an observer
sees \(A\) happens at \(t\_{2}^{\*\*}\) whereas \(B\) happens at
\(t\_{1}^{\*\*}\). According to the observer in \(S^{\*}\), \(A\) will
take place later than \(B\) and the tachyon carries negative energy
backwards in time (See Figure 1).



![[Three diagrams each with a vertical axis labelled 'time' and an arrow pointing up and two horizontal perpendicular axes labelled 'space']](tachyon.svg)

Figure 1: Spacetime diagram of
tachyon




In Figure 1 the planes represent the hypersurfaces of simultaneity. In
relation to frame \(S\) the tachyon source is at rest, and a tachyon
is emitted at event \(A\), with a superluminal but finite velocity.
The absorption of the tachyon, event \(B\), will accordingly occur
later than \(A\) in relation to the observer in \(S\), and the arrow
of trajectory is for that reason pointing into the future above the
hypersurface passing through \(A\) and standing perpendicular to the
world-line of the source. But neither with respect to the frame
\(S^\*\) nor \(S^{\*\*}\) is the tachyon source at rest and the
hypersurfaces are therefore tilted in relation to the arrow of
trajectory. An observer in \(S^\*\) observes the tachyon to have
infinite speed, and therefore the hypersurface is tilted so much that
it coincides with the arrow. The observer in \(S^{\*\*}\) is moving so
fast with respect to the tachyon source that the hypersurface becomes
titled so much that the arrow points into the past below the
hypersurface.



E. Recami (1978) tried to avoid the idea that tachyons could move
backwards in time by introducing the so-called reinterpretation
principle according to which all negative energy tachyons should be
interpreted as if they have positive energy and move forward in time.
This would mean that the causal order of tachyons should not be
regarded objective since both \(A\) and \(B\) sometimes denoted the
emission and sometimes the absorption depending on the frame of
reference. There are, however, good reasons to believe that this
suggestion does not solve the problems it was intended to (Faye
1981/1989).


### 4.3 Quantum Mechanics



Other physical candidates for backward causation can be founded in the
physics literature. Richard Feynman once came up with the idea that
the electron could go backwards in time as a possible interpretation
of the positron (Feynman 1949). In fact he imagined the possibility
that perhaps there were only one electron in the world zig-zagging back
and forth in time. An electron moving backwards in time would carry
negative energy whereas it would with respect to our ordinary time
sense have positive charge and positive energy. But few consider this
as a viable interpretation today (Earman 1967a, 1976).



More recently, the Bell type experiments have been interpreted by some
as if quantum events could be connected in such a way that the past
light cone might be accessible under non-local interaction; not only
in the sense of action at a distance but as backward causation. One of
the most enticing experiments of this kind is the *Delayed Choice
Quantum Eraser* designed by Yoon-Ho Kim et al. (2000). It is a
rather complicated construction. It is set up to measure correlated
pairs of photons, which are in an entangled state, so that one of the
two photons is detected 8 nanoseconds before its partner. The results
of the experiment are quite amazing. They seem to indicate that the
behavior of the photons detected these 8 nanoseconds before their
partners is determined by how the partners will be detected. Indeed it
might be tempting to interpret these results as an example of the
future causing the past. The result is, however, in accordance with
the predictions of quantum mechanics.



However, David Ellerman (2015) argues that interpreting delayed-choice
experiments or similar experiments as revealing cases of backward
causation or retrocausation relies on what he calls the separation
fallacy:



> 
> We have seen the same fallacy of interpretation in two-slit
> experiments, which-way interferometer experiments, polarization
> analyzers, and Stern-Gerlach experiments. The common element in all
> the cases is that there is some separation apparatus that puts a
> particle into a certain superposition of spatially
> "entangled" or correlated eigenstates in such a manner
> that when an appropriately spatially-positioned detector induces a
> collapse to an eigenstate, then the detector will only register one of
> the eigenstates. The separation fallacy is that this is misinterpreted
> as showing that the particle was already in that eigenstate in that
> position as a result of the previous "separation." In fact
> the superposition evolves until some distinction is made that
> constitutes a measurement, and only then is the state reduced to an
> eigenstate. The quantum erasers are more elaborate versions of these
> simpler experiments, and a similar separation fallacy arises in that
> context.
> 



Thus, Ellerman argues that when one describes a system in a
superposition of certain eigenstates, it does not mean that the system
is in any of these eigenstates before some measurement is carried out.
Therefore, it is wrong to interpret delayed-choice experiments, and
their like, as if the future measurement determines some past
eigenstates, which all were parts of a superposition.



In his discussion of the experimental violation of Bell's inequalities
Don Howard (1989) distinguishes, based on an earlier work done by Jon
Jarrett, between locality and separability. The locality condition
states that a measurement of a pair of objects emerging from a singlet
is statistically independent of the setting of the apparatus used to
measure its counterpart. However, the separability condition is
defined as the joint probability is equal to the the product of the
probability of each state. We know that the experimental violation of
Bell's inequalities involves the invalidation of one of these
conditions. Moreover, if we take Ellerman's argument into
consideration, the two entangled particles, although separated, are
still in a state of superposition until the measurement takes
place.



If we consider the notion of the entangled state in quantum mechanics,
we find that it is characterized as a unified, non-separable state due
to the help of the notion of superposition of possible eigenstates
represented by one common wave function for the correlated pair. Such
a superposition is neither distance-dependent nor time-dependent.
Therefore it is not surprising that based on the correct predictions
of quantum mechanics it is impossible to find support of the violation
of normal causation within this kind of experiment. With reference to
the philosophical discussion about quantum mechanical entanglement, we
can conclude that the experimental results of this sort violate the
principle of separability rather than the principle of locality.



Phillippe Eberhard and Ronald R. Roos (1989) have established a
theorem which says that if quantum mechanics is correct, it is
impossible to use quantum effects to generate a break in the chain of
normal causation. Quantum field theory does not allow any superluminal
communication between different observers. Indeed, this is not so
strange, since quantum field theory is relativistically invariant
whereas superluminal frames of reference are not. But Eberhard and
Roos' theorem does not rule out all forms of backward causation.
Two possible scenarios are still open: (1) entangled pairs exchange
some form of superluminal information (and energy) below the limits of
Heisenberg's uncertainty relations; or (2) causation may be
symmetrical so that the direction of causation in a physical system is
determined by its boundary conditions.



Costa de Beauregard (1977, 1979), for instance, has suggested that
when a system of two photons in a singlet state is measured by two
observers in two regions separated by a space-like distance, then it
is precisely the act of observation that produces the past of the
measuring process in the sense that it influences the source that
emitted the two photons. de Beauregard's idea is that the
element of reality being revealed in the formulation of the EPR
paradox is real only because it was created by actually performed acts
of observation that was propagated backwards in time with one of the
two correlated quantum objects from the measuring device to the source
of the photons.



Some physicists, like Elitzur *et al.* (2016), suggest a form
of too-late-choice experiment that supports such a time-symmetric
interpretations of quantum mechanics according to which backwards
causation plays a significant role. In the normal EPR experiment, each
measurement determines, say, the spin value of two separated, say,
electrons in a singlet state along a certain orientation of the
apparatus. The outcome then proves that the spin value of one electron
has been affected by the distant experimenter's choice of spin
orientation of the other electron. However, what Elitzur *et
al.* now imagine is a reversal setting in which a chosen spin
value determines the corresponding orientation. Based on their
analysis, they conclude that "it turns out that the orientation is
similarly subject to nonlocal effects [as the spin value.]"



Several other philosophers and physicists have come forward with
similar ideas. Aharonov and Vaidman (1997) have formulated a two
vector approach to quantum mechanics "in which a quantum system is
described, at a given time, by two (instead of one) quantum states:
the usual one evolving toward the future and the second evolving
backwards in time from a future measurement." Also Cramer's
transactional interpretation of quantum mechanics involves the idea of
a second wave travelling backwards in time (Cramer, 1986). The basic
assumption behind all of them is that in the micro-world we find only
causal symmetry, and this fact together with proper boundary
conditions can be used to give an explanation of outcomes that seem
otherwise paradoxical. Such quantum correlation experiments can,
however, be interpreted in many other ways. In the end it seems as if
it all depends one whether one assumes that Bell experiments break
with either the locality condition or the separability condition. A
time-symmetric interpretation of quantum mechanics is required only if
one believes that it is the locality condition that is violated in
order to avoid being in conflict with relativity theory.


### 4.4 Two alternatives



These alleged examples of backward causation have one thing in common.
They are all based on the idea that fundamental physical processes are
by themselves symmetric in nature. Our ordinary notion of causation
does not track any nomological feature of the world. What counts as
the cause and the effect depends on the observer's projection of
his or her temporal sense onto the world. So it is still an open
question how a coherent notion of backward causation can fit into this
general understanding of nature. The question we therefore have to
answer is the following:


2. *How can we distinguish between forward causation and backward
causation if all basic physical processes are time symmetric according
to our description of nature?*



Two very different reactions to this problem seem possible.


#### 4.4.1 Boundary Conditions



One proposal is to say that if we came across reversed cases of *de
facto* irreversible processes, such as running a film backwards in
which the cream converged in a coffee cup, such cases should be
interpreted as examples of backward causation (Price 1996). Such a
claim build on a common interpretation of time reversal invariance of
processes according to which this descriptive feature of the dynamical
equations of physics makes reversal processes symmetric in time. Many
philosophers have defended such an interpretation, in particular Hans
Reichenbach (1956, 1929 [1958]) and Adolf Grunbaum (1963). This
also led them to argued that only *de facto* irreversible
processes, such as those described by statistical thermodynamics,
could be used to defined a physical orientation of time. Thus, it
seems to be the case that the actual world consisting of mostly *de
facto* irreversible processes on the macroscopic level due to a
prevalent set of boundary conditions is temporally and causally
symmetric on the microscopic level. On the macroscopic level, *de
facto* irreversible processes emerge, because the boundary
conditions are a result of the huge degree of freedom among
microprocesses or coherence conditions forced upon the underlying
microscopic processes.



The point is here to argue that it is the absence of the right initial
or boundary conditions on the macroscopic level that makes backward
causation so rare or nearly empirically impossible. This suggestion is
based on three basic assumptions: (i) there is no objective asymmetry
in the world, causal processes are intrinsically symmetric in nature,
or causation is bidirectional, and therefore the fundamental processes
of the micro-world are temporally symmetric; (ii) causal asymmetry is
subjective in the sense that any attribution of an asymmetry between
cause and effect depends on our use of counterfactuals and our own
temporal orientation; (iii) backward causation, or advanced action, is
nonetheless possible because sometimes the correlation of certain past
events depends on the existence of causally symmetric processes and
some future boundary conditions. For instance, advanced actions in
electrodynamics require that the existence of transmitters in the
future are centered on organized incoming wave fronts; and advanced
actions in quantum mechanics require that their present states are in
part determined by the future conditions (measurements) they are to
encounter. This feature is then taken to explain quantum entanglement
and the violation of Bell's inequalities in quantum
mechanics.



A simple consideration seems to support this interpretation. Think of
a particle travelling between two boxes. The normal observer and the
counter-observer who has an inverse time sense will describe the
exchange in conflicting terms. To the normal observer Box 1, say, will
be considered as the emitter because it loses energy before anything
in Box 2 happens. Therefore, Box 2 will be considered as the receiver
since it gains energy at a later time. So in relation to the normal
observer, the particle travels from Box 1 to Box 2. The
counter-observer, however, sees the situation with opposite eyes. In
relation to him, Box 2 loses energy and not until thereafter does Box
1 gain a similar amount of energy. Accordingly, in relation to the
counter-observer, the particle moves from Box 2 to Box 1. In other
words whether a box is considered to be an emitter or a receiver
depends on the observer's time sense.


#### 4.4.2 Nomic conditions



The other proposal denies that basic physical processes are time
symmetric and argues, in contrast, that the causal asymmetry is
objective and therefore that there exists an intrinsic difference
between the cause and the effect of all physical processes. John
Earman (1967b and 1969) may be the first who argued against the
interpretation that time reversal invariance of processes is identical
with invariance under the exchange of the temporal order between
*earlier* and *later*. Two reversed tokens of the same
type of physical process do not developed in the opposite direction of
time.



Hence, backward causation should not be considered as a notion about
boundary conditions but as a notion concerned with processes that
nomically distinguish themselves from forward causal processes. Thus,
if there are processes in the world that might be seen as a
manifestation of backward causation, these are not to be depicted by a
description that leaves them to be time reversed cases of ordinary
forward causal processes (Faye 1981/1989, 1997, 2002). This
alternative interpretation rests on a basic claim and four
assumptions.



The fundamental claim is that for any observer it is possible to
identify experimentally the cause and the effect so that these remain
the same even in relation to counter-observers, i.e., observers having
the opposite time sense of ours. In support of this claim consider the
following thought experiment. Two boxes, each having a shutter, are
facing each other. Assume, ex hypothesis, that Box 1 is the particle
source and Box 2 is the particle receiver. The question is how a
normal observer and a counter-observer can come to agreement that
particles move from Box 1 to Box 2. The answer can be found through a
series of manipulations with the shutters, I would say. There are four
possible combinations of the two shutters: open-open, close-close,
open-close, close-open. Let us call any change of energy in Box 1,
regardless of whether it emits or receives a particle, \(A\) and,
similarly, any change of energy in Box \(2 B\). Whether \(A\) or \(B\)
stand for a gain or a loss of energy can be determined by weighing the
two boxes. (i) In case both boxes are closed, no particle will leave
Box 1 and no particle is received by Box 2, thus no gain or loss of
energy occurs, and both the normal observer and the counter-observer
see a situation of not-\(A\), not-\(B\). (ii) In case both boxes are
open a particle leaves Box 1 and is received by Box 2. Again this can
be observed by measuring the change of energy in the two boxes. Thus
the observers will see a situation of both \(A\) and \(B\). (iii) In
case Box 1 is closed and Box 2 is open, they will observe no change of
energy in Box 1 (because it is closed) and, since no particle is
leaving Box 1, no particle will reach Box 2 although its shutter is
open. Hence the observers measure no energy change in this box. Thus
they see not-\(A\) and not-\(B\). (iv) Finally, if Box 1 is open and
Box 2 is closed, a particle leaves Box 1, but none is received by Box
2. In other words, there is a loss or a gain of energy in Box 1, but
no loss or gain of energy in Box 2. So the observers see \(A\) and
not-\(B\). The upshot of this toy experiment is that the normal
observer as well as the counter-observer experience two \(A\)s but
only one \(B\), and one not-\(A\) but two not-\(B\)s; therefore both
will agree that the particles move from Box 1 to Box 2.



This means that what a normal observer identifies as a forward causal
process will be regarded as a backward causal process in relation to
the counter-observer in the sense that the very same event acting as a
past cause for the normal observer will act as a future cause for the
counter-observer. This indicates, too, that in relation to a normal
observer forward causation and backward causation cannot be regarded
as two different manifestations of nomologically reversible (but
*de facto* irreversible) processes since both
manifestations--the common process and the very improbable
reversed process--would develop forward in time. If this claim is
true, it implies that the description of physical processes should
reflect such an intrinsic asymmetry in a way that the nomic
description varies according to whether the process in question goes
forward or backwards in time. Moreover, we must also be able to
distinguish theoretically (and not only experimentally) between the
normal observer's report and the counter-observer's report
of the same process by a separate convention in respect to whether the
process is forward moving or backward moving. What we want is a
characterization of every physical process so that the invariance of
cause and effect corresponds to *nomological*
irreversibility.



In order to establish a nomic, intrinsic distinction between forward
causal processes and backward causal processes one has to take
departure in four assumptions. (i) Process *tokens* and process
*types* are distinct in the sense that only process types are
reversible, process tokens are not. (ii) A normal observer will
describe causal processes propagating forward in time *in terms of
positive mass and positive energy states pointing into her future*
whereas she will describe the same tokens *in terms of negative
mass and energy states pointing into her past*. This reflects two
possible solutions of the four-momentum vector in the theory of
relativity. (iii)Thus, one must distinguish between a *passive*
time reversal operation and an *active* time reversal
operation. The passive transformation is applied to the same process
token by *describing* it in terms of opposite coordinates and
opposite energy states. The active transformation, in contrast, brings
about another token of the same process type in virtue of some
physical translation or rotation of the system itself, both tokens
having the same energy sign pointing in the same direction of time.
(iv) The description in terms of positive mass and the positive
energy flow corresponds to the intrinsic order of the propagation.



Now, let us try to apply the nomic interpretation to the above
consideration concerning the exchange of a particle between two boxes.
In relation to the normal observer who describes the particle in terms
of its *positive energy component*, it travels from Box 1 to
Box 2 because Box 1 looses energy at an earlier time and Box 2 gains
energy at a later time. The same situation is by the counter-observer
described in terms of the particle's *negative energy
component* as a situation where something happens in Box 2 before
it happens in Box 1. In relation to the counter-observer, Box 2 would
not, as the boundary interpretation suggests, loose energy. On the
contrary, Box 2 would seem to gain energy, but the counter-observer
would describe the particle as a series of negative energy states
reaching into his future supposing the particle to be moving from Box
2 to Box 1 carrying negative energy. But, as we have just argued, the
particle really moves from Box 1 to Box 2, from the
counter-observer's future into his past carrying positive
energy.



Consequently, the nomic interpretation holds that in relation to our
normal time sense the causal direction of ordinary processes is
identical with that of their reversed processes. In other words, take
two tokens of a nomologically reversible process type, say \(A\) and
\(B\), and let \(B\) be the actively time reversed process of \(A\),
then this interpretation claims that \(A\) and \(B\) causally develop
in the same direction of time. So, according to this view, neither
incoming, contracting electromagnetic waves nor the decrease of
entropy would count as examples of backward causation as long as such
processes involve ordinary types of matter, i.e., matter that
possesses positive mass and/or energy pointing, in relation to our
normal time sense, towards the future. The notion of backward
causation should instead be applied to matter of a different type,
particles that appear to have, according to usual conventions,
*negative mass and/or energy pointing, in relation to our normal
time sense, towards the future but positive mass and/or energy
pointing towards the past*. Such advanced matter, if it exists,
should be distinguished from both ordinary retarded matter as well as
tachyons by always being described with respect to our time sense in
terms of negative mass and energy stretching forward in time. A
consequence is that a world in which advanced matter exists together
with retarded matter, and where advanced matter is able to interact
directly with the same amount of retarded matter, both would, in case
they actually did interact, annihilate without leaving any trace of
energy.



How and whether the notion of backward causation has a role to play in
physics has yet to be seen. But as long as no common agreement exists
among philosophers and physicists about what in the physical
description of the world corresponds to our everyday notion of
causation, it would still be a matter of theoretical dispute what
counts as empirical examples of backward causation.