In this second video on Quantum Physics and
Free Will, I'd like to look at another fascinating
theorem that digs deep into the foundations
of Quantum Theory. It is called the Conway-Kochen
Free Will Theorem.
The Conway-Kochen Free Will theorem was proved
by John Conway and Simon Kochen in 2007, and
it provides us with another robust result
which - like Bell's Theorem - highlights some
of the important philosophical issues that
lie at the core of quantum mechanics. In the
context of this particular theorem, a free
choice is defined as type of choice which
is not determined by prior conditions, that
is, not determined by the past history of
the universe (in any inertial frame). Note
that this is essentially the same definition
we encountered earlier, in my previous video,
when discussing Bell's theorem.
So what does Conway and Kochen's Free Will
theorem state? The theorem states that, if
we assume that we have a certain amount of
free will, then, subject to certain other
assumptions, elementary particles must have
free will too. Put another way, the theorem
states that - given certain other axioms - if
the two experimenters in question are free
to make choices about what measurements they
are going to make (that, is, if their choices
are not determined by prior conditions in
the universe) then the results of their measurements
cannot be determined by anything previous
to their experiments either.
This argument follows from another important
theorem, the Kochen-Specker theorem - a complement
to Bell's theorem - which places certain constraints
on the permissible types of hidden variable
theories which would attempt to explain the
probabilistic nature of quantum mechanics
in terms of a deterministic model featuring
hidden states. Kochen and Specker showed that
the properties of particles - such as the
squared spin in a particular direction - cannot
have a fixed or definite value before it is
measured. The Kochen-Specker theorem not only
shows that the result of any individual measurement
was not pre-determined independently of the
experimenter's choice of measurement, but
it also shows the impossibility of Einstein's
assumption that quantum mechanical observables
represent real elements of physical reality,
and hence - in line with non-realism - it
highlights the ever important interplay between
freedom of choice, observer and observed.
Now, coming back to Conway and Kochen's Free
will Theorem... In order to understand what
it's all about, let's go back to the same
experimental setting I introduced you to in
my previous video when talking about Bell's
theorem.
We have two experimenters, Alice and Bob,
in two different laboratories. Again, the
laboratories are space-like separated, which
means that no information can travel from
one to the other, according to Einstein's
theory of relativity, within a pre-stipulated
period of time, unless it was travelling faster
than the speed of light. In other words, the
fact that Alice and Bob are space-like separated
means that the question of who made the choice
first of what to measure is meaningless here,
because Alice and Bob's choices are not in
each other's future or past light cones. So,
according to Einstein's relativity, the fact
that their laboratories are space-like separated
means that their respective choices of measurement
cannot in any way influence each other, because
no information signal can be sent from one
to the other through the fabric of space-time.
In addition, note that either of their choices
could be said to have happened first, because
in special relativity, the time order of space-like
separated events is not absolute, but relative.
Well, turns out that this assumption is actually
one of the axioms in Conway and Kochen's theorem.
In their strong Free Will theorem version,
they call this axiom MIN, and it follows directly
from Einstein's theory of relativity. MIN
is the assumption that Alice and Bob are space-like
separated and that they can 100% freely and
totally independently choose what type of
measurement to make; that is, that their respective
choices are neither a function of the past
nor can they influence each other in any way.
The second axiom in Conway-Kochen's theorem
is called SPIN, and it is related to the Kochen-Specker
Theorem I mentioned earlier, which shows that
the properties of the particles which are
being measured in the present cannot be assumed
to exist prior to them being measured. Therefore,
the SPIN axiom follows directly from the foundations
of quantum mechanics.
Finally, the last axiom, called TWIN, is related
to quantum entanglement. It has to do with
Bell's Theorem, which - as we saw in the previous
video - describes how twinned particles can
be used to experimentally test entanglement,
that strange interconnection between particles
which Einstein called spooky action at a distance.
The TWIN axiom basically assumes this strange
interconnection to exist.
From these 3 axioms, Conway and Kochen derived
their Free Will theorem, which states that
if the two experimenters are free to make
choices about what measurements to make, then
the results of their measurements cannot be
pre-determined by anything previous to the
experiments. In other words: if we have free
will, then elementary particles have free
will too.
Again, remember that Conway and Kochen's theorem
is not in any way about proving human's free
will, but rather, the theorem takes our free
will as a starting axiom, a starting premise,
an assumption, to show that if we indeed have
a certain degree of free will, then so do
elementary particles.
"I know what I mean by humans having free
will," says Conway, "I believe, and you don't
have to, that I just picked up this pen and
it wasn't determined at the start of the Big
Bang; it's not a function of the past history
of the Universe. I think I just did that in
the last few seconds and before then, there
was nothing in the world that you could have
analysed to tell you that I would do that."
"For the Free Will Theorem, I assume that
some of my actions are not given by predetermined
functions of the past history of the universe.
A rather big assumption to make, but most
of us clearly make it. Now, what Simon and
I proved is, if that is indeed true, then
the same is true for elementary particles:
some of their actions are not predetermined
by the entire past history of the universe.
That is a rather remarkable thing."
"The particles will either emerge on the left
or right-hand side of a screen [...] and what
a particle will do is not a predetermined
function of the past. Even if you knew the
entire past history of the universe (in any
inertial coordinate frame) this would not
contain the information about what the particles
will do in the experiment."
"That's why I insisted on using this evocative
language," Conway says. "Many people thought
I should say the particle's behaviour is indeterminate.
But it would be really rude if I told you
that you were indeterminate! It's the same
property and I don't see why we should be
required to speak of it as if it were a different
property. Our theorem says that if human's
have it, then so do particles."
It is worth stressing again that Conway and
Kochen are not trying to prove that free will
exists. Their argument would be completely
circular if that was the case. What they are
doing is - by explicitly making the free choice
of the experimenter a fundamental axiom in
quantum mechanics - they are ultimately attempting
to close one of the last loopholes in Bell's
inequality tests, the so-called "free-will"
loophole.
Again, remember that an indeterministic world
is not the same as a random world. It is a
common misconception to think of the world
as being either completely random or absolutely
deterministic. Indeterminism does not need
to entail absence of causation either. Indeterminism
is just the failure of determinism. It does
not need to equate with a world governed by
completely random events or actions, but it
allows for a wide range of possible scenarios
that lie somewhere between the two extremes
where free will would be an impossibility
(absolute determinism or complete randomness).
Indeterminism is the idea that there is a
branching of possibilities lying ahead of
us, rather than just one possible outcome
uniquely determined by the past history of
the universe. Indeterminism is a necessary
condition for our everyday notion of free
will to be real. We can still have adequate
causality and partial self-determination in
a non-deterministic world. Indeterminism simply
allows for the existence of alternative futures
and pasts, as opposed to pre-determinism,
which implies just one possible future and
one possible past.
The loophole that Conway and Kochen's theorem
is trying to tackle is often called the "free
choice" or "free will" loophole. If absolute
determinism were to be true (often called
super-determinism in this context), then,
as explained in my previous video, it would
mean that all our experimental tests, including
our choices, had already been pre-determined
in advance to make us think that quantum mechanics
is correct, to make us conclude that we live
in a world that is not quite what it really
is! You may think that this is a crazy idea,
but no matter how convoluted, it still has
a few supporters, which means that more experiments
need to be done in order to close these remaining
loopholes.
Scientists around the world are working very
hard to devise experiments that can successfully
deal with these loopholes. Personally, I think
it would be great if we started performing
quantum mechanical experiments where actual
human choices were being used. So far, only
random-number generators have been used as
a way to replace human's free choices. The
main reason for this is that human action
is way too slow for the type of experiments
that are being performed so far, where we
are dealing with speeds of the order of magnitude
of c - the speed of light - and relatively
short distances between the laboratories.
If you think about it, in order for a random
number generator to function, we still need
a human experimenter to choose what random
number generator to use, and to set it up,
turn it on, and so on... So one could argue
that the same idea applies in this situation:
the human experimenter is still required to
make choices, choices which will eventually
lead to the random number generator making
its so-called free choices.
Ultimately, what we are doing is testing whether
certain variables are correlated to other
variables in such a way that realism and locality
may need to be abandoned. And in order for
the results of these tests to make sense,
either the experimenter or the random number
generator are required to be able to make
at least some of their choices 100% freely.
Despite this, I think that it'd be great if
we could experimentally put to the test the
assumption that some human choices can be
100% free, in the context of a quantum mechanical
experiment, by not having to resort to using
random number generators, but just using human's
choices, and see what happens.
This is a recent article in Nature magazine
that caught my attention. I'll quote the most
relevant parts. It says:
"The issue is whether the settings in one
laboratory are uncorrelated with variables
(hidden or otherwise) in the other. If they
are correlated, then the experiment violates
the assumptions of Bell's theorem, opening
the free-choice loophole, so called because
of how it can be closed: the only things correlated
with free choices are their effects, so (by
Einstein's principle) settings that are freely
chosen late enough would be uncorrelated with
the other variables, as desired.
Human choice and action are slow, so Bell
experiments thus far have used random-number
generators rather than free choice to change
the detector settings. There is no reason
for such random numbers to be correlated with
anything on the other side. But if one is
inclined to reject the principle of common
cause (as localists are) then one must admit
that correlations can occur without any reason.
Thus, to be rigorous, experimenters must choose
the settings freely.
Using human free-choice while closing the
separation loophole would require separating
the experimenters by much more than one Earth
diameter (only 40 light-milliseconds). Putting
one experimenter on the Moon (1.3 lightseconds
away) would also allow time for them to consciously
register the results - a requirement to rule
out a fourth and final loophole, the "collapse
loophole". This arises from the possibility
that the set of potential results recorded
by a detector does not "collapse" to an actual
individual result until observed by the experimenter,
so that before the experimenter gets involved
the result could be influenced, long after
the photon arrives, by some bizarre (but not
faster-than-light) causal influence from the
distant laboratory.
Such an Earth-Moon experiment is a worthy
challenge for the next 50 years."
Personally, I must admit that the requirement
that some of the experimenter's choices must
be 100% free from any influences in his own
past, in the same sense that it would be required
from a random number generator, sounds a bit
extreme to me. Surely there is a wide range
of possibilities other than super-determinism,
complete self-determination or complete randomness
when it comes to human beings' choices.
Requiring a human being to be able to perform
a 100% free choice, in the sense defined by
Bell or Conway & Kochen, sounds a bit unhuman
to me because - for all intents and purposes
- we are equating this human free choice with
a random choice. Is it really possible - I
wonder - to choose between up and down, right
or left, or 0 and 1 in a manner that is not
influenced in any way by our past history?
What if we have a tendency for choosing right
over left, or up over down, or 1 over 0? The
fact that we may have this tendency to choose
one option over the other would mean that
our past history would indeed have an influence
on our present choice. While there would still
be a branching of possibilities in front of
us, in this case two branches, our choice
would NOT be 100% free! There would indeed
be a higher probability that we would choose
one branch over the other! And yet, the fact
that our choice was not 100% free would not
in any way imply that it was 0% free, but
maybe that it was say... 20%, or 30% or 75%
free from past influences. The way I see it,
there is a wide range of possibilities to
consider here!
This is a very interesting topic and I will
continue discussing it in my next video - I
will take it from here, where I left.
