QUANTUM THEORY CANNOT CONSISTENTLY DESCRIBE THE USE OF ITSELF
Daniela Frauchiger & Renato Renner
https://www.nature.com/articles/s41467-018-05739-8
Quantum theory provides an extremely accurate description of
fundamental processes in physics. It thus seems likely that the theory
is applicable beyond the, mostly microscopic, domain in which it has
been tested experimentally. Here, we propose a Gedankenexperiment to
investigate the question whether quantum theory can, in principle,
have universal validity. The idea is that, if the answer was yes, it
must be possible to employ quantum theory to model complex systems
that include agents who are themselves using quantum theory. Analysing
the experiment under this presumption, we find that one agent, upon
observing a particular measurement outcome, must conclude that another
agent has predicted the opposite outcome with certainty. The agents’
conclusions, although all derived within quantum theory, are thus
inconsistent. This indicates that quantum theory cannot be
extrapolated to complex systems, at least not in a straightforward
manner.
from
https://www.quantamagazine.org/frauchiger-renner-paradox-clarifies-where-our-views-of-reality-go-wrong-20181203/
...
The experiment has four agents: Alice, Alice’s friend, Bob, and
Bob’s friend. Alice’s friend is inside a lab making measurements
on a quantum system, and Alice is outside, monitoring both the lab and
her friend. Bob’s friend is similarly inside another lab, and Bob is
observing his friend and the lab, treating them both as one system.
Inside the first lab, Alice’s friend makes a measurement on what is
effectively a coin toss designed to come up heads one-third of the
time and tails two-thirds of the time. If the toss comes up heads,
Alice’s friend prepares a particle with spin pointing down, but if
the toss comes up tails, she prepares the particle in a superposition
of equal parts spin UP and spin DOWN.
Alice’s friend sends the particle to Bob’s friend, who measures
the spin of the particle. Based on the result, Bob’s friend can now
make an assertion about what Alice’s friend saw in her coin toss. If
he finds the particle spin to be UP, for example, he knows the coin
came up tails.
The experiment continues. Alice measures the state of her friend and
her lab, treating all of it as one quantum system, and uses quantum
theory to make predictions. Bob does the same with his friend and lab.
Here comes the first assumption: An agent can analyze another system,
even a complex one including other agents, using quantum mechanics. In
other words, quantum theory is universal, and everything in the
universe, including entire laboratories (and the scientists inside
them), follows the rules of quantum mechanics.
This assumption allows Alice to treat her friend and the lab as one
system and make a special type of measurement, which puts the entire
lab, including its contents, into a superposition of states. This is
not a simple measurement, and herein lies the thought experiment’s
weirdness.
The process is best understood by considering a single photon that’s
in a superposition of being polarized horizontally and vertically. Say
you measure the polarization and find it to be vertically polarized.
Now, if you keep checking to see if the photon is vertically
polarized, you will always find that it is. But if you measure the
vertically polarized photon to see if it is polarized in a different
direction, say at a 45-degree angle to the vertical, you’ll find
that there’s a 50 percent chance that it is, and a 50 percent chance
that it isn’t. Now if you go back to measure what you thought was a
vertically polarized photon, you’ll find there’s a chance that
it’s no longer vertically polarized at all — rather, it’s become
horizontally polarized. The 45-degree measurement has put the photon
back into a superposition of being polarized horizontally and
vertically.
This is all very fine for a single particle, and such measurements
have been amply verified in actual experiments. But in the thought
experiment, Frauchiger and Renner want to do something similar with
complex systems.
As this stage in the experiment, Alice’s friend has already seen the
coin coming up either heads or tails. But Alice’s complex
measurement puts the lab, friend included, into a superposition of
having seen heads and tails. Given this weird state, it’s just as
well that the experiment does not demand anything further of Alice’s
friend.
Alice, however, is not done. Based on her complex measurement, which
can come out as either YES or NO, she can infer the result of the
measurement made by Bob’s friend. Say Alice got YES for an answer.
She can deduce using quantum mechanics that Bob’s friend must have
found the particle’s spin to be UP, and therefore that Alice’s
friend got tails in her coin toss.
This assertion by Alice necessitates another assumption about her use
of quantum theory. Not only does she reason about what she knows, but
she reasons about how Bob’s friend used quantum theory to arrive at
his conclusion about the result of the coin toss. Alice makes that
conclusion her own. This assumption of consistency argues that the
predictions made by different agents using quantum theory are not
contradictory.
Meanwhile, Bob can make a similarly complex measurement on his friend
and his lab, placing them in a quantum superposition. The answer can
again be YES or NO. If Bob gets YES, the measurement is designed to
let him conclude that Alice’s friend must have seen heads in her
coin toss.
It’s clear that Alice and Bob can make measurements and compare
their assertions about the result of the coin toss. But this involves
another assumption: If an agent’s measurement says that the coin
toss came up heads, then the opposite fact — that the coin toss came
up tails — cannot be simultaneously true.
The setup is now ripe for a contradiction. When Alice gets a YES for
her measurement, she infers that the coin toss came up tails, and when
Bob gets a YES for his measurement, he infers the coin toss came up
heads. Most of the time, Alice and Bob will get opposite answers. But
Frauchiger and Renner showed that in 1/12 of the cases both Alice and
Bob will get a YES in the same run of the experiment, causing them to
disagree about whether Alice’s friend got a heads or a tails. “So,
both of them are talking about the past event, and they are both sure
what it was, but their statements are exactly opposite,” Renner
said. “And that’s the contradiction. That shows something must be
wrong.”
This led Frauchiger and Renner to claim that one of the three
assumptions that underpin the thought experiment must be incorrect.
“The science stops there. We just know one of the three is wrong,
and we cannot really give a good argument [as to] which one is
violated,” Renner said. “This is now a matter of interpretation
and taste.”
Fortunately, there are a wealth of interpretations of quantum
mechanics, and almost all of them have to do with what happens to the
wave function upon measurement. Take a particle’s position. Before
measurement, we can only talk in terms of the probabilities of, say,
finding the particle somewhere. Upon measurement, the particle assumes
a definite location. In the Copenhagen interpretation, measurement
causes the wave function to collapse, and we cannot talk of
properties, such as a particle’s position, before collapse. Some
physicists view the Copenhagen interpretation as an argument that
properties are not real until measured.
This form of “anti-realism” was anathema to Einstein, as it is to
some quantum physicists today. And so is the notion of a measurement
causing the collapse of the wave function, particularly because the
Copenhagen interpretation is unclear about exactly what constitutes a
measurement. Alternative interpretations or theories mainly try to
either advance a realist view — that quantum systems have properties
independent of observers and measurements — or avoid a
measurement-induced collapse, or both.
For example, the many-worlds interpretation takes the evolution of the
wave function at face value and denies that it ever collapses. If a
quantum coin toss can be either heads or tails, then in the
many-worlds scenario, both outcomes happen, each in a different world.
Given this, the assumption that there is only one outcome for a
measurement, and that if the coin toss is heads, it cannot
simultaneously be tails, becomes untenable. In many-worlds, the result
of the coin toss is both heads and tails, and thus the fact that Alice
and Bob can sometimes get opposite answers is not a contradiction.
“I have to admit that if you had asked me two years ago, I’d have
said [our experiment] just shows that many-worlds is actually a good
interpretation and you should give up” the requirement that
measurements have only a single outcome, Renner said.
This is also the view of the theoretical physicist David Deutsch of
the University of Oxford, who became aware of the Frauchiger-Renner
paper when it first appeared on arxiv.org. In that version of the
paper, the authors favored the many-worlds scenario. (The latest
version of the paper, which was peer reviewed and published in Nature
Communications in September, takes a more agnostic stance.) Deutsch
thinks the thought experiment will continue to support many-worlds.
“My take is likely to be that it kills wave-function-collapse or
single-universe versions of quantum theory, but they were already
stone dead,” he said. “I’m not sure what purpose it serves to
attack them again with bigger weapons.”
Renner, however, has changed his mind. He thinks the assumption most
likely to be invalid is the idea that quantum mechanics is universally
applicable.
This assumption is violated, for example, by so-called spontaneous
collapse theories that argue — as the name suggests — for a
spontaneous and random collapse of the wave function, but one that is
independent of measurement. These models ensure that small quantum
systems, such as particles, can remain in a superposition of states
almost forever, but as systems get more massive, it gets more and more
likely that they will spontaneously collapse to a classical state.
Measurements merely discover the state of the collapsed system.
In spontaneous collapse theories, quantum mechanics can no longer to
be applied to systems larger than some threshold mass. And while these
models have yet to be empirically verified, they haven’t been ruled
out either.
Nicolas Gisin of the University of Geneva favors spontaneous collapse
theories as a way to resolve the contradiction in the
Frauchiger-Renner experiment. “My way out of their conundrum is
clearly by saying, ‘No, at some point the superposition principle no
longer holds,’” he said.
If you want to hold on to the assumption that quantum theory is
universally applicable, and that measurements have only a single
outcome, then you’ve got to let go of the remaining assumption, that
of consistency: The predictions made by different agents using quantum
theory will not be contradictory.
Using a slightly altered version of the Frauchiger-Renner experiment,
Leifer has shown that this final assumption, or a variant thereof,
must go if Copenhagen-style theories hold true. In Leifer’s
analysis, these theories share certain attributes, in that they are
universally applicable, anti-realistic (meaning that quantum systems
don’t have well-defined properties, such as position, before
measurement) and complete (meaning that there is no hidden reality
that the theory is failing to capture). Given these attributes, his
work implies that there is no single outcome of a given measurement
that’s objectively true for all observers. So if a detector clicked
for Alice’s friend inside the lab, then it’s an objective fact for
her, but not so for Alice, who is outside the lab modeling the entire
lab using quantum theory. The results of measurements depend on the
perspective of the observer.
“If you want to maintain the Copenhagen type of view, it seems the
best move is towards this perspectival version,” Leifer said. He
points out that certain interpretations, such as quantum Bayesianism,
or QBism, have already adopted the stance that measurement outcomes
are subjective to an observer.
Renner thinks that giving up this assumption entirely would destroy a
theory’s ability to be effective as a means for agents to know about
each other’s state of knowledge; such a theory could be dismissed as
solipsistic. So any theory that moves toward facts being subjective
has to re-establish some means of communicating knowledge that
satisfies two opposing constraints. First, it has to be weak enough
that it doesn’t provoke the paradox seen in the Frauchiger-Renner
experiment. Yet it must also be strong enough to avoid charges of
solipsism. No one has yet formulated such a theory to everyone’s
satisfaction.
The Frauchiger-Renner experiment generates contradictions among a set
of three seemingly sensible assumptions. The effort to explicate how
various interpretations of quantum theory violate the assumptions has
been “an extremely useful exercise,” said Rob Spekkens of the
Perimeter Institute for Theoretical Physics in Waterloo, Canada.
“This thought experiment is a great lens through which to examine
the differences of opinions between different camps on the
interpretation of quantum theory,” Spekkens said. “I don’t think
it’s really eliminated options that people were endorsing prior to
the work, but it has clarified precisely what the different
interpretational camps need to believe to avoid this contradiction. It
has served to clarify people’s position on some of these issues.”
Given that theoreticians cannot tell the interpretations apart,
experimentalists are thinking about how to implement the thought
experiment, in the hope of further illuminating the problem. But it
will be a formidable task, because the experiment makes some weird
demands. For example, when Alice makes a special measurement on her
friend and her lab, it puts everything, the friend’s brain included,
into a superposition of states.
Mathematically, this complicated measurement is the same as first
reversing the time evolution of the system — such that the memory of
the agent is erased and the quantum system (such as the particle the
agent has measured) is brought back to its original state — and then
performing a simpler measurement on just the particle, said Howard
Wiseman of Griffith University in Brisbane, Australia. The measurement
may be simple, but as Gisin points out rather diplomatically,
“Reversing an agent, including the brain and the memory of that
agent, is the delicate part.”
Nonetheless, Gisin is not averse to thinking that maybe, one day, the
experiment could be done using complex quantum computers as the agents
inside the labs (acting as Alice’s friend and Bob’s friend). In
principle, the time evolution of a quantum computer can be reversed.
One possibility is that such an experiment will replicate the
predictions of standard quantum mechanics even as quantum computers
get more and more complex. But it may not. “Another alternative is
that at some point while we develop these quantum computers, we hit
the boundary of the superposition principle and [find] that actually
quantum mechanics is not universal,” Gisin said.
Leifer, for his part, is holding out for something new. “I think the
correct interpretation of quantum mechanics is none of the above,”
he said.
He likens the current situation with quantum mechanics to the time
before Einstein came up with his special theory of relativity.
Experimentalists had found no sign of the “luminiferous ether” —
the medium through which light waves were thought to propagate in a
Newtonian universe. Einstein argued that there is no ether. Instead he
showed that space and time are malleable. “Pre-Einstein I couldn’t
have told you that it was the structure of space and time that was
going to change,” Leifer said.
Quantum mechanics is in a similar situation now, he thinks. “It’s
likely that we are making some implicit assumption about the way the
world has to be that just isn’t true,” he said. “Once we change
that, once we modify that assumption, everything would suddenly fall
into place. That’s kind of the hope. Anybody who is skeptical of all
interpretations of quantum mechanics must be thinking something like
this. Can I tell you what’s a plausible candidate for such an
assumption? Well, if I could, I would just be working on that
theory.”
@philipthrift
