I’ve been on a quest to understand quantum mechanics (“QM”)
and think I’ve actually made significant progress, even though Feynman claimed
that no one understands it. What I’m
going to write in this post is not ready for an academic paper, so I’m not
going to try to prove anything. Instead,
I’m just going to explain my understanding of QM and how it is consistent with
what I’ve learned and the results of QM experiments.
I’m not sure yet whether this explanation is: a) correct;
b) original; or c) testable. Of course,
I think it is correct as so far it’s the only explanation that seems consistent
with everything I’ve learned about physics and QM. Not only do I believe it’s correct, but I
also hope it’s correct since it has helped me to understand a lot more
about the physical world; to discover that it is false would mean that I am
fundamentally mistaken in a way that would take me back to the drawing
board. Whether or not it is original is
less important to me; as I noted before in this
post, even if I had naturally stumbled upon an explanation of QM that had
been discovered and written about by someone else, such as Rovelli’s Relational
Interpretation, I’d be fine with that because my primary quest is to understand
the physical world. As it turns out, the
following explanation is not equivalent to the Relational Interpretation
or, as far as I’m aware, any of the other existing
interpretations of QM. So, if I’ve
come upon something original, I’d like to get it into the information ether for
purposes of priority, sharing ideas, collaboration, etc. Finally, if my explanation actually is both
correct and original, I would really like it to be testable and not just
another interpretation of QM. Currently,
all QM interpretations are empirically indistinguishable. While hypothetical experiments have been
proposed to distinguish one or more interpretations from others (such as Deutsch’s
classic paper, which aims to show how a collapse interpretation might be
distinguished from a non-collapse interpretation), not only are such
experiments impossible for all practical purposes in the near future, but may
actually be impossible in principle. Of
course, even if it turns out to be just another indistinguishable
interpretation, it is already valuable (at least to me) from a pedagogical
point of view, as it clarifies and simplifies QM in a way that I haven’t seen
elsewhere. Having said all that, here is
my current understanding/explanation for QM.
Information, Facts, and Relativity of Superposition
First, let’s start with information. If I throw a rock with my hand, then that
fact – that is, the fact that the rock and my hand interacted in a particular
way – gets embedded in a correlation between the rock and my hand so that they
will both, in some sense, evidence the interaction/event. The information about that fact gets carried in
that correlation so that future interactions/events are consistent with that fact,
which is what gives rise to predictability.
The trajectory of that rock can then be predicted and calculated
relative to my hand because the information stored in the correlation between
the rock and my hand guarantees that future events are consistent with that
past event (and all past events). The
set of possible futures that are consistent with past events is so limited that
the future trajectory of the rock can be calculated to (almost)
limitless precision. In fact, the
precision to which a person could predict a rock’s trajectory is so good that
it was thought until the discovery of quantum mechanics (and specifically
Planck’s constant) that the physical world is perfectly deterministic. Many (perhaps most) physicists are
determinists, believing that the world evolves in a predetermined manner. The notion of determinism is heavily related
to Newtonian physics: If I know an object’s initial conditions, and I know the
forces acting on it, then I can predict its future trajectory.
This is certainly true to some degree. However, due to chaos, the further in the
future we go, the more sensitive those predictions are to the precision of the
initial conditions. So if we don’t know
an object’s initial conditions to infinite precision, then it’s just a
matter of time before chaos amplifies the initial uncertainty to the point of
complete unpredictability. This fascinating paper shows that
that’s true even if we are looking at three massive black holes with initial
conditions specified to within Planck’s constant. Of course, QM asserts that we can’t specify
initial conditions better than that, so this seems to me pretty good evidence
that the universe is fundamentally indeterministic.
The thing is... why should we ever have believed that
infinite precision was possible, even in principle? Instead, the amount of information in the
universe is finite, a concept reasonably well established by the entropy
concept of the Bekenstein
Bound, and also well articulated by Rovelli’s explanation that the
possible values of an object’s location in phase space cannot be smaller than a
volume that depends on Planck’s constant.
However, even if we can all agree that information in the universe is
finite, there is no agreement on whether it is constant. Most physicists seem to think it’s constant,
which is in part what gives rise to the so-called black hole
information paradox.
Part of the motivation for believing that information is
constant in the universe is that in quantum mechanics, solutions to the Schrodinger
Equation evolve linearly and deterministically with time; that is, the amount
of information contained in a quantum wave state does not change with
time. Of course, the problem with this
is that a quantum wave state is a superposition of possible measurement
outcomes (where those possible outcomes are called “eigenstates” of the chosen
“measurement operator”)... and we
never observe or measure a superposition.
So either the quantum wave state at some point “collapses” into one of
the possible measurement outcomes (in which case the wave state is not always
linear or universally valid), or it simply appears to collapse as the
superposition entangles with (and gets amplified by) the measuring device and
ultimately the observer himself, so that the observer evolves into a quantum
superposition of having observed mutually exclusive measurement outcomes. This second situation is called the Many
Worlds Interpretation (“MWI”) of QM.
I regard MWI as a nonstarter and give specific reasons
why it is nonsensical in the Appendix of this paper. But there is another deeper reason why I
reject MWI: it is a pseudoscientific religion that is lent credibility by many
well-known scientists, among them Sean Carroll.
Essentially, neither MWI nor the concept of a Multiverse (which is
mathematically equivalent to MWI, according to Leonard Susskind) is empirically
testable, which already excludes them from the realm of science. But more importantly, they both posit the
concept of infinity to overcome the fine-tuning problem or Goldilocks Enigma
in physics. People like Carroll don’t
like the notion that our universe (which appears “fine-tuned” for the existence
of intelligent life) is extraordinarily unlikely, a fact that many (including
me) suggest as evidence for the existence of a Creator. So to overcome odds that approach zero, they
simply assert (with no empirical evidence whatsoever) the existence of
infinitely many worlds or universes, because 0 * ∞ = 1. That is, infinity makes the impossible
possible. But just as anything logically
follows from a contradiction, anything follows from infinity – thus, infinity
is, itself, a contradiction.
Suffice it to say that I’m reasonably sure that at some
point a quantum wave state stops being universal. Call it “collapse” or “reduction” if you
will, but the idea is that at some point an object goes from being in a
superposition of eigenstates to one particular eigenstate. (Later in this post, when I discuss the
in-principle impossibility of Schrodinger’s Cat, it won’t actually make any
difference whether wave state collapse is actual or merely apparent.) With regard to information, some have
characterized this as keeping information constant (e.g., Rovelli), as
decreasing the amount of information (e.g., Aaronson), or as increasing the
amount of information (e.g., Davies).
Anyway, here’s what I think: the information in the
universe is contained in correlations between entangled objects, and essentially
every object is correlated directly or indirectly to every other object (i.e.,
universal entanglement). That
information is finite, but additional interactions/events between objects (and/or
their fields) may increase the information.
(Quick note: whether or not “objects” exist at all, as opposed to just
fields, doesn’t matter. Art
Hobson might say that when I throw a rock, all I experience is the
electrostatic repulsion between the fields of the rock and my hand, but that
doesn’t change that I can treat it as a physical object on which to make
predictions about future interactions/events.)
I gave an example using classical reasoning in this
post and in this paper,
but the idea is very simple.
For example, imagine a situation in which object A is
located either 1cm or 2cm from object B, by which I mean that information in
the universe exists (in the form of correlations with other objects in the
universe) to localize object A relative to object B at a distance of either 1cm
or 2cm. (As wacky as this situation
sounds, it’s conceptually identical to the classic double-slit interference
experiment.) That is, there is a
fact – embedded in correlations with other objects – about objects A and B not
being separated by 3cm, or 0.5cm, or 1000 light-years, etc., but there is not
a fact about whether object A is separated from object B by a distance of 1cm
or 2cm. It’s got nothing to do with
knowledge. It’s not that object A is
“secretly” located 1cm from object B and we just don’t know it. Rather, there just is no fact about whether
object A and B are separated by 1cm or 2cm.
(If it were simply a question of knowledge, then we wouldn’t see quantum
interference.)
That’s quantum superposition. In other words, if at some time t0
there is no fact about whether object A and B are located 1cm or 2cm apart, then
they exist in a (location) superposition.
Object A would say that object B is in a superposition, just as object B
would say that object A is in a superposition. We might call this relativity of superposition. It was in this post that I realized that a superposition of one object exists relative to another object, and both objects have the same right to say that the other object is in superposition. Compare to Special Relativity: there is a fact about an object's speed relative to another, and each object can equally claim that the other is moving at that speed, even though it makes no sense to talk of an object's speed otherwise. Similarly, there may be a fact about one object being in superposition relative to another, with each object correctly claiming that the other is in superposition, even though it makes no sense to talk of an object in superposition without reference to another object.
Whether or not a superposition exists is a question of fact. If a superposition exists (because the facts
of the universe are inadequate to reduce it), then the rules of quantum
mechanics, which depend on interference, apply to probabilistic predictions; if
a superposition does not exist, then ordinary classical probability will
suffice because interference terms vanish. If at some time t1 an event occurs that
correlates objects A and B in a way that excludes the possibility of their
being separated by 2cm, then that correlating event is new information in the
universe about object A being located 1cm from object B. Importantly, that information appears at time
t1 and does not retroactively apply.
We cannot now say that objects A and B were in fact separated by 1cm at
time t0 but we simply didn’t know.
Indeed, this is the very mistake often made in the foundations of
physics that I addressed in this
soon-to-be-published paper. Said
another way, if an object’s superposition is simply the lack of a relevant
fact, then the measurement of that object in a manner (a “measurement basis”)
that reduces the superposition is new information. By “measurement,” I simply mean the
entanglement of that object with other objects in the universe that are already
well correlated to each other.
By the way, I have no idea how or why the universe
produces new information when an event reduces a quantum superposition, but
this is not a criticism of my explanation.
Either new information arises in the universe or it doesn’t, but since
we have no scientific explanation for the existence of any information,
I don’t see how the inexplicable appearance of all information at the
universe’s birth is any more intellectually satisfying than the inexplicable
appearance of information gradually over time.
I should also mention that when I say “superposition,” I
almost always mean in the position basis.
The mathematics of QM is such that a quantum state (a unit-length ray in
Hilbert space) can be projected onto any basis so that an eigenstate in one
basis is actually a superposition in another basis. However, the mathematics of QM has failed to
solve many of the big problems in the foundations of physics and has arguably
rendered many of them insoluble (at least if we limit ourselves to the language
and math of QM). I have far more
confidence in the explanatory powers of logic and reason than the equations of
QM. So even though I fully
understand that, mathematically, every pure quantum state is a
superposition in some basis, when I say an object is in superposition, I nearly
always mean that it is in a location or position superposition relative to
something else. There are lots of
reasons for this choice. First, I don’t
really understand how a measurement can be made in anything but the position basis;
other scholars have made the same point, so I’m not alone. We typically measure velocity, for example,
by measuring location at different times.
We could measure the velocity of an object by bouncing light off it and
measuring its redshift, but without giving it a great deal of thought, I
suspect that even measuring redshift ultimately comes down to measuring the
location of some object that absorbs or scatters from the redshifted
photon. And when I say that we only
measure things in the position basis, I don’t just mean in a lab... our entire
experience all comes down to the localization of objects over time. In other words, the most obvious way (and
arguably the only way) to imagine a quantum superposition is in the position
basis.
Second, the universe has clearly already chosen the
position basis as a preferred basis.
Objects throughout the universe are already well localized relative to
each other. When an object exists in a
(location) superposition, other objects and fields are constantly bathing that
object to localize it and thereby reduce or decohere the superposition in the position
basis. In fact, it is the localizing
effects of objects and fields throughout the universe that makes the creation
of (location) superpositions of anything larger than a few atoms very
difficult. The concept of decoherence
can explain why superpositions tend to get measured in the basis of their
dominating environment, but does not explain why the universe chose the
position basis to impose on superpositions in the first place. Nevertheless, there is something obviously
special about the position basis.
Transitivity of Correlation
Because information exists in the form of correlations
between objects that evidence the occurrence of past events (and
correspondingly limit future possible events), that information exists whether
or not observers know it about their own subsystem, a different correlated
subsystem, or even a different uncorrelated subsystem.
Consider
an object A that is well correlated in location to an object B, by which I mean
that relative to object A, there is a fact about the location of object B
(within some tolerance, of course) and object B is not in a location
superposition relative to object A.
(Conversely, relative to object B, there is a fact about the location of
object A and object A is not in a location superposition relative to object
B.) Object A may be well correlated to
object B whether or not object A “knows” the location of B or can perform an
interference experiment on an adequate sampling of identically prepared objects
to show that object B is not in a location superposition relative to object
A. The means by which objects A and B
became well correlated is irrelevant, but may be due to prior interactions with
each other and each other’s fields (electromagnetic, gravitational, etc.),
mutual interaction with other objects and their fields, and so forth. Now consider an object C that is well
correlated in location to object B; object C must also be well correlated to
object A. That is, if object C is not in
a location superposition relative to object B, then it is not in a location
superposition relative to object A, whether or not object A “knows” anything
about object C or can perform an interference experiment to test whether object
C is in a location superposition relative to object A.
I’ll call
this notion the transitivity of correlation.
It seems insanely obvious to me, but I can’t find it in the academic
literature. Consider a planet orbiting
some random star located a billion light years away. I certainly have never interacted directly
with that planet, and I may have never even interacted with an object (such as
a photon) that has been reflected or emitted by that planet. Nevertheless, that planet is still well
localized to me; that is, there is a fact about its location relative to me to
within some very, very tiny Planck-level fuzziness. I don’t know the facts about its location,
but if I were to measure it (to within some tolerance far exceeding quantum
uncertainty), classical calculations would suffice. I would have no need of quantum mechanics
because it is well correlated to me and not in a superposition relative
to me. This is true because of the
transitivity of correlation: the planet is well correlated to its sun, which is
well correlated to its galaxy, which is well correlated to our galaxy, which is
well correlated to our sun, etc.
The thing
is – everything in the universe is already really, really well correlated,
thanks to a vast history of correlating events, the evidence of which is
embedded in mutual entanglements. But
for the moment let’s imagine subsystem A that includes a bunch of well-correlated
objects (including object 1) and subsystem B that includes its own bunch of well-correlated
objects (including object 2), but the two subsystems are not themselves well
correlated. In other words, they are in
a superposition relative to each other because information does not exist to
correlate them. From the perspective of
an observer in A, the information that correlates the objects within B exists
but is unknown, while information that would well-correlate objects 1 and 2
does not exist. However, events/interactions
between objects 1 and 2 creates new information to reduce their relative
superpositions and make them well correlated.
Then, because objects in A are already well correlated to object 1,
while objects in B are already well correlated to object 2, the events that
correlate objects 1 and 2 correspondingly (and “instantaneously”) correlate all
the objects in subsystem A to all the objects in subsystem B.
This is a
paraphrasing of what Einstein called “spooky action at a distance” (and also
what many scholars have argued is a form of weird or impermissible nonlocality
in QM). But explained in the manner
above, I don’t find this spooky at all.
Rather, from the perspective of an observer in subsystem A, unknown
facts of past events are embedded in entanglements within subsystem B, while
there simply are no facts (or perhaps inadequate facts) to correlate subsystems
A and B. Once those facts are newly
created (not discovered, but created) through interactions between objects 1
and 2, the preexisting facts between objects in subsystem B become (new) facts
between objects in both subsystems.
Let me say it another way. An
observer OA in subsystem A is well correlated to object 1, and an
observer OB in subsystem B is well correlated to object 2, but they
are not well correlated to each other; i.e., they can both correctly say that
the other observer is in a superposition.
When object 1 becomes well correlated to object 2, observer OA
becomes well correlated to observer OB. This correlation might appear “instantaneous”
with the events that correlate objects 1 and 2, but there’s nothing spooky or
special-relativity-violating about this.
Rather, observer OA was already well correlated to object 1
and observer OB was already well correlated to object 2, so they become
well correlated to each other upon the correlation of object 1 to object 2.
Of course,
because everything in the universe is already so well correlated, the above
scenario is only possible if one or both of the subsystems are extremely
small. The universe acts like a
superobserver “bully” constantly decohering quantum superpositions, and in the
process creating new information, in its preferred (position) basis. Still, if the universe represents subsystem
A, then a small subsystem B can contain its own facts (i.e., embedded history
of events) while being in superposition relative to A. Imagine subsystem B containing two correlated
particles P1 and P2 – e.g., they have opposite spin (or
opposite momentum). When the position of
particle P1 is then correlated (e.g., by detection, measurement, or
some other decoherence event) to objects in subsystem A (i.e., the rest of the
universe), that position corresponds to a particular spin (or momentum). But because particle P1 was
already correlated to its entangled particle P2, the spin (or
momentum) of particle P2 is opposite, a fact that preceded detection
of particle P1 by the universe.
That fact will be reflected in any detection of particle P2
by the universe. Further, facts do not
depend on observer status. An observer
relative to particles P1 and P2 has as much right to say
that the universe was in superposition and that the correlation event
(between P1 and objects in the rest of the universe) reduced the
superposition of the universe.
This
explanation seems so obviously correct that I don’t understand why, in all my
reading and courses in QM, no one has ever explained it this way. To buttress the notion that facts can exist
in an uncorrelated subsystem (and that measurement of that subsystem by a
different or larger system creates correlating facts to that subsystem
but not within that subsystem), consider this. As I walk around in the real world, thanks to
natural quantum dispersion, I am always in quantum superposition relative to
the rest of the world, whether we consider my center of mass or any other
measurable quantity of my body. Not by
much, of course! But given that the
universe does not contain infinite information, there must always be some tiny
superposition fuzziness between me and the universe – yet that doesn’t change
the fact that my subsystem includes lots of correlating facts among its atoms.
Killing
Schrodinger’s Cat
I tried to
explain in this draft
paper why Schrodinger’s Cat and Wigner’s Friend are impossible in
principle, but the explanation still eludes the few who have read it. The following explanation will add to the
explanation I gave in that draft paper. The
idea of SC/WF is that there is some nonzero time period in which some
macroscopic system (e.g., a cat) is in an interesting superposition (e.g., of
states |dead> and |alive>) relative to an external observer. It is always (ALWAYS) asserted in the academic
literature that while detecting such a superposition would be difficult or even
impossible in practice, it is possible in principle.
Let’s
start with some object in superposition over locations A and B, so that from
the perspective of the box (containing the SC experiment) and the external
observer, its state is (unnormalized) superposition state |A> + |B>. However, from the perspective of the object,
the box is in a superposition of being located in positions W and X in
corresponding states |boxW> and |boxX> and the
observer is in a superposition of being located in positions Y and Z in
corresponding states |obsY> and |obsZ>. But remember that the box and observer are,
at the outset of the experiment, already well correlated in their positions,
which means that from the object’s perspective, the system is in state |boxW>|obsY>
+ |boxX>|obsZ>.
When the object finally gets correlated to the box, it “instantly” and
necessarily gets correlated to the observer.
It makes no difference whether the quantum wave state actually collapses/reduces
or instead evolves linearly and universally.
Either way – whether the wave state remains |boxW>|obsY>
+ |boxX>|obsZ> or collapses into, say, |boxW>|obsY>
– there is never an observer who is not yet correlated to the box and who can
do an interference experiment on it to confirm the existence of a superposition. Once the object “measures” the position of
the box, it inherently measures the position of the observer, which means that
there is never an observer for whom the box is in a superposition (unless the
box is already in a superposition relative to the observer, which, as I pointed
out in the draft paper, is impossible because of very fast decoherence of
macroscopic objects).
In Eq. 1
of the draft paper, I show a simple von Neumann progression, with each arrow (à) representing a time evolution. If it’s right, then there is a moment when
the measuring system is in superposition but the observer is not. The problem with that conclusion, as I’ve
been trying to explain, is that because the observer is already well correlated
to the measuring system (and the box, cat, etc.) to within a tolerance far
better than the distance separating the object’s eigenstates |n>,
correlation of the object’s location to that of the measuring device
“instantly” correlates the observer and the rest of the universe. Once there is a fact (and thus no
superposition) about the object’s location relative to the measuring device,
there is also a fact (and thus no superposition) about the object’s location
relative to the observer. There is no
time at which the observer can attempt an interference experiment to confirm
that the box (or cat or measuring device, etc.) are in a superposition.
Therefore,
the SC and WF experiments are impossible in principle. An MWI apologist might retort that
Schrodinger’s cat is, indeed, in a superposition, along with the observer. But since there is no time at which an
interference experiment could be performed, even in principle, to confirm this,
their claim is both unscientific and useless.
They may as well say that unicorns exist but are impossible to detect.
Other
Thoughts and Implications
CCCH.
In this
post, I heavily criticized a
paper that incorrectly asserted that the consciousness-causes-collapse
hypothesis (“CCCH”) has already been empirically falsified. I did so because I despise bad logic and bad
science, not because I endorse CCCH.
Indeed, if my explanation of QM is correct, then collapse (or apparent
collapse) of the quantum wave function has nothing to do with consciousness but
is rather the result of new information produced from correlating interactions
with the environment/universe.
The
Damn Cat. What I haven’t discussed so far are “interesting”
evolutions due to amplifications of quantum events. The argument above, which is an extension of
the argument in my draft paper
on Schrodinger’s cat, is essentially that quantum amplification of a tiny
object in superposition cannot place the macroscopic box containing SC in a
superposition relative to the observer any more easily than the box itself can
naturally disperse (via quantum uncertainty) relative to the observer. And decoherence by objects and fields in the
universe makes adequate dispersion of the box impossible even in
principle. But there’s more. If I am right in my explanation of QM, then
interacting subsystems will agree on the facts embedded in their correlations. For example, if subsystem B is in a
superposition of being located 1cm and 2cm from subsystem A, then when an
observer in subsystem A “measures” B at a distance of, say, 1cm, then from the
perspective of an observer in subsystem B, B measured A also at a distance of
1cm.
In the
case of SC (and WF), I analyzed them in terms of fuzziness of objects, such as
a particular carbon atom that would have been located in the live cat’s brain
is instead located in the dead cat’s tail, thus requiring a quantum fuzziness
to span a meter or so. But of course SC
is far more interesting: in one case there is a live cat and in another case
there is a dead cat, represented by a vastly different set of correlations
among its constituent atoms.
In order
for a SC superposition to actually be produced relative to the external
observer (and the universe to which he is well correlated), it must be the case
that a “comparable” superposition of the universe is produced relative to
SC. Then, when an event occurs that
correlates the two systems – which, remember, can ultimately be traced back to
the location of some tiny particle at A or B, separated by some tiny distance –
observers in each of the two systems will agree on the correlations. So let’s say we’ve somehow created a SC
superposition. We wait a few minutes,
pop a bottle of champagne to celebrate the amazing feat, and then we open the
box to look, at which point see a live cat – that is, we (and the rest of the
universe) become correlated with |live>.
But since the correlations among the atoms in the box exist before we
open the box, then the hypothetical state |dead> must be correlated with a
universe that would have seen that exact set of facts as a dead cat. How does one measure a live cat as dead? Remember, we are not just talking about
measuring a heartbeat, etc... we are talking about a universe that is
constantly inundating the cat’s atoms in a way so that every observer in that
universe would observe a dead cat. That
is, if it were possible to produce a cat in a superposition of |dead> and
|alive> inside a box, then from the perspective of an observer inside the
box, the universe would have to be in a superposition of being in a state that
would measure a set of atoms as being a dead cat and another state that would
measure the same set of atoms as being a live cat. Ridiculous.
