From The Anthropic Cosmological Principle by John Barrow and Frank Tipler (1988):
“The
question of why does this universe rather than that universe exist is answered
by saying that all logically possible
universes do exist. What else could there possibly be? The MWI cosmology
enlarges the ontology in order to economize on physical laws.”
By the way, I have a lot of “stars” in the text
below, which correspond to notes at the bottom that give a bit of physics details
for those who are interested (it’s not necessary to read though).
One of the many problems in QM we still need to
solve is how to make sense of observers. Namely, us, the ones who perform experiments. We seem to have a peculiar
influence over what happens to particles at the subatomic level just by
observing them. Indeed, before a measurement of a particle is taken (usually
something like its position or speed. I’ll just talk about position though),
the usual interpretation, called the Copenhagen
Interpretation, says that the particle exists in a “superposition” of
states: not at any particular location. It is spread out over a certain area
and is described by a wavefunction (usually denoted by ψ). Although the
particles is more likely to be found in a particular area, it can still be
found outside this region.*1
The interpretation favoured by the Copenhagenists
is that when an observation is made, the wavefunction “collapses” to a
particular value. When we weren’t looking, it was spread out over a large area,
existing, in a sense, in many places at once, but now, it is nicely settled at
a single point in space. In the
picture below, the graph on the left shows the probability of observing a
particle in a particular location (in x and y coordinates, so two
dimensionally). This is represented by the particle's wavefunction (ψ) on the
vertical axis.*2 The particle isn’t “in” any one
spot, but spread out over an area, though it is most likely to be found at the
peak.
However, when an observation or measurement is made, the wavefunction collapses so that the particle is now in a particular spot (the spike on the graph to the right). So, as the physicist Niels Bohr said, “an independent reality in the ordinary physical sense can neither be ascribed to the phenomena nor the agencies of observations.” Observation, in a sense, brings the properties of particles into being—they never really “existed” beforehand.
This interpretation seems ludicrous, and there are
some serious issues with it as well.*3 This might just be how nature works, but fortunately, there are
also other options available to us. First, the uncertainty in our description
of QM (for example, of locating a particle) is probably just that: it is only
an uncertainty in our description,
which is tailor-made for human experience. It describes our uncertain knowledge of the world, not an uncertainty in the world
itself. There is an inherent limitation to what we can know (from our limited
senses and the fact that we have to interact with the world when we observe it)
but that doesn’t mean that the world is actually “uncertain” and existing in
many states before it’s observed. It’s naïve to assume that we can know everything through our senses and the
mathematics we have created; it’s more reasonable to assume that as creatures
living in three spatial dimensions, able to travel one direction in time and being
mostly limited to our five senses, if we dig deep enough, there may be some
things we can only understand probabilistically—but that’s not to say that this
is the way they are, just the way they are to
our perceptions. There must be a physical reality independent of our
observations even if we can’t observe it, because otherwise, what would our
probabilistic descriptions be describing? Thus, it’s important to distinguish
between the mathematics we use to describe the world, and the world itself,
which need not be constrained by our theories and human limitations.*4
This ties in with a different interpretation of QM
called the Many Worlds Interpretation.*5 In this theory, each quantum mechanical
possibility occurs in a different world. Introduced by Hugh Everett and
endorsed by many physicists today (for example, Max Tegmark, said, “Accepting
quantum mechanics to be universally true means that you should also believe in
parallel universes.”), in the MW interpretation, every quantum mechanical
possibility happens, but each occurs in a different world.*6 So everything happens,
and there are nearly infinite possibilities! So think about every possible universe,
those that are only slightly different to ours (e.g., one in which your
favourite colour is red instead of purple) and ones that
have entirely different planets, solar systems, and galaxies. In this
scenario, the observer has no magical ability to make wavefunctions collapse,
but rather, when they make a measurement, they only measure the particle’s
position in their particular universe. Everett said that “it is not so much the system which is affected by an observation as
the observer,” so the MW approach is a realist view of QM (meaning, in this
context, that each world exists whether we observe it or not).
So when a measurement is made on a system, all the
possibilities that could happen will “split” into different worlds. If one
views the universe as a whole, however, (though here, it might be better to say
multiverse) there is no real splitting and no change in the particle’s
wavefunction: the general wavefunction represents all the different particles
that exist in every universe, even though in our particular universe, it only
follows one option. The real difference is in the measuring device (or
ourselves, since we perceive the particle to be in one state or another),
because we measure different values depending which universe we’re in. Indeed,
it’s more apt to say that the measuring device splits rather than the particle
and the universe around it, because it’s the measuring device that is registering
different values depending upon the state of the particle. Barrow and Tipler
say that, “There is only one Universe,
but small parts of it—measuring apparata—split into several pieces…upon the act
of measurement.”
I find this hard to imagine physically, since, if anything in the universe splits into
multiple states, where do these copies exist? They have to be somehow distinct
from each other or else it wouldn’t make sense to talk about a “split” in the
first place. And it isn’t as though there is “the” universe, and then off in
some other plane of existence, there are various measuring devices with
different readings existing in and of themselves. I can’t explain why there
wouldn’t be as many universes as there are splits, even if, at the moment of
the split, they all start out the identically except for the reading on the
measuring device and the particle’s state. So the view of having many worlds
seems to make sense only if there are many fully-fledged universes distinct
from ours.*7 Yet later on, they mention
multiple “worlds,” each with different states for the particle that is
measured, which makes more sense. They say that “each measurement splits the apparatus (or equivalently, the
universe).” There is only one “Universe” (capital “U” to denote all the
worlds together), but this Universe represents a collection of “universes”
(each with the different possible outcomes). It is the measuring device that causes the world to split, but it is not
the only thing that exists in these other worlds.
I find this hard to imagine physically, since, if anything in the universe splits into
multiple states, where do these copies exist? They have to be somehow distinct
from each other or else it wouldn’t make sense to talk about a “split” in the
first place. And it isn’t as though there is “the” universe, and then off in
some other plane of existence, there are various measuring devices with
different readings existing in and of themselves. I can’t explain why there
wouldn’t be as many universes as there are splits, even if, at the moment of
the split, they all start out the identically except for the reading on the
measuring device and the particle’s state. So the view of having many worlds
seems to make sense only if there are many fully-fledged universes distinct
from ours.*7 Yet later on, they mention
multiple “worlds,” each with different states for the particle that is
measured, which makes more sense. They say that “each measurement splits the apparatus (or equivalently, the
universe).” There is only one “Universe” (capital “U” to denote all the
worlds together), but this Universe represents a collection of “universes”
(each with the different possible outcomes). It is the measuring device that causes the world to split, but it is not
the only thing that exists in these other worlds.
This ties in with a similar explanation of the MWI
described by Max Tegmark in various papers (using Everett’s original ideas). There
is no “collapse” of the wavefunction: it proceeds according to physical
equations.*9 It isn’t that the wavefunction “splits” into many worlds, but
that all possibilities exist, even though we only perceive one of them in a
given scenario (so it looks like a
split). There is “apparent randomness
from the inside viewpoint…[but] strict causality from the outside viewpoint,”
which means that although we can’t know which state of a particle will be in
when we measure it in a given experiment, we know with 100% certainty that all
outcomes will happen. From an “outside” point of view, we would be able to see
all the possibilities occurring, which is where the many worlds come in, since
each happens in a different “world.” This is called decoherence, when you go
from a quantum (small-scale, one world) description to a classical (large-scale)
description within one of the worlds. So it “is essentially indistinguishable from the effect of a postulated
Copenhagen wavefunction collapse from an observational (inside) point of view.”
Thus, there is no real randomness to the universe:
it only appears so to us because we cannot predict which outcome we will end up
with in our universe. Tegmark says “whenever
a quantum event appears to have a random outcome, all outcomes in fact occur,
one in each branch [universe].” There is nothing random or uncertain about
the wavefunction itself: it follows certain physical laws just like the objects
in the macroscopic world, but “observers
subjectively experience this splitting merely as a slight randomness.”
The MW theory thus has two descriptions: the
inside view, and the outside view. Tegmark describes this as the bird’s point
of view looking down on the world below (or in this case, worlds), and the
point of view of a frog within one of the worlds. From the bird’s point of
view, there is only universe described by a single wavefunction, and it does
not split into many worlds. All these “worlds” and possibilities occur
simultaneously, splitting and merging according to fixed physical laws. It is
only on a smaller scale, with the frog, that ideas about randomness and
probability make sense. The frog experiences a small portion of the full
reality, perceiving only a single world within the entire multiverse.*10 At every
instant, when there are multiple outcomes that can arise in a given situation,
the bird can see each of them playing out, all in different worlds, whereas the
frog only experiences the different worlds “as a slight randomness.” There is
no real randomness, but since the
frog doesn’t have access to any other worlds, it can only understand the world
in terms of probabilities rather than certainties. This is why mathematics is
so powerful: it allows us to temporarily rise out of the frog-level of
existence and understand what’s really going.*11
This is the basic idea of how you can explain QM
mechanics with the MW theory. It does, however, introduce many philosophical
puzzling questions, such as:
- If there are
many copies of “you” in different worlds, each slightly different, which
is the “real” you? Are they all you, are they all different people, or is
it meaningless to talk about a unified self at all?
- If the soul
exists (and we have good reason to believe that it does), then is it
spread out over the different copies of you, or are all copies but one “soulless”?
This, however, depends on the answer to the first bullet point.
- Is there a
theory of everything to describe the many worlds as a whole, or, even from
the bird’s eye view, is probability the best we could ever get?
In a future post, I’ll talk about how this can be
understood within the framework of Neoplatonic philosophy, but for now, that’s
another story
*1 This can be seen clearly in Heisenberg’s Uncertainty Principle: ΔxΔp ³ ħ/2, where Δx is the uncertainty in the particle’s position, and Δp the uncertainty in its momentum. So the more accurately you know the position, the less accurately you know its momentum/speed, and vice versa, so you can never localize a particle precisely.
*2 To be more accurate, it’s actually the particle’s probability density, |ψ|2
*3 For instance, how can our knowledge, something that exists in our minds and is, in a sense, nonphysical, affect particles outside our bodies? If there are no observers, will the world exist? Does, say, a fruit fly count as an observer? What about an unconscious measuring device operating without any human influence? And, as in Schrodinger’s cat scenario, how can a cat be both dead and alive until we observe it?
*4 Some physicists don’t like this idea, saying that the unknowable properties of particles are “hidden variables” and that the underlying reality of the world involves statistics rather than certainties. But philosophically, this makes little sense. For a related topic, check out my previous blog post Platonic Realism in Physics.
*5 Another interpretation that could also be philosophically sound is having an “Ultimate Observer,” but I won’t get into that.
*6 A simple example is a system with a particle that could be spin up or spin down. Although we describe the particle as being in a superposition of the two spin states, we only measure one of these two possibilities when the spin of the particle is measured: one in which the particle is spin up, and the other spin down, each corresponding to two different universe.
*7 It may make sense to mathematically describe only the apparatus splitting, but when you think about what physically happens, you can see that the rest of the universe will be “copied” in the other world.
*8 This is the weak anthropic principle: “weak” not because it is lacking in some sense, but because it doesn’t make any grand statement about the universe. In fact, it really just states the obvious, since everything we perceive in the universe is restricted by the fact that we exist and are able to observe it, so it must be conductive to life, otherwise, we wouldn’t be here to observe anything.
*9 The system evolves according to the Schrodinger equation at all times. If there was a collapse, the Schrodinger equation would be violated.
*10 Decoherence “prevents them from seeing…parallel copies of themselves.” (Tegmark)
*11 I don’t mean that we can get out of probabilistic interpretations, because that is embedded in our mathematics as well, but rather, we can conceptually understand the general structure of reality and what this means for the existence of other worlds, probability, and determinism.
*1 This can be seen clearly in Heisenberg’s Uncertainty Principle: ΔxΔp ³ ħ/2, where Δx is the uncertainty in the particle’s position, and Δp the uncertainty in its momentum. So the more accurately you know the position, the less accurately you know its momentum/speed, and vice versa, so you can never localize a particle precisely.
*2 To be more accurate, it’s actually the particle’s probability density, |ψ|2
*3 For instance, how can our knowledge, something that exists in our minds and is, in a sense, nonphysical, affect particles outside our bodies? If there are no observers, will the world exist? Does, say, a fruit fly count as an observer? What about an unconscious measuring device operating without any human influence? And, as in Schrodinger’s cat scenario, how can a cat be both dead and alive until we observe it?
*4 Some physicists don’t like this idea, saying that the unknowable properties of particles are “hidden variables” and that the underlying reality of the world involves statistics rather than certainties. But philosophically, this makes little sense. For a related topic, check out my previous blog post Platonic Realism in Physics.
*5 Another interpretation that could also be philosophically sound is having an “Ultimate Observer,” but I won’t get into that.
*6 A simple example is a system with a particle that could be spin up or spin down. Although we describe the particle as being in a superposition of the two spin states, we only measure one of these two possibilities when the spin of the particle is measured: one in which the particle is spin up, and the other spin down, each corresponding to two different universe.
*7 It may make sense to mathematically describe only the apparatus splitting, but when you think about what physically happens, you can see that the rest of the universe will be “copied” in the other world.
*8 This is the weak anthropic principle: “weak” not because it is lacking in some sense, but because it doesn’t make any grand statement about the universe. In fact, it really just states the obvious, since everything we perceive in the universe is restricted by the fact that we exist and are able to observe it, so it must be conductive to life, otherwise, we wouldn’t be here to observe anything.
*9 The system evolves according to the Schrodinger equation at all times. If there was a collapse, the Schrodinger equation would be violated.
*10 Decoherence “prevents them from seeing…parallel copies of themselves.” (Tegmark)
*11 I don’t mean that we can get out of probabilistic interpretations, because that is embedded in our mathematics as well, but rather, we can conceptually understand the general structure of reality and what this means for the existence of other worlds, probability, and determinism.
~~*~~
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