Tegmark’s Level III Multiverse: The many worlds interpretation of quantum mechanics


Credit: Christian Schirm via Wikipedia
Credit: Christian Schirm via Wikipedia

I recently finished reading Max Tegmark’s latest book, ‘Our Mathematical Universe‘, about his views on multiverses and the ultimate nature of reality.  This is the third in a series of posts on the concepts and views he covers in the book.  

The previous entries are:
Tegmark’s Level I Multiverse: infinite space
Tegmark’s Level II Multiverse: bubble universes

Tegmark postulates four levels of multiverse.  This post is on what he calls the Level III Multiverse, the many worlds interpretation of quantum mechanics.

In the early twentieth century, one of the mysteries of science was the constant speed of light.  The speed of light was constant no matter how it was measured.  This was in contrast to the speed of sound, or the speed of just about anything else, which varied depending on the speed of the observer.

Albert Einstein accepted the experimental evidence of the constancy of the speed of light, and explored its implications.  If the speed of light was always constant, then something else had to give.  Something that factored into that speed had to vary, something like mass, length, and time.  Exploring those implications led to the special theory of relativity.

For several decades now, one of the mysteries of science has been wave / particle duality.  We have strong evidence that light behaves like a wave, and strong evidence that it behaves like a particle.  We have similar evidence for electrons and just about any other subatomic particle, as well as atoms themselves and even large molecules under isolated conditions.

The shape of a wave is modeled in a mathematical concept called the wave function.  The particle will appear somewhere in that wave.  There is no known way to predict where in the wave any individual particle will be found.  All that can be known are probabilities of it appearing at various locations within the wave.  Bizarrely, once the position of the particle is observed, once it is measured, all trace of the overall wave instantly disappears, with only the particle remaining.

Just to be clear, this is freaky strange, and no one is certain why it is so.  Reality at the quantum level appears to be wavelike, to the degree that the wave can physically interfere with itself when split, but suddenly, instantly, becomes particle like when we look at it.  As strange as it is, this has been confirmed for decades by extensive experimental data.  It is reality.

There are a number of interpretations of what is happening.  The oldest, and for a long time the most popular, is called the Copenhagen Interpretation.  It is basically is a minimalist interpretation that says that this is simply reality, and that when a particle’s position is measured, the wave function “collapses”.  Prior to the collapse, the particle exists in what’s called a superposition.  It exists in multiple locations at the same time, but once the position is known, the existence of the particle in all but one of those locations disappears.

There are several other interpretations.  All of them must throw one or more aspects of common sense reality under the bus in order to make sense of the data.

In the 1950s, Hugh Everett came up with a new interpretation.  Everett accepted the mathematics of the wave function, but was troubled by the lack of anything in those mathematics that predicted a wave function collapse.  The only reason that the wave function collapse is thought to exist is the fact that we only observe the particle in one location once it is measured.

Everett asked, what happens if the wave function, in fact, never collapses?  If the wave function predicts two locations for the particle, then the mathematics say the particle is in both locations.  Of course, we don’t observe it to be in both locations.  So then, what’s going on?  Similar to when Einstein was contemplating the constant speed of light, something else has to give.

According to the mathematics and our sensory data, we should see the particle in only one of the locations and we should see it only in the other one.  No, the second “only” in the previous sentence is not a typo.  We appear to have two realities in which we observe the particle.  Prior to the measure, there was only one reality.  After the measure, there are two.

In multiverse parlance, the many worlds interpretation asserts that our universe is cloned every time what appears to be a wave function collapse happens.  Given that this happens an uncountable number of times per second throughout the universe, and given the large range of possibilities for each particle’s position, the number of universes being created every second is sublime.

The randomness of the particles location then is an illusion, created by the fact that we only observe the location particular to our universe.  But the wave function unfolds unabated with the particle existing in each location in a different universe.

This means that there are an uncountable numbers of you in these alternate universes, where each quantum result is manifested.  In other words, every random event that could happen, happens in some universe, and there are an uncountable versions of you living every conceivable version of your life.

In Tegmark’s framework, this is the Level III Multiverse.  It is a superset of the Level I and II multiverses, although as formulated, there’s no particular reason that its existence, or non-existence, is dependent on the other ones.  If all three levels exist, then Level III includes all the multiverses in the lower levels and reality continues to expand at an astounding rate.

Tegmark does note some similarities between the Level I and Level III multiverse.  In both, there are an infinite number of you living every possible variation of your life.  The result of every quantum possibility should be manifest in one of the Level I universes.  Of course, if they were one and the same, it would mean that remote regions in the Level I multiverse were in some way quantum entangled with each other.

Tegmark also speculates about reconciling the Level II and III multiverse, but doesn’t currently see a way to do it.

Over time, support for the many worlds interpretation has grown in the particle physics community, although Copenhagen continues to hold a plurality in most polls.  The question is, is there any way to test this idea?  Brian Greene in ‘The Hidden Reality’ identified the possibility of the uncollapsed wave interfering with itself across universes, although he notes that observing this would be extremely difficult.

Tegmark proposes another one, although it’s not one that anyone is liable to volunteer for.  The quantum suicide or subjective immortality thought experiment involves setting up a gun with a trigger set to fire if a random quantum event takes place, with a 50% chance of taking place in the first second.  The experimenter then puts their head in front of the gun.

In 50% of the universes, the experimenter dies within the first second, but in the other 50%, they live.  For each second, the probability of the experimenter being alive goes down.  After a couple of minutes, the probability of the experimenter still being alive is infinitesimal.  However, in at least some portion of the alternate universes, the experimenter lives on.

From the subjective point of view of the experimenter, the longer they live, the higher the probability of the many worlds interpretation being true.  After a few hours, increasingly unlikely events (misfire, power outage, meteor strike, etc) begin to happen to prevent their death.  If an experimenter subjectively survived this ordeal for several hours, they could have a high degree of confidence in the many worlds interpretation.  (Of course, in virtually all universes, they would leave behind grieving friends and family who would be less convinced.)

Tegmark then points out that, if either the many worlds interpretation or infinite space scenario is true, then a version of each of us will, despite its improbability, live long enough to outlast all of humanity.  In other words if is true, subjectively, you will live long enough to know it is true, at least assuming you recall reading this.  Each of us may live to be the last human in our own improbable universe, knowing the truth of the multiverse.

In the next post, we will get into the main idea of Tegmark’s book, the mathematical universe hypothesis.