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Hrvoje Crvelin

Many Worlds

Posted by Hrvoje Crvelin Oct 19, 2011

With this blog post I continue series of posts about multiverse.  So far we touched following models:

- quilted universe

- inflationary universe

- braneworld universe

- landscape multiverse

 

Before I stepped into branes I did a bit of introduction to basics of string theory and dimensions.  What lies ahead of us now is another small introduction to something you probably have heard of before - quantum mechanics.  You probably have heard of it as something that makes SciFi reality or where Star Trek is possible.  When I first met content of quantum mechanics I thought this must be some crackpot idea where due to us being limited in understanding and knowledge we create framework where "everything" is possible.  The more I dived deeper into this matter more it turned around this is a real thing and something scientists have been working on for almost a century.  Some of quantum discoveries are pretty much amazing and will lead you to question what reality is.  Bottom line is, reality is not what you see and feel, but you shouldn't worry about as quantum reality still does not affect your usual rhythm day by day.  But for past decades, achievements in field of quantum research have been pretty much breath taking and most recently we see achievements in fields of quantum computing as well (though there is a long ride yet).  The best way to understand the quantum story is to do quick trip into the past.  Brain Greene, in his book Fabric of Cosmos (highly recommended by the way), does a nice job giving historical overview of events.

dice.jpgEinstein's general relativity (I plan to spend one entire post on relativity topic once I'm done with multiverse story) and quantum mechanics have been the two greatest achievements of physics in 20th century.  As it happens, both were born in same era.  They rely on very different types of mathematics and have completely separate rules and underlying principles. General relativity breaks down at singularities and closed time loops, while quantum mechanics fails to describe the force of gravity within its framework.  This is why today we hear a lot about efforts in science community to develop theory of quantum gravity. But world at quantum level as described by quantum mechanics is sp strange and it is hard to find any comparison to what we experience in our ordinary lives. Great and late Richard Feynman (I encourage you to watch videos with him on youtube) said once: "I think I can safely say that nobody understands quantum mechanics" and "If you think you understand quantum mechanics, you don't understand quantum mechanics."  Let's explore the quantum path now.

 

Classic physics teaches us if you know where every particle is, how fast it goes and in what direction then you can use the laws of physics to predict everything.  It like those physics tests in elementary school where based on speed (or acceleration) and current location you must predict where object will be in future for example.  Quantum mechanics breaks this whole concept by saying this is not possible.  That doesn't mean quantum mechanics is incomplete or bad, but rather it gives new insight into the world we are part of.  Quantum mechanics states we can't know the exact location and exact velocity any single particle. We can know one of those, but not both.  The more precisely I know the speed, less will I know about location and vice versa.  What quantum mechanics shows the best we can ever do is predict the probability that an experiment will turn out this way or that. And this has been verified through decades of accurate experiments.  If you have 100 boxes, each with 1 electron inside, and you along with 99 friends would open them and measure electron position, you would find different results.  Do it again and you will find very close results again. The regularity isn’t evident in any single measurement; you can’t predict where any given electron will be. Instead, the regularity is found in the statistical distribution of many measurements. The regularity shows probability (likelihood) of finding an electron at any particular location.  Quantum mechanics applies not just to electrons but to all types of particles.

 

Let's push out imagination bit further.  Think of two objects.  If you have two birds in the sky each flying in its own direction, two men walking each side of the street, TV remote control and TV, any two objects with some space between - we usually see those objects as independent of each other.  In order to influence each other they have to do something to traverse the space between them.  If I'm person on one side of the street while you are the second on the other side, I need to traverse the space to reach you - either by walking to you or yelling across the street or whatever method I find suitable to reach you.  Whatever it is, something from here where I'm has to go over there where are you.  And this is in essence how objects influence each other as they never share same location.  Physicists call this feature of the universe locality, emphasizing the point that you can directly affect only things that are next to you, that are local.  For the few past decades, scientists have done experiments which have established another truth - you can do something here (eg. point A) and that has direct influence there (eg. point B) without anything being sent from here to there.  Voodoo?  Nope - just quantum mechanics.  Roughly speaking and particle wise, even though the two particles are widely separated, quantum mechanics shows that whatever one particle does, the other will do too.  No matter what distance between them.

 

To quote Greene's example, if you are wearing a pair of sunglasses, quantum mechanics shows that there is a 50-50 chance that a particular photon - like one that is reflected toward you from the surface of a lake or from an asphalt roadway - will make it through your glare-reducing polarized lenses: when the photon hits the glass, it randomly "chooses" between reflecting back and passing through. The astounding thing is that such a photon can have a partner photon that has sped miles away in the opposite direction and yet, when confronted with the same 50-50 probability of passing through another polarized sunglass lens, will somehow do whatever the initial photon does. Even though each outcome is determined randomly and even though the photons are fir apart in space, if one photon passes through, so will the other.  This is the kind of nonlocality predicted by quantum mechanics.  This property is called quantum entanglement.

 

This "spooky action at a distance", in Einstein's words who didn't like it at all, is a serious blow to our conception of how the world really works. In 1964, physicist John Bell (CERN) showed just how serious this is. He calculated a mathematical inequality that encapsulated the maximum correlation between the states of remote particles in experiments in which three "reasonable" conditions hold:

  1. Experimenters have free will in setting things up as they want
  2. Particle properties being measured are real and pre-existing, not just popping up at the time of measurement
  3. No influence travels faster than the speed of light (the so called cosmic speed limit)

 

As many experiments since have shown, quantum mechanics regularly violates Bell's inequality, yielding levels of correlation way above those possible above his conditions hold. This opens several dilemmas and it is great ground for philosophical discussions.  Do we not have free will, meaning something, somehow predetermines what measurements taken?  Are the properties of quantum particles not real - implying that nothing is real at all, but exists merely as a result of our perception?  Or is there really an influence that travels faster than light?  In 2008 physicist Nicolas Gisin and his colleagues at the University of Geneva showed that, if reality and free will hold, the speed of transfer of quantum states between entangled photons held in two villages 18 kilometers apart was somewhere above 10 million times the speed of light.  Make your pick.

 

My introduction to quantum entanglement was through Elegant Universe series based upon same titled book by Brian Greene.  So called double-slit experiment is described which shows the point and this experiment since had captured my imagination about quantum reality (or what reality really is).  To get some basics, we have to start with wave.  In nature we know many waves (electromagnetic, acoustic, etc) so we stick to something easy to visualize - water wave.  Throw a pebble into the water and you get wave.  A water wave disturbs the flat surface of a surface by creating regions where the water level is higher than usual and regions where it is lower than usual. The highest part of a wave is called its peak and the lowest part is called its trough. A typical wave involves a periodic succession: peak followed by trough followed by peak, and so forth. If two waves head toward each other (if you throw two pebbles into water at nearby locations, producing outward-moving waves that run into each other) when they cross there results an important effect known as interference.  Picture below shows it.

interference_water_waves.jpg

When a peak of one wave and a peak of the other cross, the height of the water is even greater, being the sum of the two peak heights. Similarly, when a trough of one wave and a trough of the other cross, the depression in the water is even deeper, being the sum of the two depressions. And here is the most important combination: when a peak of one wave crosses the trough of another, they tend to cancel each other out, as the peak tries to make the water go up while the trough tries to drag it down. If the height of one wave's peak equals the depth of the other's trough, there will be perfect cancellation when they cross, so the water at that location will not move at all. 

 

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Let's go now into the history.  The year is 1803 and our hero is called Thomas Young.  This is the year he performed famous two-slit experiment (referred also as Young's experiment).   In the basic version of the experiment, a coherent light source such as a laser beam illuminates a thin plate pierced by two parallel slits, and the light passing through the slits is observed on a screen behind the plate. The wave nature of light causes the light waves passing through the two slits to interfere, producing bright and dark bands on the screen - a result that would not be expected if light consisted strictly of particles. However, at the screen, the light is always found to be absorbed as though it were composed of discrete particles or photons. This establishes the principle known as wave–particle duality.

So far so good.  We learned in school about dual nature of light being both waves and particles so there is nothing new here as you already knew it.  Now we jump to 20th century.  In 1927, Clinton Davisson and Lester Germer fired a beam of electrons (no apparent connection to waves) at a piece of nickel crystal. While the details are less important, what matter is that this experiment is equivalent to firing a beam of electrons at a barrier with two slits. When the experimenters allowed the electrons that passed through the slits to travel onward to a phosphor screen where their impact location was recorded by a tiny flash (the same kind of flashes responsible for the picture on your television screen), the results were all but expected! (at this point you see where this is leading us, don't you?)   Let's take this with slow steps.

 

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A gun (obeying classical physics) sprays bullets towards a target. Before they reach the target, they must pass through a screen with two slits. If bullets go through the slits they will most likely land directly behind the slit, but if they come in at a slight angle, they will land slightly to the sides. The resulting pattern is a map of the likelihood of a bullet landing at each point.

 

Picture left showed two-slit pattern happens to be simply the sum of the patterns for each slit considered separately: if half the bullets were fired with only the left slit open and then half were fired with just the right slit open, the result would be the same.

 

Thinking of the electrons as bullets, you'd naturally expect their impact positions to line up with the two slits.  This is sane and logical thinking.  If you imagine house with two windows and you are shooting with paintballs from outside picture on left is the pattern you would get on the wall facing you inside the house.  This is what we expect particle to do.

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With waves, however, the result is very different, because of interference. If the slits were opened one at a time, the pattern would resemble that for bullets: two distinct peaks. But when both slits are open, the waves pass through both slits at once and interfere with each other: where they are in phase they reinforce each other; where they are out of phase they cancel each other out.

 

This sort of pattern is expected for photons - particles of light as showed by Young.  Nevertheless, in 1924 Louis de Broglie questioned this and introduced something called matter wave.  In 1926, Erwin Schrodinger published an equation describing how this matter wave should evolve - the matter wave equivalent of Maxwell’s equations - and used it to derive the energy spectrum of hydrogen. That same year Max Born published his now-standard interpretation that the square of the amplitude of the matter wave gives the probability to find the particle at a given place. This interpretation was in contrast to De Broglie's own interpretation, in which the wave corresponds to the physical motion of a localized particle.

 

In 1927, Davisson and Germer decided to test the whole thing.

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Now the quantum paradox: Electrons, like bullets, strike the target one at a time. Yet, like waves, they create an interference pattern.  If each electron passes individually through one slit, with what does it interfere? Although each electron arrives at the target at a single place and time, it seems that each has passed through - or somehow felt the presence of both slits at once. Thus, the electron is understood in terms of a wave-particle duality.

 

One again, we see this even if we fire electrons one by one - sequentially!  We see that even individual, particulate electrons, moving to the screen independently, separately, one by one, build up the interference pattern characteristic of waves.  If an individual electron is also a \lave, what is it that is waving?  As noted above, in 1926 it was Schrodinger who made a first guess, but it was year later Born who nailed it.  The wave, Born proposed, is a probability wave.

 

The wave-particle duality is the central mystery of quantum mechanics - the one to which all others can ultimately be reduced.

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To understand what probability wave means, picture a snapshot of a water wave that shows regions of high intensity (near the peaks and troughs) and regions of low intensity (near the flatter transition regions between peaks and troughs). The higher the intensity, the greater the potential the water wave has for exerting force on nearby ships or on coastline structures. The probability waves envisioned by Born also have regions of high and low intensity, but the meaning he ascribed to these wave shapes was sort of unexpected: the size of a wave at any given point in space is proportional to the probability that the electron is located at that point In space. Places where the probability wave is large are locations where the electron is most likely to be found. Places where the probability wave is small are locations where the electron is unlikely to be found. And places where the probability wave is zero are locations where the electron will not be found.

 

We have reached a conclusion which is far from what our common sense tells us.  But it doesn't stop there.  This is just a tip of the iceberg.  Things get even more more strange as we dive deep adding up to quantum weirdness.

OK, so there is this wave which described electron position and we call it probability wave.   As matter can't be everywhere at the same time so can't be electrons making up that matter.  Probability wave thus claims there is highest probability for electron to be where we finally observe it.  At first ball, this doesn't sound like science though in theory it does explain what has been observed above.

 

No one has ever directly seen a probability wave, and conventional quantum mechanical reasoning says that no one ever will. Instead, scientics use mathematical equations (developed by Schrodinger, Niels Bohr, Werner Heisenberg, Paul Dirac, and others) to figure out what probability wave should look like in a given situation. They then test such theoretical calculations by comparing them with experimental results in the following way. After calculating the purported probability wave for the electron in a given experimental setup, they carry out identical versions of the experiment over and over again from scratch, each time recording the measured position of the electron. Sometimes we find the electron here, sometimes there, and every so often we find it way over there. If quantum mechanics is right, the number of times we find the electron at a given point should be proportional to the size (actually, the square of the size), at that point, of the probability wave that we calculated. Nine decades of experiments have shown that the predictions of quantum mechanics are confirmed to spectacular precision.

 

Every probability wave extends throughout all of space, throughout the entire Universe. In many circumstances, a particle's probability wave quickly drops very close to zero outside some small region, indicating the overwheiming likelihood that the particle is in that region. In such cases, areas where it is unlikely for particle to be are seen to have probability wave quite flat and near the vaiue zero.  Nevertheless, so long as the probability wave somewhere in the some distant galaxy has a nonzero value, no matter how small, there is a tiny but genuine-nonzero-chance that the electron could be found there.  Looking at picture below and thinking of yourself, electrons making you up are inside you - no discussion there.  But they all have probability wave and place where they are inside you takes the place of most probable position in wave while your electron being on Mars or Andromeda galaxy is very small and somewhere within part where wave probability is very low.

wave_function.gif

Regardless of improvements in data collection or in computer power, the best we can ever do, according to quantum mechanics, is predict the probability of this or that outcome. The best we can ever do is predict the probability that an electron, or a proton, or a neutron, or any other of nature's constituents, will be found here or there.

 

OK, if this is how it works then following logical question arises; what make position on wave to be most probable one?  We saw that electron passing through double slit is sort of interfering with itself (it is the probability wave which travels through slits which can be seen as same electron being at two different places at the same time).  What makes electron materialize where really is at the end - when we measure it (or in other words, when we observe it).  What happens if we measure both slits - can we see same electron passing through both slits at the same time?  How all these electrons on same probability wave know when the one at most probable position is materialized so they can vanish (do they vanish at all)?  These are interesting questions and quite sound ones too - and of course scientists have made tests leading to even bigger surprises.

 

We do not directly encounter the probabilistic aspects of quantum mechanics in day-to-day life.  To get sense of it, think of an electron you just exhaled in room where you are reading this.  What are the chances of that electron to appear on Mars next moment.  They are not zero, but very very small.  This is because on scale set by atoms Mars is so far away which gives already small probability.  Next, there are a lot of electrons, as well as protons and neutrons, making up the air in your room. The chance that all of these particles will do what is extremely unlikely even for one is just too small.  Thus probability of discussed outcome is low - near zero (but never zero).  Einstein didn't find this whole story amusing and simply didn't agree that reality might have such bizarre elements.  Einstein argued what could be more natural than to expect a particle to be located at, or, at the very least, near where it's found a moment later? 

cop.gifThe Copenhagen interpretation was the first general attempt to understand the world of atoms as this is represented by quantum mechanics. The founding father was mainly the Danish physicist Niels Bohr, but also Werner Heisenberg, Max Born and other physicists made important contributions to the overall understanding of the atomic world that is associated with the name of the capital of Denmark (in fact Bohr and Heisenberg never totally agreed on how to understand the mathematical formalism of quantum mechanics).  It was this interpretation which was opposing to Einstein.  According to Bohr and the Copenhagen interpretation of quantum mechanics, before one measures the electron's position there is no sense in even asking where it is. It does not have a definite position. The probability wave encodes the likelihood that the electron, when examined suitably, will be found here or there, and that truly is all that can be said about its position. Period. The electron has a definite position in the usual intuitive sense only at the moment we "look" at it - at the moment when we measure its position - identifying its location with certainty. But before (and after) we do that, all it has are potential positions described by a probability wave that, like any wave, is subject to interference effects. It's not that the electron has a position and that we don't know the position before we do our measurement.

 

 

Rather, contrary to what you'd expect, the electron simply does not have a definite position before the measurement is taken.  This is a radically strange reality. In this view, when we measure the electron's position we are not measuring an objective, preexisting feature of reality. Rather, the act of measurement is deeply enmeshed in creating the very reality it is measuring.

 

This raises the question of observer's role.  The quantum world can be not be perceived directly, but rather through the use of instruments. And, so, there is a problem with the fact that the act of measuring disturbs the energy and position of subatomic particles. This is called the measurement problem.

 

The best known is the "paradox" of the Schrodinger's cat: a cat is apparently evolving into a linear superposition of basis vectors that can be characterized as an "alive cat" and states that can be described as a "dead cat". Each of these possibilities is associated with a specific nonzero probability amplitude; the cat seems to be in a "mixed" state. However, a single, particular observation of the cat does not measure the probabilities: it always finds either a living cat, or a dead cat. After the measurement the cat is definitively alive or dead. The question is: How are the probabilities converted into an actual, sharply well-defined outcome?

measurement_problem.jpg

 

Einstein didn't really buy this.  He believed in a universe that exists completely independent of human observation. "Do you really believe that the moon is not there unless we are looking at it?" he asked.  Soon, Bohr and company answered by saying if no one is looking at the moon, if no one is "measuring its location by seeing it" - then there is no way for us to know whether it's there, so there is no point in asking the question.  Einstein was still fuming at this bizarre concept.  His biggest attack against quantum weirdness was attack against something called the uncertainty principle (a direct consequence of quantum mechanics) introduced by Werner Heisenberg in 1927.

 

It says, roughly speaking, that the physical features of the microscopic realm (particle positions, velocities, energies, angular momenta, etc) can be divided into two groups. And as Heisenberg discovered, knowledge of the first feature from first group fundamentally compromises your ability to have knowledge about the first feature from second group; knowledge of the second feature from first group fundamentally compromises your ability to have knowledge of the second feature from second group and so on. As an example, the more precisely you know where a particle is, the less precisely you can possibly know its speed. Similarly, the more precisely you know how fast a particle is moving, the less you can possibly know about where it is. You can determine with precision certain physical features of the microscopic realm, but in so doing you eliminate the possibility of precisely determining certain other, complementary features.

position_energy_time.jpg

 

Einstein liked simple things.  Together with two colleagues in Princeton, Nathan Rosen and Boris Podolsky, he found what appeared to be a serious inconsistency in one of the cornerstones of quantum theory - the uncertainty principle.  Remember, the very act of observing a particle also disturbs it, Heisenberg argued. If a physicist measures a particle's position, for example, he will also lose information about its velocity in the process and vice versa. Einstein, Podolsky, and Rosen disagreed, and they suggested a simple thought experiment to explain why:  Imagine that a particle decays into two smaller particles of equal mass and that these two daughter particles fly apart in opposite directions. To conserve momentum, both particles must have identical speeds. If you measure the velocity or position of one particle, you will know the velocity or position of the other - and you will know it without disturbing the second particle in any way. The second particle, in other words, can be precisely measured at all times.  Bohr argued that Einstein’s thought experiment was meaningless: If the second particle was never directly measured, it was pointless to talk about its properties before or after the first particle was measured. It wasn't until 1982, when the French physicist Alain Aspect constructed a working experiment based on Einstein’s ideas, that Bohr's argument was vindicated (in theory, it was John Bell who came up with idea first, but technology available didn't allowed to test it). In 1935 Einstein was convinced that he had refuted quantum mechanics. He was wrong.  Why?  You could have chosen to measure the right-moving particle's velocity.  Had you done so, you would have disturbed its position; on the other hand, had you chosen to measure its position you would have disturbed its velocity. If you don't have both of these attributes of the right-moving particle in hand, you don't have them for the left-moving particle either.  Thus, there is no conflict with the uncertainty principle at all.

 

What all these tests throughout the years have shown is one really strange feature.  Even though quantum mechanics shows that particles randomly acquire this or that property when measured, we learn that the randomness can be linked across space.  They are like a pair of magical dice, one thrown in Atlantic City and the other in Las Vegas, each of which randomly comes up one number or another, yet the two of which somehow manage always to agree. Entangled particles act similarly, except they require no magic. Entangled particles, even though spatially separate, do not operate autonomously.  They way they stay entangled remains to be mystery.  Today, we have successfully tested and observed this phenomena with electrons, molecules even as large as "buckyballs", photons, etc.

 

Let's give it a try with photons now.  Particles have property called spin.   It rotational motion akin to a soccer ball's spinning around as it heads toward the goal.  Electrons and photons can spin only clockwise or counterclockwise at one never-changing rate about any particular axis; a particle's spin axis can change directions, but its rate of spin cannot slow down or speed up. Quantum uncertainty applied to spin show that just as you can't simultaneously determine the position and the velocity of a particle, so also you can't simultaneously determine the spin of a particle about more than one axis.  The experiments show that from the viewpoint of an experimenter In the laboratory, at the precise moment one photon's spin is measured, the other photon immediately takes on the same spin property. If something were traveling from the one photon to the second one, alerting the one photon that the second photon's spin had been determined through a measurement, it would have to travel between the photons instantaneously, conflicting with the speed limit set by special relativity.   Two photons, even spatially separate, are seen (and still are) part of one physical system.  And so, it's really not that a measurement on one photon forces another distant photon to take on identical properties. Rather, the two photons are so intimately bound up that it is justified to consider them - even though they are spatially separate - as parts of one physical entity. Then we can say that one measurement on this single entity affects both photons at once.  When special relativity says that nothing can travel faster than the speed of light, the "nothing" refers to familiar matter or energy.  But here it doesn't appear that any matter or energy is traveling between the two photons, and so there isn't anything whose speed we are led to measure.

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At the end of the day, two widely separated particles, each of which is governed by the randomness of quantum mechanics, somehow stay sufficiently "in touch" so that whatever one does, the other instantly does too. And that seems to suggest that some kind of faster-than-Iight something is operating between them.  According to standard quantum mechanics, when we perform a measurement and find a particle to be here, we cause its probability wave to change: the previous range of potential outcomes is reduced to the one actual result that our measurement finds.  Backup to probability wave - this means all potential positions of electron for example materialize to one that we measured in that moment.

 

Physicists say the measurement causes the probability wave to collapse and they say the larger the initial probability wave at some location, the larger the likelihood that the wave will collapse to that point - that is, the larger the likelihood that the particle will be found at that point. In the standard approach, the collapse happens instantaneously across the whole universe.  Remember, probability wave goes across whole universe.  This means once you find the particle here, the probability of being found anywhere else immediately drops to zero, and this is reflected in an immediate collapse of the probability wave. This indicates that all potential particles are connected via probability wave which once collapsed kills all other potential "same" particles riding same wave.  At the same moment.  Across the whole universe.  When I learned first about this feature it reminded me of oldish computer games where you would have big surface on which you would play, but only as you would move screen to different regions you would see objects materialize.  More modern view would be for example Google maps; depending what region you choose you get to see objects being created for selected area while rest disappears.  The mathematics of quantum mechanics makes this qualitative discussion precise and real life experiments confirms it precisely. Nevertheless, a little bit less than a century, no one understands how or even whether the collapse of a probability wave really happens.

 

If quantum theory is right and the world unfolds probabilistically, why is Newton’s nonprobabilistic framework so good at predicting the motion of things from baseballs to planets to stars?  This is because while Newton's laws predict precisely the trajectory of a baseball, quantum theory offers only the most minimal refinement, saying there's a nearly 100 percent probability that the ball will land where Newton says it should, and a nearly 0 percent probability that it won't.  Also, probability wave for a macroscopic object is generally narrowly peaked. The probability wave for a microscopic object, say, a single particle, is typically widely spread.  According to quantum theory, the smaller an object, the more spread-out its probability wave typically is.  And that’s why it's the microrealm where the probabilistic nature of reality comes to the fore.

 

Can we see the probability waves on which quantum mechanics relies?  No. As seen before, standard approach to quantum mechanics, developed by Bohr and his group, and called the Copenhagen interpretation in their honor, envisions that whenever you try to see a probability wave, the very act of observation thwarts your attempt.  When you look at an electron’s probability wave, where "look" means "measure its position", the electron responds by snapping to attention and coalescing at one definite location. Correspondingly, the probability wave surges to 100 percent at that spot, while collapsing to 0 percent everywhere else.

 

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Schrödinger's equation, the mathematical engine of quantum mechanics, dictates how the shape of a probability wave evolves in time. BUT, the instantaneous collapse of a wave at all but one point does not emerge from Schrödinger's math. So was Copenhagen approach right?  Collapse of probability wave was also a bit unlear.  Will a sidelong glance from a mouse suffice as Einstein once asked? How about a computer's probe, or even a nudge from a bacterium or virus? Do these "measurements" cause probability waves to collapse?

 

We and computers and bacteria and viruses and everything else material are made of molecules and atoms, which are themselves composed of particles like electrons and quarks. Schrödinger's equation works for electrons and quarks, and all evidence points to its working for things made of these constituents (regardless of the number of particles involved).  This means that Schrödinger's equation should continue to apply during a measurement which in return is just one collection of particles (the person, the equipment, the computer …..) coming into contact with another (the particle or particles being measured). Schrödinger's equation doesn’t allow waves to collapse.   Here is why. 

linearity.pngFirst row (a) represents probability wave function for electron at time t to be at some locattion.  Second row (b) shows this wave at t+1 time.  You can decompose wave form from first column for both (a) and (b) to two simpler pieces.  We can divide it at any number of pieces if we want.  What we get in return is less complex picture where sum of parts gives us back initial wave we started to observe.  In mathematics this feature is called linearity.  If we check first row for example, we see two spikes representing 2 high chances electron would be at given position.  What Copenhagen approach dictates is that in moment of measurement all but one spikes will collapse.  On the other hand, in no place Schrödinger's equation show any cause or result leading to collapse.  If this reasoning is right and probability waves do not collapse, how do we pass from the range of possible outcomes that exist before a measurement to the single outcome the measurement reveals? What happens to a probability wave during a measurement that allows a familiar, definite, unique reality to materialize?

 

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In 1954, Hugh Everett III came to a realize something different.  He found that a proper understanding of the theory might require a vast network of parallel universes. Everett's approach is called today Many Worlds interpretation. History says his insight was not accepted by hist peers.  Then in 1967 Bryce DeWitt picked his idea up and in 1970 placed it back to spotlight.  In essence, Everett propossed that each spike yields a reality in which electron materializes itself.  If you measured the position of an electron whose probability wave has any number of spikes, for example five, the result would be five parallel realities differing only by the location of an electron.  And since you are measuring position, that means there must be also two of you where of each will experience an electron being materialized at different location.  In this approach, everything that is possible, everything is materialized in its own separate world.

One vital aspect of the Many Worlds theory is that when the universe splits, the person is unaware of himself in the other version of the universe. This means that you who used condom during one night stand and ended up living happily ever after is completely unaware of the version of yourself who didn't use condom and now faces Jerry Springer show, and vice versa.

 

Above is called Many Worlds approach to quantum mechanics.  As we can say Many Worlds is also Many Universe then we get to the point where many Worlds approach gives us Quantum Multiverse.  And as it may come as surprise, Many Worlds approach is, in some ways, the most conservative framework for defining quantum physics.  As Brian Greene puts it, it all comes down to 2 stories; mathematical one and physical one.

 

Every mathematical symbol in Newton's equations has a direct and transparent physical world translation.  For example, x is ball’s position, v is ball’s velocity. By the time we get to quantum mechanics, translation becomes far more subtle. The mathematics of Many Worlds, unlike that of Copenhagen, is pure, simple, and constant. Schrödinger's equation determines how probability waves evolve over time, and it is never set aside - it is always in effect (it guides the shape of probability waves, causing them to shift, morph and undulate over time). Schrödinger's equation takes the particles' initial probability wave shape as input and then provides the wave's shape at any future time as output. And that, according to this approach, is how the universe evolves. It is not mathematical part which brings multiverse to life - it is physical story.  If you apply linearity as discussed above and you evolve each wave peak you end up with equally valid future points for the same observed system (eg. particle) which can only be truth if it involves two realities.  If the electron's original probability wave had four spikes, or five, or a hundred, or any number, the wave evolution would result in four, or five, or a hundred, or any number of universes.

 

When we consider a probability wave for a single electron that has two (or more) spikes, we usually don't speak of two (or more) worlds.  Usually we speak of one (ours) world with an electron whose position is ambiguous. In Many Worlds real when we measure or observe that electron, we speak in terms of multiple worlds. Isn't this confusing?  This is the point when we go back to our double slit experiment.  We saw before an electron's probability wave encounters the barrier, and two wave fragments make it through the slits and travel onward to the detector screen.  Are these two also two different realities?

 

Placing detectors at the slits to determine which one a particle is passing through destroys the interference pattern on the screen behind. This is a manifestation of Werner Heisenberg's uncertainty principle, which states that it is not possible to precisely measure both the position (which of the two slits has been traversed) and the momentum (represented by the interference pattern) of a photon.  Physicists say that the probability waves have decohered. Once decoherence sets in, the waves for each outcome evolve independently and each can thus be called a world or a universe of its own. For the case at hand, in one such universe the electron goes through the left slit, and detectors displays left; in another universe the electron goes through the right slit, and detectors records right.  And once two or more waves can't affect one another, they become mutually invisible; each "thinks" the others have disappeared.

 

This brings following question: how can we speak of some outcomes being likely and others being unlikely if they all take place?  Consider situation in which the probability wave heights are unequal. If the wave is a hundred times larger at X than at Y, then quantum mechanics predicts that you are a hundred times more likely to find the electron at X. But in the Many Worlds approach, your measurement still generates one you who sees X and another you who sees Y; the odds based on counting the number of yous is thus still 50:50 - the wrong result. Here is why; the number of yous who see one result or another is determined by the number of spikes in the probability wave. But the quantum mechanical probabilities are determined by something else - not by the number of spikes but by their relative heights. And it’s these predictions, the quantum mechanical predictions, which have been convincingly confirmed by experiments.  Nevertheless, question whether place X is 100 times more genuine than place Y, as in above example, still persists and stays unanswered even today. The lack of consensus on the crucial question of how to treat probability in the Many Worlds approach continues.  And this can easily be seen outside quantum world; when you roll a die, we all agree that you have a 1 in 6 chance of getting a 3, and so we’d predict that over the course of 1200 rolls the number 3 will turn up about 200 times.  But since it’s possible, in fact likely, that the number of 3s will deviate from 200, what does the prediction mean? We want to say that it’s highly probable that ⅙/6 th of the outcomes will be 3s, but if we do that, then we have defined the probability of getting a 3 by invoking the concept of probability. We have gone circular.

 

For all these controversies, quantum mechanics itself remains as successful as any theory in the history of ideas.  Many Worlds interpretation is clean mathematical model emerging from quantum mechanics.  Still, it may be disturbing to some people as well as it takes out of our hands any power over the quantum universe. Instead, we are merely passengers of the "splits" that take place with each possible outcome. In essence, under the Many-Worlds theory, our idea of cause and effect goes out the window.  There are many quantum features that already have been proved in reality (eg. superposition to name one) and since math fits the glove so nicely, it is hard not to wonder how this theory will end up in future (for some 100 to 200 years from now).

 

The ability to predict behavior is a big part of physics' power, but the heart of physics would be lost if it didn't give us a deep understanding of the hidden reality underlying what we observe. And should the Many Worlds approach be right, it might change our philosophy of life for good.   Many world interpretation of quantum mechanics helps you cope with your realities already now - check the following comic.

image-788.jpg

Credits: Brian Greene, James Schombert, Wikipedia, Nature, Forskning och Framsteg, Sunny Kalara

 

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