Opening The Door To Quantum Mechanics

One of the most common misconceptions about quantum mechanics is that an observation is simply one particle interacting with another particle. This false impression misses the true essence of what makes quantum mechanics philosophically intriguing.
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(Not what an observation is. And not what particles are.)
The truth is that there are no individual particles. But let’s talk as if there were for the sake of simplicity. In the same way that we talk about people even though no person actually exists.
Suppose we have a quantum randomizer which causes our particle to go in one of two directions.
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Now let’s add a second particle to our system. The first particle will interact with the second particle.
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The moment these two particles interact we say that they are entangled with one another. This is because if the first particle had gone in the other direction then the trajectory of the second particle would be completely different.
By just observing the second particle alone this will be enough to know which of the two directions the first particle went in. The second particle therefore acts as a detector for the first particle.
But what if we choose not to observe either particle? According to quantum mechanics each particle will simultaneously be in a combination of both possibilities which we call superposition.
Now suppose we observe one of the two particles. The superposition seems to disappear, and we always see only one of the possibilities.
The two particles interacting with each other is not what counts as the observation.
After the two particles interact, both possibilities still exist, and it is only after the observation that only one of the two options becomes certain. After the two particles interact, we only need to observe one of the two particles to know about the state of both of the particles. We refer to this by saying that after the two particles interact, they are entangled with one another.
So the reason it becomes certain is either because a physicist’s consciousness has a magical power or because there are also two physicists. Each one doesn’t know that he is also the other.
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This doesn’t just happen with paths. Something similar happens to the spins of two particles being entangled with one another. The spin of a particle in a particular direction can be observed to have only one of two possible values. These values are spin-up and spin-down.
CPdiagram
Suppose we also have a second particle. There are now four different sets of possible observations. Just as our previous example could simultaneously be in a superposition of two different states when we were not observing it, this system can simultaneously be in a superposition of four different states when we are not observing it.
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Suppose we briefly observe only the particle on the right.
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Suppose we see that the particle on the right is spin-up. This means that two of the four possibilities disappear. The quantum system is now simultaneously in a superposition of only two possibilities.
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This quantum system does not contain any entanglement because measuring the spin of one of these two particles will not tell us anything about the spin of the other particle.
Let us use one of these particles as a detector to determine the spin of the other particle:
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As we bring the particles together, if the two particles are spinning in the same direction then our experimental setup will cause the particle on the right to change its spin to the opposite direction.
But if the two particles start out spinning in opposite directions then nothing will change when we start out. The particle on the right is known to be pointed up whereas the spin of the particle on the left is unknown. The system consists of both of these possibilities existing simultaneously.
If we run our experiment without observing either particle. The system will continue to be in a superposition of two possibilities existing simultaneously. But regardless of which of the two states the system started in, after these particles have interacted with each other, they are guaranteed to be spinning in opposite directions. We therefore now only need to observe one of the two particles to know the spins of both particles. As a result, after the two particles have interacted, we say that they are entangled with each other.
Suppose we allow these two particles to interact and become entangled but we do not observe either particle.  The system consists of both of these possibilities existing simultaneously. It’s only when we observe at least one of these particles that the outcome of the entire system becomes certain according to the mathematics of quantum mechanics. This remains true regardless of how many particles we have.
A detector simply consists of a large number of particles. This means that if we have two entangled particles, measuring the spin of one of the particles with a detector will not
necessarily tell us the spins of the two particles. If we are not observing the detector or the particles, then the two particles will simply become entangled with all the particles inside the detector in the same way that the two particles are entangled with each other. According to the mathematics of quantum mechanics, both sets of possible outcomes will exist simultaneously.
Suppose we observe the detector – which means that we observe at least one of the many particles that the detector is made of. Once we observe the detector, all the particles inside the detector and the two spinning particles that we originally wanted to measure will all simultaneously “collapse” into one of the two possibilities.
According to the mathematics of quantum mechanics, it does not matter how many particles the system is made of. We can connect the output signals of our detectors to large complex objects, causing these large objects to behave differently depending on the
measurements and the detector. According to the mathematics of quantum mechanics, if we do not observe the system, both possibilities will exist simultaneously – at least seemingly until we observe one of the many entangled particles that make up the system.
It is arbitrary to think that the universe only “collapses” at the whim of particular people or their instruments. To paraphrase Stephen Hawking, “It is trivially true that what the equations are describing is Many Worlds.” It is not just the separate magisterium of small things such as electrons, photons, buckyballs, and viruses that exist in Many Worlds. Humans and all other approximate objects also exist simultaneously but obviously can never experience it by the Nagel bat essence of consciousness. That is, in order to experience something, you have to be it – like an adjective on the physical configuration. So you are also in each “alternate” reality but it is impossible to feel this intuitively because consciousness is not some soul that exists disembodied from the machinery. Your million clones are just as convinced that they were never you. I am also intuitively convinced that I was never you, but this is wrong physically.
Of course, we can define “I” as something different from that adjective-like Being, something different from the raw qualia, so to speak.
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We must be very clear that we are drawing lines around somewhat similar configurations, and not fashioning separate souls/consciousnesses.
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Okay, back to the QM. Here, once the particles become entangled, the two different possible quantum states are represented by the colors yellow and green.
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The yellow particles pass right through the green particles without any interaction. After the entanglement occurs, the system is represented by a wavefunction in a superposition of two different quantum states, represented here by yellow and green.
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One wave is not really above the other but this visualization illustrates how the yellow quantum state is unable to interact with green quantum state. Since the yellow wave can’t interact with the green wave, no interference pattern is created with the detectors present.
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On the other hand, with the detectors removed, the entanglement with the detectors never happens and the system does not split into the yellow and green as before. The resulting waves are therefore able to interact and interfere with each other. Two waves interacting with each other creates a striped pattern. This is why a striped probability pattern is created when particles pass through two holes without any detectors present, and it’s why a striped probability pattern is not created when particles pass through two holes with detectors present.
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Having just one detector present has the same effect as having two detectors. This is because only interaction with a single particle is required in order for entanglement to occur. But even after a particle interacts with a detector consisting of many different particles, the system is still in both states simultaneously until we observe one of the detectors.
There’s considerable debate as to what is really happening and there are many different philosophical interpretations of the mathematics. In order to fully appreciate the essence of this philosophical debate it’s helpful to have some understanding of the mathematics of why entanglement prevents the wavefunctions from interacting with each other.
The probability of a particle being observed in a particular location is given by the square of the amplitude of the wavefunction at that location.
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In this situation, the wavefunction at each location is the sum of the wavefunctions from each of the two holes.
Although there are many different places that the particle can be observed, to simplify the analysis, let’s consider a scenario where the particle can be in only one of two places. This scenario is similar to the scenario measuring the spin of a single particle in that there are only two possible outcomes that can be observed.
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The state of spin up can be represented by a 1 followed by a 0.
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The state of spin-down can be represented by a 0 followed by a 1.
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Similarly, we can use the same mathematical representation for measuring the location of our particle. We will signify observing the particle in the top location with a 1 followed by a 0 and we will signify observing the particle in the bottom location with a 0 followed by a 1.
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Let’s now add a detector indicating which of the two holes the particle passed through. We are going to observe both the final location of the particle and the status of the detector.
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There are now a total of four different possible sets of observations. This is similar to how we had four different possible sets of observations when we had two spinning particles. Although our detector is a large object, let us suppose that this detector consists of just a single particle. In the case of the two spinning particles, each of the four possible observations can be represented with a series of numbers as shown.
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The same mathematical representation can be used in the case of observing the position of our particle and the status of our detector. Here we need four numbers because there are four possible outcomes when the status of the detector is included. But if we didn’t have the detector, we would only need two numbers because there are only two possible outcomes. This is the same way in which we need two numbers for a single spinning particle.

 

The principle of quantum superposition states that if a physical system may be in one of many configurations—arrangements of particles or fields—then the most general state is a combination of all of these possibilities, where the amount in each configuration is specified by a complex number.

For example, if there are two configurations labelled by 0 and 1, the most general state would be

c₀ |0> + c₁ |1>

where the coefficients are complex numbers describing how much goes into each configuration.

 

The c are coefficients. The probability of observing the spin of the particle in each of the two states is given by the squares of the magnitudes of these coefficients. If we have two spinning particles we can have four possible observations, each of which is represented with a sequence of four numbers.

If the system is in a superposition of all four states simultaneously, then this is represented by the same mathematical expression. As before, the c are constants. As before, the probability of observing the spins of the particles in each of the four states is given by the squares of the magnitudes of each of these constants.
This same mathematical representation can be used to describe observing the location of the particle and the state of the detector. Here, the c coefficients represent the values of each of these wavefunctions at the final location of the particle when the system is in a superposition of these four possibilities:
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But if we never had the detector then each quantum state would be represented by only two numbers instead of four since there are only two possible observations. As before, the c coefficients represent the values of the wavefunction from each of the two holes at the final locations of the particle without the detector. If the system is in a superposition of both quantum states simultaneously, it’s represented mathematically as follows:
c₀ |0> + c₁ |1>
Here, if one of the c coefficients is positive and another c coefficient is negative, they can cancel each other out. On the other hand, the c coefficients would never be able to cancel each other out with a detector present. With a detector present, even if one of the c coefficients is positive and the other c coefficient is negative, their magnitudes always strengthen each other when calculating the probability of observing the particle at a certain position. But without a detector, if one of the c coefficients is positive and the other c coefficient is negative and their magnitudes are equal, then they will cancel each other out completely and provide a probability of zero.
If the particle is not limited to being at just two possible positions, then there will be certain locations where the c coefficients representing the values of the two wavefunctions will cancel each other completely. This is what allows a striped probability pattern to form when there is no detector present, and it’s also why a striped probability pattern does not form if there is a detector present.
Note that nowhere in this mathematical analysis was there ever any mention of a conscious observer. This means that whether or not the striped pattern appears has nothing to do with whether or not a conscious observer is watching the presence or absence of a detector. Just a single particle is enough to determine whether or not there is a striped pattern. A conscious observer choosing whether or not to watch the experiment will not change this outcome but because the mathematics says nothing about the influence of a conscious observer, the mathematics also says nothing about when the system changes from being a superposition of multiple possible outcomes simultaneously to being in just one of the possibilities. When we observe the system we always see only one of the possible outcomes but if conscious observers don’t play any role then it’s not clear what exactly counts as an observation since particles interacting with each other do not qualify.
There’s considerable philosophical debate on the question of what counts as an observation, and on the question of when, how, and if the system collapses to just a single possible outcome. However, it seems that most of the confusion stems from being unable to think like an open individualist – being unable to adhere to a strictly reductionist, physicalist understanding.
Some philosophers want there to be a “hard problem of consciousness” in which there are definite boundaries for souls with particular continuities. But if we just accept the mathematical and experimental revelation, we see that this ontological separation is an illusion. Instead, what we try to capture when we say “consciousness” can only be a part of the one Being containing all its observations. It is in this sense that consciousness is an illusion. We do not really say that qualia is unreal, but rather that it cannot be mapped to anything more than a causal shape that lacks introspective access to its own causes. A self-modeling causal shape painting red cannot be a self-modeling causal shape painting blue. But ultimately, the paintings occur on the same canvas.
Of course, there is a way to formulate the hard problem of consciousness so that it points to something. That which it points to is the hard problem of existence. Why is there something as opposed to nothing? This question will never have an answer. With David Deutsch, I take the view that the quest for knowledge doesn’t have an end because that would contradict the nature of existence. The quest for knowledge can be viewed as exploration of the experiential territory. If you had a final answer, a final experience, then this would entail non-experience (non-experience cannot ask Why is there something as opposed to nothing?).
Fantasizing about a final Theory of Everything is thinly veiled Thanatos Drive – an attempt at self-destruction which eternally fails; not least because of quantum immortality.