**simultaneously**act like a particle and wave. It acts like a wave sometimes and a particle at other times, but not both at the same time. There isn’t a consensus among physicists on this particular description, but I’m going to give a current mainstream description of what’s going on.

# Category: Uncategorized

# What would it be like to live in the quantum realm?

A number of interpretations of quantum mechanics postulate a “quantum realm.” These include the Transactional Interpretation.* One of its developers, Dr. Ruth Kastner, calls it “Quantumland.”

Here’s a drawing of Quantumland that Dr. David Chalmers, the noted philosopher of physics, presented in a lecture :

*The quantum realm on the left underlies our everyday world on the right.** [Image source: David Chalmers and Kelvin McQueen, “Consciousness and the Collapse of the Wave Function” **http://consc.net/slides/collapse.pdf]*

In this drawing, the waviness on the left is a metaphor for the quantum realm. It is a metaphor because these waves are not in a known physical medium. We are accustomed to water waves traveling through the medium of water and sound waves traveling through the medium of air. For example, below is an animation of a wave traveling through the medium of some kind of mesh.

*Classical wave traveling through a mesh. This is not a quantum wave due to its traveling through a medium made of matter. **[Animation by: Christophe Dang Ngoc Chan (cdang) – Own work, CC BY-SA 3.0; *https://en.wikipedia.org/wiki/Se…* ]*

Somehow, in the quantum realm, there are waves with no medium or, possibly, a medium that we can’t detect. I, for one, cannot imagine a wave travelling through no medium at all. The quantum realm, for us, is mathematical equations to which we assign physical meaning by creating metaphors.

**Ever-Changing Waviness**

The quantum realm is ever-changing wavinesses evolving into new wavinesses. It underlies our everyday physical reality. Changes in the wavinesses of the quantum realm result in changes in the probabilities of what we will observe in our physical reality.

Should some part of the quantum waviness be detected, it immediately takes form as a real particle. For example, let’s say that a part of the wavy quantum realm represents a photon from the sun. Let’s say that the math representing the waviness describes the probabilities that we will see a red photon or a yellow photon, with high probabilities that we will see a yellow one. As it hits our eye, let’s say that we see a yellow one. The waviness in the quantum realm has had real life results in our everyday physical universe.

The moment that the probabilities result in a yellow photon in our eye is the “collapse of the wave function” (as labeled in the above drawing).

**Entanglement in the Quantum Realm**

*[Image source: NASA/JPL/Cal Tech]*

If we were in the quantum realm, not only would we experience ever-changing waviness all around us, we would also, in certain situations, experience a one-ness with waviness at great distances from us. This is quantum entanglement. In quantum entanglement, waviness in one area can correlate its behavior with waviness on the other side of the universe. It’s as if time and space, as we know them, do not exist in the quantum realm.

Just as in a mystical experience, two wavinesses across the universe from each other are one. This results in two particles in physical reality correlating their behavior across the universe instantaneously. For example, two spinning electrons on opposite sides of the universe can coordinate the directions of their spin instantaneously.

Quantum entanglement is a phenomenon well-supported by mathematical calculations and experimental evidence. Though, the experiments are not conducted on opposite sides of the universe—the “opposite sides of the universe” idea is extrapolated mathematically from laboratory results.

**Living in “The ****Matrix”**

I think of the quantum realm as underlying our physical reality similarly to the way that computer code underlies what we see on our computer monitor. The code is a sea of ever-changing numbers as electricity zips through it and equations are solved. But those numbers are meaningless to most of us. For our convenience, the changing numbers of the code light up pixels on the screen. We see the changing images and text on the screen, and we grasp the meaning of the underlying computer code.

*The coding of virtual reality as in “The Matrix.” **[Image source: By Jahobr – Own work, CC0, **File:Digital rain animation medium letters shine.gif**]*

Our everyday reality is something like “The Matrix,” with the quantum world being like the computer coding underlying it all. This is not to say that we’re living in a virtual reality produced by a computer. It could, for example, be a virtual reality created in consciousness. This idea is at least as old as Buddhism but has been gaining new currency, as in the work of Dr. Donald Hoffman.

*Footnote*

*The Transactional Interpretation was first developed by John Cramer in the 1980’s with further development by Ruth E. Kastner in recent decades. For a lay explanation, see Kastner, *Understanding Our Unseen Reality, Solving Quantum Riddles*, Imperial College Press, London, 2015. Also see Kastner’s mathematical presentations for physicists in books and journal articles.

# What is the difference between quantum mechanics and quantum physics?

Quantum mechanics is the current name of the field of quantum physics. In quantum mechanics, physicists study how atoms, the components of atoms, and other tiny particles behave. These are called “quantum particles” and include electrons, protons, photons, and so on. They follow the laws of quantum mechanics.

In the early 1900’s, physicists, through experiments, discovered that atoms and their components followed different laws from those of ordinary objects like tables and chairs. The mathematical laws governing the movements and forces among ordinary objects is known as “classical mechanics” or “Newtonian mechanics.” For example, Force = Mass times Acceleration is a mathematical law of classical mechanics.

** Drawing of a photon (in green) being emitted from carbon molecules.** [Image source: Nancy Ambrosiano, Los Alamos National Laboratory, July 2017 News Release, “Single-photon emitter has promise for quantum info-processing,” (Public domain)]

When physicists realized that quantum particles do not follow the laws of classical mechanics, they called the new field “quantum theory.” At first, physicists developed quantum laws which were heavily verbal, rather than highly mathematical.

In the 1920’s, physicists developed mathematical laws which describe quantum behavior. In particular, Erwin Schrodinger and Werner Heisenberg developed the key mathematical laws governing quantum particles (Schrodinger’s Wave Equation and Heisenberg Matrix Mechanics). At this point, physicists began calling the new field “quantum mechanics” on the model of the phrase “classical mechanics.”

The term “quantum mechanics” means the same thing as “quantum physics” though the term “mechanics” emphasizes doing calculations.

# What is wave function collapse? Is it a physical event?

In one view, a wave function is a piece of math, an equation. It’s not a physical thing. So, it can’t collapse in any physical sense. The collapse is metaphorical. This is one interpretation of quantum mechanics. It’s the interpretation taught in most university classes, the Copenhagen Interpretation. However, physicists have not settled on a particular interpretation. For more nuance, see the later section “Caveat—Other Interpretations of Quantum Mechanics.”

To continue on with the view that the wave function is a piece of math: a wave function is, first of all, a function—just like the functions in algebra—a very common type of equation. The reason that physicists call it a “wave function” is that it’s an equation that when graphed, looks like waves. The accompanying image shows a graph of a particular wave function at a particular moment in time. It graphs as waves with six three-dimensional peaks:

This wave function could describe an electron in a box, possibly imprisoned by magnetic fields. The graph tells us the likelihood of detecting the electron in any particular position in the box. It gives us a set of probabilities as to the likely position of the electron when detected. We’ll need to square the amplitude (wave height) that we’ve calculated for each position to find out the probability of detecting the electron in that position.

For this graph, the calculation of the wave function tells us that the electron has an equal probability of being detected in six different positions (A, B, C, D, E, or F) and a negligible probability of being detected elsewhere.

**Collapse of the Wave Function**

Upon detection of the electron, the probabilities calculated by the wave function instantaneously convert to a 100% probability for the position in which the electron is detected and 0% everywhere else. This is the “collapse of the wave function.” All the probabilities collapse down to one position.

The upcoming 2-minute video depicts this collapse in the Double Slit Experiment. First it shows in the “Particle” segment how an everyday object like a pebble would act (still image on left). Then it shows in the “Wave” segment how an ordinary wave like a water wave would act (still image on right)

Then, it shows in the third “Quantum Object” segment, **how an electron would act**. In this segment (still image on left), it shows the waviness of the electron prior to detection. Then, upon detection when the wavy electron hits the detection screen, it shows the collapse of the electron down to a localized particle. The detection screen might be a TV-type screen with phosphor pixels that glows when an electron hits.

Click here to watch the 2-minute video of the collapse of the wave function.

## So, a spread-out physical electron wave collapses down to a tiny physical particle? No, it doesn’t.

The electron collapses down to a tiny physical particle, all right. But, according to the in the Copenhagen Interpretation, there was never any physical electron wave. The waviness of the electron prior to detection was never physical in the sense that tables and chairs are physical. If there is a wavy electron, it’s no more physical than a mathematical expression.

But here’s an alternative interpretation, it’s a waviness is in an underlying sub-level of reality. That is, it’s wavy in Quantumland where the rules of quantum mechanics apply. Not in our level of physical reality. This is the Transactional Interpretation as developed by Dr. Ruth Kastner (*Understanding Our Unseen Reality*).

Why isn’t the waviness of the electron physical in the sense that tables and chairs are physical? Because the waviness described by the wave function is no more than probabilities that something will be detected. The wave function is **not **telling us where something is. It’s telling us what’s possible and how likely any particular possibility is. And there are other non-physical aspects of this waviness. Read the next section on this if you’re familiar with the concept of imaginary numbers.

## The Wave Function and Imaginary Numbers

(Skip this section if math isn’t your thing. It isn’t essential to the basic concept of this article.) Here’s something else to consider. You know the imaginary number **i** and how it doesn’t describe anything in the physical universe? You’re never going to measure a table leg that is** i** inches tall. That’s because **i** means the square root of negative **1**. What number squared equals **-1**? There is no such number. So, **-1** has no square root. But we go ahead and call it **i** and happily calculate with it. We’re just never going to find a table leg or anything else that measures **i** inches long.

Well, here’s the punchline. Many wave functions calculate wave amplitudes which are **i** big. The implication is that these wave functions are not describing anything in our physical reality. So, the waviness of the electron prior to detection can be described mathematically, but is not a physical thing in our physical universe. It’s either just math or it’s something in an underlying reality that I like to call “Quantumland.”

## Caveat — Other Interpretations of Quantum Mechanics

In the 1920’s and ’30’s, the early days of quantum mechanics, a number of the founding fathers thought of the wave function as an actual wave. Erwin Shrodinger was in this camp. So, when reading the early literature on quantum mechanics, one will sometimes run across statements that the wave function describes a “probability wave,” with the implication that it’s a physical thing. However, few physicists today subscribe to this view. The interpretation that I’ve followed in this article is the current version of the Copenhagen Interpretation, the one usually taught in universities.

About 15 other interpretations of quantum mechanics have developed in the century since the Copenhagen Interpretation was first developed. Some of these do not include the concept of wave function collapse. Physicists who favor the De Broglie-Bohm Interpretation would say that there’s always an electron wave and it’s always guiding an electron particle: the wave does not suddenly collapse down to a particle. Physicists who favor the Many Worlds Interpretation would also say that there’s no wave function collapse.

* The probability densities are the squares of the wave amplitudes, as calculated by the wave function. The wave function yields the distribution of probability densities for detecting the electron in any particular position.

# Are electrons waves or particles?

The accompanying video demonstrates how an electron can be both a particle and a wave. (The video has two unfortunate errors in it, which I’ll point out.) The video shows how different kinds of objects, including an electron, act when they speed towards a barrier perforated by two slits. Then, it shows the pattern the objects form on a detection screen after passing through the slits in the barrier. This is the famous Double Slit Experiment. Here’s what’s going on in this video, step by step:

**How Particles Act**

“Particle” shows ordinary particles, let’s say pebbles. Particles are separate individual little things that at any one moment are in a tiny, very localized position. So, individual pebbles shoot through one slit or the other. Then, the pebbles hit the detection screen.

Here’s where the video goes off the rails. It shows a pattern on the detection screen of random dots all over the screen. Your common sense would tell you that the pebbles should form two clumps on the detection screen, one behind each slit. Real experiments show that your common sense is correct. Figure (1) by Fermilab is a more accurate depiction of what the detection screen should look like.

## How Ordinary Waves Act

“Wave,” in the video, shows an ordinary wave, let’s say a water wave. The water wave is spread out, so it goes through both slits. On the far side of the barrier, two waves emerge, one from each slit. The two waves interfere with each other. They form the crisscross pattern of ripples that we see if we throw two stones into a pond. This crisscross

pattern of ripples hits the detection screen and forms a striped pattern.

Figure (2) clearly shows how a water wave creates the crisscross “interference pattern” and marks the detection screen with a striped pattern. This is just like in the video. This striping is the signature pattern of waves interacting. When physicists see this pattern, they think “waves.”

To summarize, here are the differences from particle behavior: the wave is spread-out; goes through both slits, not just one or the other; forms two interacting waves on the far side of the barrier; and forms a striped pattern on the detection screen.

## How Electrons Act

“Quantum object” shows a subatomic particle, for example, our electron. It doesn’t act at all like an ordinary particle such as a pebble. At first, it acts more like a wave. It’s spread out and goes through both slits. It emerges as two different waves on the far side of the barrier, and these interfere with each other. The two waves form the same crisscross pattern that ordinary waves form.

But upon hitting the detection screen, the wave “collapses.” The electron wave hits the screen in one tiny spot as if it were a particle. The experiment is run over and over. One at a time, electrons flow wave-like through the barrier and collapse at the detection screen, each time hitting one tiny spot, that is, suddenly turning into a particle. Over time, a pattern on the detection screen emerges. It’s the striped pattern—the signature pattern of two waves interacting! Somehow the particles which hit the screen “know” where to land on the detection screen such that over time, they collectively seem to show the influence of the two interacting waves.

## The Quantum Wave vs. Ordinary Wave

Even though the electron acts in certain ways like a wave, there are significant differences between the wave of a quantum particle and an ordinary wave like a water wave. The electron type-wave is called a “quantum wave.” An ordinary wave is called a “classical wave.” The mathematical equations which describe the properties of a quantum wave and a classical wave are very different. While quantum waves share some similarities of behavior with classical waves, for example, creating a striped pattern on the detection screen, quantum waves also act significantly differently. Quantum waves and classical waves differ in both their mathematical descriptions and in their behavior.

Here’s a brief listing of differences between a quantum wave and a classical wave (for more detail see the article in this encyclopedia on wave):

- As shown in the video, the quantum wave collapses when it hits the detection screen and lands on it as a particle. This is called the “collapse of the wave function.” An ordinary wave retains its wave nature when it hits the detection screen.
- The amplitude of a quantum wave is proportional to the probability that the quantum particle will be detected in a specific position. In contrast, the amplitude of a classical wave is proportional to the wave’s strength.
- The equation of a quantum wave can include imaginary numbers. These are numbers that include the square root of negative 1. As no number times itself is a negative number, imaginary numbers do not refer to anything that has physical reality. The equations for classical waves do not include imaginary numbers and describe physically real things.
- It is when an electron is in the quantum wave state, rather than in its particle state, that it displays quantum weirdness: superposition (being in more than one place at the same time), entanglement (behaving in an instantaneously correlated manner with an electron as far as across the universe), quantum tunneling (appearing on the other side of a barrier despite having insufficient energy to cross the barrier), and other weirdnesses. Classical waves, of course, do none of these things.

## Wave-Particle Duality

The ability of electrons and other quantum particles to act like both a wave and a particle is called “wave-particle duality.” I’ve found that the Transactional Interpretation of quantum mechanics is able to make some sense of wave-particle duality.* This interpretation proposes that when the electron is in its wave-like state, it is not in our physical reality. That is, it’s not in spacetime but is in an underlying level of reality that we can call “Quantumland.” This level of reality, while not observable by us, is lawful in that it follows the laws of quantum mechanics. It underlies and determines the probabilities of what occurs in our spacetime.

*The Transactional Interpretation is explained in lay terms without math in Ruth E. Kastner, *Understanding Our Unseen Reality, Solving Quantum Riddles*; Imperial College Press, 2015, London.

How does the electron enter our physical reality? It interacts with something physical that is made up of lots of particles—a “macroscopic object” like a detection screen. Upon interacting with the screen, it’s suddenly a particle. This is called the “collapse of the wave function.” Since, the electron always becomes a particle as soon as it interacts with a macroscopic object, we can never observe it in its wavy state. We’re like King Midas. He could never feel his daughter’s soft hand because she turns to gold the moment that he touches her. We can never observe the wavy state of an electron because the wave function collapses to a particle when we interact with it sufficiently to perceive it.

Figure (3) depicts Quantumland on the left, the collapse of the wave function, and the resultant objects in everyday spacetime on the right. This depiction is a gross simplification because the collapse from wave to particle does not occur at the scale of entire objects like homes and picnicking families. Instead electrons, quarks, and other quantum particles are continually moving from their wavy states, interacting with others, and collapsing to particles. When they collapse, the entire atom and molecule collapses with them. Then, quantum particles revert to their wavy state, collapse again, and on and on. So, at any one moment, many of the atoms and molecules of an object are in their wavy state and many are collapsed down to particles.

## Add an Observer

This brings us to the final part of the accompanying video, “Add an Observer.” This part of the video shows the electron wave approaching the barrier. But this time, there’s a detector at the barrier watching which slit the electron goes through. This could be a human with Superman vision or a Geiger counter or another device. The device interacts with the electron sufficiently to determine which slit, so the electron collapses down to a particle and goes through only one slit.

Once past the barrier, the electron, freed from interaction, reverts to its wavy state. Upon interaction with the detection screen, it again collapses down to a particle and lands as a tiny localized dot. Again, the video incorrectly shows that after repeated runs of the experiment, random dots cover the detection screen with no particular pattern. Experimental results show that the resulting pattern on the detection screen is, instead, two clumps as shown in Figure (1).

## Consciousness and Wave Function Collapse

The role of consciousness in the collapse of the wave function has had a controversial history. In the early days of development of quantum mechanics, many of the founding fathers of the field contemplated the possibility that consciousness played a role in collapsing the wave function. Over time, this view was rejected. Considerable work was done starting in the 1950’s on the theory of decoherence. This is the theory that interaction with macroscopic particles cause collapse of the wave function. While this is a well-accepted theory, experiments in recent years also point to the possibility that consciousness can also cause collapse of the wave function. For further discussion, see the article in this encyclopedia collapse of the wave function.

## In Summary

In summary, the electron is definitely a particle when it hits the detection screen. And at other times, it’s a wave. But it’s not a physical wave like a water wave or sound wave. It’s a wave that follows the laws of quantum mechanics.

# What is the difference between a photon and a quantum?

A photon is a tiny particle of light. It is the tiniest particle of light possible in Nature. A photon can also be described as a **type** of quantum, that is, a tiny particle. Some other types of *quanta* (plural) are electrons, neutrinos, and the Higgs boson.

A quantum is the tiniest particle possible of a particular substance. For example, in the case of an electron, it’s the tiniest particle possible of negatively-charged matter. Just as a photon is the tiniest particle possible of light.

**A quantum is as small as it gets. **

This description is saying something interesting—Nature does not allow us to cut matter and energy into smaller pieces indefinitely. Let’s say that we could cut a rock down into tiny grains of sand, but there were some natural law that a grain of sand is as small as we can get. If this were true, a grain of sand would be a quantum of rock. But, of course, we can cut a grain of sand into ever smaller grains. Only when we get down to the level of electrons and other subatomic particles, does Nature call a halt to the cutting. That’s when we hit the quantum level.

In the case of light, a photon, a quantum of light, is as small as Nature allows. A single photon of light is too dim for a human being to see. It takes a few photons for us to detect light. Frogs, however, are able to see a single photon.

In summary, a photon is the tiniest possible particle of light, a quantum of light. A quantum, on the other hand, is the tiniest possible particle of **any** substance at the subatomic level and includes, for example, electrons and neutrinos. If this answers your question, no need to read any further. If you want to know more about photons and quanta, read on.

**But isn’t light a wave?**

To see how light can be divided into photons, it’s necessary to understand a bit more about light. Light travels as a wave. Specifically, it travels as an electromagnetic wave. An electromagnetic wave is an electrical wave and a magnetic wave traveling together and interacting.

As the electrical wave expands and contracts (shown in red in this image), it gives rise to a magnetic wave (blue). Then, the magnetic wave expands and contracts, giving rise an electrical wave, and on and on. This video shows the dance of electrical and magnetic waves giving rise to each other: https://www.youtube.com/watch?v=1SQV9kBN_b4

Physicists call all electromagnetic waves “light.” This includes visible light, the kind that we see with our eyes, but also X-rays, ultraviolet rays, infrared, microwaves, radio waves (which carry TV and radio signals), and others. The difference between the various types of electromagnetic waves is their wavelength (shown in image below).

So, the term “photon” can mean a particle of visible light but also a particle associated with X-rays, microwaves, or any other part of the electromagnetic spectrum.

**So, light is a wave and also a particle? **

When light, that is, an electromagnetic wave, strikes an object, it immediately collapses into tiny bits or particles of energy. (Please don’t take this literally; it’s meant only metaphorically.*) Each of these particles is a photon. It’s as if an ocean wave hits a rock and shatters into a gazillion tiny droplets. Each “droplet” of the light wave is a photon, and each carries a bit of energy. If a wave of visible light were to strike a piece of photographic film, we would be able to see the traces of all the photons which struck it. Each photon creates a tiny dot, a bit of the photo, usually a small fraction of a pixel. Together, the photons form the image.

Waves, including light waves, are spread out in space. When it strikes the film, the light is no longer acting as a wave; it’s acting as a particle. Particles differ from waves in that they are localized, that is, they have a small and definite position.

**Photons are the particle form of light. **

In summary, light acts as both a wave and a particle. When traveling, it’s an electromagnetic wave. But upon striking objects, it acts as a particle. While “photon” is the name given to light only when it acts as a particle, people may neglect the distinction. They often use the term “photon” for light at all times, whether it’s in wave form or particle form.

As a note, the term “photon” comes from the ancient Greek *photos*, which means “light” and the ending *-on*, which means “a particle.” “Photon” means literally “light particle.”

**Why call it a “quantum”?**

The general term for all types of subatomic particles which are of the smallest possible size allowed by Nature is “quanta.” “Quanta” is the plural; “quantum” is the singular. The term “quantum” comes from the Latin *quantus* which means “how much.” Electrons are the quanta associated with electron waves; neutrinos are the quanta associated with neutrino waves; etc. Just like photons, electrons cannot be further divided into something smaller, nor can neutrinos.

In its original meaning, a “quantum” is the tiniest particle of a substance that Nature allows. However, often people call any tiny particle that follows the laws of quantum physics a “quantum” even when it’s not the smallest allowed by Nature.

*Footnotes*

*Light waves don’t physically shatter when they hit objects. They interact with the objects and due to the laws of quantum physics, the waves transform into tiny energy-bearing particles, that is, photons.

The physical nature of waves at the subatomic level is somewhat mysterious. It’s still under debate due, in part, to the odd ways in which these waves behave in experiments. One view, for example, is that they are no more than mathematical expressions in the form of a wave equation which somehow create physical effects (!?). But this is diving deeper into quantum physics than is useful here.

# Why does the Born Rule predict quantum probabilities?

There’s both a mathematical explanation and an explanation based on the nature of reality.

First, the mathematical explanation: Let’s take the example of the Double Slit Experiment. A laser shoots photons one-at-a-time through the two slits of a

screen towards a photographic plate. The wave function is the equation that describes the behavior of the

photon. The amplitudes calculated for the wave by the wave function are proportional to the probability of the photon being detected in any particular position on the photographic plate.

The mathematical expressions for the wave amplitudes often include complex numbers (numbers that include the square root of negative 1). We cannot visualize such a number because what number multiplied times itself equals negative 1? There is no such number. We label this non-number as **i **and just don’t try to imagine what amount **i **really represents. Even though **i** does not describe anything that we’re familiar with in the physical universe, both mathematicians and physicists have found it useful to work equations which include** i**, that is, complex numbers.

While neither water waves nor sound waves nor any other wave that we might observe in the physical universe have amplitudes that can be measured by complex numbers, the wave function often calculates complex number amplitudes for **quantum** waves. This is a clue that quantum waves do not operate in the spacetime of our physical universe. In the Copenhagen Interpretation, the original and conventional interpretation of quantum mechanics, it’s not clear where they operate. The status of their reality is an enigma wrapped in a mystery. A bit later in this answer, another interpretation will provide more information on the issue.

But returning to the wave function in the Copenhagen Interpretation. Max Born (1882-1970) was the quantum physicist who first realized that the amplitude of the quantum wave predicts the probability of detecting a particle in a particular position. But this creates a problem. What if the amplitude includes a complex number?

A probability cannot be expressed using complex numbers. Probabilities are expressed as positive numbers ranging from 0% to 100%. That is, we can say that there’s a 50% chance when tossing a coin of getting heads. Or a 0% chance that every moment of the day will be fun. And a 100% chance that a human being will eventually die. But to say that the chances of an event are the square root of negative 1 makes no sense.

Born solved the problem by multiplying the amplitude of the wave by its complex conjugate. This squares the square root of negative 1, yielding simply negative 1. The result is probabilities calculated by the wave function are quite nice. They range from 0% to 100%.

This calculation is the Born Rule. Experimental results show that the Born Rule is accurate in calculating quantum behavior. So, not only does the rule cancel out the troublesome complex numbers, it accords with empirical results. The Born Rule is an integral part of the Copenhagen Interpretation.

However, the Born Rule does not explain what is happening in the physical universe that requires that we multiply the wave amplitude by its complex conjugate. Nor does any other part of the Copenhagen Interpretation provide such an explanation. The Transactional Interpretation does. While it would be too lengthy to fully explain this interpretation here, an example gives a taste:

Let’s say take a look again at the Double Slit Experiment with a laser emitting a single photon towards a photographic plate. Until it arrives at the photographic plate, it’s a quantum wave that physicists can calculate a wave function for. The wave function identifies the possible positions where the quantum wave could deposit its energy on the photographic plate. So far, this is like the Copenhagen Interpretation. But the Transactional Interpretation adds something new. It says that if the photon is to land on the photographic plate, an electron in the plate must take action to absorb it. Electrons in the plate must send out their own waves. When the emitting wave and the receiving wave interact, the photon transfers energy to the electron, and takes its place in physical reality at a position on the plate.

The wave function of the absorbing electron in the plate has an amplitude that fits well with the amplitude of the photon: it’s the complex conjugate of the photon’s amplitude.

But why multiply the two amplitudes? This is how we find the probability of two events occurring, in this case both the photon heading towards a particular position on the plate and an electron in that position absorbing it. When we calculate the probability of any two events, we multiply the two probabilities. For example, the chances of a baby being born a girl with brown eyes is: 1) the probability of being a girl (about 48%) **times** (2) the probability any baby having brown eyes (about 80%). We multiply 48% times 80% and get 38%. There’s a 38% chance that a baby born anywhere in the world will be a girl with brown eyes.

The emitting wave and the absorbing wave have to interact if the photon is to land in any particular position. We multiply the probability of the photon landing in a particular position (the complex number describing the amplitude) times the amplitude of the receiving wave at that position on the plate (the complex conjugate).

The Transactional Interpretation is based on Absorber Theory developed by Richard Feynman and John Wheeler in the late 1930’s. It was fully developed as an interpretation of quantum mechanics by John Cramer in the 1980’s and further developed by Ruth E. Kastner. Kastner has written technical papers on the Transactional Interpretation and also a book for laypeople, *Understanding Our Unseen Reality*. I highly recommend the book because it provides a coherent and understandable explanation of the physical meaning quantum mechanics.

# What are some good online resources that can help me understand physics better?

The Physics Classroom and Khan Academy both have excellent free on-line courses on physics, starting from the beginning. They’re step-by-step and give practice problems. On Khan Academy, if you sign in, it will keep track of your progress. It also gives “awards” like badges for good progress. Both websites are excellent. Khan Academy is a little more interactive. I have used both. To really gain understanding and certainty, I’ve done lessons on the same subject on both websites.

When I didn’t understand something in a particular lesson, I found videos on Youtube. I typed the subject into the Youtube search bar, for example, “inertia.” Then, I just started watching videos until I finally got it.

It’s important to understand all the jargon as it comes up. When terms came up I wasn’t sure of, like “mass,” I watched Youtube videos on the subject and/or googled the physics meaning. When googling, I often asked for images. Finding visuals really helps.

I’m writing definitions of physics terms in an on-line encyclopedia. It focuses on quantum physics, but many of the terms, like acceleration, are shared with classical physics. Classical physics is the first physics that you learn on websites like the PhysicsClassroom and KhanAcademy.org.

# Can quantum mechanics be understood? Does it make logical sense?

Quantum mechanics is logical. By logical, I mean that the assumptions, the principles, the equations, and the empirical data all fit together. They don’t contradict each other.

However, quantum mechanics (QM) does not fit with the assumptions and principles of classical physics (physics prior to 1900 that we learned in high school). QM is the description of the quantum world. Classical physics is the description of the macroscopic world—the world of tables, chairs, apples, etc. The two worlds are described by two different systems of assumptions, principles, equations, and empirical data.

If we attempt to view the quantum world while retaining classical assumptions and principles, the quantum world seems full of paradoxes. For example, classical physics is based on the unspoken assumption that when an object changes position from Point A to Point B, it traverses the distance in between. This assumption is violated in the double slit experiment of quantum mechanics (QM). Another assumption of classical physics is that if one knows the initial conditions of a system, one can calculate its evolution through time. Due to the true randomness in the behavior of individual quantum particles, QM violates this assumption.

*Classical physics tells us that if we apply a specific force to a billiard ball, we can predict exactly where it will roll. This is called the billiard ball model of physics.*

Neither system is particularly intuitive. Newton’s First Law isn’t intuitive: no forces are needed to maintain an object at a constant velocity. Or gravity – Newtonian gravity is action-at-a-distance. Neither Newton nor we are able to describe the underlying nature of physical reality such that action-at-a-distance occurs.

But the principles of classical physics fit together into a self-consistent logical system. Classical physics was also consistent with experimental data until the late 1800’s. That’s when scientists started investigating atoms and the interiors of atoms. And, that’s when they need QM.

QM can be seen as describing a sublevel of reality which operates on different assumptions from those of the macroscopic world.

** The green film represents ordinary reality as we perceive it with our senses. The red grid represents the quantum world, a sublevel to our reality. A wave travels through the quantum world (red grid) and creates a particle (dot in the green film colored orange or blue) in our perceived reality. [**Image source: stills from Fermilab video by Dr. Don Lincoln, “Quantum Field Theory” (in the public domain) Jan. 14, 2016; See the video below.]

The quantum world is a sublevel of reality in the same sense that computer programmers work at a sublevel of a video game. Before they key the program into the computer and see the “macroscopic” world that they’ve created, they follow rules different from those that the characters in the video game follow. The programmers can program a character to exit screen left and enter screen right—no need to traverse the distance in between. The programmers can correct an action in an earlier “frame”–no need to go back in time—they just re-type some symbols.

Later, when the game is actually playing on the screen, the characters follow different rules, more like those of our macroscopic world. For example, a character in a video game can’t correct one of her actions by going back in time (unless it’s a sci fi game).

[For more detail on the idea of the quantum world as a sublevel of reality, see this excellent short video by Fermilab. Also see the entry for quantum field theory in the quantum physics encyclopedia for laypeople QuantumPhysicsLady.org.]

Some interpretations of QM are better than others at logical descriptions of reality. The Copenhagen Interpretation, the original interpretation, doesn’t even try. The slogan of this interpretation has come to be known as “Shut up and calculate!” In other words, physicists use the highly useful math of QM in developing things like computer technology but don’t worry about the implications for the nature of reality. They know that the implications are self-consistent if we confine our attention to the quantum world; but they’re not consistent with the laws of Newton that describe our experiences in the macroscopic world of tables and chairs.

The Transactional Interpretation* does well at providing a logical description of reality. In describing QM as describing a sublevel of reality, I’ve relied on this interpretation.

In short, QM follows its own logic. As long as we don’t make assumptions based on our everyday experience or on classical physics, QM makes logical sense of experimental results.

* See the book: Ruth E. Kastner, *Understanding Our Unseen Reality.*

# Why study quantum physics?

Here’s why I began studying quantum physics. I wondered: How does this universe work? What underlies molecules and atoms? How is reality created?

Quantum physics is part of the answer—a huge part. But the trouble is, physicists don’t understand how quantum particles create the solid objects that our senses perceive. After all, quantum particles are just vibrations in what appears to be huge quantities of empty space.

Many physicists are unperturbed by this question. They use the mathematics of quantum physics for running experiments or for developing technologies, and they leave the Big Questions alone. However, some physicists/mathematicians have gone ahead and speculated about the Big Questions.

## How does quantum physics explain our perceptions of the world?

One speculation of particular interest to me is that Information Theory can cast light on this question. Information Theory reduces the universe to mathematical patterns. It reduces the vibrations of quantum particles to the mathematical equations which calculate the vibrations. These equations describe **changes** in matter and energy, what physicists call “evolutions.” The equations are not just static descriptions like the formula for the composition of water: H_{2}O.

The entire universe can be seen as an intermeshing of equations, one supplying data to another, each equation being influenced by others. The physicist, Max Tegmark, wrote the book *Our Mathematical Universe *on this premise. Another good book on the subject is *Programming the Universe *by one of the inventors of the quantum computer, Seth Lloyd.

Information Theory is illuminating. But there’s a big piece of the puzzle that’s still missing. How do mathematical equations become subjective experience? We experience colors, sounds, tastes, and other sensations as if they were out in the world. But, actually, these are our subjective experiences of electrical impulses in the brain. After all, our skulls don’t have holes in them to let the world in. The only thing going on in our brains are electrical impulses.

Here’s where **my** brain starts to hurt—our brains are, themselves, describable as mathematical equations interacting with each other. And the electrical impulses that shoot through the brain are describable as mathematical equations. And these electrical impulses arise from sense organ stimulations that are describable as mathematical equations. These stimulations arises from interactions with the external world (which, of course, are describable as mathematical equations).

But, how exactly, do we experience electrical impulses traveling through the brain as colors, sounds, tastes, and so on? **How do mathematical equations become subjective experience?**

The quantum physicist, Amit Gswami in *The Self-Aware Universe*, suggests how this happens. He proposes that our consciousness codes equations into the images, sounds, smells, and tastes of our subjective experience. In other words, the world is really in our minds. Or possibly, there is one mind, and we’re all tuned into it, each one of us experiencing it somewhat differently due to our own unique filters. The traditional Buddhist view has things to say about this.

**Is consciousness fundamental?**

This view, “Idealism,” depends on the assumption that consciousness is fundamental and matter derivative. Of course, the current scientific view that consciousness arises from brain matter, is exactly the reverse.

Some philosophers and physicists throughout history have espoused Idealism. Plato, considered one of the founding fathers of Western thought, was an Idealist. And so was the grandfather of quantum physics, Max Planck. Planck said in 1931:

*“I regard consciousness as fundamental. I regard matter as derivative from consciousness. We cannot get behind consciousness. Everything that we talk about, everything that we regard as existing, postulates consciousness.”*

Rene Descartes proposed another view called “Dualism” in the 1600’s. He saw both matter and consciousness as fundamental but also as very different substances. Dualism formed one of the basic unspoken assumptions of the worldview that I grew up with and probably most Westerners have grown up with. It is the worldview that most Westerners who aren’t paid to think, unthinkingly adopt.

Starting in the middle of the 20^{th} Century, mainstream scientists began rejecting both Idealism and Dualism. They adopted Materialism. This view is that matter is fundamental and consciousness arises from the brain. These days, some scientists, like Amit Gswami, are beginning to question Materialism. Philosophers like David Chalmers are working out the logic of Materialism and pointing out some logical difficulties that it raises. The precepts of quantum physics, in particular the precept that fundamental particles are nothing more than vibrations, can be seen to undermine the foundations of Materialism.