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]]>A scientific theory is wrong if its predictions are wrong regarding the behavior of the physical universe. Physicists have been using the principles of quantum mechanics to successfully predict the results of experiments since 1900.

During the last 120 years, physicists have conducted thousands of experiments on the tiny particles that quantum mechanics describes—atoms and their constituents. The experiment at top of mind might be the Double Slit Experiment. But there have been myriads of experiments with lasers, radioactivity, particle accelerators, etc. The equations of quantum mechanics are needed to predict the outcomes of all of these types of experiments. One book on philosophy of science described the accuracy of quantum mechanics this way:“…[T]he many predictions by which quantum theory has been tested stand up, with an accuracy so stupendous that Feynman [a physics Nobel Laureate] compared it to measuring the distance between New York and Los Angeles accurately to the width of one human hair. On the basis of these stunningly successful predictions, quantum theory, or some version of it, seems to be as true as anything we know.”*

In contrast, Newton’s laws of classical mechanics do not accurately predict the results of quantum physics experiments.

Quantum mechanics provides the equations for the technologies of our age—computers, lasers, nuclear bombs, particle accelerators, cell phones, PET scans, etc. The equations of quantum mechanics give us the control and understanding of electrons and of light that is required to think up and create these technologies. While creating a new electronic technology is not a formal experiment, it certainly is a test of the accuracy of equations. Quantum mechanics has passed this test over and over with flying colors.

This can be a confusing issue, because sometimes the original interpretation of quantum mechanics, the Copenhagen Interpretation, is taught as if it’s one and the same as “quantum mechanics.” Actually, it’s one of the many interpretations as to what the equations of quantum mechanics imply about the nature of reality. Many Worlds, the Guiding Wave Interpretation, and many others describe alternative interpretations of the physical meaning of the equations.

Any one of these interpretations, and, possibly, all of these interpretations, could be wrong. Maybe numerous universes, each with a new copy of you, aren’t created each time an electron is detected in a particular position (the Many Worlds Interpretation). Maybe a mathematical expression (the wave function) doesn’t magically create a real, physical electron (the Copenhagen Interpretation). If history is any indication, one day, physicists will find the interpretation of quantum mechanics that is the most accurate and is the most fruitful in generating further research. Or, maybe they’ll just replace quantum mechanics with a better theory.

The history of science tells us that it’s likely that the equations of quantum mechanics will someday be replaced. Quantum mechanics may be found to have been a good approximation; but there’s something closer to the truth.

This happened with Newton’s law of gravity. For almost 300 years, physicists believed that Newton’s equation for the strength of gravity is a fundamental truth of the universe. Turns out, it’s only a very good approximation. The inaccuracy becomes noticeable when objects with large masses are close together. Thus, it can’t be used to accurately calculate the orbit of Mercury around the Sun. Both are objects with large masses, and Mercury is the closest planet to the Sun. In contrast, Einstein’s General Relativity is able to calculate Mercury’s orbit. It’s a more accurate theory and, among scientists, has replaced the Newtonian equation for gravity.

But Newton’s equation is sufficiently accurate to have been used to design the moon landings of the 20th Century. And it continues to be used in the engineering of bridges and roads. It’s a lot easier to work with than the equations of General Relativity. And Newton’s equation is close enough for this type of engineering.

There are already reasons to believe that quantum mechanics will one day be superseded by another set of equations. When physicists try to combine the equations of quantum mechanics with the equations of General Relativity, they can get nonsense answers. That is, sometimes the equations result in the answer, “infinity.” Infinity is not a number, so it’s useless to physicists. When infinity comes up as an answer to an equation, it means that something is wrong. For example, you’ve divided by zero or committed some other mathematical sin.

If physicists develop an even more accurate theory that combines well with General Relativity, they will, undoubtedly, stand on the shoulders of quantum mechanics to build it. And in the meantime, look at all the electronic toys that quantum mechanics has given us!

Eventually, we may find that quantum mechanics is not completely accurate. But I started by suggesting that there’s a question even more important than the accuracy of quantum mechanics: Is quantum mechanics useful? Of course, it’s been extremely useful for developing electronic technologies. But has it been useful in forwarding scientific understanding?

Newton’s law of gravity turned out to be inaccurate, but it has been useful for hundreds of years and is still useful today. It has been useful, not only for launching rockets to the moon, but also it’s been useful in the advancement of science.

Newton’s equation for gravity has facilitated the development of many branches of science: astronomy, materials science, geology, etc. It has been an extremely productive equation that has allowed many kinds of scientists to make leaps and bounds of progress. So, while not completely accurate, it has been extremely productive.

But it’s not just Newton’s equation that was productive, it was also his interpretation (mass attracts mass) that was productive. Einstein showed with General Relativity that this interpretation is incorrect. Nevertheless, Newton’s interpretation was productive of great work, including in astronomy.

Astronomers who assumed that mass attracts mass were able to create new theories about what might be happening in the heavens. When observations showed that Uranus was not following the orbit that Newton’s law ordained, astronomers thought, “Mass attracts mass—maybe another mass is attracting Uranus and pulling it off its expected orbit.” In the middle of the 1800’s, they looked for that mass with their telescopes and found Neptune.

This pattern has been repeated over and over in science. Someone observes something and describes their observations with an equation. They explain why the equation works with an interpretation as to the nature of reality. And that gets them thinking about what they might observe if they were to make a new observation or do a new experiment. The experiments/observations tell them new things. The equation is refined or even replaced, and scientific knowledge grows to cover more phenomena with greater accuracy.

Yes! But, hey, that’s just the way it goes sometimes in science!

**Footnote**

*Richard Dawkins, *Intuition and Common Sense, Philosophy of Science. *

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]]>The post Does matter act simultaneously like a particle and a wave? appeared first on Quantum Physics Lady.

]]>Actually, matter doesn’t **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.

Matter acts as a wave when it’s not interacting with other parts of the physical universe. It acts as particle when it is interacting. We call these interactions “observations” or “measurements.” This is because they allow us to track what the matter is up to. If an electron hits a detection screen and creates a spark, that interaction allows us to observe or measure where the electron is, or how much energy it has, or other properties.

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]]>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.

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).

*[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.

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.

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]]>The post How can I teach myself quantum mechanics, step-by-step? appeared first on Quantum Physics Lady.

]]>It’s taken me about 4 years, very part-time, to get through a basic understanding of classical physics, quantum physics, a review of high school math, and first year calculus. I have about average talent at math (though I really enjoy it), a below average talent at classical physics, and some talent at quantum physics.

What it takes is an intense interest in quantum physics, patience, perseverance, and, at least some of the time, enjoyment of the learning process. All the on-line resources I describe below are free. I bought books from Amazon.

**Classical Physics First**

To understand quantum mechanics, it’s necessary to first understand regular physics (classical physics). This is because much of classical physics applies to quantum physics. When it doesn’t apply, you’re supposed to be surprised. If you don’t know classical physics and aren’t surprised, you’re not going to get what’s so unique about quantum physics—you’re not going to get why physicists are puzzled and what puzzles that they’re trying to resolve.

I studied classical physics at PhysicsClassroom and Khan Academy. I started with kinematics and kept going until I felt that I had the basics. I also worked my way through a physics textbook, reading and doing the problems: *Physics and Society* by Art Hobson, published by Pearson, available on Amazon in softcover. This is an extremely brief review of classical physics and an introduction to relativity and quantum physics. A basic understanding of relativity is important to some aspects of quantum physics.

The on-line courses are free. These resources provide practice problems with answers so that you can check your work. No calculus needed.

**Quantum Physics**

I started my study of quantum physics with videos on Youtube. These are at all different levels. I only watched ones intended for laypeople. They have little or no math. I suggest starting with the series “Looking Glass Universe” and “Cracking the Nutshell.” Try to find the first videos on quantum mechanics in each series and go from there. I also watched a huge hodgepodge of other videos until I felt oriented.

I also read biographies of the early quantum physicists. These biographies included a little science—a good way to get your toes wet. The history of quantum physics very much helps in understanding the field. This is because you’ll run across many conflicting descriptions of quantum physics principles. They were either written by quantum physicists in different time periods or written by non-physicists who don’t know that the time period matters. This can be confusing unless you understand that views of quantum physics have changed over the years.

Then, I read books for laypeople on quantum physics. The best ones so far have been *Quantum, a Guide for the Perplexed *(Jim Al-Khalili) and *Understanding Our Unseen Reality* (Ruth E. Kastner). Both authors are working quantum physicists, but the books are written for non-physicists.

**Math**

Even if you want to learn quantum physics at only a conceptual level, like I have, it is desirable to have some understanding of calculus. It may not be essential, but it very much helps. For me, it gives me a general understanding of the quantum equations even though I couldn’t possibly solve them. (I plan to keep going with calculus and maybe one day I will be able to solve them.)

Each day, I study math for about half an hour and I study or write about quantum physics for about an hour.

I reviewed a lot of math on the Khan Academy website. I knew that I needed work on manipulating fractions, logs, and exponents. You will need these skills for calculus. You don’t need much geometry but you do need trigonometry and algebra. However, I started calculus without reviewing trig and algebra.

After reviewing fractions, logs, and exponents, I started the free on-line Ohio State first year calculus course (Calculus 1151). When I ran into difficulties because of insufficient algebra or trig, I went back to Khan Academy and also Paul’s On-Line Notes and Math Is Fun.

If I need more practice problems for calculus than the Ohio State website provides, I go to one of these other math websites that I’ve mentioned. I also google “problems and solutions” for whatever type of problem I’m looking for. There are lots of these on-line that instructors kindly supply.

**Keys to Success**

- As your question suggests, take things step-by-step. Study at least some classical physics before quantum physics. Study algebra and trig before undertaking calculus.
- In math, master each step before going on to the next. If you understand a subject, you should be able to do problems without errors. If you can’t do the problems or make a lot of “careless” errors, it means that you’ve not achieved mastery. I learned something—careless errors mean that you’re still struggling with the concepts. This is true for both physics problems and math problems.
- Look up words that you don’t understand. This may mean looking them up over and over. That’s what I’ve done. This is true for both regular English words and technical words. For technical words, find pictures and animations. Usually, Wikipedia is too technical, but it provides good pictures and animations. Pictures and animations are really important for understanding physics and, sometimes, math. Also, find pictures and animations by googling. Google your topic and then, click Images or Videos. Also, search on Youtube. I’m writing an encyclopedia of quantum physics for non-mathematicians on this website. It’s not yet complete, but you can find definitions of many classical and quantum physics terms there.
- If you find a good resource at your level, but you think that you could get more from it, do it over… and over. I’ve watched short videos 8 and 9 times. I’ve read most of my quantum physics books at least twice, one 7 times!
- If you find that what you’re studying is confusing or that you’re blanking out or getting less and less out of it, stop moving forward. Find where you were last doing very well. Find at the end of where you were last doing really well, what didn’t you fully get? Was it a word (regular English or technical)? Do you need to look at pictures or animations? Do you need to work problems? Fix the issue. And then, move forward again from that point. Or you may decide that this resource is just too challenging and find another that suits you better.
- This doesn’t mean that you must master each part of quantum physics before going on to the next. This is true for math, but not quantum physics. With math, unless you master each step, you’ll crash on the next one. But quantum physics is different. I cycle through videos/books on quantum physics, getting what I can from each and deciding upon completion if I want to re-do it immediately or move on to another and, possibly, come back later. My understanding of quantum physics has built up by reading different authors, watching different videos, and just getting the feel for what is going on.

Understanding quantum physics in a conceptual way doesn’t take great talent or college training—I’m the proof of that. It takes a lot of exposure to the concepts from many different viewpoints. And it takes patience, determination, and a willingness to tolerate counter-intuitive ideas.

For me, the notion that “no one understands quantum physics” isn’t true. Through all the exposure to various authors’ viewpoints and by trying to explain it all to my husband and also by writing my quantum physics encyclopedia, I’ve built up an ability to visualize what is going on. I’ve built up a feel for how it all works.

I find quantum physics an extremely rewarding field to understand. I want to know how this universe works. Quantum physics is one path in that quest. I feel that the more people understand quantum physics, the more able they are able to perceive the truth of what is really going on. I’m not going to explain that last statement. It may become clear when you study quantum physics.

I hope that what I have written will help you (and others) to decide if you want to study quantum physics. If you decide to undertake it, I truly wish you luck and good results. If you run into problems, you can always ask another question on Quora or search the many answers to Quora questions about quantum physics.

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]]>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.

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]]>The post What is wave function collapse? Is it a physical event? appeared first on Quantum Physics Lady.

]]>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.

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,

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

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.

(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.”

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.

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]]>The post Are electrons waves or particles? appeared first on Quantum Physics Lady.

]]>“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.

“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.

“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.

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.

*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.

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).

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, 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.

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]]>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.

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.

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.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.

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.”

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.

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]]>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.

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.

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