## Saturday, August 22, 2020

### What’s “wrong” with the new definition of a kilogram.

The teacher’s perspective.

From Wikipedia: “the kilogram is currently redefined in terms of the Planck constant as approved by the General Conference on Weights and Measures (CGPM) on 16 November 2018.

The same page provides the timeline of the evolution of the definitions of the unit of mass, that for many people for many decades was known as a kilogram.

But neither Wikipedia, nor other popular or scientific sources (e.g. here; or here) do not tell us the significance of the change that happened in 2018. They all focus on accuracy, on how much more precise one kilogram can be defined now than before.

And they all ignore the methodological shift in the meaning of a kilogram, namely, they ignore the change in the in the meaning of mass.

The first meaning of mass was related to the amount of matter stored in a given amount of volume, or to the heaviness, i.e. the weight of that amount of matter.

People knew that some materials are denser than others, they could feel it. People also knew that some object are heavier than others, they could feel it, too.

So, they knew that if one takes an empty cube (or a sack), and fills it up with dense material, it will be heavy, and that was treated as “a lot of mass”. Using contemporary terminology, we can say that (without realizing it) people used two definitions of mass:

(a) mass = density * volume

and

(b) mass = weight / (the acceleration due to gravity)

In general, mass represented the amount of matter, and eventually, as a standard for that amount people used the amount of water in give volume (e.g. in one cubic decimeter, a.k.a. 1 L).

The actual standard have been changing, but the meaning of it was kept the same.

Until Newton changed it.

Before Newton, mass represented the amount of matter.

After Newton mass started to represent the amount of inertia.

To explain the meaning of mass before Newton, a teacher would have to demonstrate the fact that different materials have different density, and that when you pack more stuff in the same volume, the density and the mass (i.e. the amount of material) are proportional.

After Newton, the explanation of the meaning of mass has become more elaborated and more abstract.

We need to start from making a statement that if we would have one object (of any nature) in an empty space (for example, outside of the earth, far away from everything else) that object could have been found only in the state of rest or a in the state of a simple and continuous motion. If it would be moving, then it would be moving along a straight line traveling exactly the same distance in the same time.

Of course, I just paraphrased the first Newton’s law.

The mass or the size of the abject would not make any difference. They all would remain at rest or would travel with constant velocity (here we would have to provide the definition of velocity and explain what does term “constant” mean).

Then the second Newton’s law comes into a play.

We state that we can change the state of an object by applying to it a force (for example, by touching it). And then we observe that the state of that object changes, meaning, its velocity changes: the object may start slowing down, or speeding up, or its path begins bending (not a straight line anymore).

In the universe, nothing happens instantly – every change takes time. This is the universal law of nature.

And we observe that law in acting when we apply a force to an object that previously was at rest or was moving with a constant velocity.

We observe that velocity changing gradually.

But we also observe that how fast that change happens depends on the properties of objects.

Specifically, the rate of change of velocity depends on how light or heavy an object is.

The property of an object to keep its own state was named “inertia”.

And the mass has become the measure of that property.

“More massive” now means “more inertial”.

One kilogram became the standard of inertia “stored” in the standard of mass.

To explain the meaning of mass, we can state now that if we apply the same force to two different objects that initially have been in the same state, it will take more time for a more massive object to acquire the same change in its state as the other object.

Of course, I just paraphrased the Newton’s second law.

To explain the new, Newtonian, meaning of mass, a teacher would have to go through all the steps I just went through, but with more details, more examples, and, of course, with actual experiments.

That was not an easy task, but at least it was doable.

The new definition of one kilogram cannot be explained using any clear and understandable means; it is reachable to only scientists well versed in physics – in several different areas of it.

For the rest of folks, it is basically: “Trust me, it works”.

Don’t believe me? Try to read this piece from Physics Today(BTW: one of the best on the matter).

Trust me, it’s “dope”.

So, what should a teacher do now?

I can only share what I did this summer.

I went through exactly same explanations I used before the new definition was accepted, and added only one sentence, that today we have a new, more accurate definition of a kilogram (of course, I talked about mass and energy, and quantum properties of matter, but that was at the very end of the second semester, weeks and weeks after we covered the Newton's laws).

Based on my student evaluations, that went well.

Happy teaching!

## Tuesday, August 18, 2020

### Getting ready for the fall semester? Here are some hints.

Hi colleagues,

To help you with your preparations for the fall semester,  I would like to share with you some thoughts that are based on my personal experience of teaching in the Summer.

First, I present two unofficial feedbacks from my students (an official feedback is not ready yet) – not to brag, but just to demonstrate that at least some of my actions were appreciated by some of my students.

If it happened to me, it may also happen to you  (the past feedback is available here).

“Dear Mr. V,
I took both PY105 and PY106 this summer, and I just wanted to thank you for making the transition to online classes so seamless. I was worried about not taking physics in person, but with your approach I was able to do much better than I expected. You and the TFs have been so incredibly helpful, and I’m honestly very grateful for everything that you’ve done, considering it’s still a rather stressful time for everyone. Thank you so much once again, I hope you have a great rest of your summer.
Best”

“Mr. V,
I just wanted to personally reach out and thank you for teaching me physics this summer. I’m not a native BU student, but you made the transition easy. You always responded to my emails and my Piazza questions in a timely manner. More importantly, I don’t think I could’ve asked for a better professor. You taught me the material so well and made sure labs reflected the content we went over in class. Thank you for everything. Enjoy the rest of your summer.
Stay safe,
University of Pennsylvania,
Biology Department”

Ten general thoughts.

1. It is important to understand the difference between two forms of distant learning: “online” and “remote”. This difference is discussed in this article.

2. On-site and distant learning represent two extreme forms of a mixed-model learning, a.k.a. the Layered Classroom.

3. The results of effective teaching (i.e. the learning outcomes of students) do not depend on the format; the format of learning dictates the way teaching needs to be structured in order to achieve the best results. Technologies do not make a teacher better or worse, they just reveal how actually good or bad the teacher is.

4. No matter if students are physically present in a room, or participate live but remotely (in a lecture, a discussion, a lab team), or conduct prescribed exercises at the time of their choice (such exercises can include, but not limited to – watching recordings of lectures, discussions, experiments, reading, solving homework problems) the result of their actions depends on how good those actions have been structured by an instructor.

5. Every large class has students who prefer live participation and students who prefer to have flexibility in the time for conducting required learning actions. That is why students appreciate when they have a choice for selecting the form they prefer to use for leaning, even within the same course.

6. The most appreciated feature of teaching activities is their clarity for students, students like to understand what is happening and why.

7. Students appreciate when the lecture material, homework material, lab material and exam material are connected/correlated in a clear way.

8. Students like the feeling that they are taught by their professor. Meaning, “their professor” is the one who conducts the most of the teaching – in all possible forms. The difference between “learned from” and “taught by” is provided by the amount of the personal engagement of the instructor in the development of a course; reflected in  (1) the amount of actual interaction (at least – potential); (2) the amount of the material prepared by the instructor himself/herself.

9. The proportion of students who are engaged in learning and who are simply getting over with the course does not depend on the format of teaching.

10. Instructors act based on their own definition of learning and teaching. If learning is understood as consuming information then the source of that information does not matter, and an instructor becomes an information selector and coordinator and does not have to produce and deliver that information. In this case, teaching is not much different from training animals.

Two specific thoughts on the use of experiments in a course

1. Students like seeing their instructor doing some demonstrations (an example of a specific consequence of the general thought #8).

2. When planning a demonstration, be aware that depending on the format of your class, you may also need to think about some additional time to practice with it, and/or to organize recording of an experiment, and/or to estimate the best way to deliver a demonstration to the live audience.

Appendix

“In 1913, Henry Ford introduced conveyor-belt assembly lines at Ford Motor Company's Highland Park, Michigan factory.[6]” (from Wikipedia)

We all know that using conveyor-belt assembly lines allowed Ford to make a transition from crafting vehicles for rich individuals to mass production of cars for the middle-class Americans (who Ford help to create by paying fair wages).

This is how I imagine that happened.

At first Ford got an idea from learning about existing conveyor-belts. He called on his engineers and charged them with developing the assembly lines. When the lines were ready, he gathered all his workers and told them: “Guys, I made theses conveyor-belt assembly lines for you. Now, go in there and figure out how to use them to make cars. Once in a while a librarian will be bring you a leaflet about nuts and bolts. God speed!”

And happy workers ran to the assembly lines and picked up the tools, quickly figured out who should stand where, what tool to use, for what and how, and started making the cars.

Does not seem plausible, does it?

Of course that was not how it happened.

Of course, Ford had a team that trained workers. In fact, one of the reasons to pay workers good wage was to reduce the training cost (via retaining good workers).

Why do we talk about Ford?

To illustrate the opposite.

When COVID19 forced schools, colleges and universities to close their classroom and to through all teachers, instructors, faculty into the ocean of distant teaching, it was done exactly like in my fictional history of Ford.

“This is your computer, a web-camera and the internet access – go and teach! Once in a while our “center for teaching and learning” will email you a list of helpful hints and resources (of course, you also could have just Google that stuff, but we will pre-select it for you).”

This is an excerpt from a plan I came across.

All courses have been adapted to the … “mixed-learning” … model. Instructors began reaching out to registered students … with details on how classes would be structured and taught for the Fall 2020 semester. If you have any questions about your specific class, please reach out to the instructor listed on the Link.”

That’s it.

That's all of it.

This plan could have started from stating the central goal (BTW: the #1 responsibility of a manager) - that is to provide education of the same quality as for a standard face-to-face format (or at least as close as possible). Let be honest - the “mixed-learning” model is only a name, the real model (for 90 % of courses) is just 100 % online teaching (please note - not remote, but online!). And without making a clear goal - to keep the quality of teaching as high as before - things are getting cut: demonstration experiments are replaced with apps, labs got shorter - for the same money(!).

Why no administrator  dares to state that goal? Becasue then he or she would have to say: And this is how we will be achieving this goal!” And now we have a problem, because no administrator has sufficient knowledge about effective distant teaching strategies. In fact, almost no college and university administrator has sufficient knowledge about effective teaching strategies - period. Hence, they don't make the best decision - form the point of view of the mission of a teaching institution; they make a simplest and easiest decision - let everyone do whatever they want to. As long as students do not complain - everything is fine.

And now every instructor is figuring out on his/her own what and how he or she will do.

It is like gathering stay-home moms and telling them: “From now on, all of you have to run a restaurant”.

Do you really expect they all will start cooking like Gordon Ramsay?

For (much) more on the matter of teaching and learning:

## Monday, August 17, 2020

### The true mystery of quantum mechanics.

The true mystery of quantum mechanics
In all known experiments, all 100 % of them conducted to this day for about a century, all quantum objects have been revealing themselves as objects localized in space, i.e. as particles.

The most common examples of such experiments are:
the photoelectric effect,
the Compton’s scattering,
the Rutherford experiment (and all other collision experiments),
mass-spectrometry (including trajectory visualizing techniques like a cloud chamber),
counting techniques (e.g. a Geiger counter, a scintillation counter).

That is why each existing quantum object is called “a particle” (with a specific name – an electron, a proton, a photon, etc.).

The most puzzling feature of those particles is that even though they exist and exhibit themselves as particles, they behave in a way similar to the behavior of classical waves, e.g. the waves on a surface of water.

Our common sense makes us to believe that nothing can be a particle and a wave at the same time – they both are “size-less”, but a particle has no size because it is basically a dot, and a wave has no size because it is being spread over a vast region of space (theoretically, in the most abstract sense – over the whole universe).

And yet, in order to explain all know experiments scientists had to treat quantum objects in a very contradictory way – like particles and like waves – at the same time.

For about a century, this “contradiction” has been the source of deep confusions and intense discussions.

Those discussions had led to several famous word-tags, such as:
The SchrÃ¶dinger’s cat,
Wave-particle duality,
The uncertainty principle,
A wave-function collapse,
and also, to one of the most discussed quantum thought experiments: a double-slit electron diffraction.

Since I already have publications on those matters, I forward readers to this page.

I would recommend to start from:

Since all those pieces were a reaction to something I read, they may have similar parts, as well as ideas unique to that particular piece.

Here I just want to add two short notes – one on a wave-function collapse, and another one on the double-slit experiment.

I. A standard textbook on quantum mechanics describes two types of evolution of a wave function.

For example, Dr. Richard Fitzpatrick, Professor of Physics at The University of Texas at Austin, writes: “There are two types of time evolution of the wavefunction in quantum mechanics. First, there is a smooth evolution which is governed by SchrÃ¶dinger's equation. This evolution takes place between measurements. Second, there is a discontinuous evolution which takes place each time a measurement is made.”

This is a very common view shared by many physicists: “In general, quantum systems exist in superpositions of those basis states that most closely correspond to classical descriptions, and, in the absence of measurement, evolve according to the SchrÃ¶dinger equation. However, when a measurement is made, the wave function collapses—from an observer's perspective—to just one of the basis states, and the property being measured uniquely acquires the eigenvalue of that particular state. After the collapse, the system again evolves according to the SchrÃ¶dinger equation.”

But not all scientist share that view. Following the Wikipedia: “The existence of the wave function collapse is required in
On the other hand, the collapse is considered a redundant or optional approximation in
the consistent histories approach, self-dubbed "Copenhagen done right"
This is an illustration of simple fact that even today, almost a hundred years later after the development of the quantum theory of matter, physicists are still not united about its interpretation.

This is a notable fact.

Physicists do not have different interpretations of the classical mechanics, or classical electrodynamics. They even agree on the meaning of the special and general relativity theories.

But when they talk about quantum mechanics – they are divided.

My view on the so-called wave-function collapse is simple – it does not exist. The wave function always evolves according to the SchrÃ¶dinger’s equation, but when a quantum object interacts with a large classical system the equation is simply too complicated for scientists to solve, or even analyze – using current mathematical tools. For example, a problem with three electrons orbiting a heavy nucleolus is already borderline complicated. An act of  a measurement – as an act of an interaction between a quantum and a classical systems – is much more complicated than that. And physicists cover up their inability to solve the problem of measurements by invoking a miracle called “a collapse”.

There is no such thing as “a discontinuous evolution”. There is evolution that is too yet difficult to be analyzed.

II. One of the premises of a double-slit electron diffraction experiment is that after traveling through the slits (in any way that fits the view of an author) they do not travel using a certain path, but reach the screen via many possible paths, and for each path there is a number that is called “the probability amplitude for an electron for “choosing” that path”. And the probability for an electron to get from point A (e.g. the slit #1) to point B (e.g. a given location on a screen) is based on the sum of all probability amplitudes for all possible paths leaving point A and arriving at point B.

This picture leads to a clear and robust mathematical description, called “path integrals” – one of the most fundamental mathematical instruments used in all quantum theories.

It works.

If explains all known experiments.

The only problem with it – it contradicts the nature of the experiment used for its own development.

Electron diffraction exists. Experiments show it. those experiments have become so routine, there is a lab on that.

And yet, the notion that electrons can travel via different paths is wrong.

It is not easy to see the path of those electrons, what we see is the interference pattern on a fluorescent screen.

But we can use a robust analogy to visualize what would we see if we could see the trajectories of those diffracted electrons.

That analogy is based on the original similarity between particles and waves, or, more specifically, between quantum particles and light waves.

At the dawn of the quantum mechanics, light waves were used as a means for understanding wave-like behavior of electrons, and other quantum particles.

Light waves from diffraction patterns, electrons form diffraction patterns, hence electrons are kind of like waves.

But why don’t we use this similarity backwards?

Electrons are particles that exhibit a wave-like behavior. Light waves exhibit a wave-like behavior. Hence light is also made of particles – photons.

That was the idea the brought the Nobel Prize to Albert Einstein.

Let’s use this similarity again.

We know that light is a quantum matter formed by photons. And we know that those photons travel through a double-slit in a special way. Hence electrons, because they are also quantum particles, should travel through a double-slit in the same special way.

And that way does NOT show many possible paths – not at all!

In fact, what we see in a very standard diffraction experiment is a set of several specific trajectories.

In reality, an actual experiments is much simpler and clearer when it is done with a diffraction grating (optical – for photons, or crystalloid – for electrons).

When photons travel through a diffraction grating they travel along a small number of clear paths. It is impossible to predict which path will be “selected” by which photon, but we do NOT see photons traveling in a cloud that “collapses” when that cloud reaches a screen (again – no “wave-function collapse”!).

This pictures shows an example of those trajectories (here is a short video).
I am sure, a similar experiment with electrons traveling through a cloud chamber would show a similar picture.
This picture proves that the model of many different paths for an electron to travel from the grating (or slits) to the screen is simply wrong – despite the fact that it mathematically correctly describes the probability to fins a particle at a given location on a screen.

How can it be that a model that contradicts the physical nature of a process (traveling toward a screen), also provide correct mathematical description of the results of that process (arriving at a screen)?

There is no answer to this question.

To this day – now one knows why quantum mechanics works so well.

This experiment also shows a common methodological misconception – namely, that quantum particles travel according to the wave function provided by the solution of a SchrÃ¶dinger’s equation with the given potential energy.

That wave-function will give the probability of fining a particle at the given point at the given time – but saying that a particle can travel along many paths with different probability amplitudes is wrong – it contradicts a simple experiment.

This experiment also illuminates one of the most famous mysteries of the double-slit diffraction experiment – how do electrons or photons get through the slits? Because the way they get thought the slits (or a grating) prescribes their future behavior – particularly, the path they travel through to a screen. For example, in the picture, we see that each photon “selects” one of the three paths, the probability to travel along a different path is zero (or almost zero).

We have three possibilities to describe the behavior of particles in this experiments, and the next one is even worse than the previous one.

(A) Particles “learn” what path they have choose when they interact with the grating (or slits) and then they travel along that chosen path. If that is a case, then a particle should “learn” its path even if there is only one slit! BTW: a fact escaping the mind of an every single author discussing the double-slit electron diffraction experiment.

A single-slit diffraction is well known for light, and it should be observed for electrons and other quantum particles, as well. But the explanation should be based on the solution of a SchrÃ¶dinger’s equation for a particle interaction with a large classical object, and as we know from part II, no one yet knows how to do that (even for one slit!). Plus, this would negate the basis for the path-integral approach – if everything is “decided” at the beginning of each path (i.e. at the end of the particle–grating/slit interaction) then for each path its probability is set before that path begins.

(B) Particles “learn” what path they have to choose based on the whole system – that includes the grating (slits, a slit) and a screen. Clearly, this is even more complicated problem. The way around is to ignore the particle–grating/slit interaction and invoke the path-integral approach. But to explain how a far located screen affects the “choice” of a path we would run into a non-locality, or a faster-than-light interactions.

(C) In addition to the mystery of “learning the path”, particles may be able to “jump” from one path onto another, and back. That would definitely lead to a non-locality and a faster-than-light interactions.

This experiment demonstrates that the real mystery of quantum mechanics is not “how do  electrons travel through two slits at the same time?” (they don’t) but “how do electrons “chose” their path?”