A spaceship called Imminency III

So, our technology today causes ideas to be spread too fast to be properly tested. Is that really so bad? Perhaps the spreading of false information causes people to make bad decisions, such as whether or not one should get vaccinated during a pandemic or which president to vote for. But does that really threaten the survival of humanity? We seemed to be getting through this pandemic and although a large number of people died, it is still a tiny fraction of the total human population. Even bad presidents are eventually voted out of office. Although the next president has a lot of things that needs fixing, humanity still goes on.

So, what is really the issue with us losing the cultural mechanism? Granted. It may not be that humanity as a whole would become extinct as a result of the loss of the cultural mechanism, but there are some very seriously unpleasant states of existence before we get to extinction.

Perhaps the most important thing that is being maintained by the cultural mechanism is civilization. What do I mean by the term civilization? Basically, it is ability to live and work together with other people. Often civilization is seen as all the accomplishments such as art works of scientific achievements. However, these accomplishment are merely the symptoms of civilization. These accomplishments would not have been possible if people did not cooperate to achieve them. A single person could not have built the rocket with the capsule to land on the moon. The bigger the achievement, the larger the number of people that needed to be involved. It implies that all these people had to work together. That is only possible thanks to their level of civilization.

People are different. They have different views and convictions. If these people want to work together, they have to tolerate one another’s views, even if those views are very different. In a culture, the views and ideas may to a large extent be correlated. However, as the population of a culture increases the diversity in ideas will also increase. Therefore, the people in that culture can only maintain their cooperation if their level of civilization – the extent to which they can tolerate different views – also increases.

Warlords

So, what happens when people do not tolerate different views anymore? Does it not simply mean that they cannot work together to achieve those accomplishments anymore? Yes, that is one inevitable consequence, but there are several much more severe things that can happen. The break down of civilization effectively implies a fragmentation of the culture into several lesser subcultures. It may sound like a scenario for civil war, but there are many other ways that the fragmentation can manifest. The fragmentation may happen along class separation lines. The lower classes would them reorganize themselves into gangs, living by stealing their resources. If the government of the day can muster enough cooperation to keep these gangs in check, some form of normality can be maintain. On the other hand, if the fragmentation implies that such cooperation cannot be maintained, the gangs would become ever more powerful. The gang leaders would eventually emerge as warlords. The point where these warlords become more powerful than the government would indicate the stage where the civilization has effectively fallen.

OK so that is bad. When civilizations fall, life as we know it changes drastically. It would generally mean that life expectancy decreases. The human population would dwindle. Although it does not necessarily imply that humanity becomes extinct, it is a close second.

But why would the fast spreading of information lead to such an apocalyptic state of affairs? The reason is that there is a concomitant breakdown in cooperation. Why this is happening, I don’t know, but there is a clear increase in animosity observable in social media. Somehow, the fast spreading of information puts pressure on basic civilization. In some parts of the world there is also an observable increase in criminal activity. These observations are all pointing to an imminent fall of civilization.

That is why the spaceship is called Imminency.

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Adrift in theory space

It is downright depressing to think that after all the effort to understand the overlap between gravity and quantum physics there is still no scientific theory that explains the situation. For several decades a veritable crowd of physicists worked on this problem and the best they have are conjectures that cannot be tested experimentally. The manpower that has been spent on this topic must be phenomenal. How is it possible that they are not making progress?

I do understand that it is a difficult problem. However, the quantum properties of nature was also a difficult problem, and so was the particle zoo that led to quantum field theory. And what about gravity, which was effectively solved singled-handedly by just one person? There must be another reason why the current challenge is evidently so much more formidable, or why the efforts to address the challenge are not successful.

It could be that we really have reached the end of science as far as fundamental physics is concerned. For a long time it was argued that the effects of the overlap between gravity and quantum physics will only show at energy scales that are much higher than what a particle collider could achieve. As a result, there is a lack of experimental observations that can point the way. However, with the increase in understanding of quantum physics, which led to the notion of entanglement, it has become evident that it should be possible to consider experiments where mass is entangled, leading to scenarios where gravity comes in confrontation with quantum physics at energy levels easily achievable with current technology. We should see results of such experiments in the not-too-distant future.

Another reason for the lack of progress is of a more cultural nature. Physics as a cultural activity that has gone through some changes, which I believe may be responsible for the lack of progress. I have written before about the problem with vanity and do not want to discuss that again here. Instead, I want to discuss the effect of the current physics culture on progress in fundamental physics.

The study of fundamental physics differs from other fields in physics in that it does not have an underlying well-establish theory in terms of which one can formulate the current problem. In other fields of physics, you always have more fundamental physical theories in terms of which you can model the problem under investigation. So how does one approach problems in fundamental physics? You basically need to make a leap into theory space hoping that the theory you end up with successfully describes the problem that you are studying. But theory space is vast and the number of directions you can leap into is infinite. You need something to guide you.

In the past, this guidance often came in the form of experimental results. However, there are cases where progress in fundamental physics was made without the benefit of experimental results. An prominent example is Einstein’s theory of general relativity. How did he do it? He spent a long time think about the problem until he came up with some guiding principles. He realized that gravity and acceleration are interchangeable.

So, if you want to make progress in fundamental physics and you don’t have experimental results to guide you, then you need a guiding principle to show you which direction to take in theory space. What are the guiding principles of the current effort? For string theory, it is the notion that fundamental particles are strings rather than points. But why would that be the case? It seems to be a rather ad hoc choice for a guiding principle. One justification is the fact that it seems to avoid some of the infinities that often appear in theories of fundamental physics. However, these infinities are mathematical artifacts of such theories that are to be expected when the theory must describe an infinite number of degrees of freedom. Using some mathematical approach to avoid such infinities, we may end up with a theory that is finite, but such an approach only address the mathematical properties of the theory and has nothing to do with physical reality. So, it does not serve as a physical guiding principle. After all the effort that has been poured into string theory, without having achieved success, one should perhaps ponder whether the departing assumption is not where the problem lies.

The problem with such a large effort is the investment that is being made. Eventually the investment is just too large to abandon. A large number of very intelligent people have spent their entire careers on this topic. They have reached prominence in the broader field of physics and simply cannot afford to give it up now. As a result, they drag most of the effort in fundamental physics, including a large number of young physicists, along with them on this failed endeavor.

There are other theories, such as loop quantum gravity, that tries to find an description of fundamental physics. These theories, together with string theory, all have it in common that they rely heavily on highly sophisticated mathematics. In fact, the “progress” in these theories often takes on the form of mathematical theorems. It does not look like physics anymore. Instead of physical guiding principles, they are using sets of mathematical axioms as their guiding principle.

To make things worse, physicists working on these fundamental aspect are starting to contemplate deviating from the basics of the scientific method. They judge the validity of their theories on various criteria that have nothing to do with the scientific approach of testing predictions against experimental observations. Hence, the emergence of non-falsifiable notions such as the multiverse.

In view of these distortions that are currently plaguing the prevailing physics culture, I am not surprised at the lack of progress in fundamental physics. The remarkable understand in our physical world that humanity has gained has come through the healthy application of the scientific method. No alternative has made any comparable progress.

What I am proposing is that we go back to the basics. First and foremost, we need to establish the scientific method as the only approach to follow. And then, we need to discuss physical guiding principles that can show the way forward in our current effort to understand the interplay between gravity and quantum physics.

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A spaceship called Imminency II

Granted. One day, if humanity needs to take a spaceship to another planet to survive, the knowledge of how that spaceship needs to be maintained would be a technology that humanity depends on for its survival. But what about today? Although there are a large variety of existing technologies, none of it involves the survival of humanity as a whole, right? That depends on how you define technology.

Technology

What is technology? It is the knowledge of how to use the resources at our disposal to make devices that serve specific purposes. Well, it does not have to involved physical devices. Technology can also be represented by methodology – techniques of how to do things. Often the use of specific tools requires some sophisticated knowledge.

If we see it broadly enough, almost all the knowledge that we have can to some extent be seen as some form of technology. Perhaps it would be a stretch to think of the waltz as a form of technology, but that may be the exception.

So what technology, seen in this broader sense, is vital for the survival of humanity today? Well, in this broad sense, the technology of acquiring and maintaining knowledge is in itself also a technology. In fact, the mechanism for the way humanity learns and uses knowledge can be seen as a technology. When viewed in this way, it is clear that such a technology would be something that humanity needs for its survival.

This technology has a name. It is called culture. One may think of culture as things like theater, cuisine, fashion, etc., but culture is much more than that. These things are high culture, which is just a tiny part of culture. One may think that culture is a fixed rigid thing, but that is not the case. It evolves and changes as time goes by. One may think of culture as just a collection of traditions and activities, but in fact, it is a mechanism.

Culture is the most important mechanism by which humanity maintains its survival in an ever changing world. If we lose it, we are in a serious situation. I’m not taking about “losing our cultures,” instead I’m referring to losing the mechanism of culture.

Culture is a feedback system that filters new ideas and maintains the best among them. For this to work, it is important that new ideas are tested before they are propagated through the population. This mechanism is under threat today. The rate at which ideas are propagated far outpaces the rate at which these ideas are tried and tested. The result is that false information is spread far and wide. People are responding to it with detrimental consequences. This process erodes the very mechanism of culture and thus threatens the survival of humanity.

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A spaceship called Imminency

What would happen if there is a technology that humanity depends on for its survival and then they forget how to maintain that technology? Yes, it is a rhetorical question. But why would there be such a technology? Humanity evolved as a species that survives without the need for any special technology. Don’t they?

To illustrate a scenario where such a thing can happen, I’ll tell a story. It is a story about a situation that can happen at some point in our future.

Far into the future, the people of earth realized that life on earth is doomed. To save humanity, they built a vast spaceship and called it Imminency. Then they loaded it with all the knowledge of mankind. A large number of people entered the spaceship, taking with them all the resources they would need for a long journey through space to a different planet where they hope to establish a new home for humanity. If this mission would fail, humanity would cease to exist.

The journey would take several generations to complete. Therefore, each new generation needs to be taught how to maintain the life support systems of the spaceship.

So, here we have that scenario that I talked about at the beginning.

For a while it worked, but humans are humans. Their ideas drift. The human mind is capable of much diversity. It is inventive and resourceful. So at some point some very clever people came up with reasons why children should not be taught all this knowledge of the technology. And so it happened that, after a few more generations, the knowledge of how to maintain the technology that keeps humanity alive got lost.

Slowly, the life support systems started to fail, but nobody knew how to solve the problem. They did not understand the technology and did not know how to fix the failing systems.

I don’t like stories with bad endings so I won’t leave this one in such a condition. Fortunately, in the vast libraries that was loaded onto the spaceship at the beginning the knowledge of how these systems work and how they are to be maintained still existed. Some young people then got hold of this knowledge and they started to fix the systems.

Obviously I have some other reason for telling your this story, but I’ll leave that for another day. In the meantime, you may think about this story and what it means.

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Non-commutation

It is believed that the non-commutation of operators is a characteristic property of quantum mechanics. So much so that axiomatic mathematical structures are developed specifically to represent this non-commuting nature for the purpose of being the ideal formalism in terms of which quantum physics can be modeled.

Is quantum physics the exclusive scenario in which non-commuting operators are found? Is the non-commutative nature of these operators in quantum mechanics a fundamental property of nature?

No, one can also define operators in classical theories and find that they are non-commuting. And, no, this non-commuting property is not fundamental. It is a consequence of more fundamental properties.

Diffraction pattern

To illustrate these statements, I’ll use a well-known classical theory: Fourier optics. It is a linear theory in which the propagation of a beam of light is represented in terms of an angular spectrum of plane waves. The angular spectrum is obtained by computing the two-dimensional Fourier transform of the complex function representing the optical beam profile on some transverse plane.

The general propagation direction of such a beam of light, which is the same thing as the expectation value of its momentum, can be calculated with the aid of the angular spectrum as its first moment. An equivalent first moment of the optical beam profile gives us the expectation value of the beam’s position. Both these calculations can be represented formally as operators. And, these two operators do not commute. Therefore, the non-commutation of operators has nothing to do with quantum mechanics.

So what is going on here? It is an inevitable consequence that two operators associated with quantities which are Fourier conjugate variables would be non-commuting. Therefore, the non-commuting property is an inevitable result of Fourier theory. Quantum mechanics inherits this property because the Planck relationship converts the phase space variables, momentum and position, into Fourier conjugate variables.

So, is Fourier analysis then the fundamental property? Well, no. There is a more fundamental property. The reason why Fourier conjugate variables lead to non-commuting operators is because the bases associated with these conjugate variable are mutually unbiased.

We can again think of Fourier optics to understand this. The basis of the angular spectrum consists of the plane waves. The basis of the beam profile are the points on the transverse plane. Since plane waves have the same amplitude at all points in space, the overlap of a plane wave with any point on the transverse plane gives a result with the same magnitude. Hence, these two bases are mutually unbiased.

Although Fourier theory always leads to such mutually unbiased bases, not all mutually unbiased bases are produced by a Fourier relationship. Another example is found with Lie algebras. For example, consider the Lie algebra associated with three dimensional rotations. This algebra consists of three matrices called the Pauli matrices. We can determine the eigenbases of the three Pauli matrices and we’ll see that they are mutually unbiased. These three matrices do not commute. So, we can make a general statement.

Two operators are maximally non-commuting if and only if their eigenbases are mutually unbiased

The reason for the term “maximally” is to take care of those cases where some degree of non-commutation is seen even when the bases are not completely unbiased.

Although the Pauli matrices are ubiquitous in quantum theory, they are not only found in quantum physics. Since they represent three-dimensional rotations they are also found in purely classical scenarios. Therefore, their non-commutation has nothing to do with quantum physics per se. Of course, as we already showed, the same is true for Fourier analysis.

So, if we are looking for some fundamental principles that would describe quantum physics exclusively, then non-commutation would be a bad choice. The hype about non-commutation in quantum physics is misleading.

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