Curiosity is Not Uniquely Human
But our ability to question the fundamental nature of reality is (as far as we know). We should embrace that.
If I had the time, I’d go back to college. Specifically, I’d do Columbia’s MA in the Philosophical Foundations of Physics (yes, an Arts degree in Physics). David Albert is one of the directors of the program, and he’s one of my favorite physics communicators (I’m not sure how he’d react to that label, though) along with Tim Maudlin and Sean Carroll.
For most of the last 100 years the idea of a Philosopher of Physics was met with skepticism, at best. Go back further and every physicist was a philosopher. For thousands of years the most curious among us have followed that curiosity, driven by the most fundamental of questions—what is the world made of, how did everything come to be, where do the forces come from, what came before, what comes next.
As technology advanced and industrialization took hold, the practical applications of physics took on a new importance, and the specialization required became ever deeper. Curious minds were discouraged from asking questions that don’t have practical answers. Physics became high energy physics, and the price tag for any experiment that would push the boundaries of our existing models became (relatively) enormous.
But humans are still curious, and unfortunately my curiosity tends to find me in places that are hard to comprehend without a lot of education. I have an undergraduate degree in what is essentially Technical and Scientific Communication (it’s called Professional Communication, but it was basically a mix of I/O psych, communications theory, technical writing, and interdisciplinary studies).
Most of my writing is about the tech industry in general, and the intersection of AI and Product Management in particular. It’s easy to forget that physics, and the 3,000 plus years of epistemic exploration that preceded modern physics, provide the foundation on which everything I write about is built. Literally and figuratively.
The scientific method can be traced back to as early as 3,000-1,000 BC based on the Edwin Smith papyrus, Aristarchus of Samos figured out the Earth orbited the Sun and that the stars were “very distant suns” around 300 BC using geometry and parallax, J. J. Thompson discovered the electron in 1897, and then proposed what has become derisively called the “plum pudding model” of the atom—which was totally wrong—but by using the mathematics related to the spring restoring force he stumbled into an atomic model with electron configurations that were close enough to the Rutherford model to lead Hans Geiger and Ernest Marsden to perform an experiment that revealed what became our modern understanding of the atomic nucleus.
Anyway, my point is this: there have been people asking what and why going back as long as we have written records, and I doubt that started with writing. So, with that, I want to share a few of the things that drive my curiosity. Things that I find endlessly compelling and make me keep asking “why?”.
But first, context. A lot of context. It’s important that you see the lens through which I view these topics, so I have a story to tell.
Einstein, Bohr, and the Foundations of Modern Physics
In 1935, Albert Einstein, Boris Podolsky, and Nathan Rosen published a paper titled “Can Quantum-Mechanical Description of Physical Reality be Considered Complete?”. This is commonly referred to as the “EPR Paper”, and the thought experiment proposed is often called the “EPR Paradox”. I’m not going to try and explain the whole thing here—partially because I’m layman and partially because if you aren’t already aware of this you probably wouldn’t find my rough explanation all that compelling—but the summary is basically this: Quantum entanglement, and in particular the behavior of entangled particles separated and then observed, seems to violate relativity if the quantum mechanical wave function is a complete description of the physical system. The relativistic violation comes in the form of the measurement of the spin state of one of the the particles instantaneously effecting the other particle, no matter how far away it is (yes, I know it’s more complicated than this, and there’s the criterion of reality from the paper, but that’s just another way of phrasing the relativistic violation).
So, very long story short: Einstein had some problems with quantum mechanics as it was being interpreted at the time. Ultimately, this led to his gradual slide into irrelevance. Those of you who’ve seen Oppenheimer might remember the conversation between the two about a scientist losing relevance—this is Einstein talking about what happened to him after he began questioning the Copenhagen interpretation of Quantum Mechanics, the preferred interpretation of Niels Bohr, who relentlessly campaigned for its acceptance to the exclusion of all alternatives. Bohr’s approach to physics was very much the precursor to “shut up and calculate.”
It is wrong to think that the task of physics is to find out how Nature is. Physics concerns what we can say about Nature.
- Niels Bohr
Bohr, and the Copenhagen interpretation of quantum mechanics, are very much focused on utility over philosophy. There was intense pressure to not pursue metaphysical interpretations of quantum mechanics. This could partially be seen as pragmatic—during World War II every moment spent pursuing the philosophy of physics is a moment not advancing its practical applications—but it had a long-lasting chilling effect on the philosophy of physics and foundational physics, a chill that has really only started to thaw over the past few decades.
It took almost 30 years, but in 1964 John Stewart Bell published “On the Einstein Podolsky Rosen Paradox”, in which he builds on the work of Bohm and Aharonov (two people, particularly Bohm, that were considered on the fringe by the Bohr acolytes) and essentially proves mathematically that there are constraints on the statistical measurement outcomes of more complex entanglement experiments. These were called the Bell inequalities.
It took a long time for our engineering to advance sufficiently to be able to fully perform every variant of the experiments necessary to bring the error all the way down to the constraints predicted by Bell, but over the last few decades of the 20th century, experimentalists John Clauser, Alain Aspect, and Anton Zeilinger performed all of the iterations of the experiments necessary to prove Bell right: any physical theory of reality cannot be both local and real. In other words, the universe we live in is not locally real. Local meaning objects can only be influenced by their surroundings at the speed of light (aka the speed of causality) and real meaning stuff has definite properties independent of observation.
To reiterate: the universe in which we live is not locally real, and this has been proven experimentally through results that can only occur in a nonlocal physical reality, defined through rigorous statistical calculations. For this work, Clauser, Aspect, and Zeilinger were awarded the 2022 Nobel Prize in Physics.
The EPR paper was written assuming locality. The implication being that the wave function can’t be a complete description of reality. However, later on Einstein began to contemplate non-locality. In a letter to Max Born in 1947, Einstein used the now-famous phrase “spooky action at a distance”, as he described how much he disliked this aspect of quantum mechanics. I have to imagine that this result, proving nonlocality, would be bittersweet for Einstein: vindication that something wasn’t fully understood, while also disturbing that physics does not always, as he put it, “represent a reality in time and space.”
I cannot seriously believe in it because the theory cannot be reconciled with the idea that physics should represent a reality in time and space, free from spooky action at a distance
- Albert Einstein, in a 1947 letter to Max Born
What should we make of this? I honestly have no idea. I don’t even want to attempt an analogy, and thinking about this one can feel some empathy for Bohr and the early pioneers of quantum mechanics. It isn’t hard to identify the religious connotations of the concept of non-locality—there exists some fundamental aspect of nature where time and location lose meaning to us, but is inexorably linked to and required for, well, everything based on how we define everything. Beyond this, even if you set aside any potential religious implications, there are still the implications that quantum mechanics challenges determinism, or a Einstein put it, “God does not play dice with the universe.”
The Copenhagen interpretation introduces the idea that particles have no defined properties until they are measured, which then requires “measurement” to be defined, leading to the “measurement problem”, all to avoid confronting some implications of the other interpretations (which I won’t get into here, but if you’re curious, go read about the Everettian interpretation). I think this discomfort with the implications of quantum mechanics drove both the preferred interpretation taught throughout most of the 20th century (and still taught today as the standard accepted interpretation), and the early efforts by Bohr and others to discourage questioning the metaphysical implications of quantum mechanics. Here’s the first part of that earlier quote from Bohr:
There is no quantum world. There is only an abstract quantum physical description. It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about Nature.
- Niels Bohr
I’m not explaining all this to prompt existential dread, but rather to provide sufficient context for the concepts I’m about to share. This article is about curiosity—specifically what I’m curious about—and in order to understand why I find these things curious, you need to be able to feel the mystery of them the same way I do, hence all the context.
We’re almost there, but I need to give you one example to help you see the connection between the physical world and the abstract mathematical world:
This thought experiment is about the questions you ask, and how the answers become less physical the deeper you go.
You’re told that the electron was deflected by an electric potential. So you ask, “what is an electric potential?”
“The electric potential is a scalar field,” you’re told.
“Ok, what’s a scalar field?” you ask.
“A scalar field is an assignment of real numbers to space-time points.”
So real numbers in space are making the electrons change direction?
I’m glossing over a lot of detail—voltage gradients and virtual photons with negative momentum being exchanged and all kinds of stuff. Things that no one considers to be “real”, just convenient mathematical conventions to help us make predictions so we can build things and make predictions. But going back to scalar fields—and fields in general, the fundamental part of quantum field theory—I don’t think anyone actually believes that physical reality is comprised of a bunch of numbers assigned to points in space-time (unless you’re Max Tegmark, I guess, but that’s an entirely different story). So the question is: if our universe is not locally real, and we are able to make fantastically accurate predictions using mathematical structures that don’t seem to have any metaphysical properties, how do we interpret the elements of those structures that extend beyond, through, and around what we consider to be our physical reality of three dimensions of space and one of time?
And so we arrive at the end of the preamble. I hope I’ve provided the right amount of detail to provide enough context without getting too stuck in the weeds. The most important things to keep in mind as you read through the rest of this are these two points:
The universe, our reality, has been experimentally proven to be not locally real—particles can interact across vast distances instantaneously as though they were actually physically located next to each other.
We’ve spent almost 100 years discouraging students from pursuing the philosophical and metaphysical implications of quantum mechanics, and instead have told them to “shut up and calculate” by saying quantum mechanics only applies to the smallest of scales, and is only relevant to measurements.
Spinors and the Spin-Statistics Theorem
You might have heard that electrons have something called 'spin.' While it's natural to picture electrons as tiny spinning balls, the reality is much stranger.
In quantum mechanics, electron spin isn't something physical like a ball just much smaller. Instead, it's a special property that we describe using math tools called spinors. Here's a simple way to understand how weird spinors are: Imagine turning something in a complete circle (360 degrees). Usually, it ends up exactly as it started, right? But spinors are different - when you turn them one full circle, they're actually upside down! You need to turn them twice (720 degrees) to get them back to where they started.
If you’re familiar with topology you may recognize this as a property of Möbius strips: you start at one point, follow a straight line completing one complete circuit and you end up where you started but on the opposite side (e.g. if you started on the exterior you’ll end up at the same spot but on the interior), and another full circuit will bring you back to your true starting point. Now, in this case you are still in a 3-dimensional space and the effect is due to topology, but it can be a helpful way to visualize the phenomenon of a 360 degree rotation resulting in returning to an inverted version of the starting point. Here’s an animation from The College of Wooster Physics Department that demonstrates exactly this:
This isn't just a mathematical trick - there seems to be a fundamental connection with the physical nature of reality at work. Spinors help us describe particles like electrons and protons, which we call fermions in the standard model. These particles follow a special rule called the Pauli exclusion principle, which simply means that no two fermions can be in exactly the same place and state at the same time - it's the reason solid objects don't pass through each other and why atoms and molecules stay distinct and stable.
Fermions have half-integer spin values (1/2, 3/2, 5/2, etc.), the impact this has on their wave function (antisymmetric) causes them to obey the Pauli exclusion principle. Bosons (photons being the one you’re likely the most familiar with) are integer spin meaning they have no problem passing right through each other, which gives us all the wonderful effects we see with light, such as constructive interference. This is the essence of the Spin-Statistics Theorem, proven by Wolfgang Pauli (of the Pauli exclusion principle) in 1940. It uses the mathematics of quantum field theory and relativity to show the deep, fundamental connection between a particle’s spin and its quantum state—everything, literally everything in the universe, follows from this connection.
So the fact that the mathematical description of fermions includes a property that involves rotations that both violate our common sense and experience of the world around us while also explaining a fundamental physical property of matter itself probably means something, particularly given the validation of Bell’s inequalities proving the universe is not locally real.
I frequently find myself contemplating what this means physically and have to stop myself—the structure of the question itself is already setting me up for failure.
Black Hole Entropy and The Holographic Principle
Have you ever seen a real hologram? The ones where everything is green and it’s a small image you can peer into and around?
It’s flat, but you can look around the image. As you tilt the image or move your head around, you actually seem to see inside the image, as though the image is a window into another world with three full dimensions. Stop for a minute and think about that. Somehow, a flat plane is showing you more information than your intuition would tell you should be present. Three dimensions worth of information is being encoded on a two-dimensional surface, and then the light that bounces off of that surface into your eyes is recreating that three-dimensional data. This is all being done with interference patterns. The actual image itself, if you were to look at the photographic plate under a microscope, looks more like a moire pattern than the final resulting image.
The light bouncing off of the photo constructively and destructively interferes to reproduce the light-field that was present in the original scene. The reason the hologram is always monochromatic (usually green), is that the light needs to be coherent so that it all reaches the right places at the same time, and different wavelengths of light can have different scattering and absorption properties.
So what does this have to do with black holes? We’re getting there.
The Bekenstein Bound
In 1972 theoretical physicist Jacob Bekenstein first proposed that black holes must have entropy, and that the maximum entropy is defined by the area of the event horizon, and not the volume of the interior of the black hole. Later, in 1981 he published his paper "Universal upper bound on the entropy-to-energy ratio for bounded systems" which led to coining of the term “Bekenstein bound”, which proves that the upper limit of the entropy of any region of space is defined by the area of a sphere enclosing that region of space.
So if you could take all of the knowledge of humanity, high resolution scans of every square millimeter of the surface of the earth, the recorded positions of every molecule of gas in the atmosphere every millisecond going back 10,000 years, and whatever other information you want to fill up a whole bunch of hard drives (use your imagination), and then you took all those hard drives out in space and started compressing them down, smaller and smaller, eventually you would compress them smaller than their own Schwarzschild radius and form a black hole. The Bekenstein bound says that all of the data on all of those hard drives could be encoded on the surface of the event horizon. You wouldn’t need the volume of the space to encode the data.
This is profoundly strange. Area is a squared value, volume is cubed. Area has two dimensions. Volume has three. Wouldn’t one more dimension—one more degree of freedom—fit more information? Think back to that hologram, where the entire light-field of a three-dimensional scene is encoded on a two-dimensional photograph.
AdS/CFT Correspondence and Holography
In 1995 Gerard ‘t Hooft and Leonard Susskind published “The World as a Hologram”, in which—I’ll just let Susskind explain it:
The three-dimensional world of ordinary experience—the universe filled with galaxies, stars, planets, houses, boulders, and people—is a hologram, an image of reality coded on a distant two-dimensional surface.
- Leonard Susskind
According to Susskind, he had this revelation as he was walking past an exhibit on holographic photography and began to opine on the way a three-dimensional scene could be encoded on a two-dimensional surface. He had been discussing black hole thermodynamics with ‘t Hooft and made the connection.
Three years later, on January 1st 1998, theoretical physicist Juan Maldacena published another one of those papers with a cryptic, mouth-full of a title: “The large N limit of superconformal field theories and supergravity.” The shorthand for what this paper proposes is the AdS/CFT correspondence, and it shows a mathematical equivalence between different theories of quantum gravity in n dimensions, and quantum mechanical theories in one fewer (n-1) dimensions. To put a finer point on it, the AdS part represents the “interior” volume with gravity and four space-time dimensions, and the CFT part represents the “surface” surrounding the interior, but without gravity and only three space-time dimensions. The interior is generally called the “bulk”, and that outer surface is the “boundary”. This paper has become one of the most-cited papers in high energy physics.
This mathematical equivalence has been a valuable tool for theoretical physicists as the same phenomena can be described in both the bulk and on the boundary, and one very obvious case where this could be valuable (assuming any of this is actually correct) is quantum gravity and doing away with the singularity inside a black hole. Since the boundary is n-1 dimensional from the bulk, and without gravity, there is no singularity on the boundary.
For Susskind and ‘t Hooft, they see the Bekenstein bound and the AdS/CFT correspondence as inexorably linked: if everything in the interior (the bulk) can be described by what’s happening on the n-1 dimensional boundary, that would make the universe a hologram. Hence, The Holographic Principle.
Do I believe that we actually live in 2 spacial dimensions instead of 3, and that the 3rd dimension is a holographic illusion that gives rise to relativity? I have no idea, and it wouldn’t make any practical difference to our day to day life one way or another. However, I find the idea fascinating, and when I think about non-locality, and how direction and distances mean different things when the number of dimensions change, I can’t help but wonder if there’s a deeper connection.
Closing
I could keep going, but that’s enough for now. Maybe next Friday I’ll write about the Higgs potential and the origin of mass.