My last post was a little ranty, perhaps. So lets be fair to the physicists. What physicists mean by randomness is that when they run an experiment, unpredictable results are seen. Furthermore, when viewed in aggregate, these unpredictable results perfectly match probability distributions of a certain sort. And given that there are no parameters one can control in these experiments to predict what the answers will be, the reasoning goes that we might as well consider them as random, and build our theory accordingly.
This is fine, IMO, so long as you’re not trying to build an ultimate theory of physics. It’s a good idea, even, in the same way that spherical cows are a good idea. However, if you’re trying to get the answer right, and describe the smallest levels of physical existence, then, by definition, mere approximations won’t cut it.
However, this assertion, on its own, probably doesn’t say, or explain enough. For instance, what about Bell’s Inequality? Bell’s Inequality experiments absolutely rule out local realism. Local hidden variable theories simply can’t work. Isn’t that reason a strong indicator that there is inherent randomness in the universe?
In short, no. This is because I can simulate Bell’s Inequality results in the comfort of my own home without resorting to quantum randomness once. This is doable because Bell’s Inequality says nothing about non-local hidden variable theories.
The most well known of these is Bohmian mechanics, an approach that was first presented in 1927. This method has been thoroughly explored by physicists, but most of them walk away from it fairly unsatisfied, because it requires that every point in the universe can have instantaneous interactions with any other. The math of Bohmian mechanics is set up to ensure that the answer comes out exactly as it does for classic QM, while keeping the system deterministic. But, given that this doesn’t add any expressive power, and makes the model non-local, that feels like a fairly poor compromise.
Fair enough. But Bohmian mechanics isn’t the only way to build a non-local theory. As we’ve pointed out on this blog, if you’re looking for a background independent model of physics, you have to start thinking carefully about how spatial points are associated with each other. And if you follow this reasoning in a discretist direction, you generally end up building networks, whether you’re into causal set theory, loop quantum gravity, quantum graphity, or any of the other variants currently being explored.
And, as soon as you start looking at networks, it’s clear that there are perfectly decent ways of non-locally connecting bits of the universe that are not only self-consistent, but provide you with tools that you can use to examine other difficult problems in physics.
If I seemed to be disparaging physicists for not considering hidden determinism in the universe in my last post, that was not my intention. I certainly don’t mean to poke the finger at any specific individuals, but I do believe that poking the finger at the culture of physics in this regard is important.
We have experimental evidence of the non-locality of physical systems. However, we have no evidence that the universe runs on a kind of non-computable, non-definable randomness that flies in the face of what we know about information and the mathematics of the real numbers. Doesn’t that mean that we should be working a little harder to put together some modern deterministic non-local theories? Is it really better to hide under the blankets of the Copenhagen interpretation because this problem is hard?
After all, while issues of interpretation are broadly irrelevant given most of the day to day business of doing physics research, there is the small matter of quantum mechanics and relativity remaining unreconciled for the last hundred years. I would venture to propose that if we ever want to close that gap, having the right interpretation of quantum mechanics is going to be an important part of the solution.
Ars Technica has a nice article on a piece of theoretical work done by J D Bancal, et al. The upshot of it is that if your explanation for how quantum mechanics works is anything other than non-local, leaves open the possibility of faster-than-light communication. (Thanks to Dan Miller for pointing me at it.)
I have mixed feelings about this idea, as I’d love for faster-than-light communication to be a possibility, and am delighted that someone has come up with a way of determining whether it can be done. However, the flip side of this is that I’m pretty certain that QM is fundamentally non-local, as I outlined in my post on replicating particle self-interference. The notion here being that non-locality doesn’t rule out discrete models. If anything, it supports them, as it encourages to think of wave-functions as sets of non-locally distributed points, either finite or otherwise.
What this result doesn’t say, unless I’m missing something, is that the currently fashionable, complex-number-based model of QM is literally true. You can still take exactly the same result and reframe it in terms of another equivalent model, such as Bohmian mechanics, for instance, and get something that looks completely deterministic.
Hence, while the result is nifty, the goal posts for viable theories of physics remain doggedly where they were.
In the last few posts, I’ve talked a fair bit about relativity and have struggled to make my thinking on the subject clear enough to read. What that process has revealed to me is that some topics in science are just hard to talk about. In part, that’s because they’re counter-intuitive, but there’s a lot more to it than that. A lot of what’s going on is, I’d propose, social, and deeply concerning about how we engage with science.
Open any number of pop-science books that attempt to give you a grand overview of the universe and somewhere near the start there are usually the same two chapters. One of these is on relativity and the other is on quantum mechanics. These chapters are the author’s attempt to explain the ‘wacky’ things that happen in physics. In most cases, the author ends by saying something like, “this might sound incredible, but it’s what we see in experiments, so suck it up”.
And this is usually where real scientific dialog with the public stops. Subsequent chapters in these books are usually short on specifics and relatively thick on prose like “Geoff and I were sitting eating a sandwich, feeling sad, and suddenly it occurred to me that if we ran the same simulation backwards, it would give us the eigenvectors we were looking for, only with the parameters inverted! We raced back to the lab without even finishing our lunch!”
Different books make the break in different places but the effect is usually the same. The physicist in question gives up on trying for an intuitive explanation of what they were doing and resorts to personal drama to try to retain reader interest.
Underpinning this switch is the belief that the only way to really understand the ideas being discussed is to do the math. Without the math, you just can’t get there. At some level, the math is the understanding. I take issue with this notion pretty strongly. Not only is it dead wrong. It’s counter-productive. In fact, it’s an angry badger driving a double-decker bus into the side of the temple of science.
Let’s go over some of the problems that this ‘math equals understanding’ approach creates.
First, it causes the public to disengage. People feel that if they aren’t good at math, they’ll never get it. Yet life goes on, so science can’t possibly be relevant to them. And, at the end of the day, this creates funding problems.
Second, and far worse, is that the people who do the math and get the answer right feel like they have understood it, even though deep down, it still doesn’t make any sense. They sweep that feeling under the rug and press on but become increasingly defensive when pressed on topics that make them feel uncertain. This just makes the gulf between scientists and everyone else all the wider.
On top of this, attempts to communicate the math, rather than the meaning, to the public end up creating a folk-notion of how physics ‘has to be’. This creates a whole stew of junk reasoning when people try to extend that folk-notion. For instance, in relativity, people are told that you can’t go faster than light because if you did, you’d be travelling backward in time in someone else’s reference frame. This is incredibly, insanely wrong. And it’s just one step from there to “if I go faster than light I go backwards in time”.
Perhaps most horribly of all, this process creates physicists who can’t uncouple the tools they’re used to using from the problems they’re trying to solve. This creates massive blind-spots in the reasoning of some of our brightest and finest researchers, because these people are never tested to see whether they have understood the principles in the absence of the math.
Here’s an example from relativity: “spacetime exhibits Lorentz-invariance”. This might sound fine, until you think about the fact that we can only ever examine spacetime by passing things through it. We have no idea what properties spacetime exhibits, because we can never directly test it. All we can know about is the things we can observe. Saying that test on moving objects yield a pattern of Lorentz invariance is fine, but often, that’s not what’s said.
Here’s another relativity example from my own life. I sat down in a cafe a few years ago with a grad-student in particle physics to talk over some things I wanted to understand. We got on to the subject of using a compact dimension for spacetime interval in the way I outlined in the last post. He pulled a face.
“I don’t think you can do that with just one dimension,” he said. “I think you need three.”
We debated the point for some time, even breaking out some equations on a napkin. In the end, he still wasn’t convinced, though he couldn’t say why, or point out a hole in my reasoning. All this despite the fact that his math skills were far in advance of my own.
Why did he make the assertion that he did, even though fifteen minutes of basic logic crunching could have demonstrated otherwise? Because the way relativity is taught makes use of the idea of Lorentz boosts. People use six dimensions to model what’s going on because it makes the math easier. They never just use one dimension for s. This fellow, extremely bright and talented though he was, was wedded to his tools.
So where do we go from here? What do we do? If science has a problem, how do we solve it?
I’d propose that all math can ever do is supply a relation between things. “If this is true, then that is true”. Math gives you a way to explore what the implications of an idea are, without ever saying anything about the idea itself, other than whether it’s self-consistent. In essence, math in physics tries to describe how things behave solely in terms of constraints, and without ever trying to provide an implementation. In other words, it deliberately avoids saying what something means, and says only what it does. This is because meaning, I’d propose, is a property that comes with a choice of specific model.
This is why physics tends to become fuzzy and unsatisfying when it diverges from physical experience. We can describe relativity or quantum mechanics easily using math by defining the constraints on the behavior we see. However, we are used to having a specific model to back our reasoning up–the one provided by intuitive experience of the world. When that model goes away, we lose touch with the implications of our own logic.
Does this mean that we are forced to rely on math for insight at that point, as is commonly proposed? No. In fact, I’d suggest that the reverse is true. This is the point at which we should trust math less than ever. This is because self-consistency is only as good as the conjectures you apply it to. I think it was Bertrand Russell who said that from a false premise you can prove anything. The only way to determine whether our physical premises are correct is to have more than one way at arriving at confidence in their validity. That’s why physical intuition is a vital tool for preventing self-consistent nonsense from creeping into theory.
Hence, instead of just leaning on our analytical crutch, we should strive harder than ever to find metaphors for physical systems that do work, and which bring phenomena such as relativity within easy mental reach.
And this, to my mind, is exactly where digital physics can help. Digital physics asserts that we should only consider a physical theory reasonable if we can construct a viable implementation for it. If a system is self-consistent, but non-implementable, then we shouldn’t expect it to match nature, as nature clearly is implemented, by virtue of the fact that we are witnessing it. By requiring concrete implementations, we force ourselves to create metaphors with which to test our understanding.
In other words, if the math leaves us asking the question, ‘what does it all mean?’, then we haven’t done enough digital physics yet.
Does this mean that any one of the implementations we pick is correct? No. In fact, the more workable implementations, the better. Digital models are not theories.
Does it mean that digital physics represent a substitute for mathematical reasoning? No, of course not. Math lies at the heart of physics. It just can’t exist in a vacuum of understanding.
Digital physics, then, is a different tool, through which the set of theoretical models of nature can be tested and understood. It’s a way of ruling out theories that don’t add up even if the math works out. It is, I would propose, the best antidote to Geoff and his half-eaten sandwich that physics has going for it.
This week, I had a very interesting discussion with someone who I had never met, who had a digital physics idea that they wanted to share. I found myself in the position of giving feedback on work I was not familiar with, and it occurred to me that I should say something about it on this blog. I want to make it clear how I feel about citizen scientists, the concept of ‘crackpots’, and digital physics in general.
First, let us be completely honest. Digital physics is considered a crank topic by many mainstream physics. You need look no further than the blog of Lubos Motl to see just how fervently this is felt, or the level of anger that that can be directed towards the notion of a discrete universe.
For the most part, the reasons for this contempt are down to laziness. Those who don’t care to engage assume that a digital universe must involve a cartesian spatial grid on which some number of cells are turning on and off–the classic CA approach. This picture looks utterly incompatible with either quantum mechanics or general relativity, so they consider the entire notion to be stupid.
Those who do engage attempt to transfer the familiar tools they are used to using, the Minkowski metric, quantum fields, etc, into the discrete domain without modification. When they discover that this approach fails, they consider that they have given the idea a try and that it’s clearly inadequate. Usually, they do not look any deeper.
However, there is another reason why people have contempt for discrete approaches. That’s because they are both intuitively easy to grasp and easy for amateurs to explore with computers. This means that a great many people who are fascinated by science can perform basic simulations and become excited with the suggestive patterns that they find. Feeling that they have something to contribute, these people suddenly become the most vocal, amateur, would-be contributors to physics.
For professionals who have worked hard to carve out a place in an extremely competitive field, suddenly being vigorously courted by people claiming to have new physical theories can be galling. This is particularly true when those doing the courting have no notion of what has been tried already, incomplete grounding in physical mathematics, and an apparently unshakeable conviction that they have discovered something immense.
The simple fear of an encounter with someone who might be like that is enough to send some physicists running. I know because I have seen them run.
What is utterly stupid about this state of affairs is that those members of the public who are most interested in physics and most willing to engage often end up feeling the most shut out. Physics, particularly particle physics, is a field struggling for funding at a time when the cost of running groundbreaking experiments has skyrocketed. To throw away contact with those members of the public most likely to act as cheerleaders for the field doesn’t help anyone. Furthermore, disengagement from a public who want to exercise skepticism means that confidence in abstruse domains of physical theory, such as string theory, becomes ever harder to attain. How are the public to differentiate between M-brane theory and their own concoctions when dialog is expected to be one-way, as if from priests to the masses? The answer is, usually they do not, and frankly, should not.
How do we fix this? Work is needed on both sides. The physics community needs a better attitude towards so-called ‘crackpots’. Often such people are usually not crazy or stupid, just untrained and enthusiastic. Physics needs to find more things for interested members of the public to do, and more explicit ways for amateurs to help out. It needs to swallow its fear of strange people (an irony in itself). Guidelines for public engagement need to be written, to ensure that there is more of it, not less. If there are common misconceptions about physical theory that amateur theorists fall foul of, they need to need to be pooled, and collated as a series of challenges.
Having said this, the bulk of the work lies on the shoulders of aspiring citizen scientists. Professional physicists hold themselves and each other to incredibly high standards. They have little patience for would-be contributors who seemingly do not. This means that anyone from outside the field who wants to join in needs to do their level best to hold themselves to levels of rigor at least as high. Their work needs to be transparent, fully logical, and expressed in terms that makes it as easy as possible for physicists to read. Anything less than that is simply not good enough.
I have been incredibly lucky. My wife is a prize-winning astronomer. My housemate is a cosmologist. I have many dear friends who are physicists and mathematicians. Without exception, they have called me out when I have made statements I cannot substantiate. They have forced me to examine my own work with a critical eye. They have been unrelenting in making me describe what I have actually achieved, not what I would like to imagine I have done.
I believe that all citizen scientists can do this. Furthermore, we can do it for each other. We can, and must, exercise the highest degree of skepticism in our own work that we possibly can. Otherwise, we will never be heard, and the science we love will pay the price.
In this blog, we’ve talked a lot about particles, relativity, quantum mechanics, and even the reason for the universe itself. One important topic that I haven’t yet covered is spacetime. Where does it come from and why does it take the form that it does? Any Grand Unified Theory that we’d like to propose can’t just satisfy itself with describing the matter and energy that makes up the things we see. It also has to explain how the gaps between the things come to be there. In other words, it needs to be ‘background independent‘.
This feature has also been conspicuously absent from all of the research I’ve shared so far. In each case I’ve outlined, I’ve simulated space by sprinkling dots onto a preexisting smooth surface and hooking them up to those nearby. This isn’t good enough. In fact, it’s avoiding one of the hardest problems of the lot, and the physics community know this. If you look at any of the most promising research on discrete approaches, the main focus is on the structure of spacetime itself and how it changes. From that, it’s felt, everything else can spring.
People have had mixed success in this regard. There’s loop quantum gravity, which has been a relatively successful physical theory. However, at least as I understand it, it presupposes structures that have the four dimensions of spacetime we expect.
There’s the theory of causal sets, which starts with nothing but the idea of a partial order, and which can derive something roughly spacetime-like from it. However, reconciling it with quantum mechanics has proven tricky.
Then there’s causal dynamical triangulation, which has successfully assembled spacetime-like structures out of very simple raw ingredients. However, those ingredients once again have an implicit four-dimensionality built in at the smallest scales.
Do I have a model of spacetime to share with you that’s better than any of these? No. Categorically not. As with all of my research, I’m deliberately not trying to do physics directly. Instead, my goal is simply to illustrate ways that discrete techniques might make solving thorny physics problems easier, and to add to the theoretical toolkit with tricks from computer science.
What I do have is a way of building large, irregular networks from scratch that behave like smooth spatial surfaces, while using no geometrical information whatsoever. I’m going to share it with you over a sequence of posts. You’ll have to assess for yourselves whether you think it’s a good fit for nature.
As a starting point, let’s look at a simplified version of the problem. We’ll forget about time, and concentrate on only a single dimension of space.
Imagine you have fifty friends who you’re playing a party game with. The aim is to use your cellphones to form an invisible circle. When the circle is finished, you’ll be able to call Alice. Alice will then able to call Bob. Bob can call Cindy, and so on. At the end of the chain, Zachary can call you and tell you what message he received. The message will have gone through everyone in turn.
Each person is allowed to store the numbers of up to two friends on his phone. They can swap their numbers for others by calling one of their contacts and saying ‘who do you know?’ and picking which numbers to keep or discard. They can also say to someone, ‘you’re my friend now’. They can’t say anything else, or rank the contacts they receive by name or number.
At the start of the game, the numbers in everyone’s phones are random. How do they organize themselves into a chain?
As party organizer, you have one extra perk you can use if you want to. You can add people to the party one at a time if you like. If you decide to do that, people will receive their random phone numbers when they join, and the numbers they receive will always be for people who’re already at the party.
In the last couple of posts, I’ve been showing you how to go about simulating quantum effects in the comfort of your own laptop. Sound impossible? It should do.
Quantum Mechanics is usually described as mysterious, truly random, and inherently non-computable. We’re told that it’s a topic that should cause us to ask deep and difficult questions about the nature of reality, and that it might even be connected to human consciousness.
This, in my humble opinion, is hogwash. I think QM is straightforward, mundane, and something that can be understood concretely by anyone by using simple algorithms. No complex numbers. No wave equations. No Hilbert spaces. This is not to say that I have a new theory of physics to trumpet, because I don’t. My purpose is simply to demonstrate that if people are having trouble reconciling Quantum Mechanics with Relativity, it might simply be because they’re looking in the wrong place.
Last time, I got as far as showing you how to make a self-interfering excitation wave. Let’s remind ourselves what that looked like.
Mostly, at this point, this just looks like a pink smush. Not terribly impressive. So in order to show you a little more about what it can do, let’s first cover a little background about the nature of waves to make sure we’re all on the same page.
Issac Newton thought that light was made up of particles and everyone agreed with him for a while. Then Robert Young came along (as well as several others), and pointed out that light experiences diffraction, and so it had to be a wave.
Cut two slits in a cardboard sheet and shine a light through it, and you get wave interference on the other side. Here’s his famous sketch of the process.
And here’s what that looks like if you hold a second screen up to look at the pattern that the interference makes.
As you can see, we get stripes. The reason why this pattern is important is because if light is a particle, it can only be in one place at a time, and so can’t interfere with itself. So getting a pattern like this shouldn’t happen for particles.
So before we get on to talking about quantum effects, let’s first check to see how our excitation wave works when we put it through a screen with two slits in it. We do this by taking our network and cutting a line in it. Then we only allow nodes on either side of the line to join up if they’re sitting very close to a pair of points we’ve selected.
Here the wave has hit the first screen, and is just starting to peek through the two holes.
And here the waves from the two holes have started to overlap.
The results look a little fuzzy perhaps, but our method appears to be working. Try comparing it to Young’s sketch above. However, I still haven’t said anything about quantum effects. And that’s where things get interesting. So next time, I’ll make a point of revealing all.