Physical theories are often presented as a description of what’s really going on. Forces act on a baseball, causing it to fall. Atoms collide and fuse in the heart of a star, releasing heat and energy. Science is true, as is often said, and our scientific theories encapsulate this truth. But this isn’t entirely true. 

The probability distributions for hydrogen in different energy states.

For example, quantum mechanics is a strange, sometimes confusing theory. Objects can be particles and waves. They do strange things like tunnel through barriers, and can even appear and disappear.  Given all this strangeness, what’s really going on? What’s the true nature of quantum reality? It depends on which approach you want to take. In one view quantum objects are described by a wave-like probability function. When you interact with or “observe” the object this “wavefunction” collapses into a definite state. That’s view commonly presented, but a quantum system can also be described by its transitions between energy states. Since this uses a mathematical method involving matrices, it’s known as matrix mechanics. Both wavefunctions and matrix mechanics give the same results, but their view of what really goes on is very different. Then there’s the path integral method. Rather than a wavefunction or matrix transitions, path integrals imagine quantum objects can take almost any path between two states. By summing all the possible paths you can derive the odds that it will occur.

The matrix transition version of quantum theory doesn’t care about the wavefunction.

So which one is true? Are quantum objects distributed waves of probability? Are they simply transitions between energy states? Do they take an infinite number of paths between states? Each of these models make the same predictions, so one version is no more “true” than the others. What happens in practice is that we’ll use whatever method is useful at the time. They are equivalent models, so the best model for the job is the one we’ll use. The only reason the wavefunction view is so common is that it’s the version usually taught to introductory students.

You might think this uncertainty of truth is due to the behavior of quantum physics itself. It’s so strange and counterintuitive that we can’t wrap our puny brains around what’s really going on. But the same thing occurs in lots of other fields. Even something as straight forward as basic Newtonian physics.

In the path integral view many potential paths are summed.

Toss a baseball in the air and Earth’s gravitational force pulls it down. The force of gravity is a simple truth, right? While we often describe classical motion in terms of forces and acceleration, we can also describe it in terms of energy and momentum. In the Lagrangian and Hamiltonian approach, the path of a baseball is the optimized path among possibilities. In this view a baseball’s path is the extrema of an energy equation, and force can be derived as a necessary consequence of this. In the relativistic view the baseball follows a geodesic, which is the minimal path through space and time. So is a baseball’s motion due to a gravitational force, an energy extrema, or a spacetime geodesic? As with quantum theory, different approaches yield the same result. They are mathematically equivalent, so we can use whatever method is most useful at the time.

At its core, science is less about truth and more about models. The metaphysics underlying a model is useful only as far as it allows us to make better predictions, generate new ideas, or bring models together as a cohesive whole. This is why we have no problem using classical gravity to calculate the path of a spacecraft through the solar system, while using special relativity to account for the Doppler shift of the spacecraft’s radio signals. It’s why we can use quantum physics to study atoms in the morning, and general relativity to study black holes in the afternoon. In regimes where models conflict with each other it isn’t a failure of truth, but instead shows an opportunity to develop a better model.

It could be that with each better model we move closer to the truth about reality. The truth is out there, and science strives to move towards that truth. It’s a common view, and certainly the search for truth has driven many scientists to develop better and better models. But the real power of science is the recognition that what we have are models. Our models can be powerful, but they are always a bit tentative. There’s always a chance that they might just be an illusion of truth.

The post The Illusion Of Truth appeared first on One Universe at a Time.

Elon Musk thinks we probably live in a virtual universe. Meanwhile scientist have shown that wormholes can be traversed by spacecraft. Perhaps they’re used by nearly a trillion alien civilizations that live in our cosmos. 

At its core, science focuses on evidence. Models are tested against the evidence we have, so that over time a confluence of evidence allows us to refine scientific theories into something that’s reliable and predictive. There’s always a chance that a newer, better theory will replace an older one, but our focus on evidence keeps us from straying into wild speculation.

That doesn’t mean we can’t sometimes speculate about what might or might not be. Exploring “what if” models can be a great way to push back against the assumptions of a model. Debates about metaphysics and the philosophy of science can help keep us honest about the limits of a theory’s power. While these speculations aren’t necessarily science, they play a role in the scientific process. Unfortunately there is often confusion in popular media about the difference between what might be and what is.

Take, for example, the idea that we live in a virtual universe. The basic argument is that if it’s likely that civilizations far more advanced than ours can arise in the universe, and they have a good chance of simulating aspects of their past, then odds are we are living in a simulated world. Statistically its more likely that we are a simulation of pre-singularity humans than actually living in that rare time period. The argument is a philosophical exploration about the limits of what we can know, and has a long history tracing back to descartes’ demon and Plato’s cave. The often-referenced work by Nick Bostrom doesn’t claim we are living in a virtual world, but rather argues we can’t simply discard the idea out of hand.

Then there’s the idea that wormholes might be traversable. Wormholes are a hypothetical idea that has been studied for decades, including how they might be traversed. The latest work on the idea focuses not on spaceship travel, but on how microscopic wormholes might allow elementary particles through. It’s a mathematical study of the limits of general relativity. It’s less about proving wormholes real and more about pushing an established model until it breaks to see how it works.

But what about alien civilizations? Have we finally proved they’re out there? No, the latest paper on alien civilizations is a study of the observational constraints on alien civilizations. We now have a good handle of just how many potentially habitable planets there are in the Universe, at least on a broad order of magnitude. They’re extraordinarily common, and that means there could be trillions of alien civilizations out there. There could also be no civilizations other than ours. It really comes down to how rare the formation of life on a world actually is. Even if civilizations are common, it’s quite likely that we simply won’t meet up with them.

While each of these ideas might be true, there currently isn’t evidence to support them. They may lead us to new ways of seeing the Universe, or they may just end up a false, but cool, story.

Paper: Nick Bostrom. Are You Living In A Computer Simulation? Philosophical Quarterly, Vol. 53, No. 211, pp. 243-255 (2003) DOI: 10.1111/1467-9213.00309

Paper: Gonzalo J Olmo, et al. Impact of curvature divergences on physical observers in a wormhole space–time with horizons. Classical and Quantum Gravity, Vol 33, No 11 (2016) DOI:10.1088/0264-9381/33/11/115007

Paper: A. Frank and W.T. Sullivan III. A New Empirical Constraint on the Prevalence of Technological Species in the Universe. Astrobiology, Vol 16, No 5 (2016) DOI: 10.1089/ast.2015.1418

The post Cool Story, Bro appeared first on One Universe at a Time.

If you ever want an interesting conversation with a physicist, ask them about free will.

On a basic level, free will is the ability to choose between different possible outcomes. For example, Neo freely choosing between the red pill and the blue pill in The Matrix. Most of us feel like we have this ability to choose. Our inner dialog seems to have an act of choosing between options. But a basic assumption of physics is that the universe is governed by physical laws which strictly limits the behavior of physical objects.

In classical Newtonian physics these laws are deterministic, meaning that if you knew the exact initial state of a system, you could predict the state at some future time. At no point would the system choose one outcome over another. It doesn’t make any sense to say that a baseball chooses to fall under the influence of gravity, for example, any more than it would for a skydiver to jump out of an airplane and then choose not to fall. Free will doesn’t come into it.

You might think that quantum theory gives you an out, since quantum mechanics is not deterministic, but that isn’t the case. Free will requires a choice between outcomes, not simply a probabilistic outcome. A common misconception in quantum theory is that quantum objects like photons electrons conspire to prevent us from knowing about a system. In the mathematical formalism of quantum theory, however, the probabilistic outcome is determined by the state of the system. Randomness is not free will.

What’s interesting about all this is that the usual metaphysics of quantum theory assumes some form of free will. Experiments such as the EPR Experiment presume that the observer is free to choose what to measure independent of the state of the quantum system. So basically we assume free will within a system that has no free will. No one ever said that physicists made good philosophers. Of course the counter argument is that even with this implicit observational free will, the predictions of quantum theory match reality to an extraordinary precision. Newton made incorrect assumptions about the nature of space and time, but his physics still works quite well. The same can be said of quantum theory.

There are approaches that try to overcome this metaphysical paradox, such as superdeterminism. The basic idea is that there are non-local “hidden variables” in a quantum system, but that they occur through the historical interactions between system and observer rather than being a real-time conspiracy of the quantum system. The downside of this approach is that the EPR experiment is agnostic on superdeterminism, so you’d need a different kind of experiment to test it. Since quantum theory already works quite well, superdeterminism is relegated to the back burner of physics. It might be interesting in the future, but for now, who cares?

Just to be clear, the fuzzy metaphysics physicists typically use doesn’t mean quantum theory is unfounded. It does, however, point to an interesting conundrum in modern physics that we haven’t fully resolved. Since free will seems intuitively correct, most physicists hold onto it without really thinking about it, and since it works well enough for most physical systems, there’s no real push to change.

But given what we know about the universe, how could we do otherwise?

Paper: Sabine Hossenfelder. Testing superdeterministic conspiracy. Journal of Physics: Conference Series 504 (2014) 012018. arXiv:1105.4326 [quant-ph]

The post Wants And Needs appeared first on One Universe at a Time.

Everything you experience is experienced from your personal perspective. That seems like a rather obvious statement, but it also applies to humanity as a whole. Everything we experience in the universe is from our point of view. Cosmologically that view is a very narrow window. Humanity has only been around for a moment of cosmic time. We see the heavens from the vantage point of a small rock orbiting a medium star. Our comprehension of the universe is framed by the biases of our primate minds.

It is this idea that is encapsulated by a philosophical idea known as the anthropic principle. Of all the ideas in astronomy and cosmology, the anthropic principle is perhaps the most controversial. Despite its name, there are in fact several variations of the anthropic principle.

The Weak Anthropic Principle states basically what I summarized in the first paragraph. Our view of the universe is not random. It is biased by the fact that we are observing it. For example, we observe a universe that is billions of years old because it takes billions of years for planets to form and life to evolve.

The Weak Anthropic Principle is simply a reminder that we shouldn’t read too much into observations that seem special. I live in the United States, so a random sampling of people around me finds that most speak English as their first language. I can’t presume however that humans speak English as their first language, because my sample is biased by my location. Someone living in Japan would find that most people speak Japanese.

The Strong Anthropic Principle is more controversial. It states that the universe as a whole must have conditions necessary for life such as ours to exist. For example, gravity in three spatial dimensions allows for stable planetary orbits, but gravity in four-space doesn’t. If the universe had expanded more quickly than it did, then stars and galaxies wouldn’t have formed. Too slowly and it would have collapsed back on itself.

On the one hand the strong principle is rather obvious. If the universe was too different from the way it is (gravity too strong, speed of light too small, etc.) then we wouldn’t be here. But this fact is sometimes used to argue a stronger version of the principle. Specifically, the fact of our existence means the universe must be fine tuned to a set of conditions that allows us (or a similar sentient species) to exist. This idea was first proposed by Brandon Carter in 1974, and it has stirred controversy ever since.

But that’s a story for another day.

The post Self Centered appeared first on One Universe at a Time.

I’ve been getting a flurry of emails from revolutionary armchair scientists again, largely due to the recent post I wrote over at Starts With A Bang! Whenever several new theories arrives in my mailbox, they all start sounding the same. A bit of praise for my article/website/etc. and then a long diatribe on the errors of modern science followed by a link or attachment for the new and revolutionary idea. The genius of these new ideas are self declared, much along the lines of Vizzini in The Princess Bride, who declared that compared to him, the great philosophers were morons. Although its easy to see the absurdity in a self-declared scientific genius, it is similar to an attitude taken by some scientists with a dim view of philosophy. Plato, Aristotle and Socrates may have been deep thinkers, but philosophers are idiot scientists.

Except they aren’t.

Of the big three philosophers, Aristotle is most often claimed as a scientist. That’s likely because of the three Aristotle’s philosophy is most similar to that of modern science. He didn’t conduct experiments, but he did take the position that observation of physical phenomena could lead to understanding of the world around us. He talked about cause and effect, and developed a set of rules that he argued governed (or at least described) the behavior of the universe. Aristotle’s cosmology held as the dominant model of the solar system until the 1500s.

Plato’s Timaeus looked at aspects of the physical world, which Plato distinguished from the eternal world of forms. In his physical universe matter consisted of the elements earth, air, fire, water, and ether. The idea that matter could consist of a mixture of different fundamental things helped give rise to the idea of chemical elements centuries later. Plato also explored the way in which the universe could have arisen in the first place. His ideas were deeply influential to medieval philosophers and theologians, and led to concepts such as the ex-nihilo origin of the universe. This later inspired Georges Lemaître’s proposal of the big bang.

Socrates famously never wrote anything down, but his ideas come to us through Plato’s writings. Socrates is most famous for his method of getting to the truth of things by asking questions rather than assuming knowledge. It’s an approach that inspires much of modern science. Socrates also explored aspects of metaphysics. In Plato’s dialogues, for example, Socrates is seen to emphasize mathematics as a description of the world, which is a foundational aspect of modern science.

Of course the works of Plato, Aristotle and Socrates inspired later philosophers to explore other aspects of the cosmos, from Descartes’ exploration of the nature of space and time, to Karl Popper’s ideas of falsifiability, all of which has heavily framed modern science. Although we praise Newton’s work as a scientist, one of his largest influences was his philosophical position on what constitutes a scientific model.

Despite this, philosophy and philosophers are still viewed as rather useless to scientists. Part of this is due to the fact that modern science relies on observational and experimental evidence as the final arbiter of truth. In a contest between experiment and theory, experiment always wins. Philosophy is often seen as arguing over things that are either unanswerable or answerable by experiment. Why spend days arguing over the number of teeth in a horses mouth when all you need to do is find a horse and start counting?

Our modern world is so deeply rooted in scientific thinking that it can be difficult to recognize the philosophical roots of our modern worldview. It’s easier to think of past generations as wrongheaded and ignorant rather than adherents to a different metaphysics. And this is one of the reasons science needs philosophers. It’s always good to have a bit of pushback against your assumptions. Philosophers aren’t scientists, so they are free to explore ideas that (at least for now) are scientifically unproductive.

And that’s part of the reason I don’t really mind the Vizzini’s of the world. Most of their ideas are easy to disprove, and it’s always good to see things from another perspective. If all else fails, I could always challenge them to a battle of wits.

The post Plato, Aristotle, Socrates? Morons appeared first on One Universe at a Time.

Ludwig Boltzmann was a physicist who developed statistical mechanics, which connects Newtonian physics of particles to thermodynamics.  Boltzmann’s kinetic theory not only explained how heat, work and energy are connected, it also gave a clear definition of entropy. While this revolutionized our understanding of everything from heat to the universe, it also led Boltzmann to a rather puzzling idea known as a Boltzmann brain.

The pressure, temperature and volume of a gas is known as the state of the gas. Since these are determined by the positions and speeds of all the atoms or molecules in the gas, Boltzmann called these the microstate of the gas (the state of all the microscopic particles). For a given state of the gas, there are lots of ways the atoms could be moving and bouncing around. As long as the average motion of all the atoms is about the same, then the pressure, temperature and volume of the gas will be the same. This means there are lots of equivalent microstates for a given state of the gas. Basically what Boltzmann found was that the entropy of a system in a particular state depends on the number of equivalent microstates that state has.

This explains why entropy within a system increases.  Odds are, any physical system you have will tend toward a state with more microstates, since a state with few microstates (low entropy) is statistically much less likely to happen. But of course the catch is that statistically improbable is not the same as impossible.  Boltzmann supposed that if the universe were a vast sea of particles, it would be possible for particles to come together to form the state of your conscious brain, just as it could come together into the universe we see around us.  But which is more likely?

It is kind of like the classic example of monkeys banging on typewriters (or astrophysicists on laptops).  Let them bang around randomly for long enough, and there is a chance they will type out the complete works of the Library of Congress.  Of course it is far more likely that they will bang out To Kill a Mockingbird. In the same way, if the universe is a collection of microstates, then it is more likely to find itself in a conscious state that thinks it is in a universe rather than the entire universe itself.  That is, a Boltzmann brain is more probable than a universe.

Just to be clear, should not be seen as convincing evidence that you are a brain in a vat, or that we are all living in a virtual world. The idea of a Boltzmann brain is much like the idea of Schrodinger’s cat.  Both are examples of physical models taken to their extreme to find weaknesses in the model. In the case of Boltzmann brains, one flaw is the assumption that universe is simply a collection of microstates.  We now know that the universe began as a low entropy state of high density and temperature (aka the big bang). It then progressed via the laws of physics into atoms, stars, solar systems and a rocky little world where living things evolved over billions of years.  Your brain and the Library of Congress are not random states, but what hydrogen does over 13.8 billion years.

At each stage in the history of the universe, the overall entropy has increased.  Pockets of lower entropy such as living organisms are only possible due to higher entropy sources such as the Sun.  In the same way refrigerator can make things cold (lowering their entropy), but it must use energy to do so, and it creates more waste heat than it removes from the fridge. Overall entropy still increases. This, by the way, means the next time someone uses thermodynamics to deny evolution, you should point out that by the same argument their refrigerator shouldn’t exist.

A basic diagram of eternal inflation.

Of course there are those that argue the ordered universe solution to Boltzmann’ brain is simply kicking the can down the road.  While it is true that the early universe was a low entropy state, that doesn’t explain why it was a low entropy state. One solution to that is early cosmic inflation. The kind that BICEP2 hopes to have found. While inflation can solve the low entropy problem, it can also allow Boltzmann’s brain to reappear.  That’s because there are versions of inflation where regions of the “multiverse” are inflating all the time.  In this model our universe just happen to arise out of a local inflationary fluctuation. But if that’s the case, what is to prevent a Boltzmann brain from arising from a smaller fluctuation, and which is more likely?

All of this is pretty speculative, so it’s important not to take the idea too literally. What makes the Boltzmann brain idea interesting is that it helps us examine the most bizarre and puzzling aspects of our physical theories.

It’s enough to baffle anyone’s brain.

The post Boltzmann’s Brain appeared first on One Universe at a Time.