Cosmic Invariance

If the universe is truly cyclic in nature, does that mean its evolution is as well? In cyclic cosmologies, the universe expands from a singularity and evolves, mostly according to Newton's laws of motion (let's leave quantum effects out of the picture for now). From the starting singularity, there's a burst of energy and expansion. As particles expand outward, they come into contact with one another - they trade energies, repel, coalesce with new momentum and continue on their way. In this respect, the analogy of a game of pool is very apt. Think of the starting singularity as the initial break and the subsequent motions and interactions all under the control and guidance of Newtonian mechanics. If you knew the exact position and momentum of each and every particle, you could figure out where any one would be and what it would be doing a billion or one hundred billion years from now. In short, the universe is deterministic and clockwork for the most part. Furthermore, and more to the point of this post, the universe appears to be a closed system like a box of gas or a pool table with balls in motion on it.

Henri Poincaré. Note the spiffy glasses and awesome beard.
Why did I shave?

In the late nineteenth century, mathematician Henri Poincaré, as part of an attempt to solve the infamous "three body problem" (in short, how three objects would move under the influence of mutual gravitational pull) stumbled upon something he called the Recurrence Theorem. This was the heyday of statistical mechanics and Boltzmann's descriptions of entropic forces and the evolution of closed systems was in many ways the central focus of physics. What Poincaré discovered, put simply, was that if you started a closed system (one free of outside physical influence) in any particular configuration and let it evolve according to Newton's laws of dynamics (motion), and if you had an infinite amount of time to wait and observe, that system would eventually return to its initial configuration, not just once, but over and over again. The fewer the components you have the shorter the recurrence time would be and the more you add, the longer you'd have to wait. The universe is home to more particles than can possibly be imagined, so the recurrence time would be huge - but if the universe is really eternal (and closed), it is virtually guaranteed to return to its initial state and evolve precisely along the same lines all over again.

Think about what that means for a moment. Every single event in the history of your life, in the history of the universe, would be bound to repeat itself, over and over and over again - with no variation within those particular evolutions. How long would we have to wait for one recurrence time for the universe? A box with sixty particles in it has a recurrence time of the present age of the universe. In other words, it would take a box of sixty particles nearly 14.7 billion years to return to its initial configuration, statistically speaking of course. By comparison, a typical macroscopic object, made up of much, much more than sixty measly particles, has a recurrence time would be 10^{1,000,000,000,000,000,000,000,000} seconds. (Carroll, 205-206).

The idea of recurrence seems much more profound than mere fate. A typical determinist may look at the universe and say, "Well, it's all in motion like a train and cannot be stopped." Life unfolds, the universe evolves and there's no tampering with it. It's almost like a movie playing itself out, but that analogy isn't quite right because it's as if we, the observers are part of the movie too. Our reactions to it, indeed, even whether we recognize it as such, has already been determined as part of the story. But if Poincaré is correct, and he is mathematically, if not physically, then it's a movie on repeat - a disc stuck in a dvd player, but you'd never recognize it as such. If a cyclic cosmology is correct and the universe indeed goes through expansion and contraction phases infinitely into the future with a sort of bounce in between, then certainly some, though probably not all, of the expansions may create histories that look exactly like our own, given we wait long enough. The life you experience now may be the very first of a series of repetitions you can do nothing about or control - or, it could be the 1,000,913,456th. It may happen all over again in the very next cycle the universe goes through, or it may take another ninety evolutions, but here you'd be all over again - with the same joys and frustrations, accomplishments and failures.

Even more interesting: in an endlessly cycling universe there are bound to be cycles where the history or evolution is dramatically different. Ones in which no sentient life forms exist or evolve at all, for example. Or, it could have evolutions that are quite similar, but subtly different (from a cosmic perspective at least). There could be alternate histories and evolutions where Hitler was never born (a favorite for alternative history science fiction fodder), or where you were born in another country, to another set of parents (but would it still be you?). All it would take is the subtle displacement of a single hydrogen atom or a change in vector of a single electron to change the whole subsequent history of the universe, giving birth to different realities and different histories each time the universe expands anew.

Could you be born into a family of Wookies because an electron
zigs instead of zags in the next expansion cycle of the
universe?

Is it true? Are we doomed (or blessed) to live the lives we have now forever? For truly any other evolution, no matter how slightly different, would result in an us that is not us and therefore different. This reality is all that we have. Well, there's a couple of snags that complicate Poincaré's picture:

1. What we know of quantum mechanics seems to suggest that there is an inherent level, not of randomness, but probability to reality itself. Virtual particles pop into and out of existence, leaving their mark, no matter how subtle in a myriad ways - causing black holes to evaporate or contributing to mysterious macroscopic behaviors like the Casimir Effect. In short, ephemeral instability and unpredictability have a subtle effect on macroscopic objects and their motion or movement. If such events truly are part of the fabric of reality, they would perpetually disturb the motion of electrons and other subatomic particles and alter the history of each subsequent expansion or history. Would it still be possible for the same evolution to occur, down to the same perturbations? Maybe. Probably, given that you had an infinite amount of time to sit around and wait, but the recurrence time would be even more monstrously huge.

2. On a more concrete level, we know that the universe is expanding. Leave aside whether or not the universe is indeed closed or open, or if we're one pocket universe nestled in a multiverse of other universes - cosmologists know that objects in the universe are moving away from one another. Not only that, but they're doing so at an accelerating rate. In short, that's bad news for cyclic cosmologies. When is contraction going to occur? By what means? It seems like expansion will continue into the future unchecked, stretching the particulate matter of the universe into a thin gruel spread over even more unimaginable distances. It's hard to imagine a spontaneous contraction that would reverse then start the cycle all over again. It seems far more likely that the universe will suffer entropic heat death and it'll all end in a Big Freeze.

3. Even more basically, cyclic cosmologies may be inherently incorrect, the reason stated in point #2 being just one flaw of such theories (see earlier posts).

4. Even among those who embrace cyclic cosmologies, like Roger Penrose, there are those (again, like Penrose) who believe that events in one expansion cycle effect events in the next. Penrose believes that events in the previous cycle have left imprints on the Cosmic Microwave Background that are visible today. Those imprints, speculated to be caused by supermassive black holes near the end of the contraction of a previous cycle, surely would affect the motion of particles in this expansionary phase. In short, there is no repetitive, or recurring cycle as events in one cycle have specific effects on the next.

Granted, I'm no expert, but I tend to think that while recurrence is a pretty thought-provoking and amazing idea to think about, it has no strong scientific backing. Poincaré's math is solid. If you really did have a closed system and we only considered Newtonian physics, recurrence would occur. Unfortunately (or fortunately), I don't think the universe is quite as neat or simple as a box of gas.

Carroll, Sean. From Eternity to Here: The Quest for the Ultimate Theory of Time. London: Plume Books, 2010.

On Cyclic Universes

How old is the universe? Did it have a beginning or is it eternal? There is no more fundamental a question in cosmology than the question of the origins of the universe we see around us, nor one more vexing to theoretical physicists.

The most commonly accepted answer to the above question is the Big Bang model, which states that the universe began, actually started from "nothing," 14 billion years ago. Before this time, the entirety of the universe was shoved into a "point" so small and so dense that the laws of physics, the notion of the dimensionality of space and the flow of time are incomprehensible to us as we understand them today. Why do we think this? Simple. We just rewind what we see happening before us today. Edwin Hubble discovered that the universe was expanding. Not just expanding, but expanding at an accelerating rate. In fact, the further out we look from where we are in the universe today, the faster cosmological structures like galaxies appear to be receding from us. If the universe is expanding, the thinking goes, then at one point in time, everything must have been close together. Using Einstein's theory of general relativity, which explains gravity and it's effect on objects that occupy space-time, theorists can rewind the clock back to the point where it all began. Well, almost to that point. It turns out we can only see back to within 300,000 years of the bang itself. Before this era, the universe was still so energetic and dense that visible light couldn't travel freely about the universe. It wasn't until it began to cool and expand that light began to move from one place to another, transferring information about separated points in space to each other. Before this time, we rely on general relativity to explain what was happening given certain expected energy levels and masses present in the early universe. The equations are reliable and have let us know much about the time before us, but at a certain point, they begin to break down. If you rewind back far enough, well past that 300,000 year limit, the equations begin to break down. The assumption is that this point in time is the beginning and the expansion that followed is all there really is to the universe - a rather unsatisfying conclusion to say the least (even if it may be true). Could there have been more?

Paul Steinhardt at Princeton University certainly thinks there's room for more. In a 2007 article in Seed Magazine, he phrases it this way:

The big bang is formally defined as the moment when the equations say that the temperature and density of the universe became infinite, and it is impossible to extrapolate back any further. Concluding that this represents the beginning of all space and time is suspect, however, as Einstein himself once pointed out. Properly construed, finding that the temperature and density become infinite is an indication that the mathematical equations underlying general relativity have become invalid, not that this is when the universe began.

There are many models for eternal universes out there right now. One of the more interesting ideas put forward by theoretical physicist and mathematician Roger Penrose is a model of a cyclic universe that is eternal and oscillating. The argument goes something like this: the universe has always existed and is eternal and we are living in one of an infinite number of permutations and lives of the universe. The basis for this belief stems back to the days of Einstein, who himself played with the idea of an oscillating universe in the 1930s. He postulated that the universe has existed forever and that each cycle begins with a bang and an outward expansion, followed inevitably by gravity getting a hold of the expansion and slowing it down before reversing it altogether, collapsing the universe back down to a single point for the process to begin again. This is a very simplistic explanation, and there are far more sophisticated explanations for a Big Bounce theory of the universe, but you get the basic idea.

The question is: is there any evidence of such cycles? The light barrier mentioned earlier is certainly an obstacle to seeing back past this point for confirmation of the universe's other lives. It may very well be impossible to know anything for sure about the universe before the big bang, however, Roger Penrose thinks he's found a clue in the cosmic microwave background radiation, the remnant radiation of the earliest times in the universe discovered  in 1964 and which NASA's WMAP space probe has been dutifully mapping. The CMB shows a relatively uniform energy prevalent throughout the observable universe that is a relic of a time when the universe was small and uniform. After expansion and cooling, minor variations in the CMB provided a structure around which galaxies eventually formed. Penrose and colleague Vahe Gurzadyan recently published findings of a series of concentric circular patterns in the CMB that they argue are a sign of pre-Big Bang activity. The circles are areas of small temperature variation between one spot and its neighboring spot in the universe. What could have caused these structures is a mystery, but Penrose has suggested that they are the result of collisions of supermassive black holes causing the creation of uniform spheres of of gravitational waves that radiated outward from the collision and left an imprint on the CMB straight through to the current era.

Ripple Patterns in the WMAP CMB data noticed by Penrose

Other scientists remain skeptical. Earlier last month, physicists Hans Eriksen and Ingunn Wehus conducted a study of the same data examined by Penrose and his colleague and found the exat same evidence of concentric circles. They then built thousands of random simulations of expansion models from the Big Bang to the present and found that the circles showed up in the random models as well. What does this mean? Erikson and Wehus think that it may just be part of the structure of the universe for some reason. No matter how the CMB varies in the models, it still produces the circles. Moreover, they may simply be evidence of processes that occurred in very early times, before the universe expanded and settled and allowed light to travel freely throughout, hiding the evidence of causation. Sounds reasonable enough. I don't have a PhD in math or physics, but it would seem to me that anything that occurred before the Big Bang would in a sense be erased by the condensation of the universe that the cyclic models suggest. Any patterns created by gravitational waves due to colliding supermassive black holes would be erased as the fabric of space were warped back down to a point and a new expansionary phase would create new patterns.

Nevertheless, the idea of a cyclic universe is intriguing, even if we don't have solid evidence of its existence. For one thing, it gets around the sticky point of what caused the Big Bang in the first place if absolutely nothing existed before by simply asserting that everything that currently exists has always existed. Forever. The universe is eternal and we're just in one of its infinite phases. Cyclic theories aren't the only eternal models of the universe, however. It has rivals with names like baby universes and eternal expansion, that are equally intriguing and probably worth covering in future posts.