First posted 24 Nov 2003. To check on any updates to our knowledge, you can visit Nasa.
We know our universe pretty well, right? Galaxies contain stars, around which orbit planets. The odd comet or asteroid zips around. And there is dust, like what gives Saturn those cool rings. We can see these things all around us, reaching to the edge of the visible universe.
All of this stuff is made of matter, which most of know is made up of protons, neutrons and electrons. Some of us know that protons and neutrons are actually constructed of more fundamental particles called quarks and that there is a small host of other fundamental particles out there. We have a pretty good idea of the mass, electric charge and spin of each of these particles.
Sounds good. Well imagine my surprise when I learned that all the particles we know of make up only about 5% of the estimated mass-energy content of the universe, and that its very existence is a fluke!
What's the matter?
Cosmologists are able to measure the orbital motion of galaxies within clusters, and of stars within galaxies. The velocities they have measured are greater than can be attributed to the gravitational field generated by the mass of visible matter. When we calculate the mass that must be 'out there' to account for the observed velocities, we learn that visible matter makes up only 15% of total matter in the universe.
The rest is called Dark Matter, and we know precious little about it. We reckon that it is made up of Weakly Interacting Massive Particles (WIMPs!), that it formed into structures as the universe cooled after the Big Bang, and that the visible galaxies we see formed around/within these structures.
The Dark Side, continued
But wait, there's more. It turns out that matter (including Dark Matter), makes up only about a third of the Cosmological balance sheet. The remainder, about which we know next to nothing, is called Dark Energy. How do we know it's there? Well, we've wondered for some time whether the universe is destined to go on expanding or to collapse upon itself in a Big Crunch. Scientists have measured very closely and learned that the rate at which the universe is expanding is actually accelerating. Well, first, this means there's no Big Crunch in our future. But second, it leads us to ask what force is counteracting gravity to cause this acceleration. Dark Energy is the place holder for this variable.
That bursts our bubble a bit, huh? Well, we should consider ourselves lucky - really. It's a fluke that there is any visible matter at all. As Einstein's famous equation shows, mass and energy can be converted between one another. This was happening at a fantastic rate in the earliest moments after the Big Bang. Particles burst into existence, accompanied by their mirror-cousins, anti-particles. Usually, particles and anti-particles ended up slamming into one another and annihilating to form energy again. But one time in a billion a particle was created without an anti-particle. This slight asymmetry led to the existence of the visible matter that we observe (and are made of) today. We are but an asymmetric excess!
Here's lookin' at you kid. You're one in a billion. But you've got a way to go before you really understand your universe.
First posted 21 January 2005. Questions of consciousness. Questions of the role of subjectivity. Questions of time. Questions of a Platonic reality. All still central to what keeps my curious mind busy... Penrose was the adviser of another of my scientific heroes: Julian Barbour.
Roger Penrose, the Oxford Physicist, is not convinced: quantum theory, he believes, is incomplete. In The Road to Reality he argues that a further revolution is required in quantum mechanics, as indicated by its inability to address the reduction process for the wave function (and thereby its inability to 'join up' with classical physics) as well as troubling incompatibilities with general relativity.
The time asymmetry associated with the wave function reduction (or collapse) upon measurement of a quantum system contrasts sharply with the symmetry associated with the propagation of the wave function itself. The latter can be made sense of moving either backwards or forwards in time; the former works only moving forward.
A more familiar time asymmetry, the one we experience every minute of every day, is grounded in the extraordinary nature of the Big Bang itself - its strikingly low entropy. The Big Bang was so ordered that the ever-decreasing order of the universe is a probabilistic near-certainty. This is what lies behind the 2nd law of thermodynamics and the 'arrow of time'. It points to the peculiar behaviour of gravity at cosmological singularities - not only the Big Bang but (less spectacularly) black holes.
The presence of this time asymmetry in both the reduction of the wave function and in the Big Bang suggests that gravity might play an important role in wave function reduction. Discovering this role would amount to a revolution that could well resolve the 'measurement paradox' and render quantum mechanics consistent with general relativity and contiguous with classical physics.
According to this idea, it is the gravitational effects of the classical measuring apparatus (and other macroscopic entities in our everyday world) rather than the perceptions of any observer that bring about the collapse of the wave function. As such, the reduction is an objective rather than a subjective one. This takes the conscious observer from the limelight of quantum theory. How does this happen? As the wave function propagates through time, non-uniformities develop in the distribution of energy and matter among its superposed states, and at some point become gravitationally significant. The gravitational interaction with the measuring apparatus (or other macroscopic entity) then brings a collapse into a measurable single state.
Although Penrose takes the consciousness out of quantum reduction, in The Emperor's New Mind he puts quantum reduction centre stage in consciousness, thereby turning the world (as seen by conventional quantum theory) on its head. These same quantum gravitational effects account for the difference between consciousness and artificial (computer) 'intelligence', and Penrose calls upon them in his rejection of the computational theory of mind. There are things - including non-algorithmic, non-computable ones - that the human mind can comprehend while no computer (Turing machine) possibly could. This is in keeping with Godel's theorem, which states that no formal mathematical system (or at least none of the richness required to handle even common arithmetic) can be complete. There must always be truths that cannot be expressed without recourse to 'meta-mathematical' language that is not part of the formal system.
Penrose suggests that our access to such truths is due to quantum fluctuations, gravitationally induced, within the brain (he suggests maybe in the microtubules of the neurons' cytoskeletans). Multiple states may exist in superposition in our brains until gravity triggers a collapse to a specific state, with resulting (possibly non-local) effects on our neural states. This is something that is not possible (at least for now) with computers.
There is a deep connection among the time-asymmetry of the wave function reduction, the behaviour of gravity at singularities and the presence of non-algorithmic (non-computable) elements - including consciousness - in the world. This helps to explain the relationship among Penrose's "Three Mysteries":
There is also an "Escher element" to the relationships among the three mysteries. Escher was an artist (and obviously a mathematician) whose works included paradoxical staircases and streams that seemed to always lead in one direction (up or down) yet returned to their own source.
In Penrose's three world / three mystery model, a small portion of the mental world is all that is needed to capture the mathematical one (since we obviously spend lots of time considering other things). Similarly, a small portion of the mathematical world is applied to the collected (total) formalism of physics, with much else being dedicated to other questions. And finally, only a small portion of the physical world (that part that makes up our cells) is drawn on to explain the mental one. Each part is able to 'swallow' its neighbour in an illogical, unending cycle.
Penrose believes that the secret to this mystery of the mysteries is that all these worlds are in fact one. Perhaps in a holographic, holistic, non-local sense like that evoked by David Bohm, another of my creative scientific heroes?
First posted 28 June 2006. My view of time and consciousness is surprisingly close in this 11-year old post to what it is today, even though I had not been exposed at that time to the main elements that now underpin my reasoning.
Several pairs of unreconciled truths (as in best operating guesses) interest me deeply: Quantum mechanics & General relativity, Determinism & Free Will, Materialism & Consciousness. These pairs are not unrelated, could indeed be different manifestations of the same chasm. The paradox that may interest me most of all captures aspects of all three and is almost certainly inextricably entwined with each, and that is: Space-time & Temporal becoming.
The paradox has two elements. The first, in a nutshell, is that our best understanding of space-time tells us that it is a complete, unchanging, four-dimensional (perhaps with seven further dimensions wrapped tightly around themselves, unextended) whole, but our direct experience is of a temporal flow with each moment different from the last. All is constant, yet the only constant is change itself.
The second is that while space-time itself has no privileged set of parallel planes that can be called Nows (each inertial frame parses out space and time in a different way, with the Nows as planes at different angles to one another) , we each indisputably experience a clear distinction among past, present and future. The flow from the latter to the former hearkens back to the first element of the paradox.
In an interesting paper, entitled "The Physics of 'Now'", James Hartle takes us some of the way towards a reconciliation.
Space-time is a four-dimensional grid, with each point being an event. If we label one axis as the the speed of light multiplied by time and the others as the space dimensions, then one can imagine two cones, extending in opposite directions parallel to the 'time' axis and meeting at a designated point, or event. The one pointing back toward the Big Bang is the past light cone for that event, and the one opposite it is the event's future light cone.
There is a reason these are called light cones: given the chosen units of the time axis and the fact that nothing can travel at speeds exceeding the speed of light, all points (events) within the 'backward' light cone can be said to be in the given event's past, they could have played some part in the evolution that led to the given event's occurring. Similarly, all points in the future light cone can possibly be affected by this given event. Points outside these cones cannot be said to be in the given event's past or future. They are what is called 'space-like' separated from it.
If we imagine that event or point as being one of many that make up the history, or world line, for a person as that person travels through life (and space and time!), then, within that person's frame of reference, the plane that runs through that event and is perpendicular to the time axis might be defined as a Now or instant for that person.
But the thing is that that person's frame of reference is not privileged, is nothing special. So although it might be called a Now for him, it is not a Now for the universe. Other people could be travelling at very great speeds relative to him, and their Nows would be askew with respect to his.
As it happens, all we humans exist very close to one another (on a cosmological scale), and we move only at very low velocities relative to one another (as compared to the speed of light). So our Nows are for all intents and purposes not only parallel but even simultaneous. Still, this is just a local accident.
Why do we distill the time dimension from the space ones and experience it as a flow from future to past? Hartle believes it is a function of the way that we collect and process information. Placing humans within a broader set of entities he calls Information Gathering and Utilising Systems (IGUSes), he models a simple IGUS to demonstrate his thinking.
In essence, we have 'registers' for current input and for memories of past input. These registers contribute directly to conscious thought both directly and indirectly, the latter through subconscious updating of our 'schema' or underlying operational models for dealing with the world around us.
In any moment, or more to the point, at any event along our world-lines, the 'current input' register is populated by what we are experiencing, the remaining registers are populated by what we experienced in each of several immediately preceding moments. The direct 'feed' from the 'current input' register to conscious thought gives the sense of Now. The fact that any brain state enfolds information from previous brain states ( in the other registers), gives a sense of both a past and of a flow to time. The future is not represented in any register but is rather the object of calculation in both conscious and subconscious processing.
But why does this flow move in one direction rather than the other, or rather than in both? Hartle appeals to two old dears of physics, the 2nd law of thermodynamics (which states that entropy must always increase), and the nature of electromagnetic radiation. I've talked about the first elsewhere. The second is worth mentioning a bit more about. Anything we see has radiated from some source. Electromagnetic radiation only ever travels in that one 'direction' - from source outwards.
In a sense, then, the past can simply be defined as the direction in time from when radiation strikes our retina to when it is (was) emitted. Information only travels that way. Since gathering and processing information is what we do, we naturally take on or assign this direction a prominent place, simply through our interactions with the world.
As ever, I'm sure that I've been less than perfectly true to Hartle's original argument, so do read his paper.
I will say, though, that I think he leaves two questions unanswered. They may well fall outside the scope of his work, but they are related and interesting. First, Hartle mentions repeatedly that we EVOLVED into the IGUSes we are, to process information as we do, because that is what worked. He is doing nothing more than making one specific reference to the accepted truth of Darwin's thesis. But when one thinks of space-time as a four-dimensional, unchanging and complete totality (as I believe it is), one can't help but think differently about evolution.
We no longer say, things are this way because they evolved to be so, and they evolved to be so because being so conveyed survival and reproductive benefits. That is all true WITHIN the time dimension, but within the eternal space-time picture, that we are this way is just that we are this way. Both our present state of evolution and every other step in its past and future exist eternally. So one then asks, why is THAT so? Why is it that this relationship within four-dimensional space-time exists? I don't have an answer. It is just SO.
Second, it is simple enough to refer to a given event on my world-line, look into the 'current input' register and say, "That is my Now". But the interesting point is that EVERY ONE of the points on the 'conscious' segment of my world line is a conscious now, and every one exists eternally, side-by-side, as it were, in space-time. Why do I not experience them all at once. Why do I only experience THIS one and now THIS one?
I do have my own answer to this question, and it is that we ARE experiencing ALL of our Nows eternally, although somehow only ever in one channel at a time. Every instance from our first sentient experience through to our last is experienced by us eternally. Each exists at some event in space-time, but all are there in the eternal 4-D block that is existence. So we don't get life-after-death as such (because the 'after' shows that we are talking within the time dimension with that phrase), but we do get eternal life! And that eternal life is no better or worse than each instant that you live. Moments of suffering are eternal, as are moments of elation, despair and euphoria. Drink deep. Live it up!
In his 2004 essay, Goedel and the End of Physics, Stephen Hawking conducted a U-turn. A past believer that the hunt for the Theory of Everything (or Grand Unified Theory - GUT) would be successful, perhaps even in the near future, Hawking decided that the same reasoning as Goedel applies to mathematics also suggests that such an all-encompassing theory is not possible.
Goedel's theorem states that no finite system of axioms can prove every result in arithmetic. Goedel draws on self-referring and self-contradictory statements to make his point. An example of such a statement is "This statement is false." Think about it. The statement he used was a mathematical one, and the proof involved other important points, but Hawking draws on this one specifically when he extrapolates from maths to physics.
If the system we seek to describe is the universe, then we have a problem - we can't step outside of the system to view it from on high. We, our apparatii and our equations are all part of it. So any physical theory seeking to describe and predict the universe is self-referencing in the way that Goedel's statement was. Perhaps, then, it shouldn't be surprising that the Standard Model of particle physics and the General Theory of Relativity (which explains gravity, the one thing NOT explained by the Standard Model) are incompatible.
Hawking's argument is not a proof, but rather an analogy. Even if Hawking is wrong in saying that the theory of everything is unreachable, his essay is useful reading for someone interested in the biggest questions about the universe.
First posted 31 Oct 2003. I definitely still think there is infinite diversity out there, including many versions of 'me'. I tend now to think of it more as the existence of every possible experience from every possible perspective.
See Scientific American: Parallel Universes [ COSMOLOGY ]; Not just a staple of science fiction, other universes are a direct implication of cosmological observations
Buckle in, 'cause this one's a helluva ride - a real head spinner. You can read the whole article via the link above, but I'm dying to try to summarise it, to see how much of it I 'get'. The gist is that our universe is just part of a multiverse, or actually a part of four tiers of multiverses, with the result being that (based on simple probabilities) an infinite number of you's and me's are 'out there' living through every permutation of our lives. I hope only a few of the me's out there are suffering from my cold at the moment.
Our Hubble Space
The article starts by defining our universe as our visible universe. Since light travels at 300 million metres per second, and since the Big Bang happened about 14 billion years ago, our visible universe (or Hubble space) is a spherical space with a radius of about 10^26 metres. (The article says 4x10^25). This visible universe's radius grows (by definition) by one light year (roughly 10^16 metres) each year, and the light we see emanating from the edge of our Hubble space was emitted at the beginning of time.
Level 1 Multiverse = The Universe
The first level of multiverse, then, is the collection of Hubble spaces. This is what I have always considered and shall continue to call The Universe. If we assume (as current observations suggest) that the overall universe is infinite and that matter is roughly evenly spread throughout it, then there are an infinite number of these Hubble spaces, all with the same physical laws as ours. Now, pick one of those other Hubble spaces. What is the probability that the interaction of fundamental particles and forces over the lifetime of that space just happen to produce another you? Surely unbelievably small. But is it zero? It seems irrational to assume that the probability of another you in any other given Hubble space is absolutely zero, since you have already appeared once, after all. Let's say the chance is one in a gazillion, with a gazillion being the biggest number imaginable. Then there must be another you out there, because any non-zero probability, no matter how small, when applied to an infinite number of cases, will be realised.
Saying that there must be other you's living through every possible permutation of your life is just a special case. We could simply say that anything that is possible (i.e. has non-zero probability) exists. So, somewhere out there is a you with 9 fingers, a you with a squeaky voice, a you who didn't propose to your wife, a you who likes Abba songs, a you who only carries 20p pieces in his pockets. There is you who slept late on your 19th birthday, not to mention a you whose life is exactly the same as yours in this Hubble space. Now you see just how infinite infinity is!
Level 2 Multiverse = The Multiverse
There are a couple of ways to think of a level 2 multiverse, which I will call just The Multiverse. At heart, The Multiverse (i.e. Level 2) is a collection of an infinite number of Universes (i.e. Level 1s), each of which can have very different physical 'constants'. We can think of these Universes as bubbles of non-stretching space within the eternally inflationary Multiverse. Alternatively, we can view The Multiverse as a cycle of continuous birth and destruction of Universes, perhaps with black holes as the agents of mutation and birth. From either angle, we could never communicate between Universes (or gain information about another one), because they are either moving apart from one another at faster than the speed of light or only 'touch' at singularities, through which no information can pass. Still, the existence of The Multiverse would explain the otherwise tricky and highly improbable fine tuning of our own Universe. If ours is just one of an infinite number, then it is no longer surprising that so many specific variables (density fluctuation, relative weights of elements, etc) have values just right for allowing life to emerge and evolve. As regards the multi-me's and multi-you's, if the infinite size of our Universe guaranteed that they were out there, then the existence of The Multiverse, containing an infinite number of Universes, really cements it!
Level 3 Multiverse = Many Worlds (from quantum mechanics)
A level 3 multiverse is another name for the infinite collection of worlds in the 'Many Worlds' interpretation of quantum mechanics. Each quantum event causes a split between worlds, with one proceeding along possible route 1 and the other along possible route 2. Each of those 'worlds' contains an entire Multiverse (i.e. Level 2). Since there are an infinite number of quantum events, there are an infinite number of such splits and an infinite number of worlds, one for each thread that winds its way forward through one 'choice' after another. I (as in this specific Doug in this specific level 1 and 2) only have access to, only experience one of those threads. The other me's see only their specific threads. But all threads exist.
The me's in different Hubble spaces live separate but parallel lives in a different part of space-time. The different me's within the many worlds (Level 3) are not separated from me in spatial terms but in dimensional terms within the overall wave function for the Level 3 multiverse. You can think of these worlds as being perpendicular worlds, as opposed to parallel ones. Jointly, they require an infinite number of dimensions, which the 'Hilbert Space' of the wave function has. Ouch, that hurts my head.
Anyway, the existence of this level depends on whether the wave function's evolution through time is unitary (no, I don't know what that means), which is as yet uncertain but is consistent with observations and wider theory. In one sense, it doesn't matter, because if physics is unitary, then Level 3 adds nothing that doesn't already exist in Levels 1 and 2. No more possibilities are generated, just additional copies of ones that already exist.
Level 4 Multiverse = All possible mathematical structures (or, a bridge too far)
Just a few words on a final, highest level multiverse. The wave function of quantum theory and level 3 multiverse is a mathematical structure, and most physicists today see the universe as fundamentally mathematical. Why not, then, allow for an infinite number of level 3 multiverses corresponding to any imaginable set of (mathematical) laws? Fine with me, but you'll need to check with all the other multi-me's individually.