Was Einstein Right About Quantum Mechanics?

Most of us who follow physics know Einstein's famous response to quantum mechanics (QM): "God does not play dice!" Many writers consider this quote as an indication of his refusal to accept the randomness of QM phenomena, and they consider it to be one of Einstein's biggest mistakes. The author of "Is The Cosmos Random?" in Scientific American's September 2015 issue, having reviewed much of Einstein's written work and correspondence, argues otherwise (a subscription is needed to read it online). A fresh look at what Einstein thought about QM could lead to new approaches to how we think about quantum phenomena, especially how we interpret the experiments that reveal its trademark quirky behaviours.

Einstein's "hidden variable theory" – that there must be one or more underlying variables to explain the seemingly random (and spooky) nature of certain particle processes - was debunked by John Bell in the 1960's. Based on his theorem, a series of elegantly designed experiments were carried out in the 70's and 80's to test the hidden variables theory. Those results argue very convincingly against hidden variables (at least local variables). The principle of locality means that an object can only be directly influenced by its immediate surroundings, whether it is an object pushing it, for example, or energy or a force field acting upon it. In this case there is no evidence that some hidden force field, or as yet unknown particle, acts on the subatomic particle in question, influencing its behaviour. It's just, according to any observations we can make of it, autonomously random.

Subatomic particles do some very weird things. Their behaviours point to a built-in randomness at the quantum level of reality. Particles also don't seem to play by the same rules of space and time that we do at our everyday scale of physics.

Excited atoms, for example, emit one or more photons when they return to ground state, but exactly when and in what direction those photons are emitted are entirely random. Similarly, exactly when a particular radioactive atom emits a beta or gamma particle, or a gamma photon, is purely random. Despite this, both radioactivity and the emission of light follow predictable rules of physics at the macro or everyday level, so that such phenomena can be drawn as predictable curves on graphs even though the individual particles themselves act entirely randomly.

In one version of the famous double slit experiment, electrons are shot one at a time through a barrier, which contains two thin slits, toward a detector screen. Electrons are used in this example but in theory this experiment can be carried out with any subatomic particle because they all follow the same quantum rules. Individual impacts are recorded as discrete points on the detector, as we might expect. However, the impacts are randomly placed on the detector, even though each electron is shot in an identical manor. Like the previous examples show, the electrons have a probabilistic (random) nature, revealed here by where they hit the detector.

This built-in randomness at the particle level cannot be explained by classical mechanics. In classical mechanics, one action always leads directly, and reliably, to another action. Classical mechanics describes a clockwork universe in other words, where every outcome in nature is ultimately predictable. The double slit experiment reveals that at the subatomic (quantum) level, nature is not predictable but entirely random EVEN THOUGH those same electrons, observed at the macro scale, follow Michael Faraday and James Maxwell's predictable classical rules of electromagnetism. You have here two layers of reality, where predictable physics is built upon an unpredictable probabilistic base.

The double slit experiment reveals an additional and even more perplexing subatomic reality. When electrons continue to be shot through the slits, another phenomenon emerges. An interference pattern builds up, like waves interfering with one another in a wave tank. This is not only direct evidence for the dual particle/wave nature of subatomic particles. It also reveals that individual particles, each one hitting the detector in a purely random location, somehow manage to build a distinct pattern AS IF they know how future electrons will contribute to the interference pattern. The experiment can be repeated over and over. Electrons will hit the detector in different random order each time but every time the same interference pattern builds up. This implies that the particles are acting outside the boundaries of time, as we understand it. A particle somehow "knows" the end result as it leaves the electron gun. According to special relativity, no particle can travel faster than the speed of light, back in time in other words, to plot out its contribution.

Space somehow also seems to have a different meaning on the subatomic scale. This example involves quantum entangled particles. To make an entangled pair, for example, you can allow an unstable spin zero particle to decay into two spin ½ particles. One will be spin up and one will be spin down. Other than their opposite spins, these particles will have identical quantum numbers. They will be identical twins in other words. When the entangled particles are shot off in two different directions, they seem to communicate information to one another, instantly, even though one particle may, by the time it's measured, be across the universe from its entangled partner.

Particle A's spin might be measured (it has a 50% chance of being either spin up or spin down) at some point. When A is measured and found to be spin up, at that instant, Particle B's spin is confined to spin down. Before measurement, both particle spins are said to be in a superimposed up/down state. Collapse of one into spin up instantly forces the other, wherever it might be located, to collapse into spin down state. This experiment reveals the spookiness of the EPR (Einstein/Podolsky/Rosen) paradox, and it can be reviewed on Wikipedia both here and here. Both entries describe the phenomenon in great detail. The question for us is how does one particle "communicate" wavefunction collapse to its partner instantly across any distance? This goes further than breaking the light speed barrier because it is instant. It is as if physical space does not exist for the entangled pair. They are instead acting like one single particle.

All these phenomena have been exhaustively experimentally verified. As we try to swallow those facts, we seem to be left with two unsavoury choices: Either we accept at face value the fact that phenomena occur randomly and in ways that don't make sense in terms of how we understand space and time. Or, we cling to the hope that there is some predictable and sensible underlying reality and we just haven't found it yet. If we chose the latter option, we are treading toward Einstein's ruled out hidden variables.

George Musser, the author of the Scientific American article, offers us possible outs for both of these choices. First, there is good evidence that reality is actually like a layer cake, where probabilistic and predictable phenomena are layered on top of one another. Which type of behaviour you observe depends on which scale you are observing. If you are focused on behaviours the quantum scale, you will find probabilistic behaviour. Zoom out and look at the same physical system at the everyday scale and you will likely find predictable classical behaviour. What looks purely random at one scale averages out to be predictable behaviour on a grander scale. For example, consider a single isolated atom in the vacuum of space. It could have any random kinetic energy, but it has no temperature.* If you place that atom together with a few million of its friends, you can now measure a specific temperature that is reliably determined by measuring the average kinetic energy of the atoms EVEN THOUGH that mixture consists of atoms that have all kinds of random kinetic energies as they mill about and collide with one another. Temperature is a predictable phenomenon that follows classical rules. It is also an emergent phenomenon that does not exist at the quantum scale.

Musser offers even more layers of phenomenon in the example of weather. At the quantum level, the gaseous particles in air behave randomly. Get them together in measurable volume and you find they perfectly follow predictable gas laws of behaviour (again, it is thanks to averaging out billions of atoms). Now put two or more different large-scale air masses together and you've got the unpredictability that accompanies any weather forecast. The more days out you try to forecast, the more unpredictable it gets because now you are dealing with the physics of chaos theory. Chaos emerges from a non-chaotic initial state. Take a long view of weather over several seasons and once again the numbers come back into predictable line as climate data. Perhaps, considering this, it isn't too much to accept that our predictable world is built upon the zany behaviours of quantum particles.

Second, we can wonder if there is any possibility of some kind of reality underlying the quantum scale of physics, implying that QM is actually only part of an as yet unfinished theory. This, according to Musser, is really what Einstein was getting at: He wasn't arguing against randomness so much as he was arguing against taking the random behaviour observed at face value. There's a subtle difference between taking that stand and resorting to a hidden force or particle. The layer underpinning QM could once again be deterministic in nature. Consider this possibility: All the countless random directions in which a photon can be emitted from an atom could represent countless possible realities at our scale (the multiverse people thoroughly explore this possibility). Here is where I veer off: We observe just one of these possibilities but on its scale, its reality could consist of ALL the possible directions, simultaneously. We observe the photon emitting in just one specific direction, and it looks totally random to us. But add all the countless possible angles of emission and imagine all these realities simultaneously coexisting, from the photon's perspective. From its perspective, it actually achieves all possible emissions. This, then, is what the quantum world looks like to the quantum particle. We, on the other hand, see only one emission and it is random. If we follow the SA article's logic, we can call this difference an abrupt transition from one scale to the next (while maintaining that both realities are valid WITHIN their own scale).

Richard Feynman came very close to describing quantum phenomena the same way. To describe electron and photon interactions, he started from the standpoint that the particles are waves and they move from point to point as a wavefront. A wavefront, unlike a point, takes numerous paths to get from A to B, rather than just one path. To translate that into mathematical quantum jargon, you call the particle a probability wave, and it doesn't take numerous paths. It takes ALL paths. This approach assumes that a particle, just like larger objects, follows the principle of least action. By assigning arrows that follow each possible path (in theory there are countless paths remember) and rotating them as you go, you can get a measure of how difficult, or how long and convoluted, each path is. By adding up all the arrows as vectors, you get a final vector called the amplitude of the wavefunction. This is the path integral that the particle takes from A to B, which also happens to always be the shortest route it can take, and also happens to be the path, the straight line, that we observe. This might seem like a pointless exercise, all this fanciness just to get back to the particle's observed trajectory. However, there is an important point to it, that ALL possible trajectories DO contribute to the path integral, even routes that take the photon all around the universe between A and B (those paths don't contribute very much). Conceptually, this process introduces a whole new way to think about a particle. The path integral forms the basis of the famous Feynman diagrams, I'll mention later. I don't know if he ever thought of those infinite paths as a physical reality or strictly as a mathematical method. I don’t think he ever couched it in the kinds of terms where you think of the process as a kind of scale transition from quantum to our macro scale, where one path as an observable phenomenon emerges from a state of "all possible paths taken."

When you think about this, you might see how it mingles with Max Tegmark's multiverse theory, in particular his level III many-worlds interpretation. Feynman himself suggested a closely related multiple histories interpretation of QM.

This underpinning (and unimaginable) possible quantum reality (all paths taken) could be thought of as a kind of nonlocal, or global, hidden variable. It acts not directly on particles but redefines them within their scale instead. It would result in a superimposed multiverse (existing strictly at the quantum scale with only the possible very rare exception of quantum tunneling). It would contain all quantum possibilities of all quantum processes that ever have and ever will occur in the universe. In such a quantum reality, each electron in the double slit experiment does, in fact, take every possible trajectory to the detector. In an instant, each particle has already built the interference pattern. From inside our macro-scale perspective, we observe only an artifact of that reality or, better put, we observe a different (emergent) reality where a single random path is observed and an interference pattern mysteriously builds up. The double slit experiment, therefore, becomes an opportunity to glimpse a direct translation of quantum reality into our "macro language." We don't see the ultimate reality of all those trajectories taking place at once (the source of the random strikes on the detector) and that's why our observations don't make sense to us. They do make sense, however, from the all-paths taken quantum path integral perspective.

We can see that the quantum entanglement phenomenon can also be a translation of quantum reality that we are reading in our macro reality terms. In such a quantum world, each of the two electrons shoot off in every possible direction simultaneously. In that quantum reality they are everywhere at the same time, and they are indeed part of a single entity, because their quantum states are superimposed (they share the same total momenta, angular momenta, and energy).

It seems confusing because most of the time we don't need to look into QM weirdness. In many cases, we can accurately describe a particle's behaviour as if it is a point-like particle that travels in a straight line. Think of the Rutherford gold foil experiment, in which an alpha particle** is shot at a relatively big gold atom. The occasional collisions between that particle and the nucleus can be described using classical dynamics. The alpha particle is deflected as if it were a small hard ball. Many other experiments also reveal the point-like nature of particles. Only experiments cleverly designed to single out quantum behaviour reveal it. Entanglement experiments tell us that it is useless to visualize electrons or photons or any subatomic particles as point-like particles. They never are point-like, except when we translate them into our scale (the alpha particle - nucleus collision though tiny is observed in our scale). Sometimes the translation seems seamless. A particle is observed as clearly a point-like particle or a wave. Sometimes it's almost lost (as in two entangled electrons experiment). What we observe is muddled.

Wave function collapse, from this perspective, is not a process (there is actually no mathematical framework describing this process by the way). Instead it is the transition from the quantum scale to the macro scale. We don't see a quantum particle/wave at all. We don't see any collapse. When we do see a "particle," it is the artifact-like trace of what that path integral represents in our reality, at our scale.

From a statistical standpoint, it looks as if we are measuring only one (random) degree of statistical freedom from within a quantum reality that contains countless degrees of freedom. In most experiments, what we observe is actually the path integral of all the possible degrees of freedom in that quantum system. Because they are path integrals, all the quantum randomness fits seamlessly into our perception of reality, in the same way that temperature makes sense – from a distance. The clever electron version of the double slit experiment is one of the few exceptions where one single (random to us) degree of freedom is plucked out at a time.

This statistical treatment brings to mind recent work done on a mathematical object called the amplituhedron. I wrote an article on it here. Like a multifaceted higher-dimensional jewel, its volume can calculate the probabilistic outcomes of particle collisions inside colliders, a very tedious job that is usually done by large computers, or it could be done by resorting to drawing many hundreds of Feynman diagrams. The amplituhedron is like a shortcut that circumvents those calculations and goes directly to a geometric assessment that can be quickly processed. The researchers also calculated a master amplituhedron that contains an infinite number of facets, analogous to a full circle (where every direction is represented) in two dimensions. Its volume, in theory, represents the total amplitude of all physical interactions in the universe. Lower dimensional amplituhedra live on the faces of this structure and represent our observations when a finite number of particles collide.

Both Feynman diagrams and the amplitudehron seem to do the same thing. The Feynman diagrams take the scenic route (it takes so many of those calculations) and the amplitudehron takes the direct route. Both can predict the probabilities of creating various kinds of particles when two massive particles collide with each other in a collider. Both serve as a kind of translator taking information from the quantum scale that we can't directly access and turning it into a macro-scale form we can observe.

Using a scale approach eliminates the need to make an unsavoury choice between "quantum-scale phenomena are random and don't make sense" and "there must be some hidden variable somewhere." Instead we come to a single consistent conceptual framework and we could say that Einstein was right after all. There is a hidden nonlocal variable in the sense that quantum reality is all possibilities at once. It can differ from reality at the macro scale because phenomena unique to the macro scale are emergent. The shift from one reality to the other is a shift in scale, where emergence takes place.

The question of whether an electron is physically real or not takes a back seat to the question of what scale we're talking about. What does this mean for the reality of a subatomic particle? For those readers who hope for a physically real particle, the picture here once again seems to strongly suggest that reality at its most basic level is strictly built of potentiality. Reality itself is redefined as a scale-dependent concept. We could argue that what we measure and observe in our quantum experiments (an electron doing something funky) is as real as all-paths-taken (the electron being in all places at once) and vice versa. In the same way that temperature is a real phenomenon to us but not to a subatomic particle, a path integral is real at the quantum scale but not to us. To us it is just a particle moving in a straight line from A to B. It might not satisfy some readers to say that a real object such as a chair, for example, consists of a collection of the statistical average of all possible quantum potentialities. How do we even experience the separateness of objects then? I would answer that "chair-ness" is an emergent property that is physically real to us at our scale.

There is an unexpected upside to this approach. The Holographic Universe principle provides a consistent (different) explanation for quantum entanglement but it takes the randomness of free will away in the process, something most people find abhorrent since we sense we can make random choices and change our futures. I tackled that principle a few years ago in this article. Thanks to the layer-cake nature of scale, we can retain our unpredictable free will even though the cells in our brains behave according to established predictable physical and chemical laws (two different scales). What this approach forbids is applying rules that work for one scale to another scale. The branch of psychology that tackles our conception of free will (ego, moral directive, our subconscious dreams, etc.) doesn't use the same language as neuroscience (axons, glial cells, receptor flooding, neurochemical reactions, etc.) for good reason. In physics, it can be all too easy to forget that caution, especially when many of us carry in the back of our heads the idea that there is one ultimate reality that should work in all cases, no matter what our perspective is. When it comes to quantum phenomena, we're lost.

When I say "rules" I don't mean that physical laws change from one scale to the next, nor am I suggesting that spacetime is something different at the quantum scale (no one knows what spacetime is at the quantum scale). I am also not suggesting that quantum phenomena could actually ever be observed (what do you bounce off an electron to "see" it without affecting it?) or verified directly. I mean the rules of observation and interpretation have to be scale-dependent. Just because a particle acts like a tiny hard ball in one experiment doesn't mean that the particle really is a tiny hard ball. I only argue that we can use a scale-dependent approach that borrows from the science of emergent phenomena to interpret what is going on in the double slit and entanglement experiments at the quantum scale.

*Here I mean only classical temperature – thermal motion or the degree of "hotness." The particle will have entropy as well and it can be precisely measured. Those entropies can in theory be added up and averaged to get temperature as well. That's the thermodynamic approach. In fact, temperature theory is quite complex (simply google "temperature"). I intend only the most basic classical kinetic approach in my example.

 ** An alpha particle is a helium nucleus consisting of protons and neutrons. According to QM, even though it is composite, it has its own specific de Broglie wavelength and acts just like any other singular quantum particle.

"How can we see something from the origin of the universe?"

Physicists have a lot of very good evidence that the universe inflated from a singularity, a single point, approximately 13.8 billion years ago. Some of the evidence comes indirectly from mathematical models, but physicists can also detect and investigate the echo left from this time because that echo remains today. The entire universe is bathed in a sea of microwaves, called the cosmic microwave background (CMB). The CMB is direct evidence for the Big Bang theory, as it is called. If you have an old TV set you can see CMB photons contributing to the static on the screen. This echo is still here because it has nowhere else to go.

The unimaginable energy (here, think about all the current matter and energy in the entire universe squeezed into a microscopic space) of the Big Bang unleashed a fury of extremely energetic photons called gamma rays. They shot around in every direction, crashing into other particles. Some of those photons are striking Earth today billions of years later, but as microwaves rather than gamma rays (fortunately). About 300 photons are flying through very square centimeter of space right now. There are so many of them, only a tiny fraction of them have stuck other particles and transferred their energy into other forms. Where are they coming from?

To get our answer we need to take a look at the expansion of the universe. No one knows why the universe expanded from a single point or what existed, if anything, before that. What physicists do know is that the Big Bang was the origin of both space and time, as we understand it. Space and time are described as dimensions in a four-dimensional theory called general relativity. Physicists can theoretically trace events back to about 1/32nd of a second after the universe popped, or banged, into existence. Before that time, current theories about how space-time operates break down into nonsense, so it is impossible to peak into the very first moments of our universe.

Shortly after the Big Bang (a tiny fraction of a second), the universe, according to most well established theories, went through a brief period where its expansion rate increased to faster than light speed. Physicists can prove that galaxies farthest away from us are also traveling away faster than light speed because we are now once again in an era of accelerating expansion. These two periods of accelerating expansion owe themselves to different mechanisms.

All of this faster than light business does not violate the special relativity rule that says that nothing, even light, can travel faster than light speed, because space-time ITSELF is the thing doing the moving, or expanding in this case.

How can we see the CMB when it is the oldest stuff in the universe? Shouldn't all those photons be invisible because they are moving away from us faster than they could travel toward us? The CMB permeates the entire universe. That includes the part of the universe that is not moving away from us faster than light speed. This is the CMB that is detectable. Everything is traveling away from everything else in the universe but the expansion is cumulative. You can't even detect it on the scale of our own galaxy but as you get further and further away over great distances, that miniscule expansion rate accumulates so that as you observe regions very far away, you are seeing photons coming from very old stars and their motion is approaching light speed. There is evidence of a much larger invisible universe outside the boundaries of the visible universe. Photons in this outer region will never reach us so it is invisible to us. When you look at the oldest stars you are seeing stars that are long burnt out. You are seeing the light that shone from huge white-hot stars that were born when the universe was just hundreds of millions of years old. In other words you can see ghost of stars that once were. There may currently be new stars in that region that are generations younger but their light hasn't reached you yet.

Expansion of the universe had a significant effect on CMB. Each photon travelling randomly through space travelled while that space expanded. As space expanded, the wavelength of each photon was increasingly stretched across it. What started as very short wavelength gamma photons are now long wavelength microwaves. We can no longer see them because they are now in the invisible part of the spectrum. If you could put on glasses that let you see in the microwave spectrum, you would see the universe glowing all around you. You might be wondering: does this mean that those photons lost their energy to space somehow? No, although this "tired light" hypothesis had some traction decades ago, apart from colliding with other particles and transferring their energy, photons retain as much energy as when they were created. There is no "friction" in the vacuum of space.

An important point to keep in mind is that there is nothing outside the universe, at least according to most theories. A common analogy used to think about the expanding universe is an expanding balloon, but there are some key differences. While a balloon expands into the space around it, there is no space for the universe to expand into, not even a vacuum. The surface of the balloon is a two-dimensional surface expanding outward, whereas the universe is expanding spatially in three dimensions. You can get a simplified idea of what the expansion looks like if you draw a few dots on a balloon with a marker and then blow it up. The dots grow further and further apart from each other as the balloon expands. In reality, however, the dots, which are galaxies of stars, are embedded in the substance of the balloon. A better analogy might be raisins moving apart from one another in a rising loaf of bread. There is an additional quality of space-time that the balloon doesn't illustrate. All the matter dotted throughout the universe affects space-time. It stretches space-time's four-dimensional fabric. Space-time stretches as the universe expands, taking everything in space along for the ride, but matter itself also stretches space locally. Like a bowling ball on a trampoline, a massive object such as a galaxy makes a depression in space-time, except the depression is in four dimensions rather than in three.

Space-time is also a relative fabric. The theory of special relativity says that how a section of space-time looks and behaves depends on how fast you are traveling relative to it. Think of an object like a spaceship travelling close to light speed through space relative to you. In other words it could be flying through space past you as you float in a space station. Its spatial length would appear to be squished. It would look like a short squat ship. It would appear as thin as sheet of paper if it were going almost exactly light speed. People on the space ship wouldn't notice anything weird. The ship's time frame would also stretch. Those people could travel to some planet light years away, settle down and colonize, and still be decades younger than you when they returned for a visit. The movie, Interstellar, illustrates this unsettling effect very well. Exactly at light speed, relative time stops altogether. If you could hitch a ride on the back of a photon, your children would live their lives, the entire history of mankind would play out, in fact the universe would unfold to its end around you and you would not have time to even blink. It would all play out instantly to you. Time also plays this tricky maneuver at the event horizon of a black hole. In this case, time slows down relative to the space around it because space-time around a massive black hole is stretched infinitely by mass concentrated to a point of infinite density. Here, too, however, the rules of physics break down and there is speculation about exactly goes on inside one.

If we get back to CMB for a moment, there is another way to think about why those original photons are still everywhere. Because the universe is a self-contained expansion of what was originally a singular point, there is no location in the universe that you can label as the starting point of that expansion. The entire universe is the starting point. Although scientists (correctly) talk about the oldest stars being those that are farthest away from us, it can be a bit misleading. It doesn't mean that space-time is youngest in the center, and that center is surrounded by older shells of space-time. The space-time of the whole universe is the same age. The whole universe is that point in space 13.8 billion years after it started to expand. That being said, there are older and younger stars. The oldest stars, mentioned earlier, first began to shine just a few hundred million years after the Big Bang. Thanks to the universe being a giant self-contained Big Bang, we can see almost the entire evolution of the universe just by observing photons of light. All the ghosts and echoes of the past are still there. From Earth, distant stars are moving away in all directions. They are red-shifted, or Hubble shifted. The most distant stars are the oldest stars and they are moving away fastest. This is not because Earth is in the center of the universe. It is because everything is moving away from everything. If you could jump into a wormhole and travel instantly somehow to any distant planet in any distant galaxy, you could look up in the night sky there and see the same phenomena. Distant stars would be moving away in all directions and the oldest most distant ones would moving away fastest, approaching light speed.

By mapping out the ancient CMB photons across the visible sky, scientists can glimpse what the very young universe looked like. Its energy wasn't perfectly homogenous. Those slight variations in density created tiny gravitational pockets into which matter tended to clump, forming the first stars and galaxies. Those ancient photons could not travel freely when they were first created. The universe was so dense and energetic that they constantly banged into electrons and protons. When the universe was about 380,000 years old, the density of electrons and protons was low enough that photons could travel for distances between them. From then on, they were free to travel not outward into the universe but in all directions as the universe expanded outward. That is why we can see back into the universe's past only up to 380, 000 years after the Big Bang. By observing a similar map of neutrinos, however, physicists hope to see the ghost of an even younger universe, because neutrinos escaped and began to stream long before photons could. The tricky part here is that neutrinos are themselves almost ghostlike particles. They are very difficult to detect.

Nerd In Vegas

We were newbies. At 50, it might seem difficult to manage not to have gone to Las Vegas even once. My husband signed up for the November Rock n' Roll Race along with a handful of good friends so I tagged along. We've been curious for years: What the heck is Las Vegas?

Note: All prices except stated otherwise are in American dollars as of November 2015. Right now us Canucks are paying an additional 30% thanks to our weak dollar. The prices are included because part of my argument here is whether it was worth it or not. We wanted to stay on the strip and have what we thought would be a real Vegas Experience. Quite a few friends we talked to usually stay off-strip for a little as $50/night and pay much less for restaurant meals. This is our experience along with a little additional information attained through some online sleuthing.

As we landed I could see the city hovering in the desert like a mirage. Even in daytime, it is alluring at first sight, full of promise and magic. We chose a rental car and except for a few misleading exit signs the drive to our hotel was straightforward. Our friends chose to take a taxi to their hotel. Here's where things begin to get interesting, and none of us, even non-newbies, knew any of this. Just to get in a cab in Las Vegas you are charged $3.30. There is an additional $1.80 surcharge for airport pickup/drop-off. There are waiting time fees. Some cabbies will tell you there is an additional mandatory tip as well. In Edmonton, you just get in the cab and the metre tallies up your minutes. I think in most cities it's a pretty standard interaction. Here fares are murky, and often way too high. There is much written online about Las Vegas cabbies taking the long haul route to your destination. They will drive to hell and back to get from point A to point B and being a newb you don't know any better. I sensed this when some friends and we took a cab from our hotel to Freemont Street. According to the map it's a straightforward jaunt from the MGM Signature, where we stayed, to the end of the strip. At night, we were turning off and on ramps and speeding around other cars. The ride was $30, too steep really.  After a little online sleuthing to see what other people have experienced, I have this tip for other newbies (if there are any left in the world besides us): say, "Please take the most direct route. I don't want to go on the freeway."

Joe booked a room for us at the Signature at MGM Grand. The drive to the three towers, the valet service offered, and the grand lobby entrance all make you feel you are in for an exclusive and ritzy experience. There was a hiccup when we checked in. Joe paid for four nights through air-miles, a third party provider, and there was no record of us in their books. After much rummaging through printoffs and waiting around, we managed to produce our confirmation number. I don't know whether air miles or the hotel dropped the ball there. We also dropped the ball by not having all documents within easy reach. Newbie note: make sure you have every document with you and handy, especially if you book through anywhere but the hotel directly.

Our room was very nice with a lux marble tiled bathroom (which is emphasized on the website, of course). For the base price I thought it was a fairly decent deal for a very good room, around $240/night (Canadian). This was the standard price we got while using air miles. If there is a sale, you won't see that reflected in your air mile usage.  It varies by time of year and who you book with, in American dollars, it costs about 30% less, and I would recommend it both for good service and for proximity to the strip (while still being quiet). We found out from friends staying there with us that these rooms are owned and then rented out as hotel rooms, a cool idea. They don't have pressure-sensitive minibars (thank you) but instead have a mini kitchen. If we were to stay there again, we would have asked for the kitchen utensils (not in room but supplied if you ask) and then go to Walgreens on the strip for yogurt, fruit and muffins for every breakfast except for one (rationale coming), for convenience in the morning, a healthier option, and because it is much cheaper.

Not so cool were additional rates charged. First, to print off a few race registration sheets cost us $9. Even less cool was the fact that the MGM pool complex unknown to us was closed for the season (although in fairness I rechecked the website and it does state clearly it is closed now; maybe we arrived just as it closed). We were looking forward to the lazy tube ride and the pools.  Not being able to use any of this, we were charged an additional $29 (American) per day for a resort fee. Really guys?  If the complex was still open, according to the hotel website you must pay for a spa pass of $25 (American) per day per person in addition to the resort fee. Huh? To rent a tube for the lazy river costs an additional $16. To rent a cabana is free (and Tripadvisor reviewers warn that this is the only place you will find shade when it gets fiery hot in summer). The catch there is that you must buy at least $400 (American!) in drinks/snacks to qualify I believe that's for two and it goes up from there, according to a reviewer question on Tripadvisor from 2012. The website only states that a minimum food/beverage purchase is required. We still had access to the hot tub and pool of our tower, however, and we had the place almost to ourselves. Still, I think you can see where this is going. $240/night quickly balloons to almost $1000/night and you still must find breakfast and dinner somewhere and some kind of nightlife. If that is in your budget I say go for it but I would have been miserable spending a fortune just to stay comfortable there in the summer, and I'm still a bit peeved about it in the winter, frankly. Lesson: Everything costs in Vegas. By the way, a newbie tip here is that many add-on fees are not easy to find on hotel websites, especially the pricey strip hotels. I wonder how many people arrive to a far more expensive stay than what they planned on. I find this business approach insulting to guests who are paying a premium for good rooms in a good hotel. For comparison, I experienced one-on-one service with unlimited activities, full access, and almost free amenities including drinks and great local healthy food at an ecoresort in Costa Rica a few years ago, called Playa Nicuesa Rainforest Lodge. I just checked the website: It's $230/day during the green season (when we stayed), very exclusive (can get there only by plane and then boat) and a hell of a lot more fun. If you read some of my other articles you know I try to be ecologically responsible. On this point I argue that even a non-ecoloving person would prefer this other option, although admittedly you will not find sequins, high heels, "call girls" or slot machines. How ecofriendly is Vegas, I wonder?  I'm going to get to that.

When we landed we wanted an early supper so we set off exploring. The towers are connected nicely to the MGM proper, a fairly short walk that includes moving pedways. Once in MGM Grand, however, we entered an endless smoke-and-racket filled casino that is a maze to navigate through. I don't spend time in casinos so its appeal is limited. Good restaurants, or at least restaurants with celebrity chef names attached to them, branch off these gambling caverns. All other high-end hotel complexes we visited were the same in this regard. You had to walk through the casino to get to a good restaurant, to see a Cirque show, to get out of the hotel, to get anywhere actually. And every one is a maze.

Here is one thing I just don't get. All these restaurants seem to open into the smoky casino air. Not only is it unappetizing to walk through a cloud of smoke to eat, but you are also entering a cavern within a cavern. There are no windows anywhere. I don't understand the appeal of a $150 Gordon Ramsey steak dinner (for some wine and dessert, add $100, and I mean per person here). Even if the décor in these restaurants is really stunning (at least what I could see peeking in).

We kept on and made our way to the monorail station. If you want to see the main highlights of the strip, buy a day pass. For two of us it costs $24, one of the few charges I felt was totally reasonable as it connects you quickly to several key tourist destinations on the strip (traffic on the strip at night is too congested for a car but I had a reason for the car rental, coming up). By now it was dark and the strip lights were indeed dazzling. We had found ourselves buying a Fat Tuesday drink on the way (a boozy slush drink in an insulated cup). These were indeed good and every flavour we tried was delicious. We found it fun a bit thrilling to walk around with a boozy drink all over Vegas as it is most definitely legal to do so within the city. They are $15 each and $10 if you bring back your cup to reuse. I give them an eco nod for the reusing option. There are Fat Tuesdays and their knock-offs all over, almost as many as there are Starbucks. The Starbucks in our hotel charged twice as much as the ones near the strip. As breakfast options are limited right at the towers (there is only one small café and Starbucks) it seemed natural to just get two lattes, two yogurt/fruit cups and a doughnut for breakfast, until we got our bill, $45! With that option shut down, we reacted by going big and going tiny on following mornings. On Sunday morning before the race, we opened our wallets and enjoyed the champagne brunch at the MGM. It costs about $28 each, a great deal compared to Starbucks, and it was good! Great food, great service, lots of choices, wonderful champagne orange juice. We took our time, got very full and got giggly. I consider that a worthy indulgence. It got our spirits up when we were starting to wonder about this whole Vegas thing. To go tiny we trekked to the food court in the MGM. Perfectly acceptable breakfasts can be had here on a much smaller dime. Still not uber-cheap by any means. And where can a soul get a piece of fruit or vegetables to nibble on? God help vegans in Las Vegas.

What got to me, and I think to my friends and possibly most visitors as well, is that absolutely nothing is straightforward. What should be a simple walk down the strip is in fact a maze. Before you know it you are finding yourself walking up across a pedway into yet another hotel, and more specifically into its rambling casino. It may be Bally's or Paris or New York, New York, Caesar's Palace or the Venetian. Regardless, you will be fighting your way through a smoky casino maze to get to any of the "good" stuff like miniaturized versions of Paris. Or Rome. Or something. Getting off at monorail stops is no different. Your first sight will be maybe a few shops and then a casino. I would think more than a few people start to get as creeped out by this as I did. Even if you choose to simply walk the strip, you are in a noisy congested maze of people, sights and lights. Tack three times onto to any length walk you plan to make. Forget Google's walk time estimates. They're no good here because time and space in Vegas operate according to their own mysterious physics.

On this point I found myself experiencing a really odd mix of emotions. It is overwhelming and in a vague sense alluring. At low moments I felt like part of herd of cattle marching to some unseen slaughterhouse and I started to feel manipulated, as if "They" are going to get my money one way or another and I will eventually realize I am powerless to stop it. I started to feel really angry toward "Them." I was going to have my own Vegas vacation on my own goddamn terms, thank you! As a tourist, it is hard not to feel more than a bit manipulated or at least micro-managed. Who are "They" I wondered. I will get to that.

Despite this, we found our way to small treasures. There are very good little eateries all around the artificial cities and there are cheap eats on the strip but you generally must look for them. For example, Jean Philippe Chocolates and Pastries in the Bellagio, is a really wonderful place to stop and eat. This man is a world renowned pastry chef. The cascading glass chocolate fountain is dazzling and the pastries and treats are beautiful to the eye and welcomed by the taste buds. We got some great savoury crepes there. The salmon in mine was astoundingly fresh, as fresh as seafood right off the shores of Vancouver Island. This led me to research, and perhaps it is no surprise that Vegas boasts one of the most sophisticated food supply infrastructures in North America. Ingredients are shipped fresh and fast from around the globe, and you can find everything here from fresh wild salmon to sea urchin to any caviar you desire, etc. For a steep price, however. And served in a cavern. There is great pizza to be had in a shop in Ceasars Palace. There is a fantastic pub with a really good beer list in The Venetian. Most of these offerings were on the reasonable side and they were all very good. I don't know what the right way to do Vegas is but this approach seemed like a sound option. We also got to try White Castle fare and Crispy Crème doughnuts, two American treats that have been on our to-do list for some time. I suppose the other option, if you have a big budget or simply want to do Vegas BIG, is to try several high-end famous chef restaurants. There are many. However, I did find it somehow distasteful to discover that Mr. Ramsey represented himself in at least three eateries, covering the entire price spectrum. It seems a bit obvious that this is easy money for an already wealthy man. And what do I get for this? Certainly Mr. Ramsey himself is nowhere to be found. Perhaps a plaster likeness of him would yell at me as I walk into his restaurant: "You STUPID COW!!" This idea in general somehow seems a bit dated to me. I go back to my earlier comment that if I want to spend money on a chef eatery, give me a chef in his own native restaurant where he lives and creates, where he sources his ingredients from the local farms. He doesn't have to famous. NOW I will happily give over $300 to enjoy a truly transcendent culinary adventure. But not here in this fake jungle. It's on principle now. And the principle, I learned online is called "the concept-driven restaurant." This, along with craft beers, is a new trend and Vegas is playing catch-up.

I found to my surprise stunning art in Vegas. It is all around to be had for free. You just have to enjoy it. To get to that patisserie I mentioned we walked through the Bellagio conservatory and the Fiori di Como – the glass ceiling flower art – in the hotel lobby. I spent several minutes aiming my camera upward to photograph it. And I spent several minutes just looking at it, so beautiful! The glass artist, Dale Chihuly, is very accomplished and he was commissioned to make this piece in 1998. It cost $10 million to create and consists of 2000 hand-blown glass blossoms that weigh 40,000 pounds all together, all supported by a 10,000 pound steel armature. Between 2 and 5 am every day, a team of about eight engineers clean and maintain it. This piece reminded me of my most favourite glass art, the modern stained glass windows in Hereford Cathedral in England. The windows were inspired by the poetry of a 17^th century Hereford poet, Thomas Traherne. My sister bought this poetry book for me when we visited there on a walking holiday. It is spiritual poetry that is stunning in its descriptive powers of the human heart, as stunning as the sound of the organ and singers in that wonderfully atmospheric cathedral. Now in Vegas, does the Fiori di Como achieve spiritual depth (or height)? Should it? I read online that many people come just to see the flowers and many of them sit under them for hours contemplating them. Others lay on the floor to see them best. Could they be so hungry for something beautiful in a real sense? I was.

In the following days, I looked for art and found it in installments, sculptures, and in galleries. It is good art, or at least art that made me stop, think, examine and question. Picasso and Salvador Dali works could be found as well as other artists I had never heard of that I thought were even more fascinating. There is a gallery devoted to the work of a Russian artist in the Forum shops at Caesars Palace, that is just, how can I say this, utterly intriguing.

While Joe ran a half-marathon, I thought to myself as I explored: Vegas itself is a marathon. I need stamina to get to all the places I want to see, and I need to pace myself and guard against sensory exhaustion. It is both feast and assault to your senses. There is beautiful and even sublime if you look. There is also tacky, gross, depressingly sad and just plain weird. It is both thrilling and disorienting. I kind of loved it a little bit, but in the same way as the line in the movie Backdraft, "The only way to beat fire is to love it a little." You need to be on guard in Vegas. I could sense its predatory nature and, in fact, I suspect predation is really what Vegas is all about. It is sometimes subtle. It knows that you are going to eventually say to yourself, "Well I'm here so I might as well . . ." and that is when you begin to contribute your share to the massively expensive infrastructure that is Vegas. It is a machine carefully designed to relieve you of your money, and it will most often do it while you are enjoying yourself.

It feeds on your weaknesses: shopping, gambling, drinking, eating, and sex in any way you can imagine it, and pride too because there seems to be an unwritten rule here: don't look cheap or poor. You can look tacky though, and in fact here I think tacky gets you fashion points. Newbie tip:  Especially if you have a bit of a psychological interest, watch people's faces while they walk, while they eat, and while they party and gamble. I felt sometimes I was witnessing seethingly powerful forces in our collective unconscious at work as I walked, especially after dark. I felt my own mysterious urges and thoughts stream upward to greet me at strange and unexpected times. I knew I was experiencing only the glitzy shell of Vegas, but I could vaguely sense something ugly deeper inside, truths about Vegas that maybe cabbies, the police and social workers know too well. There is also raw celebratory energy in places and I could see many people simply letting loose according to what appeared to be a more innocent agenda. Is that so bad? I let it take me over a few days later as I danced with our friends at the open-air concert on Fremont Street. It felt good to let it all go. It feels as good now to let the little kid inside gawk around inside fake Venice, Rome and Paris. They are fun; we both enjoyed walking around in them. But these themed places will never age gracefully like the originals. There is a brutal obsolescence built into them, because what's currently "in" changes on a dime, and I can feel they are already missing the mark. Look with your rose-coloured glasses and there is romance in Vegas too, even if it comes from a fake streetlamp shining gold light onto fake cobblestone. There are numerous places to stop and steel a kiss with your sweetheart.

We spent lots of money to see "O" on our first night there and it did not disappoint. These Cirque du Soleil shows offer magic and awe and they are gloriously beautiful. We see the traveling shows whenever we can in home in Edmonton. This was our chance to see a permanent show. The technical achievement of it utterly fascinates me as I think about it. Newbie suggestion: do see at least one show in Vegas. I think a burlesque show or magic show could be equally fun. It was a good introduction to Vegas because Vegas itself, I was learning, is theatre. As long as I kept this knowledge in mind, I enjoyed my experience and let some of its magic in. Even the ubiquitous casinos are theatre, really. There is a spectrum on offer from techno-new (MGM, Bellagio) to an old school glamorous/a-little-sleazy. I am thinking of the quite wonderful but horribly smoky Golden Nugget casino on Freemont Street. It was interesting to compare that hotel lobby and casino to the newer monstrosities on the strip. That older building is more humanly sized and it instantly feels just a bit less intimidating. I wonder if the strip development overdid it. Had it gone too far and made us feel more uncomfortable than comfortable? Judging from how popular the strip seems to be, I might be alone in that thought. As a group, we ate dinner at Vic and Anthony's in the Golden Nugget. It is elegant, intimate and totally overflowing with the glamorous atmosphere of what I imagine as "Old Vegas." I loved the swooning voices of the rat pack in the background as we enjoyed a memorable dinner together. Newbie tip: this is a place I would definitely go for a quintessential steak dinner experience in Vegas: really good, not crazily expensive and worth every dime.

It is in a way wonderfully fitting to take in the Mob Museum near Freemont Street. If you wonder like I did how Vegas got to be what it is, this is a fascinating place to dig in and investigate. Money, crime, and power families – in there you see both the glamorous lifestyle of the mob bosses and their women as well as the ruthless and short lives of made men. There are intriguing connections to the Kennedy assassination, to Cuba, and even to the recent European soccer scandal there. Old Vegas came to be when the mob found a city to invest in. The mob was cleaned out of Vegas in the 1980's with a series of high-profile investigations and arrests (and here you can find some very interesting origins of modern investigation techniques such as the witness protection program and the switch to trying people according to connections to criminal activities rather than according to each individual crime). I think admission was around $20 each, money well spent!

Las Vegas, I learned online, is always transforming itself. The mob gave Vegas the blueprint that corporations now use to develop it further, bigger, better. At least they hope it's better. I'm not convinced. It seems people love Vegas to party, gamble, be someone different, and play, but it is a slick operation that takes as much money as it can psychologically muscle out of you. It can leave you high and dry to fly home, defeated and wondering what just happened. There is a lot of "I hate Vegas" online I quickly found out, and the reasons seem to be similar to the letdown I felt there, rather than just those that lose big at the tables, although I suspect there are countless people who lose homes, cars, etc. in the casinos. Travellers are more sophisticated than ever. People have more vacation options too. They can see real European cities in their own unique way. They can travel to out of the way countries to eat the exotic foods there, and they can experience local cultures. People are savvy and they can smell a tourist trap. Vegas, it seems to me has done it all way to obviously. What it offers is something like Velveeta processed cheese. You know you can get real artisanal flavourful cheese elsewhere, and probably for much less. More than a few of my friends seem to be kind of sick of the place, especially those that have been there a few times. Will millennials buy the hype? Are the swank nightclubs enough for them when there are better ones arguably in Europe and most have been there too at least once? Those kids are even more critical of everything than we are.

Christmas is approaching and it likewise promises magic as well as a rosily unrealistic expectation of loving family harmony for the holidays. The reality is extra stress and cost, a few tensions here and there among family, and if I am lucky a few moments of rest. It is not a very restoring experience. Yet I feel the Christmas magic enter me and I love that feeling of anticipation. Even though I am definitely old enough to know better, and I know I am going to get cranky putting up the tree again and I'll need a stiff drink or two before the holiday is over, I love the theatre and ritual of it. How different is that from the Vegas Experience? Maybe there is something in our hearts that desires it. Christmas, however, is at least anchored by family bonds and by something spiritual and historic. Vegas is anchored only by money. It's ultimately sadly hollow. If we go there hungry, we will go home even hungrier.

Is Vegas on its way down? Will millennials embrace this kind of "more is more" mentality? Or have they had it with the baby boomer greed they had to grow up living with? Time will tell. More pressing is the question of whether Vegas will survive climate change and the deep drought threatening the water supply of Lake Mead. When we arrived I could see the steep dried white backs of the lake against Hoover Dam, stark evidence of a severe and increasing water shortage. Although you can quickly forget Las Vegas is actually located somewhere on Earth, it is indeed plunked down in the middle of Mohave Desert. The only water supply is the Colorado River, and it is being way over-used in the continuing drought experienced there. The city invested more than $1 billion to build new intake valves at the bottom of the lake behind Hoover Dam because the water level is falling below the present intake. It also cut its water consumption by 23% while the city grew by 500,000 people.

It seems that while the city itself is not in denial, the tourist zone is. I never saw a low-flush toilet or low-flow showerhead. Our room instead had a deep Jacuzzi tub. It seemed at least the tourist zone is ultimately unsustainable, and that is where almost all the investment money is. Imagine summer temperatures continuing to rise and at some point, being virtually unlivable. Will resorts build giant air-conditioned domes over their resorts, thus making the experience even more claustrophobic? Perhaps some enterprising CEO will capitalize on climate change and create an enclosed Moon or Mars experience, so you can feel like a new world colonist while you gamble. I never saw a single recycling bin anywhere, and in Vegas you quickly realize how much plastic and other waste you create when you rely on take aways and disposable drink cups. Perhaps city management thinks it’s a lost cause to get drunk people to recycle their garbage. So much trash is thrown right on the ground and many people are hired to discretely clean that up all day and night. I can just imagine how large the local landfill must be and how fast it must be filling up. Something is going to have to give at some point if climate change continues on this trajectory, as it is expected to. The twenty-somethings I know are more than a bit peeved that we baby boomers have done so much damage to the planet. Vegas could be the lightning rod for that resentment, rather than the escape destination it hopes to continue to be.

However, Las Vegas also seems resilient and the corporate machine here is very intelligent. In fact, I find myself wondering what kinds of secret algorithms CFO's, or gambling managers or whatever they are called, employ in the money-generating gaming rooms. Who so cleverly designed the disorientating passageways that funnel humans into casinos? I admire how seamlessly it seems to work. Still, surely CEO's know the world is changing fast and that even a denial as solid as the Hoover Dam can't win out over reality. Will Vegas reinvent itself as the Green Gaming City? Will solar panels outshine hotels as we fly in? And why aren't there already solar panels everywhere? It's not a new technology and it is now quite affordable, an investment that would in fact reduce energy bills and save money. Will we ever see native gardens planted among the buildings? How about greenhouses somewhere close by to supply food?

Caesar's Entertainment, which owns Caesar's Palace, Paris, Bally's, Flamingo, Rio, Planet Hollywood, Harrah's Las Vegas and the Quad, launched a Codegreen program in 2008. To see a review (as of 2013), read this case study. You have to purchase the PDF to read the entire paper. Frankly I find it very light on current specifics and heavy on future plans and initiatives. MGM Resorts, the other big corporate player in Vegas, owns MGM Grand, Bellagio, Mandalay Bay, The Mirage, Monte Carlo, New York-New York, Luxor and Excalibur as well as the new CityCenter, a massive strip complex that includes new conference facilities. It launched its own program called Green Advantage. In 2013, 12 MGM properties were certified as Greenleaders by Tripadvisor. Mandalay Bay announced it plans to install the second largest rooftop solar array in the U.S. (finally! and I will believe it when it actually happens). To get an idea of how MGM Resorts is attempting to go green, watch this October 2015 Bloomberg video. Don't expect hard facts here either, but instead beware of too much of what I call corporate-speak. My response to both programs is yes, you are making strides in building more efficient energy production facilities and recycling cardboard (things that reduce your bills and thus your bottom line), but you are light on details about true eco-responsibility, and you are not doing nearly enough to address your critical water issues. In the video the sustainability officer (yes MGM has one to its credit) states that when they constructed their latest LEED-certified CityCenter, they did not want to look anything like an ecoresort. It needed to look glam and shiny, in keeping with what they think tourists are attracted to in Vegas. But will younger tourists continue to find that attractive? I seriously wonder.

The world and how we relate to it is changing fast, I think if these corporations have a fatal flaw it will be that, like a large ship, they are too heavily invested to turn on a dime. They might be too big to keep up with rapidly changing demands. One thing is clear: they understand that at least selling green is important to today's tourists. They are under pressure to promote a glamorous green. Is it real or is it window-dressing, because it seems to me they no longer have the option of green-washing if they want to survive. Convention attendees, coming from companies that are practicing green initiatives, expect their convention center to be practicing them too. Most tourists are going to demand that as well. It doesn't feel good at all to know I am being far less ecofriendly in Las Vegas than I am at home. This city is clearly under environmental stress and I only exacerbated it with my presence there.

Nevada is a beautiful state and when we drove out of the city to hike I couldn't help but wonder why Las Vegas couldn't embrace its natural surroundings rather than build replicas of elsewhere to attract people. Will people game and have fun in a natural setting? I think so.

If you go to Las Vegas, try the Red Rock Canyon. It's about 40 km (26 miles or so) out of the city (the reason for the car rental). We had time to explore the interpretive centre, which is very well done. Knowing nothing about desert flora and fauna, and the history of people there, it was really fascinating to learn. The exhibits are set up to make that easy and fun. We found that in mid-November the temperature is perfect, for example, mild 20C in the day and a refreshing 14C at night. After reading several blogs online about other people's experiences, I think this is a much better time to visit than during the heat of summer. In summer, prepare for 40C and much larger sweaty crowds everywhere.

We hiked the Calico Tanks, called the quintessential hike online. It is both challenging (some route finding skill is good) and so very beautiful. This was my one must-do as I had never hiked in desert before. How the light plays on the colourful rock and craggy ancient trees is stunning. There are indeed water tanks hidden in the large crevice, and I'm sure that animals and people have used that secret source for thousands of years. They were low but there was standing water even during this extended drought Nevada is experiencing. Do hike this if you can, but don't if you have knee problems. Do wear shoes with good grip as you will need that. And bring at least 1 litre of water for your hike (more in summer). If I were to do it again I would backpack in a nice picnic to enjoy with Joe at the end where we reached a summit that overlooks Las Vegas in the distance. There we could enjoy the city from a new perspective. I would also sign in at the signup book at the interpretive centre just so that they know we are out there.

I really wonder how Las Vegas is going to adjust or if it can. I would like to say I am above the unevolved thrill of Vegas but I am not, at least not completely. She left her mark on me as this article attests. Still, I know there are far better places to experience out there in the world. As our plane took off, I watched the dark and glittering city disappear behind me and I felt glad I experienced it. But, Vegas lived up the image of a mirage in the desert. At first, it seems to promise so much but, at least for average working class people like us, it ends up delivering very little. 

Amplituhedron (For the Rest of Us)

There has been a lot of buzz over the last two years about a geometric shape called the amplituhedron. It has its own Facebook page (with the bold statement "I am the shape of the universe") and more than one jewelry vendor sells trinkets designed after an artist's rendering of its shape shown in several articles. In more scientific circles there are "amplituhedron" discussion groups, where the nature of space-time itself is energetically debated.

The amplituhedron is a new mathematical object coined by its discoverers Nima Arkani-Hamad and Jaroslav Trnka in 2013. The excitement about this object is not only that it might be a first tentative glimpse into the secret nature of space-time. It also questions our concept of space-time itself, the brainchild of Albert Einstein and others and one firmly entrenched in how we think the universe works. When we look into the amplituhedron, we might be peering into something deeper and more fundamental than space-time.

As exciting as this breakthrough is, it is very challenging. There is a wide chasm between the extremely technical and difficult to understand original article and popular accounts of it in magazines like Discover and Scientific American. It's not easy to know the science behind the amplituhedron, or how it fits into modern theoretical physics and there are misconceptions online about exactly what this object can and cannot tell us about the nature of reality at its most fundamental level.

Introduction

I usually start my investigations at Wikipedia. In this case Wiki offers perhaps the most concise treatment you're going to find, to a fault really. It also tells us nothing about why it's caught our scientific attention like it has, why it's so special. I think it's much better to start with Natalie Wolchover's very good article in Quanta magazine, called A Jewel at the Heart of Quantum Physics. Here she tells the compelling scientific story of the amplituhedron. I hope to build on that story here and try to work out why and how you get to the structure itself.

The amplituhedron is a mathematical object that exists in a branch of theoretical physics called quantum field theory (QFT). Quantum field theory is a conceptual and mathematical framework for studying the behaviours of subatomic particles. It is in some ways an extension of quantum mechanics (QM), the theory that governs how individual particles behave. In QFT, you can describe not just the individual behaviour of particles but how they behave together in space and time, how they act in a field that has spatial dimensions in other words. Think of electrons moving in an electric field for example. We can use QM to describe the workings of a single electron. We move on to describe its motion and behaviour with other electrons and with photons if we use the simplest and best understood branch of QFT called quantum electrodynamics (QED). QFT is a very powerful and very quickly expanding field of study. Like a block party that's getting out of hand, the branches of the theory extend outward to talk to other theories and there are many cases in which QFT's do not agree with each other and some do not even speak the same language. Usually, the very idea of what the particles "live in" varies with the QFT you choose.

As newcomers to theoretical physics we can be happy just to understand the basics of Einstein's 4-dimensional space-time. Yet even here, once we dig a bit deeper, we find that space-time comes in different forms depending on what kind of action we want to describe. If we want to talk about a problem in special relativity, the space-time we use is a simplified type of 4-dimensional smooth Lorentzian manifold called Minkowski space. If we want to describe how space-time stretches and bends under gravity, we use tensor fields in the Lorentzian manifold described by general relativity. We can also assign various symmetries to the mathematical structure of space-time. Usually this is done to simplify the solution to a particular problem (the link above is an excellent lecture all about symmetry in physics). Many space-time theories are physical theories - they are abstractions or models of the physical (real) entity of space and time, but they are not the entity itself, a point that I wish to stress in this article.

Space-time is just one of many mathematical models that attempt to describe the dimensions of space. In theoretical physics, space as a real entity no longer exists. It becomes one of a large number of possible mathematical models, which can house specific particle fields, symmetries and dimensions. They can also have unique dynamics. General relativity space is stretchy but special relativity space isn't. Many of these models are inconceivable in our everyday world.

The amplituhedron exists in a very specific mathematical space described by N=4 supersymmetric Yang-Mills theory. This space is a mathematical model and the amplituhedron is mathematical object within it, and it is defined by its own mathematical space called the positive Grassmannian. It is not important to memorize these terms but instead to grasp that the space we are talking about is not real physical space. You cannot go out and find Yang-Mills space somewhere. It is a simplified system or approach to tackling a complex problem in a new theory. For example, a physicist can put a new theory into N=4 supersymmetric Yang-Mills space and see how it evolves in it. Is it solvable for example? We can think of N=4 supersymmetric Yang-Mills theory is a simplified unreal universe that is perfectly symmetrical and has no gravity. We don't know if the supersymmetry (this article link is an especially good introduction) this theory describes exists in reality or not. No supersymmetric particles have been found yet - particle physicists are looking for them. In this case supersymmetry does the all-important job of simplifying matters - when solving for this theory you can swap out bosons, fermions and scalar fields and the predictions of the theory don't change. N=4 super Yang-Mills, derived from a simple 10-dimensional theory, is closely related to the most popular 11-dimensional string theory called M-theory or matrix theory. The amplituhedron is the result of working string theory into twistor space or twister geometry (this is how we get to the geometrical object), which happens to have the same dimensionality as 3+1 Minkowski space-time.

When this was done, researchers noticed something very unexpected and that is what I wish to focus on here. The real jewel is not so much the pretty colourful object sometimes dubbed the "shape of the universe" but instead the hint that it is making to us - that a geometric approach to understanding space-time might reveal new insights into how it works.

Two Pillars of Theoretical Physics Re-Examined

Like the space-time in which it is formulated, the amplituhedron is not a real object. It is a tool, a spookily efficient tool that greatly simplifies how physicists calculate something called scattering amplitudes. You can try out an introductory lecture on scattering amplitudes by the lead author himself, Nima Arkani-Hamad, at Cornell University. There, you can get a sense of why he is so passionate about this research in general as well. We'll get to this most important part but first, when physicists look at the calculations involved in creating the object it appears that two things we take for granted in physics, two conceptual pillars if you will - locality and unitarity - no longer look fundamental but instead seem to be emergent properties of reality. Much of the internet buzz focuses on this.

Locality

Locality has been on shaky ground for several decades now. Non-locality (Einstein's spooky action at a distance) is probably one of the first stinging slaps we feel when we begin to explore quantum physics. Quantum mechanics is to blame. The principle of locality states that an object is only directly influenced by its immediate surroundings. For an action at one point to influence an action at a distant point something like a wave, a particle or an energy field must carry that influence. However, a measurement on one of a pair of entangled particles causes simultaneous collapse of the wave function of the other particle no matter how far away it is, even it it's across the universe. This phenomenon, called quantum entanglement, has been experimentally verified. Therefore, QM might not be a local theory (if you get into this, you will find controversy around this. A number of experts do not accept non-locality despite the evidence, and some have found ways around non-locality, hence my use of "might").

But special relativity (SRT) is a local theory. It requires that no influence can travel faster than the speed of light. If we get back to our opening QED example (electrons and photons in space) of a QFT, we get our first taste of just how utterly complex QFT really is. Under most interpretations of quantum entanglement, understanding QM demands that we discard locality at the subatomic particle level. Understanding SRT demands that we must accept locality, however, because we must have it in order for the theory to make sense. It prohibits any influence from traveling faster than the speed of light through space. And yet QED, which gives a complete mathematical description of how light and matter interact, is built on QM and seamlessly incorporates SRT. To see this contradiction between QED and SRT in action so to speak, I recommend that you examine the famous double-slit experiment.  In two past articles I wrestle with the implications of this experiment: What Is An Electron REALLY? - scroll down to the subheading Young's Double Slit Experiment Peers Into a Secret Quantum World and The Universe Is Real and Not Real - scroll down to subheading What Young's Double Slit Experiment Says. As you mull over this experiment yourself, I don't think it is too much of a stretch to accept the possibility that locality could be emergent rather than fundamental.

Before I go on, I should mention that not all researchers agree that locality and unitarity are in fact emergent phenomena in the amplituhedron theory. Some experts prefer the term "derived" instead because, they argue, when we look at N=4 supersymmetric Yang-Mills theory by itself, both locality and unitarity are preserved exact and they can both be derived from the mathematical description of the amplituhedron developed in this theory. However, as the paper's authors argue, locality and unitarity are not required in the mathematical description of the amplituhedron itself so they can be thought of therefore as emergent phenomena in that they don't necessarily exist at the quantum scale but they show up at the macro scale.

Emergence is any property, law or phenomenon that occurs at macroscopic scales but not at microscopic scales, even though a macroscopic system can be thought of as a conglomerate of microscopic elements. In this case, both locality and unitarity might arise in the system as we move from the microscopic quantum or particle scale up to the macroscopic or everyday scale we ourselves experience and can test. There is a subtle but important distinction between emergent and mathematically derived. The paper's authors go on to make a case for a connection between these "emergent" phenomena and the indeterminism in QM. This is an important little point because much of the excitement in the physics community stems from these two being emergent. I invite you to be the judge. As food for thought, try this exchange on phsyics.stackexchange.com, where the question of emergence versus derived is tackled by a physicist from England.

Unitarity

This phenomenon - the second of two widely accepted beliefs in physics - is just as deeply ingrained in our logical minds. Like locality it makes sense and to consider otherwise jolts us. To describe unitarity we must delve into probabilities. The amplituhedron, and quantum mechanics in general, are all about probabilities, thanks to the uncertainty principle that underscores the theory. You have probably heard of the electron cloud inside an atom. It's a region around the nucleus where an electron might be because we cannot know exactly where it is at any given moment. Put more precisely we can know either the electron's momentum (and velocity) or its position but we cannot know both simultaneously no matter how carefully we measure them. Uncertainty is built into the quantum system. We can however assign probabilities to these values, and we can sum up or integrate the probability densities at all points inside the electron cloud (a tedious process!) and they will add up to one - meaning that there is absolute certainty the electron is in there somewhere.

Particle physicists, those people who smash particles together to see what happens, rely heavily on probabilities, or probability amplitudes or scattering amplitudes as they are most often called, in order to anticipate which particles will come out in any given particle collision. For example, smashing two gluons together in a collider does not give you a single standard result, a consistently identical set of particles every time. The particles, and their momenta, can vary each time even under identical conditions. This is the experimental verification of uncertainty. You might be most likely to get a particular outcome (there is a high probability density for example that two gluons will come out) but there are always less likely possible outcomes as well to consider (a gluon and two photons might come out instead, adding up to the same total energy) and all of these, which approach an infinite number, must be added to get that perfect value of one. You can call it the conservation of probability. We are going to delve deeper into this kind of scenario because atom smashing probability calculations are exactly how the amplituhedron came to be, and exactly why it is such a remarkable breakthrough.

The amplituhedron theory suggests that at a very fundamental level of reality unitarity doesn't have to be conserved. Like locality, it is emergent. Here is a possible explanation of why that might be the case, and it comes from how Arkani-Hamad himself talks about it in his paper: in any collision event, all the probabilities of what will come out and with what energy is actually infinite (meaning unitarity is conserved), but the system of particles in the collider must be finite in reality and this is where unitarity falls down and is not conserved.

You could also argue that both locality and unitarity fail because the measurement itself fails, in the case of black holes in particular. If you could measure a phenomenon and go smaller in scale, down to Planck scale (which is about 1.6 x 10^-35 m), the energy you would need to make your measurement would approach infinity. To measure or "see" something you need to detect it - hit it with a particle and let the particle bounce back. A (big wavelength) visible photon definitely won't cut it. A smaller wavelength electron won't do; even a tiny wavelength ultrahigh-energy gamma photon won't work. Even if you could measure it, infinite energy focused on an infinitely small spot would form a black hole, making any measurement attempt impossible, and therefore you can't address the validity of locality or unitarity at Planck scale and lower - the scale in which subatomic particles live. For those black hole enthusiasts, one can also argue that black hole information loss also destroys unitarity.

Keep in mind that mathematically speaking the amplituhedron does not require either locality or unitarity yet in the Yang-Mills theory in which it is formulated both are preserved. Does the possibility that locality and unitarity are emergent phenomena hint that the fundamental reality of the universe is different than what we know of it through quantum mechanics and general relativity? One of the most mystifying things in theoretical physics is that these two vastly successful theories do not talk to each other (they don't commute) and yet the universe seems to be a single seamless reality. Many theorists hope that the amplituhedron or a related theory might be a first (baby) step toward a new framework that can describe both the quantum world and gravity. What the geometric structure of the amplituhedron can do in terms of particle physics calculations offers perhaps the most compelling hint that this theory or one like it might someday reveal a more fundamental simpler unified reality. By discarding Feynman diagrams and using the geometry of the amplituhedron instead, one can drop even the familiar notions of position and time to calculate how particles behave. What does this mean for our notion of space-time?

Is the Amplituhedron a Look at Reality Through A New Kind of Magnifying Glass?

When particle physicists try to predict the outcomes of various particle collisions, they must preserve the unitarity of the system. In a way it is like balancing a chemical equation by adjusting the number of atoms on each side of the equation except that in this case probability is balanced or conserved rather than the number of atoms. Unlike chemical equations, the process of calculating all the probability amplitudes is almost impossibly difficult. Even a very simple 2-particle gluon-gluon collision into 4 less energetic gluons requires a computer to do the work. As the number of particles involved in a collision increases, so does the complexity of the calculations.

1) The Amlituhedron as a Powerful New Method


The amplituhedron is all about particle physics, the branch of physics that studies the nature of particles that make up matter and energy. We often think of subatomic particles as the smallest possible physical objects, like specks of dust. However, subatomic particles are currently understood as excitations of quantum fields, and that is why quantum field theory is used to investigate these particles. The ultimate quantum field theory is the Standard Model of particles. The supersymetric and string theories mentioned, including N=4 supersymmetric Yang-Mills theory, are extensions of the Standard Model.

Particle physicists study the behaviours of subatomic particles and look for new theoretical particles by smashing atoms and particles together in high-energy colliders. Those theoretical particles that belong to supersymmetric theories, for example are suspected to be very massive and very unstable. We don't observe them in everyday matter because they should live only in a very high-energy environment, the kind of environment a high-energy collider can replicate. This is how physicists hunt for these exotic particles and finding them will help answer fundamental questions about why matter and energy is the way it is in our universe.

2) Feynman Diagrams

When two particles are smashed into one another at almost light speed, they are annihilated and a multitude of new particles scatter from the impact, created from the relativistic mass of the original particles (recall that mass is equivalent to energy). In order to predict and identify specific particles, many of which do not exist outside of atoms such as gluons, physicists use something called scattering amplitudes. These are complex numbers that, when they are squared, give probabilities for incoming particles to scatter into particular outgoing particles. In theory you can calculate scattering amplitudes by drawing Feynman diagrams of the collision, using a set of schemes called perturbation theory. It's a way of describing a complex system in terms of a much simpler one. You take a simple system that has a known mathematical solution, add "disturbances" to it, and then measure what happens to the system. Your results are called corrections.

The calculation of scattering amplitudes requires large complex integrals over many variables. They are complicated but they do have a regular structure and they can be represented by Feynman diagrams. The diagram offers a simple visual representation of a huge arcane and abstract formula.  A generic Feynman diagram is shown below.

Krishnavedela;Wikipedia

This one happens to represent a particle-particle interaction. Particles (of momentum p) correspond to the solid lines and the dotted line corresponds to a virtual particle of momentum k. This diagram could represent two electrons interacting through the exchange of a virtual photon, or two neutrons interacting through a virtual pion or two quarks interacting through a virtual gluon. The inner dotted line represents a virtual particle, which is never directly observed and never stays behind as a product. What it does is mediate the interaction. Most often you will see it drawn as a blue squiggly line.

We would be done here if this were the whole story to particle interactions but according to Feynman's work on path integrals, there is actually an infinite number of paths a particle can take from the left side to the ride side. Theoretically it could take off, go around the universe, interact with an enormous number of other particles and come back. Not surprisingly, this introduces complexity to the Feynman diagrams. The diagram above describes the case where the momentum (or energy) of the virtual particle is fixed. It's completely determined by the momenta of the external particles. It is also the sum of their momenta, and most of the contribution to the amplitude comes from this single interaction (called a tree diagram). However, there are many possible ways to get from a to b. There are cases (in fact an infinite number of cases) where the momentum of the virtual mediating particle is not fixed. These are higher order corrections to the perturbation theory. They can be drawn as loop diagrams (the loop or loops is/are drawn where the dotted line is located). These diagrams - one loop (2nd order), two loops (3rd order) and so on - are notorious for being difficult to solve. As you go up in order your corrections contribute a smaller and smaller fraction of the total amplitude. At the same time, the number of equations goes up - in alarming fashion. Loop diagrams indicate collisions where virtual particles interact with each other before branching out as products and these virtual particles can have very high momenta and very complicated interactions.

3) Beyond Feynman Diagrams

In 1948, the Feynman diagram method was a huge breakthrough in particle physics. Finally you had a way to visualize what was going on at the particle level, but what you get is a frustratingly complex picture for all but the simplest of particle interactions. N=4 supersymmetric Yang-Mills theory beautifully simplifies the way-too-heavy Feynman diagram method. How it does this is a question of math. Why it does this is a source of wonder. This theory has three symmetries in it and we can eliminate a large number of scattering amplitudes (corrections) by requiring that each amplitude conform to the three symmetries. Ordinary Yang-Mills theory describes electrodynamics and quantum chromodynamics. It works very well to describe the behaviours of electrons and quarks in other words, and it can be thought of as a very good physical theory. The supersymmetric extension of it, though very useful, has not been found in nature because no supersymmetric particles have been discovered (yet). It is a drastically simplified version of reality and therefore it is considered to be a toy theory rather than a physical theory. I say this as a reminder that neither Feynman's infinite integrals nor the geometric structure of the amplituhedron are meant to be understood as physical processes in nature. If you could look at what's going on with an impossibly powerful magnifying glass (and not make a black hole) you would not see infinite summation arrows or Feynman diagrams or amplituhedrons. I hope I am not insulting you but I continually find myself wanting to do this.

To do the amplituhedron simplification, two mathematical tools are used - twistors and Grassmanians.

First, Andrew Hodges discovered in 2005 that scattering amplitudes could be modeled using a construction called twistor diagrams. You can see examples of them in Wolchover's article. By using a set of formulas called recursion relations, discovered by Ruth Britto, Freddy Cachazo and Bo Feng, hundreds of Feynman tree diagrams could be translated into just a few twistor diagrams. These diagrams encode scattering information as something called multidimensional contour integrals. They basically provide the instructions to construct the positive Grassmanian, which is a high-dimensional structure called the amplituhedron.

The most interesting part here is that the physicists working on this found that the twistors encoded the information in a different way than Feynman diagrams do. Locality and unitarity are not required in the twistor formulation, while both are essential to calculating the Feynman diagrams. The mathematics behind twistor diagrams is difficult because it deals with many-dimensional spaces. Twistor-string theory lives in 9 + 1 space-time dimensions. Twistor space has 6 dimensions and the space-time in which the Feynman diagrams live is 3 + 1. The startling point is that all these theories map onto each other under specific supersymmetric conditions (a surprise in itself). You can reverse the process to get the scattering amplitude by mapping twistor space back onto 3 + 1 space-time. In other words, the amplituhedron is an unreal structure living outside of ordinary space-time, but the particle collisions described by it are real and do live in space-time. For a technical account of this process try Freddy Cachazo's The Geometry of Trees.

The numerous Feynman tree diagrams are encoded in the volume of a positive Grassmanian, a structure in algebraic geometry that is called a convex polytop. An example of a typical one, in three dimensions, is shown below.

The amplituhedron is the particular geometric structure you get when you input scattering amplitudes. To see an artist's rendering of it, see Natalie Wolchover's article A Jewel at the Heart of Physics.

Conclusion

The Feynman diagrams, the twistor diagrams and the positive Grassmanian (the volume of the amplituhedron itself) all encode the scattering amplitude information of particles when they collide with each other, but they live only inside drastically simplified quantum field theory. The relatively simple and elegant structure of the amplituhedron, living in the unique and unreal multidimensional space of N=4 supersymmetric Yang-Mills theory, encodes the same information as the over-encumbered Feynman diagrams that live in our familiar Einsteinian 3 + 1 space-time.

It is hard to ignore the fact that the amplituhedron is a pared down theoretical space where locality, unitarity and even our notions of time and space do not necessarily exist and yet this geometry does the most efficient job of describing particle behaviour. If we could magically look directly at the particles interacting would we see something purely geometric in nature? This is the over-step I try to warn about even though it is very alluring. What the amplituhedron really means is hard to know but it does kind of tap familiar imperfect space-time on the shoulder and ask, "What gives?"