2011-03-02-Zeno

 

I first heard of Zeno’s paradox a little over a decade ago and it has always fascinated me.

The scene is Achilles racing a tortoise, who has a head start. In order for Achilles to reach the tortoise he must first run to where the tortoise started, but by that time the tortoise has moved a bit further ahead, and when Achilles reaches that point the tortoise has moved a bit further still. Even though the distances between them keep getting shorter there is an infinite amount of halfway points that must be overtaken before Achilles reaches the tortoise, and crossing an infinite amount of points, however small, would take an infinite amount of time, therefore motion is impossible and Zeno concludes it to be an illusion.

 

That’s the story anyway*

 

Pondering this during sleepless nights, my amateur philosopher solution had always been that while trying to divide space into infinite and increasingly smaller units, one must eventually hit a limit. An indivisible quantum of space. This would limit the halfway points to a finite number (the same would go for time at the planck scale) and make it possible to cross the threshold (however, if you want to make the infinite steps truly work we could incorporate the theory of relativity to the paradox thusly). This then played into my other sleepless-night-question concerning whether time and space were continuous or granular (if time is granular and builds upon itself it is at least conceivable that the future does not exist. Not until we actually get there anyway).

But just as I was satisfied with my granular space/time idea I remembered Zeno’s Arrow Paradox, which gives the example of an arrow in motion. If we freeze-frame time and look at the snapshots; the individual grains of time, we find that every snapshot contains the arrow occupying a certain space. And since it is where it is and cannot occupy a space where it is not, motion is again impossible at any given moment.

This then leads us back to the nature of time. If time is granular and at any given moment motion is impossible, then time might just be a handy tool used to differentiate between one arrangement of matter and another arrangement of the same matter, meaning that it’s an adaptation and not a fundamental force of nature, which then means… yep, you guessed it, time is an illusion too!

Are these just word games or is motion really an illusion? Heck, is reality an illusion?”

The short answer is, yes. The longer answer is, how the hell should I know?

 

2011-03-07-Slits

Known for a couple hundred years, the double slit experiment clearly demonstrates that we, as middle size creatures (with the subatomic on one side of the scale and stars on the other) evolved not to understand reality as it is, but to survive in our environment by perceiving reality through practical illusions (look at any solid object in front of you right now and realize that it is literally almost entirely empty space. Doesn’t feel like it though does it? It feels like stuff*BAM* reality is faking you out every second of your life). Intuition, human logic or armchair philosophy simply cannot predict experimentally proven subatomic reality.

The double slit experiment demonstrates the particle-wave duality of matter. Photons are fired at two slits and the result is an interference pattern. So it looks like light acts as a wave interfering as it passes through the slits resulting in enhanced and cancelled bands on the screen behind (the same thing you would see when you drop two pebbles in a pond). So far your mind is intact.

Now fire individual photons, one at a time. You would expect to see them pass through one or the other slit and hit the screen behind creating two bands. And when it is calculated to see which slit a particular photon has passed through, this is indeed what happens. Now fire photons one at a time without detection, and watch as they hit the screen one at a time and build up an interference pattern! (this experiment has also been done with electrons, and even molecules!). This means that each particle passes through both slits at the same time and interferes with itselfThis is the stuff we are made of. Lol wut? Yeah.

The Heisenberg uncertainty principle tells us that particles do not have precise locations, only potential locations (which is why in Star Trek the transporters work with the aid of ‘Heisenberg Compensators♣♣”).

The wave-particle duality of matter is a paradox, and it can be interpreted as either a fundamental property of the universe, or a limitation of the observer. I have no preference.

On the one hand it’s incredibly frustrating to realize that reality is not what we understand it to be from everyday experience, and the deeper we probe the more it looks like our perceptions of reality are just an emergent consequence of macro evolution. The actual nature of reality does not seem to have our experience in mind at all. On the other hand it’s amazing that animals which evolved to survive mundane earth conditions can actually grasp at the fabric of reality and question and even break through our limitations to explore counterintuitive results that explain a realer reality than we have ever understood before.

Contemplating all this I’ve always craved answers. Why is it that the wave function of an electron only collapses when it is observed? Why doesn’t it just exist somewhere for sure? WTF electron!?


2011-03-16-Cave-

Reality is an illusion.

Yea, this idea has been around for ages. Whether you are reading philosophy and find Plato’s allegory of the cave intriguing or you buy into the concept of Maya in various Indian religions, you can find this sort of thing alluded to here and there, time and again. The difference between armchair philosophy and modern scientific approaches however is that the ideas being speculated about should be able to be proven, mathematically, experimentally and make predictions that can be tested. This is not to say that philosophy isn’t worth discussing but rather, at some point the discussion has to break down with no where else to go unless it is further informed by science. What’s interesting to me is a discussion that is on going, with evidence on the horizon waiting to be discovered. That being said I’m going to touch on a couple subjects that seem to blur the lines between science and science-fiction. The difference being that in theory, with time, these ideas can be developed and proven or disregarded.

 

The Holographic principle of the Universe: I’ve talked about the granular vs. continuous nature of space/time in the previous posts and here once again this issue arises. In black hole physics when an object falls though the event horizon, the information/entropy of that object is lost. This fact on its own presents a problem for the second law of thermodynamics, but as information is added the surface area of the black hole’s event horizon grows. This means that the three dimensional information of the object in the black hole can be preserved on the two dimensional surface of the event horizon. This was the stepping stone used in 1993 to suggest that the whole universe might in fact act as a hologram. With the outer boundaries of the universe being a huge 2-d sphere made up of planck length sized bits of information which represent all of the information contained within the 3-d universe inside. This would make everything we experience one big illusion. Space and gravity as we perceive it would be nothing more than a side effect, a projection, of this physical structure. The three dimensions that we move in and everything you perceive to be real would in fact be wholly fake.

The idea of course seems counterintuitive because we know that the volume of the sphere would be able to contain more than the surface. This is why Craig Hogan of Fermilab predicted that our universe, at the fundamental scale would be larger than the planck scale making the ‘pixels’ of our universe much larger than the ‘actual’ pixels thereby being able to fill the void. This means that at the fundamental scale, our universe would be blurry, much like an overblown digital image. And this is the evidence they are searching for.

(The German gravity wave detector/experiment GEO600 has run into interference and noise that they had not expected but seems to agree with Craig Hogan’s predictions of space-time breaking down from a continuum into a grainy structure at these scales. This is not yet conclusive, but it is a very exciting clue. We might be in a cave reverse to Plato’s wherein we are the objects that are in reality mere shadows on a surface.)

Or (quickly) we could be the shadows themselves according to M-Theory, where our familiar 4 dimensional existence is actually the boundary of an even larger five dimensional holographic space.

 

The Simulation Argument: This is basically the Matrix (or less popularly but more accurately ‘The Thirteenth Floor’) with a serious probability argument as a backbone. This argument not only has the most profound implications but also the most entertaining and satisfying (to me).

Nick Bostrom of Oxford proposes this idea. He argues that at least one of the following propositions is true:

1)    All civilizations at our level of development are very likely to go extinct before reaching a “posthuman” technologically mature stage

2)    The fraction of technologically mature civilizations running ancestor simulations is almost zero.

3)    You are almost certainly living in a computer simulation.

 

If we accept that an incredible amount of computing power will be available in the future, detailed simulations of the past would likely occur similar to current ‘unsophisticated’ simulation games. These simulations would be fine-grained enough for the simulants to be conscious. The simulated universes would vastly outnumber actual universes and therefore it would be irrational to assume that we were part of the original universe. If we do not believe that we are currently living in a simulation then it is also not rational to believe that our descendents will run ancestor simulations. Therefore if our civilization comes to a point where we do run detailed ancestor simulations we could strongly rule out proposition 1 and 2 and conclude that it is very likely indeed that we ourselves are in a simulation.

Simulations can be stacked within themselves and no one ‘reality’ could ever be sure that it is at the bottom. The simulation runners would be godlike to the simulants in that they would be omnipotent and omnipresent and this could have interesting consequences. An afterlife could be a real possibility as part of the simulation and could be run on any number of religious lines. If the simulation was designed to bear out any specific religion we could see the consequences and prophesies of these religions come true. We actually could have been switched on six thousand years ago with light from distant stars in travel and fossils in the ground designed to fool us. Or maybe we all departed from Zeus a bit early when we really should have held on. Valhalla, I am not coming!

Bringing my 3 part series full circle, the most interesting part of this argument is that it would answer my question of why an electron does not have a definite position but only exists in potential until observed. It would be explicable by comparing it to a less sophisticated video game where environments exist in potential but are only defined when needed/observed, just like the collapsing of a wave function!

Admittedly ‘out there’ it is still the best explanation I’ve had on this subject, and being a pattern and answer seeking animal I am happy to have this sort of an explanation to satisfy my search. I enjoy the mind bending implications of this idea, but remain a skeptic. Until further notice.

In conclusion, reality seems likely to be an illusion in every sense of the word. But don’t take my word for it, I might just be a zombie designed to fool you into thinking other minds exist.

 

 

*One of the solutions offered to Zeno’s paradoxes comes from the idea of a convergent infinite series, meaning that it is possible to calculate that an infinite amount of fractions that get progressively smaller total a finite number, not an infinite one.

Planck length of space is 10-35m and may be relevant here (though this may be different from an indivisible unit).

Planck time is the amount of time it takes a photon to travel one planck length, 10-43 seconds.

♣♣When Star Trek technical adviser Michael Okuda was asked by Time magazine how the Heisenberg Compensator worked, he replied “It works very well, thank you.”