Artificial Intelligence, The Brain as Quantum Computer – Talk about Disruptive

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Originally posted on CloudRamblings:

Brain_Area_Functions

The AI side of the equation

I started my career studying Artificial Intelligence at MIT.  Back then the researchers thought that we would have computers that were smarter than humans in short order.  What I discovered after observing what the AI people had done was hardly anything close to “intelligence.”   Marvin Minsky called the bluff and wrote an article back in the day basically spelling out in a somewhat comical way that using the variable “learning” in a computer program didn’t mean the program learned anything.

What we have done with AI since then is to build smarter and smarter algorithms and if there is a learning variable in those programs it doesn’t mean those programs are learning anything either.    Some of these algorithms running against massive data stores like the contents of the internet and with virtually unlimited processing power can appear to produce answers to questions…

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A simple guide to to Blockchain and a compelling use case: Voting Election Democracy Worldwide Zero-Fraud

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Originally posted on CloudRamblings:

Mandel_zoom_07_satellite

(Mandelbrot Set signifying the alarming simplicity and yet powerful possibilities of some simple math)

The Blockchain is useful for financial, legal and other applications in general not just for Bitcoin.    It is a new enterprise grade technology that disrupts a lot of existing trust and transactional  systems.

Properties of the Blockchain:

1) You have a unique code which nobody can fabricate themselves from anything you do.  They can’t “be you” without stealing it from you.

2) Other people have a way of determining that you and only you have the code, so assuming you haven’t lost it, other people know you are who you say you are.

3) When you do a transaction (buy something, send someone money, vote, sign your will, sign a contract) the information recorded on the blockchain in an indelible manner and copied hundreds/thousands of times.  The blockchain is publicly viewable by all proving that…

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Privacy! This is egregious and illustrative example of way over the line behavior.

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Originally posted on CloudRamblings:

holding hands

I have written about Privacy before.   It is a topic I feel personally very strongly about.  Here is my other blog entry in which I specify what I think should be legislated to help bring some sanity to the privacy debate.

A Case Study

This morning I read an article in buzzfeed:

uber-executive-suggests-digging-up-dirt-on-journalists

The article purports that in a “closed” meeting an Uber executive suggested (possibly jokingly although the article seems to make that unlikely) that Uber could create a slush fund of $1M to fund operatives who would discover information about reporters who report negatively about Uber and leak that information to the press to hurt those reporters.   He said that in particular that he had specific personal information on a reporter at BuzzFeed who is critical of Uber that he could release that would be damaging to her.

This is a nightmare scenario.   We…

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Is Deep Learning AI going to result in human intelligence or better anytime soon – the setup?

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Originally posted on CloudRamblings:

Does a significant advance like the recent advances in AI presage a massive new potentially dangerous robotic world?

ai_robot_a0755080-cb27-4e42-8132-d441a6d813ca-1020x612

Elon Musk Stephen Hawking, Bill Gates and others. have stated that recent advances in AI, specifically around CNN (Convoluted Neural Nets) also called Deep Learning has the potential to finally represent real AI.

This is exciting and worrisome if true.   I have been interested in this problem from the beginning of my career.   When I started doing research at MIT into AI I had kind of a “depressing” feeling about the science.   It seemed to me that the process the brain used to think couldn’t be that hard and that it would take computer scientists not very long to try lots of possible approaches to learn the basic operation and process of how people “abstract and learn” to eventually give computers the ability to compete with…

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Virtual Virtual Reality, Virtual Anthropomorphic Reality, Virtual Functional Reality, Virtual Extended Reality

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Originally posted on CloudRamblings:

Virtual Reality

I categorize virtual reality into these 4 different types.   They are progressively more difficult technologies but each will progress independently.   VVR, VAR, VFR, VER represent the 4 ways VR technology can be used.   VVR is about creating false worlds or artificial computer generated worlds.  VAR is about transferring ourselves in the real world virtually.  VFR is about using using VR for functional purposes like building things.   VER is about extending our perception to new senses and new environments that require our brains to adapt to these new senses.

Networking

Ten years ago people at home frequently had thousands of bits/second to their home and their phones or data communications over wireless was practically nonexistent.  If you had it, very slow at hundreds of bits/second.   Ten years later cell phone 4rth generation LTE is common which allows communication at 10s of millions of bits/second…

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Sometimes we have to understand what we don’t know

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Originally posted on CloudRamblings:

man in wheat field

You will find it hard to find someone as enthusiastic about the potential of science and how it could benefit us.    However, there are several things I think everyone should be aware of in spite of our amazing advances.

Our knowledge is recent in most fields.   Something I say is that “man has really been AWARE for about 100 years.”  What I mean by this is that 100 or so years ago we looked into a human body and saw gross organs and had no idea what they did or how they worked.   100 years ago we barely learned that there was a speed limit in the universe and bizarre things like space and time can be warped and we had no inkling of quantum mechanics.   We fared the seas and land of the earth but had no idea of the environment or our potential impact…

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An Uncommon Man and the surprising nature of our universe, Roger Penrose and reality Part 4

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roger penrose

Sir Roger Penrose, Oxford Univ

Is he the most brilliant man ever?

Part IV Coincidence or Reality

This series of blogs is intended to give you as simple as possible understanding of the actual universe we live in which surprisingly does not have 3 spatial dimensions and a time dimension.    In fact the universe we live in called Twistor Space is 5 dimensional and there is no time dimension.  In Twistor space rays of light are points and things we see as points in space-time are rays in Twistor space.   Our mind creates a radically different view of reality because the purpose of a brain is to predict things so that the living thing with the brain can survive not to give the most accurate view of reality.

This is a complex topic.  I highly suggest you read the articles in sequence starting from the first:

Here is the series on Roger Penrose and Reality:

Part I

Part II

Part III

Part IV

Part V

Part VI

One of the first things Roger did was to try to understand spinning particles

Here is a graphical representation of a spinning electron for instance.

spinor

It is a good idea to start with particles to understand one of the most basic and perplexing things about reality.    All particles spin for some reason.   We classify all particles by the amount of spin they have so understanding this perplexing property would be a first step.

Interestingly, spinning particles can be represented by using a complex number to represent the angle of the spin.  When saying complex numbers I mean:  A + Bi    where i = -1^0.5.   The geometric equivalent of the complex number was a Riemann sphere which has as one of its axis a complex dimension.

riemann sphere

The angles of the spinning can be translated to a second number that you can conveniently put with the part of the complex number.

Roger invented Spinors to represent spinning particles and it worked.   It turns out that Spinors rotate differently than what we imagine.  They rotate through 720 degrees as in the graphic below.

Spin_One-Half_(Slow)

So, it seems a convenient mathematical trick that you can represent this using a complex dimension and all the math works out when you combine these things, multiply or add them together but that’s just a math coincidence right? It is assumed there is no actual complex dimension that the spinning particle inhabits.

Mathematically this is convenient.  However, what does it mean to have a complex dimension in reality?  When Penrose did this I don’t think even he imagined at the time that reality had a complex dimension.   Nonetheless, inventing Spinors had a positive effect on Rogers career.  Spinors did help people visualize spinning particles and more important were found useful to calculate things.

You can think of the complex dimension as the angle of spin of a particle rather than try to imagine what a complex dimension might be.

Roger and other physicists were confused about what the significance of the fact that complex numbers keep appearing in quantum mechanics, not just in spin but everywhere in quantum mechanics.

In Newtonian physics before Einstein and the 20th century we had formulas that said if you launch a ball with such and such a force it will go here in 10 seconds. According to Newtons law it went exactly there.  In quantum physics it could go 100 miles from there.  It’s likely it will go close to where Newtons formula said but in fact in the quantum world we really live in, it could go almost anywhere. Everything is a probability and in some universe the ball does go 100 miles from where it would in Newtonian world.

So, quantum mechanics doesn’t tell us where the particles will go exactly.  It tells us with what probability it will go here or go there.  Those probabilities can be calculated very accurately with Schroedinger’s equation and nature follows the Schroedinger equation to MORE digits of accuracy than Newton’s law ever did!   So, that’s amazing.

When we calculate the value of Schroedinger’s equation we don’t get the probability but something else we called the amplitude.   The amplitude is a complex number.  So, where do we get the “probability?”

You take the complex number called the amplitude that is the solution to Schroedinger’s equation and do a simple mathematical trick of reversing the sign of the second part(which is then called the conjugate), multiply it by the original the result was a pure real number with no complex part and turns out to be the number which if you threw that ball a trillion times it would show up there exactly that number of times (in proportion to the number of course).   So, it turns out that you took the result of Schroeder’s equation and after you did that funny multiplication produced the probability to an amazing level of accuracy.

This is the math trick physicists depend on:

(a+bi) * (a-bi) = a^2 – b^2*i^2 (i^2 = -1 of course) so

(a+bi) * (a-bi) = a^2 + b^2 = probability particle appears here

These “amplitude” numbers that come from Schroedinger’s equation can be added or multiplied to represent different physical things that happen in the real world. The math of complex numbers works perfectly to reproduce the physics we see. The result is exactly what we observe to an unbelievable level of precision.

It is not at all obvious why the amplitude is complex, except that Schroedingers equation was arrived at by thinking of very elementary ideas of energy in systems and the natural solutions to the equation results in complex numbers.  So, it wasn’t like Schroedinger pulled this out of his hat as random.   This was a description of reality that made sense.  It’s just that the solutions you calculate when you do the math are complex valued results.

A success of sorts.  It works but at a huge cost.  We had to turn our entire conception of the universe on its head.   Worse than that, we’ve had to give up all conception of the universe and think of the world as a set of equations.

The 4rth multi-verse

One theory of physics says that any consistent system of mathematics that describes a possible world actually exists.  Thus there may be infinite universes with different sets of theories and we happen to inhabit the one that includes complex numbers.  There may be universes that don’t have them.  Who knows.

If imaginary numbers are necessary to compute the answers to simple algebraic equations then nature would naturally have an imaginary dimension because it is constantly solving such equations in the process of the world simply working the way it does.

The point is that to our surprise in most cases when the math produces a result that seems crazy, we have found that nature actually does what we thought was crazy.  Physicists have been caught trying to out-elegant reality too many times.   So, some now believe that math is the ultimate reality and that all possible mathematical realities exist somewhere.

The 20th century is replete with accounts of physicists including Einstein himself who would reject the mathematical results of his theories.  Initially when his General Relativity predicted the existence of black holes he denied they were actually possible.  When people showed how they would arise he tried like other physicists to show how they weren’t possible.  When his general relativity showed the universe wouldn’t be stable and would be contracting Einstein believing in the steady state as most physicists did at the time introduced a fudge factor to keep the universe at a stable steady state.  It was only a few laters that we discovered the universe was expanding and Einstein realized he didn’t need his fudge factor.  Amazingly, the fudge factor turns out to be real too.   So, amazingly frequently in physics when the math says X is possible, we discover that X is true.

So, this makes us think if our resistance to the idea that the amplitude in Schroedinger’s equation reflected the existence of an “imaginary” complex dimension is again our inability to simply accept what the mathematics is telling us.

Nonetheless it is extremely hard to understand what a complex dimension means or looks like.

Another way to think about complex dimensions

Roger is in a sense trying to give us back a conceptual geometry to re-imagine our world.   In the case of Spinors we could imagine the complex mathematical description of a spinning particle with a geometrical object called a spinor.

If we think of the amplitudes as something spinning then the complex dimension of amplitudes may be thought of as just a the angle of the spinning particle in another way, not the spinning of electric charge but maybe something else, the flavor is spinning.

In Penrose Twistor theory, Twistors have 5 dimensions 2 complex dimensions (4 including the real and complex).   So, you have to imagine something spinning in multiple ways simultaneously.  Hence it is twisting.

Does an amplitude really exist?

Imagine that we question the reality of anything we don’t see.  So, we say the proton and electron are imaginary and that the only things real we will admit to are the things we can see like the baseball, the pitchers hand, the air.  Let’s say we assume the electron and proton are convenient  mathematical things and don’t exist in reality.    The problem with this is that understanding the nature of the elements allows us to understand why some materials interact with each other chemically, why some materials are metals and conduct electricity.  The mathematical contrivance of the proton and electron, the model of the atom seems to have legs.  Is reality composed of atoms or do we really think it’s a convenience.   Everybody agrees today that atoms and electrons exist.  We have seen them in electron microscopes.  Well, the amplitude and the Schroedinger equation have legs as well.  Serious legs.

We don’t see amplitudes directly in nature.  As far as we know an amplitude can’t exist in nature right?  It has a complex portion and space can’t have a complex portion in it, right?    So, what do we make of these amplitudes?  Well, for the last 100 years physicists just assume that it’s math, not think about what it means or try to imagine what the world looked like.  Roger Penrose just couldn’t do that.  He had to come up with some way to think of these things.

There is no way to get rid of these complex numbers.  They are not a trick of math.  They seem to be as real as the real portion of the wavefunction.  Yet for the last 90 years we have operated as if the only real thing is the probability which is the complex conjugate product.   We don’t know even know why we multiply the amplitude by its the complex conjugate and get the probability.  It just works.

Why multiply complex conjugates to get the probability?

So, jumping ahead a little I will explain that in Penrose Twistor space when two particles have mass and a gravitational wave passes through the spinning particles it causes the amplitudes of the particles to multiply by their complex conjugates.  According to Twistor theory a gravitational wave causes the amplitudes to multiply in this weird way I described above naturally without contrivance.

The math of Spinors in Twistor space is such that a gravitational event produces decoherence and the effect we call consciousness.  

Using Spinors and Twistors is resulting in a lot of coincidental physics we see that explains perplexing unknown reasons for things.  Why do we multiply by the complex conjugate to get the probability?  Because that is the math that happens when gravity interacts with Twistors.   In physics this is not a proof of anything. Until we have experimental data that is predicted by Twistor theory we can’t say such coincidences are proof.

You can see that gravity in Twistor space is integral part of the theory combined with quantum theory.   Previously in physics these two theories never met. Gravity was about things of the Earth size 10 ^ 20 times bigger than the typical Spinor particle size.   We talked earlier how physics works at the scale of 10 ^ 75 or 10 ^ 1 and here is an example.  Gravity acts at this micro level because the masses are large compared to their distances of separation.

So, what is Twistor space and what does it mean to say “build a reality on complex dimensions?”

What is Twistor Geometry?

A little history : Twistor Revolution

Roger invented Twistor theory as a complement to Spinor Theory around 1970. Initial progress after Roger’s invention of these mathematics was slow.  He then invented these tools called Twistor diagrams to help do calculations which later turn to be incredibly useful.  However, as cool as Twistor theory was it didn’t generate much interest until 2003 more than 30 years later when Edward Witten from String Theory fame discovered a relation between String Theory and Twistor theory.  Among other things Edward Witten discovered that you could put strings into a twistor universe and it worked.

Soon after that Andrew Hodges and other people discovered a beautiful connection between Twistor Diagrams and Quantum mechanics resulting in the discovery of the Amplituhedron in 2010 which has caused an exponential jump in our ability to calculate quantum particle interaction results.  For this alone Twistor theory became in indispensable tool in the physicists arsenal.   With it you could calculate things that before had been intractable.

In 2011 people started talking about the Twistor Revolution.

In 2013 gravitation physicists started finding the connection of Twistor theory and quantized gravity. Twistor theory seems to have united physics from particle physics to quantum physics, string theory to Gravitational theory. It is producing remarkable achievements in all these fields simplifying and solving thorny problems explaining completely mystifying things.

As you can see this is all very recent.  Witten’s discovery was just over 10 years ago and most of the other advances are in the last 3 years.   We are seeing a jump, a disruption in physics.   I am explaining something that really has not hit the public eye yet.

So what is Twistor space?

In Twistor geometry there are 2 real dimensions, 2 complex dimensions and another dimension  = 5 total.  This is one more than the 4 we think of in our Minkowski space of X,Y,Z and Time.  The 5 twistor dimensions are not at all like the space time we are used to.   In other words there is no “X” coordinate or surprisingly no T (Time) dimension.   We say they are emergent. They are in there but not as dimensions.

In Twistor geometry X, Y and Z  and T are calculated  from TWISTOR space in a way that whole lines in regular Minkowski space like a light ray become a point in TWISTOR space.

Points in Twistor Space

twistor p05

The entire path of a light ray in what we see as Minkowski space as a brilliant laser light shining along a line in space for instance would be nothing more than a point in Twistor space.

One obvious question is why do we “see” a line, “see” something that occupies multiple points in space it seems when in fact it is only a single point in Twistor space?  Well, first we never see a single photon of light anyway.   We see a collection of photons that are interacting with air and dust particles composed of billions of particles each.  So, we don’t see Twistor space. We see at our level the interactions of a billion billion particles.  That’s one answer.

Even if we go to the microscope and look we don’t see a ray of a photon.  We see a measurement we take which identifies a particular point the photon occupied.  We never see it actually move, like the Zeno paradox the light particle we presume moves but whenever we take a picture, i.e. a measurement it decoheres and we see a specific point.  We visually think of it is as a ray of light.  We draw it’s motion as a ray but we never see it as a ray.  All we see are points when we observe it.   What the light particle is actually doing when we aren’t observing it we don’t have anyway of really knowing.  Our brains fill in the motion and make it look continuous.

From the point of view of the light particle it is in all places simultaneously it will ever be.  This is because for the light particle time is not moving.  It exists at a particular moment in time and that is it.

I have thought about this and thought about this and tried to understand what does it mean.   The light particles appear to be a point fixed in space and time.  Our perspective as traveling observers lets us see portions of the light wave in different places but it really exists in a number of places simultaneously in our Minkoski space because of how we perceive it.

Photons and other particles moving at the speed of light are actually motionless and are like the girders of our universe sitting there forever locked in one place and time for everything else to move around.

Lines are important constructs in Twistor space.  Intersections of lines are where interactions happen.

Let’s look at some other “mappings” in Twistor space to Minkowski space.

Lines in Twistor Space

A line in Twistor space becomes a point in Minkowski space.   How can a point be a line again?  In Twistor space anytime we measure occurs at an intersection of lines in Twistor space.  In other words the “particle” we see is simply the convergence of several lines in Twistor space.  The measurement paradox we discussed earlier is starting to start to make sense.

In Twistor space the points where lines come together corresponds to the instant we are able to perceive reality.   In that instant, things have specific times, sizes, places.  The world is real.  In-between the intersections there is no reality, so perception.  You have to get to an intersection to “see” things.

How bizarre, this starts to explain why we have the perplexing “measurement” problem.  Our reality consists of the collection of all the intersections in Twistor space.  This is what we see not just in the measurement devices we create in physics but we see through our eyes and ears or noses.  This is mind blowing to think about but clearly for me anyway gives me a much better way to think about the measurement problem and about the “fuzzy” state.

The “fuzzy” state we call quantum coherence is simply between the intersections. In Twistor theory what we do is compute the transition from one point to another.  These calculations produce the measurements we see.   What should also start to become clearer is that since what we calculate is our space and time dimension values.   They emerge from the calculation as the result of the interaction.  Twistor space doesn’t require that Space and time dimensions have locality.   Space and Time emerge from Twistor theory as calculations.  This makes a lot of sense when you think of some of the problems I described in physics.

Twistor space is composed of light rays (Spinors) as the basic building blocks of the universe.  These points in Twistor/Spinor space create space in some literal sense.  Each Spinor is its own space and only when it interacts with other Spinors do we have the chance to “see” space.   Space could be infinite with infinite Spinors or Twistors floating in Twistor space.   Only when Twistors interact do we “see” and so our perception is simply a perception of the interactions of Twistors.  When they aren’t interacting we have no perception, i.e. we have no conscious sense so

Consciousness is the perception of Twistor interactions.

Gravity is one of the glues that causes Twistors to interact and if the Twistors are aligned by gravity and the mass of the Twistors into a “space”.     Gravity helps to form the structure of the universe and bring Twistors into coherence helping to form the universe and create the interactions we see.

Gravity is the glue of Twistor space

So, Twistor space is point-like, i.e. points are where lines converge.  Lines are particles and points are light rays.  Sort of the inverse of what we think of reality at our macro dimensions.   Don’t give up.  This will become clearer.

I15-56-spinnet

The point-like character of TWISTOR space means that to get from point A to point B you perform a “calculation” the result places you at a different point adjacent to the point you were at.

If 2 particles interact it is represented in Twistor space by an intersection, where two lines intersect is an “interaction” or “measurement.”  Between interactions there is no reality.  Twistor space is therefore not tied to space and time the way our reality seems to be to us.  Time and space emerge from calculations mapping the Twistor space back to Minkowski space.

One can think of the lines as particles hidden in some alternative reality that pop out when an intersection occurs or you can think of the lines as simply the next state as in a finite state automata as in a Turing machine.   Interactions lead to interactions lead to interactions each calculable with a probability of options to the next set branching out to all the possibilities.

Our perception is simply the collection of interactions we observe.

The Unitary Principle

Quantum mechanics has a rule that the sum of all the possible things that can happen must add up to 1, not 1.4 or 2 or 0.5.  One of the possibilities must happen, not 2 of them or half the time nothing happens.  In quantum mechanics this rule is simply assumed.  There is no apriori reason to assume 2 things couldn’t happen.   Like multiplying complex conjugates to get the probability there is no obvious reason WHY only one thing can happen or not.   After all, lots of bizarre things happen in the experiments we do in quantum world.

However, when you look at it in Twistor space the possibilities all emerge as lines from a point in a n-dimensional space.  When you look all the possibilities emerging from a point they form a unitary circle around the point.  If you think of 2 dimensions the possibilities naturally fill out the 360 degrees around the point.   Therefore all the possibilities fit in this 360 degrees and a particle doesn’t exist on 2 lines at the same time, a particle is a line.

It emerges as a property of the geometry of Twistor space that unitarity is a derived.

It just is that from any point all that can happen is all the lines out and the sum of the lines is all the possibilities.  Thus the unitary principle is derived from the geometry of the space.

These may not seem like big deals to you but for physicists these are deep and hard problems to explain.

Space and Time emerges from Twistor theory naturally

The idea that our idea of space and our idea of time emerges from a new theory is critical and has been known for some time because our space and time are not fundamental we have discovered.   They can be bent, expanded, compressed, disappear or stop so they are not fundamental.  Sorry if that is alarming but the experiments clearly show this.  It is apparent from the previous experimental evidence presented that space and time are not really very solid concepts to base reality on.

In Twistor space we calculate the space and time values for an intersection of lines like we would compute velocity by dividing distance covered by time.  Velocity is a concept not a real property of things and it is relative depending on who is viewing it.   In a similar way space and time are computed and not a real property of things.  It depends on the intersection of lines in Twistor space (interactions of particles).   They could compute so that what we see as “non-local” is perfectly okay in Twistor space.  Things appear where they do to our eyes or measurement devices because that’s where the calculations of the mapping from Twistor space makes them appear and when.

Space and time are not really very solid concepts to base reality on.

Dr Nima Arkani-Hamed says: “The notion of space-time itself is breaking down” because as you try to probe to smaller and smaller dimensions we run into logical contradictions.

One way to think about this is to think of the problem we have imagining “quantum fuzz.”   In the quantum world we are taught that things are in all places at once and that things are indeterminate.  Only when we make a measurement do we see particles at places with specific locations and times, values.   We always wonder how the universe looks when it is in the “fuzz” state.

PW-2013-05-23-hydrogen-wavefunction1

A quantum microscope actually shows what quantum fuzz for a hydrogen atom looks like.

The measurements are the fundamental thing that we perceive as reality.

Basically the universe is “invisible” most of the time and only when we “look” does it decide to “decohere” and look like it has a place and existence.  This fuzziness leads to all kinds of conceptual problems that bedevil physicists.   For nearly 100 years since we first discovered the reality of quantum mechanics we have struggled to understand how nature pulls off the trick of “cohering” when we decide to look.   There are no less than a dozen distinct theories with no proof for any of them what happens in decoherence and it is called the measurement problem.   Basically the measurement problem is that we don’t understand why measurement causes the world to change, how long it takes to change and what happens before it changes or after.

By definition we cannot see what is happening in the quantum fuzz because by trying to see what is happening we trigger the measurement problem and the world decoheres and essentially laughs at us and says: “Ha, here I am.  I’m really here not in all those other places.”   Yet when we aren’t looking the world seems to progress as if it was in superposition of many many possible places (remember lines in Twistor space).   This perplexing puzzle has boggled all physicists since the original experiments confounded us and we are no less confounded today nearly 100 years later.

If you think of TWISTOR space particles (Spinors) go from point to point in TWISTOR space where lines intersect.  Between the intersections one interpretation is there is no reality.  It’s not that things are in a fuzzy state.

Consciousness is a consequence of lines crossing in Twistor space.

Lines in Twistor space cross.   When they do an interaction happens and “reality” happens in our Minkowski space.  We only can perceive the interactions when the lines cross.    We can compute what happens at each intersection point using a combination of Twistor physics and regular quantum physics but if space is discrete which seems likely then maybe nothing exists between the intersections.  It’s simply a computation of one intersection to all intersections possible from that point.

Two particles could interact which are in vastly different location in X,Y,Z space or the result of the next place you see a point could map to many different non-local positions in X,Y,Z,T space.    Twistor space therefore doesn’t have a notion of locality like Minkoski space.   That is critical to explain some really puzzling things in the quantum explanation of the universe.

The simplest non-locality problem,  a single particle

Penrose points out one of the simplest non-locality problems or conundrums is simply a single particle.  In our quantum understanding a particle can appear in anyplace with a probability.   That’s cool.  We can all sort of imagine that.  However, quantum mechanics also says that the particle “disappears” from all other possible places it could be.  This information that the particle has appeared HERE and not HERE has to be transmitted throughout all of space instantaneously because a particle NEVER can appear to pop out in multiple places.   So, this is pretty basically the simplest way to understand how F’d up physics is.   We don’t understand how particles can do what they do.

We have this fundamental conundrum that when a particle decoheres it has to perform a seemingly impossible task of disappearing simultaneously from all possible places it could have appeared just a moment ago.   This fundamental oxymoron of physics is the purest simplest way to understand how the non-locality is so fundamental a problem.  All the other non-local quantum properties are similar in nature.  Two particles or three particles can be entangled and when they suddenly appear as a result of an interaction simultaneously no matter if the particles are separated by billions of miles their state becomes fixed and immutable and all other possible states are eliminated all over the universe instantly.

Scientists have measured the speed at which this “cancelling” other possibilities is transmitted and it is at least 1,000,000 times faster than the speed of light.

Complicating this is Bell’s theorem which puts constraints on non-locality making it impossible for their to be hidden connection between the particles we don’t know about.   Every way we look at it the physics seems to be conspiring to make Minkoswki space locality not exist.  Physicists have been brought to the point of virtual insanity it seems finally suggesting that we need a theory of reality where there is no locality where locality emerges! This is contrary to our 3 dimensional Minkowski idea of space time.  Locality is simply the idea that things must take place close to each other in the X,Y,Z dimensions to effect each other.

Physicists needed a theory which abandoned X,Y,Z but this is hard to do, harder than simply living with the conundrums of quantum physics so they punted on it for 100 years!

In Twistor theory individual particles are called Twistors and they are independent from each other and their separation is constrained by gravity.  Waves of gravity shake the grid of Twistors and cause interactions as well as bend the Twistors into shapes like Einsteins general relativity predicts.   Discrete Twistor space encompasses gravity, quantum mechanics and general relativity the holy grail of physics that Einstein himself sought.   In a sense Roger Penrose is Einsteins natural successor in the quest for understanding the ultimate reality that Einstein sought.  He has possibly accomplished what Einstein never had the math to do.

When we look at smaller and smaller portions of space we have to use higher and higher energy beams to explore.  This seems contradictory but the fact is that it is the smaller particles that are the more energetic.  E = 1/λ (wavelength) so as the wavelength shrinks the energy of the particle increases.   At some point the space-time becomes so energetic that it creates a black hole and by physics definition it becomes impossible to see.   Does that mean that at the planck length space becomes discrete?  Maybe.  It makes sense.

String theory says that strings are composed of energy that vibrates.  These strings are on the order of the size of the planck length which is considered the smallest possible length.   It doesn’t make sense for space to go smaller than the planck length along several lines of reasoning it becomes nonsensical to talk about lengths smaller than that.  As I’ve pointed out before numerous aspects of a number of theories produce infinite results when you assume that space is continuous.  We get around this by subtracting out the infinities and that works because the infinities are the result possibly of continuous math including the infinitely small which doesn’t exist.  There are other ways of concluding that space can’t be continuous.

Is time continuous?  If everything else in the universe isn’t continuous it seems extremely unlikely time is continuous.    We have struggled with the concept of time.  How would we know if time stopped or if moments of time were spaced inconsistently?  From the planck constant we can compute the time it takes at the speed of light to cross one planck distance.  This is considered the planck time and the minimum time likely.  It is 10^-40 seconds.  If true then there is a lot potentially going on that we haven’t probed yet.  We have only ever looked at events of around 10^-16 seconds.    If 10^-40 is the minimum time interval then 10^24 time periods pass between each of the smallest times we have ever observed.   That’s a lot of time between the smallest times we have ever seen.  It would be hard to distinguish this time from continuous time.

For similar reasons to space it is logically inconsistent with numerous aspects of physics if time were continuous therefore it is likely time is quantized and the only contender is the planck time.    One wonders what nature is doing with all the time between what we consider the smallest amount of time we’ve ever observed.  It could do a lot of stuff.   So, this represents interesting question that I have no idea if anybody has really probed.

It is only today that people are taking seriously Roger Penrose’s idea that Twistors and Spinors could really be the underlying reality of our universe.

I15-56-congruence[Twistor universe 4 dimensional + 1]

We live in a Twistor universe that appears to us because of our macro senses as a Minkowski universe (3-dimensional + time).   Presumably if our senses were confronted constantly with macro twistor geometry manifestations we would see twistor space but since for macro level things the best approximation is Minkowski space our brain gives us the impression we live in a 3 dimensional world with a separate time dimension.  We know our brain interprets reality, sometimes filling in details.  There are many examples of this.   Here is a simple example I find amazing:  here.   There are many such examples including the Escher drawings where the brain interprets things.   There is a lot of pre-processing and much of what we ultimately feel from our senses is processed information that is made to appear consistent so we can operate in the world.

Presumably if we immersed ourselves in a twistor universe from birth where twistor space phenomenon happened regularly (10^-10 cm) we would perceive twistor space.  Our brain would probably find a way to enable us to see twistor space as reality but we are too big and very few things we interact with demonstrate twistor space oddities so our brain pops a visualization which is how it interprets the universe which we call the Minkowski style universe.   It’s a nice linear universe with time that moves nice and smoothly forward and space looks continuous.   We know these things are NOT true in the real world.

In a twistor universe there are 5 dimensions, 2 of which are complex like the spin example above.   Time and x,y,z are not dimensions like we think of them.  They are mapped as ratios of each other into complex numbers.  Time and spatial dimensions are part of ratios in a Twistor space mixed up with each other.  It’s not trivial to imagine how this is like our reality but it is a valid mapping and whether it exists in reality or not it is mathematically more consistent with our universe than Minkowski space.   Here are some mappings from Space-time Minkowski space to Twistor space.

I15-56-twistorspace

From what physicists can see today it is much simpler to think of physical laws and all the peculiarities we see in quantum mechanics, trying to solve problems with quantum gravity, string theory, calculating things in quantum mechanics, unification of all physics and everything when it is done in twistor space.   Some of the laws of physics like Maxwell’s equations become as simple as Newtons laws of motion.  Problems with non-locality and wave-function collapse disappear as problems.

Roger has uncovered the real universe.

We do not live in a universe of 3 dimensions and time.  We live in a universe of 5 dimensions.   Our brains interpret reality to be convenient for us to operate.   Our brains fill in information and give us a reality that is not necessarily “reality.”   Such observations go back to Plato and original philosophy.  We have direct evidence of this “infilling” with simple experiments you can do.   Try this,

Twistor theory is a translation of conventional space and time into a new set of dimensions.   Essentially you can map Minkoski space time (3 physical dimensions and a time dimension) to a 2×2 dimensional Twistor space.   I say 2×2 because the twistor space is 2 dimensions with 2 complex dimensions.  What is a complex dimension?  It is not really complex.  It is a regular dimension but it is simply that the laws of physics of particles in those dimensions operates as if the complex dimension really exists and operates as if complex numbers really existed.

The easiest way to think of these complex dimensions are the spinning of particles in different directions.  This is the best analogy I can think of.

From Scientific American:

Using twistor concepts, theorists have now shown how all the dimensions of ordinary space—and even time—can pop out.  Many theorists find it quite natural that spacetime would be derivative. Andrew Hodges of Oxford points out that we do not perceive spacetime directly; we infer that events happen in specific locations at specific times from the information that comes to us. “This idea of points of spacetime as being primary objects is artificial,” he says. Indeed, the concept of distinct positions and times breaks down because of the gravitational warping of spacetime and the notoriously spooky connections between quantum particles.

This series of articles :

Here is the series on Roger Penrose and Reality:

Part I

Part II

Part III

Part IV

Part V

Part VI