# Sir Roger Penrose, Oxford Univ

## Is he the most brilliant man ever?

# Part II

I told you a little about how our reality is definitely not the Minkowski 3 space and 1 time dimension we perceive. Almost all physics agrees that our ultimate theories of the world are not likely to be limited to these 4 dimensions.

In order to understand what the problems that this new reality Roger has uncovered is needed and why our perceptions of a 4 dimensional universe are not consistent with reality you need to understand some of the perplexing things that force Physicists down the road to consider something else.

### Some other interesting paradoxes science has uncovered

Richard Feynman said: “If you think you understand quantum physics, this is proof you don’t.” If Richard Feynman didn’t understand quantum physics, then you don’t either and neither does anyone else. That is not to say you aren’t as smart as Feynman but the experimental results we’ve been getting over the last 100 years or so challenges anyone to come up with a reasonable explanation.

## 1) The measurement problem : Decoherence

When we do a measurement in physics it causes something nobody expected. We still haven’t figured out if it is the human doing the measurement that is critical or if it is an artifact of the simple process of interaction with matter that forces this change. We call this change decoherence or a “collapse of the wavefunction.” What this means is that until we make a measurement, the particles we are attempting to measure are in a fuzzy quantum superposition of all possible states they could be in and therefore are in no particular state. Sometimes this is called the quantum fuzz. Nature seems to prefer to in most times be in a indeterminate kind of being in all places it could be all states it could be while we don’t look.

By definition you can’t observe the quantum fuzz because the instant you attempt to observe it, it collapses and acts like regular particles. So quantum fuzz or the coherent state of particles is unobservable by definition. We can’t look to see what’s happening because by definition the instant we look it collapses. Isn’t that a pisser?

The other place I know in physics we see this definitional type of impossibility is black holes. A black hole is defined by the event horizon where you can’t know, can never know what happens behind. For all intents the horizon of a black hole is the edge of our universe because anything beyond the black hole event horizon is gone forever and no information about what is behind it can ever come back by definition.

Going back to Quantum mechanics and decoherence what this means practically is that a set of particles in this “quantum superposition” or quantum fuzz is in effect everywhere throughout all of space even possibly thousands of miles from here at the same instant of time filling space as if it was a presence everywhere. It seems the particles appear to be evolving as a wave together interfering with other waves acting differently than if they were particles figuring out what to do when we decide to look. When we look the wavefunction collapses the particles become particles and “choose” a state usually the least energy transition from the previous state, what physicists call the eigenstates of the system, and the system acts like it wasn’t a wave anymore. As soon as we look away it seems to go back into its fuzzy state acting like waves filling space.

How can a particle jump between a wave filling all of space and a particle with only a specific location and then go back to a wave instantaneously (1,000,000 times the speed of light or more?)

As you can imagine this is bizarre enough behavior to constitute a really mind bending set of explanations. Physicists actually punted on this problem for 50 years or so preferring not to think about the headache producing problems of decoherence and just focusing on developing the math of how matter acts while in the coherent wavelike state. In the meantime more than a dozen theories of what happens including something you’ve probably heard of called Many worlds interpretation became popular.

## 2) The collapse is instantaneous in all of space simultaneously.

At the instant we measure the particles they all take up real positions in space become real particles with definite energy. When this collapse happens the entire wavefunction spread over thousands of miles instantly (1,000,000 times faster than the speed of light at least from our measurements) disappears and no longer exerts influence on far away particles. It acts completely differently than it did an instant earlier.

This is true whether we are measuring 1 particle or more that are separated by thousands of miles. They will all instantly (1,000,000 times faster than the speed of light or more) turn into real particles in space with defined results from quantum physics and disappear from the rest of space.

It is almost as if these particles when they are in the coherent phase are right next to each other in another dimension that allows them to be in instantaneous contact even though in the 3 dimensions we see they are separated by thousands of miles. Unfortunately such a simple explanation that maybe there is another dimension that particles touch is outlawed by something called Bell’s inequality. So, we have proven experimentally that there can’t be some simple explanation like this for this behavior.

## 3) Nature does a calculation that seems impossible

We know the formulas for quantum physics. We have demonstrated they work for 2 particles and more to incredible precision. In fact the results from these calculations are the most proven most accurate calculations we have ever had for any physics. We know to 10 digits of precision that quantum mechanics calculations are precisely and completely accurate prediction of what is happening in experiments. It is the most successful scientific theory ever.

Testing the theory on larger aggregations of particles turns out to be extraordinarily hard not because the experiments are hard but because the calculations are unbelievably difficult.

The fact is that the quantum foam allows almost an infinite number of possible outcomes from any experiment means that to calculate what the result from any experiment we are going to do we are forced to examine nearly an infinite number of possible results and add them up to produce the result. Somehow nature does this calculation instantly choosing the best least energy path effortlessly.

When we build a bridge we do a lot of calculations of what happens when you exert a force here or there. After the bridge is built these calculations which are quite complicated sometimes in our computers is done by the molecules of the bridge instantly. They react to the forces and we intuitively understand how that could be.

This could be looked at as similar to what the particles are doing with quantum calculations but it is fundamentally different. In quantum mechanics nature picks a “random” result with some probability distribution. It does this in such a way that it appears as if all possible results actually happen and we just happen to be in a universe where one of the possible results happens. If we repeat the experiment with even the very same exact particles at a different time the results will interfere with previous results and future results so that overall all the results we get from all our experiments fit a probability distribution perfectly to within 10 digits of accuracy.

We have shown through Bells inequality that no other unknown force could be impacting the selection of random states chosen by nature. It isn’t that we don’t have all the information to predict what the final state will be. The underlying process is truly a random process. There is no other information we are missing. This has been proven experimentally.

## 4) Natures calculations solve problems we know are incredibly hard

When a photon hits the clorophore molecule of a green leafed plant the photon is turned into a free electron that travels to the place in the plant where it is able to split a CO2 molecule into carbon and oxygen. This travel is done using something called quantum tunneling. The electron finds the least possible energy path to get from a to b. To do this on our computers is an impossibly hard problem. It is estimated that the plant using quantum tunneling photosynthesis is at least 10 million times more efficient than if the energy were transmitted using conventional macro atomic reactions. In essence the plant couldn’t possibly survive on harvesting energy from the sun without quantum tunneling. It would die from lack of energy.

We have used quantum tunneling in computers and electrons as a side effect to make them fast and to perform certain electrical features we need at incredible speed and using very little energy. See Tunneling Diode.

### Quantum computers

We are now building quantum computers that can do astonishing things that are infinitely better at solving some problems. The easiest way to think of this is to imagine that in a quantum computer all we do is run a quantum experiment every time we want to do an operation. We observe what nature does and we then simply report the answer from nature. Nature does the calculation. How it does it we have no idea. It seems impossible however, it does and we therefore can utilize it to do incredible feats of computation.

It is as if engineers had a “reference bridge” built. When they want to compute what forces are on the bridge at any point they have some devices actually exert the forces asked for and measure the forces on the parts of the bridge in interest and report back to the computer what the measured forces are instead of computing the forces using Newton’s mechanics. Such a solution is impractical for most engineering problems but it’s how we leverage the phenomenal compute power of the underlying reality we live in to solve problems for us.

D-Wave, a company from Vancouver area has built the only commercial quantum computers. It’s latest model can put 1152 qubits into superposition. In effect all 1152 qubits can be simultaneously in all possible states of 1152 bits simultaneously. In practice what we do is load up the qubits with the states that we want to do the computation on (the numbers that represent the things we want to operate on.

Let us say we wanted to find a particular pattern in 32,000 patterns. We would load the 32,000 patterns into a subset of the D-Wave qubits. We would need only 15 or so but we might have additional information in the patterns we want, so it could we could use any number of qubits from 15 to 1152.

When we want to find if there is a matching pattern or a specific matching pattern all we do is twist some electrical fields which constrain the path of the qubits similar to the minefield an electron passes through the plants leaf to get to the CO2 molecule. The path is represented as hurdles the patterns have to get through to emerge, essentially electrical walls of different heights depending on the bits we are looking for. All we need is one operation to perform the match.

The quantum computer allows the one result which matches the barriers we set up just as the photon slinks its way through the barriers in the molecules as it goes to its destination the pattern that matches emerges magically in one step from the quantum computer. In a normal computer matching algorithm this would take 32000 operations.

If the numbers had been organized in systematic way by putting them in a sorted key we could have done the match using a conventional computer in square root of the number of operations or maybe 200 operations. The quantum computer did it in one operation and it didn’t need them sorted beforehand. We could do the searching algorithm in one step if we had 32000 computers at our disposal. Each computer would do a test against one pattern in its memory in one step. Somehow the quantum computer acts as if it is 32000 computers doing the test against all 32000 numbers simultaneously. Some have said that the quantum computer is using 32000 different universes to calculate the result.

Another more perplexing ability leverages the ability to do this quantum tunneling in a different problem. We want to find the fastest way to our destination in the bay area. There are thousands and thousands of roads and an exponential combination of roads, billions of possible paths. We have GPS’s which seem to do this pretty good and fast. However, these algorithms usually solve what is called a local minimal solution. They find roughly the fastest way but they may in some cases fail to come up with the true fastest path. I think we’ve all experienced this problem. The computers in the GPS’s that do the solution take millions of steps to solve this problem and do so imperfectly. A quantum computer solves this problem for the best solution in a single step. More incredible, It is not tricked by what appears to be a fast route. It finds the actual fastest route as if it had searched all the billions of possible paths in one step.

I am simplifying this a little. It is not always one step in a quantum computer. It depends on the number of factors but in any case for problems of this type which can be translated into problems that are similar to what quantum mechanics does the quantum computer can be in effect infinitely faster than a semiconductor logic computer.

## 5) Quantum foam, virtual particles exist empty space is bubbling hot with particles

Empty space is bubbling with particles of all types. There is no such thing as empty space. This is surprising to many people. Quantum mechanics tells us that at any instant in time a particle could bump into any combination of virtual particles and make a transition to a huge number of possible other particles and combinations of particles resulting in a constant jumbling. This is not a violation of conservation of energy because there is always a balanced pair of (what is called) virtual particles that exactly cancel each other out. If the collision with a virtual particle happens the resulting particles must always obey the laws of nature conserving energy, angular momentum and of course the schroedinger equation.

Let’s say a proton and an anti-proton appear out of nowhere. These particles can exist for a short amount of time, enough time to bump and interact with the real particles in our universe and cause them to undergo transformations or produce new particles that weren’t there before or they could just appear and disappear doing nothing. Space appears to be a bubbling stew with things popping out all the time only to fall back into the stew after a short time.

This is not some joke. When we do experiments in the LHC in Switzerland the results are billions of interactions many of which involve particle interactions with virtual particles and changes that directly prove that this bubbling foam really exists. Further it has been shown that even in the space of a black hole boundary virtual particles pop in and out of existence. When those particles pop up one inside the black hole event horizon and one outside the event horizon it is possible in some cases for the particle outside the event horizon to escape it’s cousin and emerge into space out of nowhere. Hawking was able to show this radiation was real and that this was dubbed Hawking radiation. It led to the bizarre result that black holes actually radiate energy not just suck energy in.

## 6) Time contracts with speed and mass

The speed of every particle in the universe is constant going the speed of light at all times. This may seem ridiculous statement but it is true when you take into account the particles speed through time. Some particles travel at the speed of light through space but travel through time at zero speed. Some particles travel at close to the speed of light and travel slowly through time. Some particles travel slowly in space and fast through time. Essentially Vx^2 + Vy^2 + Vz^2 + Vt^2 = c^2 (the speed of light.)

Einstein showed in his paper in 1905 that our perspective on something traveling at close to the speed of light was distorted and that some observers see some things happen at different times and possibly even in different sequences than others who observe the same thing.

The particle of light is from its perspective stuck in one instant in time but because of our relative motion we perceive it as traveling through space and time.

This is sometimes called the twin paradox. One twin is going close to the speed of light to travel say to Alpha Centauri the closest star system. The twin on a space ship going at 99.9% of the speed of light would see the distance between Alpha Centauri and the Earth shrink. Space itself as well as time appears to shrink or expand depending on our perspective. The other twin would see his brother take years. When he got back from Alpha Centauri the twin who travelled would be years younger than his brother.

Einstein showed that time is a dimension as are space dimensions. They all distort, shrink and expand arbitrarily depending on our perspective. That’s bizarre and makes you wonder if space and time are really real. How could space contract? How could I see 2 events occur in one order and someone else see them happen in a different order?

## 7) Entanglement – Particles can effect each other instantaneously even when separated by millions of miles

Two or more particles are entangled in some scenarios when they are created together or go through an experiment simultaneously which drives them to defined complimentary states.

When particles are entangled they maintain a connection even as they travel apart from each other. This is what we talked about earlier where the particles that are entangled act as if they were right next to each other in some other dimension we can’t see even if they travel all over the place in the 3 dimensions we see.

We have created entangled states of 80+ particles at one time. Let us just consider 2 particles entangled and flying apart from each other. They may be billions of miles from each other. When we shine a light on one (force decoherence) and the particle appears with definite position and state the other particle no matter how far away it is will instantaneously become a particle, lose its coherence and act like a billiard ball I described above revealing its true position and properties and not interfering with other particles but bounce off them like a solid particle.

## 8) Quantum Turing Zeno Paradox

Many particles decay after a certain “lifetime.” This is well understood and will happen with remarkable precision. However, Turing wondered if a watched kettle would boil in quantum mechanics. A similar paradox is that when you look at an arrow moving at any specific point in time you don’t see it moving but obviously it is moving. In this case Turing asked if a particle would decay while we looked at it. In fact they don’t.

A particle can be stopped from decaying endlessly simply by “watching it.” Any number of minor disturbances where you can see the particle on a regular basis apparently prevents it from decaying. This is also known as stopping unitary time.

There are numerous paradox’s in Quantum mechanics that seem to be related to when you observe something as if nature knew we macro human level creatures were watching. Other theories simplify this to any system that perturbs a coherent system in some “amount” causes it to decohere or prevent it from going into a coherent state. If decaying particles change state and require that they first go into a coherent state before they change state then by watching the particle we prevent it from going into coherence and evolving. We stop time.

## 9) Space can contract or expand faster than the speed of light

Like bizarreness #6 above space can contract or expand much faster than the speed of light. During the inflationary period of the universe if it existed it is assumed that space expanded at a prodigious rate that within less than a microsecond most of the universe we see today was created consisting of billions of light years of space in all directions.

Simply accelerating to high speed can cause an arbitrary contraction of space to the thing undergoing the acceleration as their perception of both time and space changes. This contraction is real to them in the sense that the distance they cover is amplified at a fantastic rate (although to them the distance itself will have shrunk to the stationary observer the distance will still be enormous.

This all implies that space and time are fungible quantities that don’t exist as real world entities because they seem to be able to be expanded or contracted at arbitrary rates depending on an observer. The expansion and contraction happens in the eye of the observer telling us that real distance means nothing. It is expandable and contractable at an instant and arbitrarily and can then be unexpanded similarly. Absolute distance or absolute time mean nothing in that everything is relative. It’s a simple matter of units. 4 Billion miles or 4 inches. The distance seems irrelevant because we can change the interpretation and travel it in a flick of an eye or take all eternity depending on our perspective.

During inflation space expanded at an unbelievable rate or was it that time slowed at an unbelievable rate so that our perception of space and distance changed? Maybe space didn’t expand at all but time contracted at a prodigious rate.

## 10) We live in a 2-dimensional universe

A surprising fact discovered by the professor I have taken Physics classes at Stanford from is that the amount of mass you can cram into a black hole is limited by the size of the black holes surface area, not its volume. If I try to pack stuff into a unit volume of space I can do so only up to the limit of the surface area of the space not the volume.

That’s strange in itself. It implies we don’t live in a 3-dimensional universe at all. That we perceive a 3-dimensional universe could be no more than an artifact of our senses, our brains interpretation of what it takes in via our senses. The fact is that we don’t really have full access to 3 dimensions and that if we try to access every place in 3-dimensions we will find ourselves limited and unable to access every point.

We are not sure what to make of this. Are we smashed against the side of a black hole? Are we projections from a 2-dimensional world like a hologram?

## Interpretations of Decoherence

These are just some of the perplexing results of our physics experiments. They have challenged everyone from Einstein who was a long opponent to quantum physics even as he won the nobel prize for figuring part of quantum physics out. He made the famous quote: “God does not play dice.” I mentioned the quote from Feynman no slouch in the brilliance department and every physicist I have talked to professes that these real experiments challenge the mind to make sense of them looking at our 4 dimensional world of time and space.

The standing rule in physics has been since scientists discussed this in the 1930s was called the Copenhagen interpretation. At Copenhagen physicists agreed to table trying to understand physics from a physical point of view but to simply apply the Schroedinger wave equation and compute results. They gave up trying to “understand” quantum mechanics, decoherence, the nature of reality and to become mathematicians when it came to quantum mechanics.

This is important because Penrose was an algebraic geometry mathematician and understood everything in terms of visual representations but every other physicist said: I give up. I’m not going to try and imagine how this is possible. I’m just doing the math and telling you the answer. Penrose wouldn’t do that. He needed to try and conceptualize in geometry and his mind what was going on.

In these paradoxes above most physicists simply accept them as facts, do the calculations and don’t worry about how this could actually be. We did the experiments. The results are bizarre but as scientists we have to accept the data as real. It is repeatable and our calculations using the math we have created works perfectly. So, we have stopped trying to imagine how or why the universe does these things and simply accept it does.

Since Copenhagen more than a dozen other interpretations have emerged including the multi-worlds theory which if you subscribe to this theory then all simultaneous possible worlds that a particle could be in exist. In this way the particle is actually in a specific place or time however it is in a different one in each world. This makes the problem of decoherence go away because essentially the particle or particles split when they went into coherence into all possible subsequent states as different real universes. All these universes exist and all possible states are realized. We just happen to be in the universe that the one we observe the particle doing X. Many Worlds is actually the most believed theory today by physicists. Even Steven Hawking has fallen into this camp. I want to brag a little that when I first heard of the measurement problem I came up with many worlds conceptually. The problem with many worlds is just as bad as decoherence though because how can all these universes be created? It does seem troubling!

Another view on decoherence is very recent and says that space itself has memory and learns, like evolution. In this model there is only one world but particles behave in what appear to be random probabilities because the space underneath the particles remembers all the other states of the particle or particles and keeps the particles or space producing what appears to be randomness.

Other theories of decoherence are for instance the Penrose quantum gravity interpretation of decoherence. The Consistent histories interpretations, the pilot wave interpretations. All in all there are about a dozen different theories for the measurement problem. Surveys show physicists are split amongst all the theories but none seem to have garnered enough support to be considered really “the truth.”