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Archive for the ‘physical sciences’ Category

Gravity, Relativity and Quantum experiences: searching for a consensus.

“Quantum Mechanics is very impressive. But an inner voice tells me that it is not yet the real thing. The theory produces a good deal but hardly brings us closer to the secret of the Old One…I am at all events convinced that He does not play dice.”

– Albert Einstein
(in a reply to one of Max Born’s Letters in 1926)

Every time the word ‘quantum’ is used to imply some surrealistic idea, I quiver with apprehension. So much has been said about the so called ‘uncertainty’ lying deep within it, the ‘nonlocal’ connivance of the non-classical world and the weird notions of ‘probability’ and ‘wave function collapse’ that the shroud of mystery around the theory thickens by the moment.

There are countless half-boiled hypotheses that claim to link animal consciousness and the concept of ‘soul’ to principles of quantum physics run across the information highway and a casual mind is easily attracted to one or the other.

Despite being the most validated theory of all physics, Quantum Mechanics is still viewed by many as something that essentially needs adjustments in order for it to conform to our common-sense view of the classical world. But there is this larger majority of physicists and cosmologists out there who are convinced that it’s our classical world-view that needs revision – the world wide struggle for a unified theory of the forces tell the tale. Roger Penrose, celebrated mathematician and theoretical physicist, belongs to the first group. He suspects that the cause of failure in unifying the theories lies in a perspective difference.

QM and Relativity

There are four fundamental forces in the universe: electromagnetism; the strong and the weak nuclear forces, and finally gravity. General Relativity attributes gravity to the effect of matter on space-time fabric. Imagine a stretched sheet of rubber to represent the fabric of spacetime and a few iron balls placed on it to represent stars and planets and other massive celestial bodies. The dents made on the rubber sheet by the iron balls can be regarded as the geometric alterations caused by the presence of matter in spacetime. A smaller iron ball when set to roll over this sheet, moves uniformly forward until it falls into one of the deeper dents caused by larger iron balls than itself. Analogously, the orbits of celestial bodies are due to a curved or bent space surrounding the larger body. This effect is ‘gravity’, says Einstein.
Quantum Mechanics (QM) and Quantum Field Theory (QFT) have been able to explain all the fundamental forces except Gravity in terms of particle interactions; the Standard Quantum model of fundamental forces considers gravity as an attractive force mediated by the exchange of gravitons.

“Although this tension between relativity and quantum mechanics may be mostly dormant at the energies that are currently experimentally accessible, there are situations where the interaction between the matter fields and quantum fields and the gravitational field becomes relevant. For example, physically realistic models of the universe predict an initial singularity. At this singularity, classical physics breaks down and it is assumed that a quantum theory of gravity, i.e. a theory combining general relativity with quantum physics, will be necessary to probe the physics of the early universe.”

Nevertheless, both Quantum Mechanics and Relativity give excellent testable predictions and are widely accepted as useful but unproven and ‘incomplete’ models of some deeper reality.

Penrose’s views

Penrose derives his inspiration from Einstein, who believed that a theory incorporating the relativistic nature of gravity and the non-classical nature of Quantum world data would be possible only by correcting Quantum mechanical notions rather than Relativity. Einstein was definitely disturbed by the anti-relativistic findings arising in the quantum scheme of things and the indeterminacy popularly called Heisenberg’s uncertainty principle.
But Penrose is more bothered with two things about QM; in fact the first one takes root from the second:

The first is about the ability of a quantum particle to be simultaneously present at two different locations, even though larger chunks of matter don’t seem to do that despite being made up of the very same quantum particles. Simply speaking, why is it that an electron, in the famous double slit experiment, appears to be present simultaneously at two places, while a person or a chair does not appear to do that? The second is about taking the ‘mathematical’ process of wave function collapse (‘State-vector reduction’) for real.

Collapsing Wave functions: real or mathematical?

A photon is emitted from a source in the direction of a receiver. On its way a half silvered mirror is kept. In a non-mathematical language, we can say that the probability of the photon passing through the half-silvered mirror and hitting the receiver is 50% and the probability of it reflecting off the mirror is also 50%. But going through the real mathematical representation denoting the states of the photon, a subtle but relevant problem is revealed: The probabilities of whether the photon hits the receiver or not spring up only after the photon encounters the mirror. Before hitting the mirror, nothing can be said about the route of the photon in terms of probabilities; the photon is said to be in a combination of states – “it will pass through the mirror” and “it will bounce off the mirror”. (Other situations can also be imagined up, where more than just these two states could exist.).
This kind of “combination states” are not just products of theoretical experiments, they have been demonstrated for real in countless occasions ; the most intriguing being that of the double slit experiment, where a single photon is seen to pass thru two adjacent slits simultaneously!

The real fate is decided after the interaction of the photon with the mirror. What is “spooky” about this interaction is that only after this can we calculate the probable fates mathematically. The generally accepted interpretation of this scenario is that the mirror represents a part of the experimental apparatus and the interaction of the photon with the mirror is equivalent to a “measurement process” which causes the split-up states (fates) of the photon to abruptly collapse into a single state. Before “measurement” there is only “it will pass through the mirror” and “it will bounce off the mirror”. After measurement there is either “it will pass through the mirror” or “it will bounce off the mirror”. The interaction of the photon with the mirror resulting in collapse of split-states into a single state is termed “decoherence”.

This view, called the Copenhagen Interpretation or formerly, the Bohr-Heisenberg interpretation, (after its most famous patrons Neils Bohr and Werner Heisenberg) is more of a colloquial representation of a mathematical statement. Bohr himself had suggested on many occasions that physical properties can be meaningfully ascribed to the object only in relation to some actual experimental results. He also held that the quantum scheme of wave equations is a mere symbolic representation that is useful for making predictions and it doesn’t directly depict any aspect of reality whatsoever. Note that this is starkly different from the widely held misconception that Copenhagen Interpretation demands a conscious observer to perform the act of measurement for the “mysterious” collapse of states to occur (the “collapse” part was actually a later addition by John von Neumann)

Penrose acknowledges that his approach is that of a realist – one who maintains that all physical theories worded in mathematics correspond to some aspect of objective reality out there, however small the accuracies of experimental observations be.
The standard interpretations of the quantum experiments do not say what exactly happens during decoherence; not even in theory. Penrose finds “decoherence”, a real process where relativistic gravity could come into action. Also, he believes that the experimental evidences of finding the same quantum particle (electrons, photons etc) at two different places should be a real phenomenon – something which happens out there.

His approach can be summarized in a very simplified form as below:

General Relativity proposes that if a piece of matter exists in a region of spacetime for a sufficiently long duration, the geometry of that region of spacetime is altered accordingly and gravity is a result of this alteration of spacetime (recall the iron balls and rubber sheet analogy).

It follows therefore that if an electron or any quantum particle really exists simultaneously in two regions of spacetime, then each of the duplicates should possess mass and therefore alter the geometry of its regional spacetime, resulting in gravitational fields of their own.

But to keep one duplicate of the particle away from the gravitational influence of the other requires energy. The interacting gravitational fields destabilize the split-states causing them to “decay” (collapse) into one or the other classical alternative.

If the whole system is left totally undisturbed by other environmental factors, then the split-up (duplicated) state of the quantum particle will remain stable for a time period inversely proportional to the energy needed to prevent the gravitationally induced decay.
This decay process is conveniently named Objective Reduction (OR for short), meaning that the process is not an artifact of the ‘act of observation’ or the ‘experimental apparatus’. Thus gravity is nicely woven into the scheme of quantum experiences.

As we can see, to take the ‘wave-collapse’ concept in the literal sense of the word or as a symbolic representation of reality is a matter of choice, so long as we can generate mathematical expressions that predict experimental outcomes. And for a physical theory, that’s what matters the most.

The important thing to note is that, as Penrose pointed out in several later interviews and lectures, in most occasions, mass movements in the environment itself result in (gravitation induced) collapse of states. The decay-time relationship with gravitational self-energy works perfectly well only in situations where the particle under observation is kept isolated from all environmental influences.
Thus as per Penrose’s interpretation, every piece of matter irrespective of macroscopic or microscopic state, can exist simultaneously in two or more split states like the electron in the slit experiments. What causes them to be seen as a single deterministic mass in our classical world is gravity.

Where does consciousness and mind come into all this? How do brain cells utilize spacetime to generate something as bewildering as ‘consciousness’?

 

More of that in part 3 of Quantum Consciousness: How physics changes the way we look at mind.

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Non-computability – Gödel, Turing machines and brain

 

This article is a subsection of the main article
How physics changes the way we look at mind

The current (and almost universally) accepted view on consciousness is that it is an emergent phenomenon arising from the complex interconnections and communication among neurons. Artificial Intelligence researchers latch their idea of a robotic equivalent of the brain on this concept of consciousness. Basically they believe that the creation of an ‘intelligent’ processor is only hindered by the tedious job of writing out algorithms powerful and complex enough to mimic brain’s functions.

But is that optimism farfetched?

Kurt Gödel’s incompleteness theorem doesn’t actually set some arbitrary limit to the process of acquiring knowledge through human or machine effort. And Penrose doesn’t say it does either. The Incompleteness Theorem is cited by Penrose as an example of how human brain can go beyond a computer or a robotic processor brain. Computers and Artificial intelligence devices function on the basis of ‘formal logic’ based programs (or algorithms for short) that tell them to deduce or derive results in series of logical steps. Penrose argues that such an operation can be used to trick the computer easily so that the computer will soon start contradicting its own logic and break down presumably.

Take for example the simple old puzzle:

If the barber shaves all those who do not shave themselves then who shaves the barber?

The simple tit-for-tat reply that pops into your mind now may be: Another barber!

But that answer is too tricky for a computer to arrive at, if it follows logical algorithms, even though a twelve year old can really “see through” the puzzle’s logic. And this is what Gödel’s theorem basically says. Rudy Rucker, in his book Infinity and the Mind: The Science and Philosophy of the Infinite, has simplified Gödel’s Incompleteness Theorem through an excellent example in a stepwise manner.

 

Think over this:

  1. Someone introduces Gödel to a UTM, a machine that is supposed to be a Universal Truth Machine, capable of correctly answering any question at all.
  2. Gödel asks for the program and the circuit design of the Truth Machine. The program may be complicated, but it can only be finitely long. Call the program TMP for Truth Machine Program.
  3. Now, Gödel writes out the following sentence: “The machine constructed on the basis of the TMP will never say that this sentence is true.” Call this sentence G for Gödel. Note that G is equivalent to: “Universal Truth Machine will never say G is true.”
  4. Now Gödel laughs and asks the Truth Machine whether G is true or not.
  5. If the Truth Machine says G is true, then “Universal Truth Machine will never say G is trueis false. If “Universal Truth Machine will never say G is trueis false, then G is false (since G = “Universal Truth Machine will never say G is true). So if the Truth Machine says G is true, then G is in fact false, and UTM has made a false statement. So UTM will never say that G is true, since UTM makes only true statements.
  6. We have established that UTM will never say G is true. So “UTM will never say G is true” is in fact a true statement. So G is true (since G = “UTM will never say G is true”).

And having tricked the Truth Machine, Gödel triumphantly declares: “I know a truth that Truth Machine can never utter,”

 

 

You may have a hunch: “isn’t this a problem of the language we use?”
The answer is NO.
The original incompleteness theorem is mathematically worded. The above simplified version using linguistic conundrums is just an abstraction of the real one. Gödel’s Incompleteness Theorem is a real problem that is faced by artificial intelligence researchers at least on theory level; the fact that we have not been able to attain any sort of complex thinking in machines doesn’t preclude incompleteness theorem from interfering in these matters.

Roger Penrose suggests that the ability of human brain / conscious brain to “go out of the labyrinth of axioms and find the truth outside” is due to the quantum nature of consciousness. He suggests that human consciousness may depend on some new, as yet unknown, quantum physics that has significant role in the neuronal processes of the brain.

More of that in the coming sections of How physics changes the way we look at mind.

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