It From Bit Or Bit From Us? Majid Karimi Research Group on Foundations of Quantum Theory and Information Department of Chemistry, Sharif University of Technology
On its 125 th anniversary, July 1 st, 2005 issue of Science highlighted several questions for which we do not have any answer. Do Deeper Principles Underlie Quantum Uncertainty and Nonlocality? How and Where Did Life on Earth Arise?
concept of information
Brukner and Zeilinger s informational interpretation of quantum mechanics Roederer s, pragmatic definition of information
We would like to show that to what extent (if any) these new approaches (information base approaches) may have the power to resolve these mysteries about quantum physics and life.
Information: From Aristotle to Landauer & Wheeler Information: From Aristotle to Landauer & Wheeler I think of my lifetime in physics as divided into three periods. In the first period. I was in the grip of the idea that Everything is Particles. I call my second period Everything is Fields. Now I am in the grip of a new vision, that Everything is Information John Archibald Wheeler, Geons, Black Holes, and Quantum Foam. Aristotle believed that the universe was entirely ordered by the metaphysical forms. The form informs matters, the matter materializes the forms Information referred to the processes by which a form (or idea or essence) entered into something material and gave it a specific shape or character, thus in-forming it.
Information: From Aristotle to Landauer & Wheeler Maxwell s demon Maxwell (1871): discussion about the limitations of the second law of thermodynamics Szilard (1929): The decrease of entropy by intelligent beings The relationship between information and measurement (information gain)
Information: From Aristotle to Landauer & Wheeler Mathematical theory of communication Hartley (1928): The idea of using logarithms to measure of information content Shannon (1948): mathematical theory of communication
The fundamental problem of communication is that of reproducing at one point either exactly or approximately a message selected at another point anything is a source of information if it has a number of possible events. any signal carries information about a source if we can predict the state of the source from the signal. Shannon ingeniously showed how the concept of information could be used to quantify facts about contingency and correlation inausefulway
Quantification of information Reduction of information to a mathematical formula Resemblance between information theoretic Shannon entropy and the thermodynamic Boltzmann entropy Brillouin (1951) free information bound information interconvertibility of information and negentropy
Information is physical Landauer(1961) discovered that logical operations that get rid of information, such as erasure, necessarily require the dissipation of energy. the erasure of 1 bit of information requires a minimal heat generation of KTln2.
Information is physical Information is stored in material system in accordance with the laws of physics and, information is transferred from place to place by physical means. So, information is not a non- physical entity Information handling takes place in the physical world
It from Bit J. A. Wheeler believes that information is the fundamental category from which all else flows, in other words, physical existence, at the deepest level is composed of information or bits. It from bit symbolizes the idea that every item of the physical world has at bottom - at a very deep bottom, in most instances - an immaterial source and explanation;
Quantum Mechanics Quantum Mechanics has two conceptual kinds of problems: local-realism (nonlocality) measurement problem Niles Bohr: There is no quantum world. There is only an abstract quantum physical description. It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about nature
Brukner and Zeilinger s interpretation The whole physical description is based on propositions we have knowledge or information about an object only through observations. The only way we are able to understand any phenomena in nature is through the epistemological structure of classical physics and everyday experience
A system is nothing else more than a construct based on a complete list of propositions together with their truth values (1)The velocity of the object is (2) The position of the object x is v From the theorem of Bell and Kochen- Specker we know that for a quantum system one can not assert definite truth values to all conceivable propositions simultaneously
In an attempt to describe quantum phenomena we are unavoidably put in the following situation: 1) the description of a quantum system has to be represented by the propositions which are used in the description of a classical system 2) those propositions cannot be assigned to a quantum system simultaneously. How to join these two, seemingly inconsistent, requirements? Knowledge and information
Finiteness of Information indefiniteness of the truth values for complementary propositions is due to that: The information content of a quantum system is finite
A quantum system cannot carry enough information to provide definite answers to all questions that could be asked experimentally. Then by necessity the answer of the quantum system to some questions must contain an element of randomness.. This kind of randomness must then be irreducible, that is, it cannot be reduced to hidden properties of the system. Otherwise the system would carry more information than what is available.
Irreducible randomness results from the finiteness of information How much information a quantum system can carry? The principle of quantization of information states that: An elementary system carries 1 bit of information.
Randomness must be irreducible because if it could be reduced to hidden properties, then the system would Do Deeper Principles Underlie Quantum Uncertainty and Nonlocality? The state of an elementary system specifies the answer to a single yes/no experimental question Elementary systems cannot carry enough information to specify definite answers to all experimental questions that could be asked Questions lacking definite answers must receive a random outcome
according to the Bell s theorem, any local realistic view of the world is incompatible with quantum mechanics In other words, Bell demonstrates that for entangled state, the explanation of all correlations between two particles with a local realistic model is impossible. This conflict between local realistic view and quantum mechanics has led to numerous experiments, interestingly, all of which support quantum mechanics. This means that if nature is governed by the predictions of quantum theory, the locality principle is simply wrong, and our world is nonlocal.
Entanglement they consider the case of two Qbits systems carrying therefore 2 bits of information, i.e. representing the truth value of two propositions. the Bell states:
In which way do these four states carry two bits of information in a nonlocal way? if we ask the two questions whose answers describe the result of a joint observation: Are both spins in the same direction along x? Are both spins in the same direction along y? then we end up with a maximally entangled state. yes, yes" yes, no" no, yes no, no" Entanglement is explained as arising when all of the N bits of information associated with N elementary systems are used up in specifying joint rather than individual properties, or more generally, when more of the information is in joint properties than would be allowed classically
The ultimate goal in Brukner and Zeilinger s approach Information is a fundamental notion which the inherent nature of quantum particles and quantum processes are based on its concept. External reality depends as well on our experimental answers to questions about the quantum events Reality and information are two sides of the same coin. It does not make sense to talk about reality without the notion of information about it, and it is pointless to talk about information without something where it refers to. What can be said about reality, defines what can exist.
Information is the irreducible kernel from which everything else flows. Then the question why nature appears quantized is simply a consequence of the fact that information itself is quantized by necessity. It might even be fair to observe that the concept that information is fundamental is very old knowledge of humanity, witness for example the beginning of gospel according to John: "In the beginning was the Word".
the more contentious question becomes whether or not physics needs another, richer concept of information than Shannon s definition. what is the meaning of information? Does information, as mentioned above; really play an active role in physical processes to shape the Universe? If so, when and where does information begin to play an active role, actually controlling processes in the Universe? Are information and information processing exclusive attributes of living systems, related to the very definition of life that entangled with concepts such as meaning, intention and specific functions? where is there room in physics for the notion of information, not merely in the static, passive and technological sense, but in the active life, observation and meaning sense? How does a lofty, abstract notion like meaning or intention emerge from the blundering, purposeless antics of senseless atoms?
Pragmatic Information Roedere emphasizes that to address and answer these questions, a definition of this ubiquitous concept must be found that is truly objective and independent of human actions and human- generated devices To accomplish this idea, he turns to the process of interaction as the underlying basic, primordial concept
Pragmatic Information he divides all interactions between two bodies into the two major categories: Force-field driven interactions between elementary particles and ensembles of particles in the physical domain, Interactions between classical mass points elementary particles in the quantum domain gravitational interaction between macroscopic bodies Information-based interactions between certain kinds of complex systems that form the biological domain, interactions between an insect orbiting around light bulb and this light source, interactions between microorganisms and imbalance in concentration of glucose, interaction between instrument and object during a physical measurement.
Pragmatic Information
interaction in informational base is an arrangement in which the presence of a specific form, shape or pattern in complex system A (the emitter) not its field, energy or forces leads to a specific, univocal change in complex system B (the recipient). Roederer defines pragmatic information as that which represents the univocal correspondence between pattern and specific change
Pragmatic information does not appear as an active, controlling agent in the physical interaction processes. This concept plays no active role in the abiotic world, unless an observer such as life form (or device designed and built by intelligent beings) intervenes for measurement or modeling without observers, there is no information Roedere posit : information is the defining concept that separates life from any natural (i.e., not made) inanimate system.
life is information at work, therefore, information appeared, in its fundamental pragmatic form, when and where life appeared in the universe and, conversely, life appeared whenever and wherever information-driven interactions began.
It From Bit or Bit from US? Wheeler s Meaning Circuit dictum : Physics gives rise to all phenomena, Phenomena in turn give rise to chemistry, biology and communicators Questions of communicator lead to measurement and the laws of physics. The laws of physics result from our observation of the universe What is the relationship between information and reality? What is the relationship between physics and reality? What is the role of physics? It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about nature