Monday, January 9, 2012

The Information theory and the Universe

The Information and the Universe

An abstract of my theory:

The WAR: Susskind-Hawking battle, where Leonard Susskind and Gerard 't Hooft publicly 'declared war' on Hawking's solution!

From this video:

Stephen Hawking argued that small bits of information are lost when black holes evaporate. Susskind maintained that because this would violate the basic laws of physics, it couldn't be true. Susskind's theory that the universe is really holographic proved Hawking wrong.

The Susskind-Hawking battle, where Leonard Susskind and Gerard 't Hooft publicly 'declared war' on Hawking's solution, with Susskind publishing a popular book (The Black Hole War: My battle with Stephen Hawking to make the world safe for quantum mechanics) about the debate in 2008.

Susskind's long battle (20 years) with Hawking lies at the center of his book. The two disagreed fundamentally.

A black hole packs enough matter or energy into a small enough volume of space and it will collapse into a ball of intense gravitational attraction. You might expect that inside a black hole all the information in whatever formed it like stars, planets, civilizations… had been destroyed; but most physicists believe that black holes do hold information. But if they didn’t, their very existence would undermine one of science’s most important laws, the second law of thermodynamics.

The entropy of a black hole scales with its area rather than with its volume, since entropy is normally an extensive quantity that scales linearly with the volume of the system. This odd property led Leonard Susskind at Stanford University, and Gerard 't Hooft at Utrecht University to propose the holographic principle, which suggests that anything that happens in a volume of spacetime can be described by data on the boundary of that volume.

A lot of physicists searched for a quantum description of gravity for decades without finding the answer. But they do have a few pointers -they know that whatever makes up space-time should come in bite-size chunks measuring just 10-35 meters, the Planck length. So if you broke space-time up into little boxes, each a Planck-sized cube, you’d expect there to be roughly one bit of information per box.

But this picture is frayed by black holes. Instead of having one bit of information for every little volume, they seem to have one bit per patch of surface area.

If black holes obey the second law, they can’t just wipe out information. Where do they store it all? Well, black holes have something else that can never decrease -their surface area. Jacob Bekenstein of Princeton University and Stephen Hawking worked out that the surface area and the disorder in a black hole must be proportional. In information terms, there is roughly one bit per Planck area.

So information appears to be related to enclosed surface area not volume.

In a single cubic centimeter, there are 1099 Planck boxes to stick bits of information into; the surface of a single cubic centimeter has space for only 1066 bits.

Locality is the idea that points in space are separated and distinct from each other and that forces have to travel between them.

The holographic description of nature is distressingly awkward, says Stephen Shenker at Stanford.

Anyway to describe nature properly, we need to find a theory that lives in a two-dimensional space but can reproduce events in three spatial dimensions. Physicists were persuaded of this possibility only in 1998, when Juan Maldacena, then at Harvard, found a real theory that was holographic. He was trying to work out how a black hole could be made of strings.

The total information content of the observable universe is bounded by a finite number given by the area of a cosmological surface divided by the Planck area. This is referred to as the holographic principle. The current bound is roughly 10122 bits, but in the past it was smaller, varying like t2 in the early universe.

Planck area = 2.61223 × 10−70 m2

Iuniverse ≤ 10122

According to the holographic principle, this huge number represents an upper bound on the information content of the universe.

My view: the Information and the Universe

Physical information refers generally to the information that is contained in a physical system. In quantum information is important, for example in the concept of quantum entanglement to describe effectively direct or causal relationships between apparently distinct or spatially separated particles.

Quantum information is physical information that is held in the "state" of a quantum system. The most popular unit of quantum information is the qubit, a two-level quantum system.

Quantum information differs from classical information in several respects, among which we note the following: it cannot be read without the state becoming the measured value, the state may be in a superposition of basis values.

The states in which a qubit may be measured are known as basis states (or basis vectors).

Quantum phenomena have some remarkable functional properties, such as nondeterminism and nonlocality.

Entanglement is a nonlocal property that allows a set of qubits to express higher correlation than is possible in classical systems.

A quantum system is moving from a superposition of multiple possible states to a single definite state, without the intervention of an observer or measurement.

The qubit has some similarities to a classical bit but is very different. Like a bit a qubit can have two possible values, a 0 or a 1. The difference is that whereas a bit must be either 0 or 1, a qubit can have the values 0, 1, or a superposition of both.

The qubit state is a linear superposition of the basis states. This means that the qubit can be represented as a linear combination of form |0 and |1:

|ψ› = a|0 + b|1

where a and b are probability amplitudes and both are complex numbers..

When we measure this qubit in the standard basis, the probability of outcome |0 is |a|2 and the probability of outcome |1is |b|2. Because the absolute squares of the amplitudes equate to probabilities, it follows that a and b must be constrained by the equation:

|a|2 + |b|2 = 1.

because this ensures you must measure either one state or the other.

The states in which a qubit may be measured are known as basis states (or basis vectors).

A quantum state is a set of mathematical variables that fully describes a quantum system; a quantum state of a system characterized by a set of quantum numbers and represented by an eigenfunction.

The energy of each state is precise within the limits imposed by the uncertainty principle but may be changed by applying a field of force.

That is why different quantum states for a physical system show discrete differences in the value of the variables used to define the state. The spin of an isolated electron can take on one of only two values; there are no other quantum states available for the electron and no intermediate values, since spin is quantized. The quantum state is sometimes described by a set of quantum numbers that pick out the appropriate values for describing the state.

A quantum state is a set of mathematical variables that fully describes a quantum system; a quantum state of a system characterized by a set of quantum numbers and represented by an eigenfunction.

Mass and energy in the universe remains constant under all current accepted cosmological models.

The observable universe consists of the galaxies and other matter that we can in principle observe from Earth because light from those objects has had time to reach us since the beginning of the cosmological expansion.

The total mass for the observable universe is Muniverse = 3.35 × 1054 kg; this is an estimation based on critical density.

Because the gravity can not compress the universe beyond the Planck density I calculated the minimum volume of the Universe, Vmin is equal with the mass of the Universe divided by the Planck density: Vmin = Muniverse / ρP

Vmin = 3.35 × 1054 kg / 5.1550 × 1096 kg/m3 = 6.498545 × 10-43 m3

This means no singularity, energy is not infinite, density is not infinite, volume is not zero, and space time curvature is not infinite.

Here is an incomplete list of physical implementations of qubits: Photons, Coherent state of light, Electrons, Nucleus, Optical lattices

An approximate calculation gives the number of atoms in the observable universe to be close to 1080.

This means today the number of qubits of the universe is bigger than 1080 qubits.

Individual photons of light show great promise as quantum bits of information (qubits) in a quantum computer because they can travel great distances through optical fibers or even air without losing their quantum nature.

Extremely low frequency (ELF) is a term used to describe radiation frequencies from 3 to 300 Hz. In atmosphere science, an alternative definition is usually given, from 3 Hz to 3 kHz. In the related magnetosphere science, the lower frequency electromagnetic oscillations (pulsations occurring below 3 Hz) are considered to lie in the ULF range.

One of the difficulties posed when broadcasting in the ELF frequency range is antenna size. This is because the antenna must be at least a substantial fraction of the size (in at least one dimension) of the wavelength of the frequency of the EM waves. A 1 Hz signal would have a wavelength equal to the distance EM waves travel through a given medium in 1 second.

I calculated the lowest number of qubits after Big Bang: min Iuniverse .

I calculated the max number of qubits, max Iuniverse if the universe will be made of photons with the 1Hz frequency.

To calculate the total amount of information that could be processed, we have to assume that the universe has a minimum temperature, below which no energy, no information can be extracted.

Speed of light c = 2.99792458 × 108 m s−1

Planck constant h = 6.62606896 × 10-34 J s

Planck energy EP = 1.9561 × 109 J

Planck angular frequency fP = 1.85487 × 1043 s-1

min Iuniverse < Iuniverse < max Iuniverse

Muniverse × c2 / EP < Iuniverse < Muniverse × c2 / h

3.35 × 1054 × (2.99792458 × 108)2 / (1.9561 × 109) < Iuniverse < 3.35 × 1054 × (2.99792458 × 108)2 / (6.62606896 × 10-34)

15.392 × 1061 qubits < Iuniverse < 4.544 × 10104 qubits

The Big Bang

I answered to this question:

Physics major question: Big Bang: What Banged?

The Big Bang is the dominant (and highly supported) theory of the origin of the universe.

What Banged? In my view: a qubit of information (a photon) with a very high oscillation frequency.

The frequency of the qubit:

fQ = (Energy of the universe) / h = Muniverse × c2 / h = 3.35 × 1054 × (2.99792458 × 108)2 / (6.62606896 × 10-34)

fQ = 4.544 × 10104 Hz

Like I said before:

"In the beginning was the qubit" Adrian Ferent


In my view Susskind’s first mistake: he is talking about bits of information, but today information is measured in qubits.

I do not agree with Susskind-Hawking: the information is located on the ‘area’ of the universe. In my view the information of a system depends of the energy of the system, we need energy to change the state of the qubit.

Susskind is talking about Hawking’s thought experiment; there is one bit per Planck area. This is wrong because inside a Planck volume the Planck energy EP = 1.9561 × 109 J.

Today there is more information inside the universe then on the edge of the universe.

The photons from the edge of the universe can not record all the changing information from the whole Universe. All the qubits like photons, electrons, atoms…are generating a lot of information.

Information is lost in the quantum system trough interaction with an observer.

The information within the quantum states cannot entirely be retained once the system has collapsed from a superposition of states into a specific state. That lost information can never be retained, as opposed to classical theory where information transformations can be reversed to obtain a history of the previous states of the system. That’s why in my view Susskind, Hawking, Gerard 't Hooft…theory is wrong.

When a measurement of any type is made to a quantum system, decoherence breaks down and the wave function collapses into a single state.

Susskind is talking about the information from a book; to have a correct discussion we can not mixed bits with qubits, to describe a system we have to stay at the quantum level.

I calculated precisely the lower bound , the lowest number of qubits after the Big Bang:

min Iuniverse = 15.392 × 1061 qubits.

I answered to physics major question: Big Bang: What Banged?

In my view: a qubit of information (a photon) with a very high oscillation frequency, fQ = 4.544 × 10104 Hz.

"In the beginning was the qubit" Adrian Ferent