Mirror Convexure Infinity

REACHING MIRROR INFINITUDE OF CONVEXURE

THE NEVER ENDING FASCINATING INFINITE REFLECTION

For over a hundred years, man has pondered the puzzling mirror condition of infinite reflections.

The Big Brain specifies reaching infinity through the use of various mirrors. Previously, Plano mirrors were used for this experiment, exhibiting the infinity of seemingly endless reflections. This time, the choice of mirrors include two convex mirrors. These are questions surrounding this experiment:

1) Is infinity reflection state achieved?
2) Is infinity reached faster or slower with convex mirrors compared to plano mirrors?
3) How is the speed of infinity defined?

To answer these questions, one must consider two models. One is purely mathematical and theoretical and the other is the real world actual experiment. For our purposes, both are important. First, the obviates of this experiment include the tiny minute offset of the mirror positions that result in the image shifting position as it continues towards an infinite state. This upsets the infinity purity.

The limit of count (black rings) is eight reflections with two convex mirrors

The second real world factor is the the light reflected by a number images become dimmer and dimmer, thus limiting the actual number of reflections. Contrast also becomes less and less. Resolution degrades. In the case of the convex mirror images, the images become smaller and smaller until finally they merge with the finite microscopic silver grains and the compositional material of the mirrors. The smallness of this effect can be negated by telescope and then followed by a microscope, to make the tiny images larger. However, this has limits, unlike the infinity being sought. We therefore postulate in the real world, one must determine the number of visible reflections en-route towards infinity, where infinity is considered condition that is actually never reached with mirrors in the real world. Reaching infinity means the reflections will continue on and on without stopping. But, are there other types of mirrors in the Universe of the macro or the microscopic and the quantum realities that surround us?

Numbered reflections

SETUP
The cost of this experiment is 60 cents. Two plastic quality convex chrome "mini blind spot" mirrors were obtained from Wenzhoushi Senhu Locks, part number #SF-011. One mirror is placed on the table. Next to the mirror is a box. A piece of tape is applied to the top of a second mirror and the mirror is connected to the box, parallel to the base mirror, and are concentrically adjusted. The infinity of reflections are observed and recorded.

LINKS
Mirror - Wikipedia, the free encyclopedia
en.wikipedia.org/wiki/Mirror
A beam of light reflects off a mirror at an angle of reflection equal to its angle of .... mirrors placed exactly face to face can give an infinite regress of reflections.

Look into Infinity: Reflection & Light Science Project | Exploratorium ...
www.exploratorium.edu/snacks/look_into_infinity/index.html
Look Into Infinity. Images of images of images can repeat forever. If you have ever been between two mirrors that face each other, such as in a barber shop or a ...

Infinity is weird… even in infinity mirrors! | Skulls in the Stars
skullsinthestars.com/.../infinity-is-weird-even-in-infinity-mirr...
30 Jul 2011 – I was recently looking into the optics of a so-called “infinity mirror”, ... be produced by the reflection of the first image in the mirror behind him: ...

Why do Parallel Mirrors produce infinite mirrors?
www.physicsforums.com › ... › Introductory Physics
6 posts - 4 authors - 2 Oct 2009
Why do Parallel Mirrors produce infinite mirrors? Introductory Physics ... From where shall I start? Do you know the laws of reflection?

Reflecting Infinite Reflections
reflectinginfinitereflections.blogspot.com/ 18 Aug 2007 – Simply ... its a collection of pictures taken with digital cameras (mostly, I think) and mirrors .. to .... guess what ... generate Infinite Reflections.

Shooting Challenge: Infinite Loop
gizmodo.com/5809926/shooting-challenge-infinite-loop - Cached8 Jun 2011 – Though, technically, you should know that mirrors won't create infinite reflections - they're actually countable. It's a bit of a sidebar, but I found ...

Quantum Space

BIG PROPELLER-CHIP BRAIN SPACE EXPLORATION
BIG BRAIN CREATES QUANTUM WORLDS DIVISION FOR STUDY OF QUANTUM  SPACE

The Big Brain has formed the Quantum Space Division, i.e. The Quantum Worlds Exploration Division, which will explore strange new worlds that exist beyond the microscopic space end of the size spectrum. The project will explore perplexing "quantum world things" that traverse past the increasingly small realm of nanotechnology, and zoom deep down within the embedded and perhaps limitless infinitely shrinking zonal space of the ultimately weird and not-understood Quantum Effects.

According to research sources, i.e. Quantum Reflection

The purpose is to create a platform for exploring the phenomenon of quantum reflection, taking and applying Quantum Reflection to a level incorporating added dimensional Quanta and to theoretically represent their predicted or simulated behaviors and effects. 

TOOLS
Even when dealing with the theoretical, special research tools are required for experimentation, simulation and investigation of various scientific principles. For this reason, the QuadLyzer was invented and built.

Quantum Reflection
university.iosonofabio.fastmail.fm/talks/Quantum_Reflection.pdf

Quantum reflection is a classically counter intuitive phenomenon whereby the motion of particles is reverted "against the force" acting on them. This effect manifests the wave nature of particles and influences collisions of ultra-cold atoms and interaction of atoms with solid surfaces.

Quantum reflection of cold atoms from surfaces occurs on the attractive tails of long-range atom surface potentials, and takes place at mesoscopic distances on the order of a fraction of a micron.

Because of that, studies of quantum reflection are closely related to studies of the long-range atom-surface interactions and contribute to our understanding of the interface between quantum world and the macroscopic world in general.

Observation of quantum reflection has become possible thanks to recent advances in trapping and cooling atoms. Utilization of this effect has only begun and holds many exciting promises. The goal of the workshop is to present the recent results and applications of quantum reflection in the areas of atomic, molecular, optical and surface physics, and to discuss its potential for science and technology, notably for the understanding of quantum mechanics, for realization of experiments testing quantum electrodynamics and gravity, and for applications in the fields of quantum optics and nanotechnology.
Institute for Theoretical Atomic Molecular and Optical Physics
http://www.cfa.harvard.edu/itamp/

MESOSCOPIC
Mesoscopic physics is a sub-discipline of condensed matter physics which deals with materials of an intermediate length scale. The scale of such materials can be described as being between the size of a quantity of atoms (such as a molecule) and of materials measuring micrometers. The lower limit can also be defined as being the size of individual atoms. At the micrometer level are bulk materials. Mesoscopic and macroscopic objects have in common that they both contain a large number of atoms. Whereas average properties derived from its constituent materials describe macroscopic objects, as they usually obey the laws of classical mechanics, a mesoscopic object, by contrast, is affected by fluctuations around the average, and is subject to quantum mechanics.
http://en.wikipedia.org/wiki/Mesoscopic_physics

In other words, a macroscopic device, when scaled down to a meso-size, starts revealing quantum mechanical properties. For example, at the macroscopic level the conductance of a wire increases continuously with its diameter. However, at the mesoscopic level, the wire's conductance is quantized - the increases occur in discrete, or individual, whole steps. During research, mesoscopic devices are constructed, measured, and observed experimentally and theoretically in order to advance understanding of the physics of insulators, semiconductors, metals, and superconductors. The applied science of mesoscopic physics deals with the potential of building nano-devices.

SIZE OF MESOSCOPIC
There is no rigid definition for mesoscopic physics, but the systems studied are normally in the range of 100 nm (the size of a typical virus) to 1 000 nm (the size of a typical bacterium). 100 nanometers is the approximate upper limit for a nanoparticle.

From Discussion
http://www.physicsforums.com/showthread.php?t=560069
Quantum mechanics basically takes the wave mechanics of classical physics and applies it to individual particles. There are a few differences that crop up when you do this, but I think the main concept here carries over pretty well-- the concept of interference. In classical wave mechanics, we have Huygens' principle, which says that every part of a wave acts like sources for how the wave evolves forward in time. Also, we have the "superposition principle", which says that every solution to the wave equation that comes from one source just adds up with the solutions that come from all other sources. This means in classical waves, the waves get a high total amplitude wherever there is constructive interference, and low total amplitude wherever there is destructive interference.

SUPERPOSITION PRICIPLE

In quantum mechanics, we also have a superposition principle, except now it applies to individual particles. It basically says that anything that we can describe as something that can happen to an individual particle can happen in superposition, so what 'actually happens" is a kind of constructive sum over all these "possible happenings." This is the spirit of the Feynman path integral approach, for example. So using this mathematics, what has a high probability of happening is what receives constructive interference over this sum, and what has low probability is what destructively interferes. This is a key point-- each individual term in the sum starts out equally likely, even ones that correspond to absurd behavior, but the absurd behaviors cancel each other out, sort of like monkeys voting in an election.

In the case of reflection, we find that the presence of the mirror allows a certain behavior to receive constructive interference, which would not if the mirror were not there. The new behavior is "angle of incidence equals angle of reflection", and the mathematical property of that type of solution is that it exhibits "stationary phase." Stationary phase means the phase of the type of process (so how quickly the amplitude of the process varies over the set of very similar processes) is not varying over the physically allowed process, but does vary rapidly as soon as you test a non-physical process. Thus, the "angle of incidence equals angle of reflection" gives an extremum in the phase as you vary over a range of possible processes-- in this case, it is the minimum time to get between specified points A and B. Without the mirror, the only minimum time is the straight line between them. With the mirror, a second possibility emerges, the local minimum in time that comes from an equal angle of incidence and angle of reflection path between A and B that glances off the mirror. (It takes more time than the straight shot, but less time than all its neighboring paths, so it exhibits stationary phase and so constructive interference when you add the neighboring amplitudes.)

This still doesn't answer what the mirror is doing that allows for this new stationary phase solution. The classical answer to that is that the mirror acts like a source of waves that cancel the incident wave within the mirror, and constructively interfere to make a reflected wave. Quantum mechanically, the mirror creates a boundary condition on the photon wave function that forces the wave function to go to zero at the surface of the mirror, and this constraint suffices to give the reflected wave when you apply the superposition of wave functions analyzed in terms of all the modes that obey that constraint and have the energy of the incident wave. You could even do it with quantum field theory, and one way to picture that would be to say that the incident photon is destroyed by the mirror, but its energy must be accounted for, and since the mirror is elastic, it must use the energy to promote a "virtual photon" to the status of a real photon. What's more, the virtual photon not only has to have the energy of the original photon, it must also have a wave function that resonates constructively with the original photon-- in other words, it is indistinguishable from the original photon, so is ruled by the same wave function, and that wave function must experience constructive interferece (for all the above reasons) to have a reasonable probability of actually happening.

So you may be surprised to find there is not just one answer to your question, and there might be new possible answers in a few more centuries, but the key idea is constructive interference set up by the way the mirror is required to prevent the photon from crossing its flat surface, yet energy is also required to be conserved. Generally, we're happy if we have one way to think about it that gives good results and seems simple enough for us to understand.

Quantum mechanical tunneling and reflection simulation
http://www.youtube.com/watch?v=cV2fkDscwvY

What is Quantum Tunneling?
http://www.youtube.com/watch?NR=1&feature=fvwp&v=cTodS8hkSDg

More Links
http://en.wikipedia.org/wiki/Quantum_reflection

Quantum Reflection from an Atomic Mirror
george.ph.utexas.edu/papers/reflection_atomic_mirror.pdf

Counter-Intuitive the Laws of Quantum Physics
Researchers at the Fritz Haber Institute in Berlin report on the observation of a text-book quantum effect that nicely reveals how counter-intuitive the laws of quantum physics can be. Considering only classical mechanics, a particle moving towards a cliff would, inevitably, fall over (and down) the cliff wall, simply because the force is acting in this direction. In stark contrast, the wave-particle-duality of quantum physics allows for a particle (e.g., an atom or molecule) to bounce back from the edge of the cliff unscathed. This is known as quantum reflection and is responsible for the observation of non-destructive reflection of the weakest bound molecule known, the helium dimer, from a reflection grating. The findings have been published in the journal Science.

http://presse.fhi-berlin.mpg.de/832?lang=enhttp://presse.fhi-berlin.mpg.de/wp-content/uploads/2011/02/brevia5.jpg

Artist’s view of quantum reflection of a diatomic helium molecule in front of a solid surface. The attractive force between the surface and the helium dimer (van-der-Waals force) forms a deep canyon in front of the hard wall. The helium dimer survives this impact, because the dimer actually never comes into this canyon but bounces off the edge of the cliff.

Quantum reflection of ultracold atoms from thin films, graphene and semiconductor heterostructures
http://iopscience.iop.org/1367-2630/13/8/083020/fulltext/
 http://www.staff.ncl.ac.uk/nick.parker/images/SOL2.jpg

BRIGHT SOLITARY MATTER WAVES:  The quantum wavefunction of a BEC satisfies a nonlinear Schrodinger equation.  Under attractive atomic interaction, self-trappedwaves of matter known as bright solitary waves can be supported.
 Sufficiency conditions for quantum reflection
http://iopscience.iop.org/0295-5075/51/4/381

http://ej.iop.org/images/0295-5075/51/4/381/Full/img26.gif