"To fully understand this reality, we must take into account other dimensions of a wider reality" (John Wheeler).
"No theory of physics that deals only with physics will ever explain physics" (John Wheeler)
Wormholes
In physics, a wormhole, also known as an Einstein-Rosen bridge, is a hypothetical topological feature of space-time, described by the equations of general relativity. It consists essentially of a "shortcut" through space-time. It consists of two parts: an origin A and an end B, such that an object located at A, passes instantaneously to place B.
The name "wormhole" comes from the following analogy, used to explain the phenomenon. Suppose the universe is the surface of an apple, and a worm travels over it. The distance from one side of the apple to the other is equal to the shortest path (geodesic) that the worm has to travel on that surface. If the worm were to dig a hole directly through the apple the distance it would have to travel would then be less.
Traditionally, the concept of the existence of a fourth spatial dimension has been used to explain the phenomenon.
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According to Einstein's theory of relativity, black holes and wormholes can exist in our universe. Both types of holes are related: a wormhole has a short lifetime and joins two black holes. But these are theoretical speculations. There is no evidence for their actual existence.
Time flows more slowly in a gravitational field. In the extreme case of a black hole, where gravitation is enormous (gravitational collapse occurs), time practically stops and space practically disappears: all points in space are the same point.
Tunnel effect
In quantum physics, the tunnel effect is a phenomenon in which a particle jumps over, penetrates, or passes through a barrier of potential energy greater than the total energy (potential + kinetic) of the particle itself.
This phenomenon was born with the discovery of natural radioactivity by Henri Becquerel in 1896. For example, alpha particles (Helium nuclei) "escape" from an unstable (radioactive) atomic nucleus.
The tunnel effect is explained by the wave-particle duality. The particle has an associated wave that extends beyond the potential barrier. Part of the wave is reflected by the barrier and part passes through it. The wave can collapse as a corpuscle in that region. The wave function describes (according to Max Born's interpretation) the probability of the particle being at each position in space. Born himself recognized that the phenomenon of the tunnel effect is not restricted to quantum physics alone. According to quantum cosmology, the universe appeared from a quantum blur, coming into existence through the tunnel effect and evolving since then.
The tunneling effect has important applications in modern devices, such as flash memory, tunneling microscope, LED diodes, transistors, semiconductors and superconductors.
Formalization in MENTAL
Here we are interested in integrating both phenomena (wormholes and tunnel effect) by formalizing, in their qualitative aspect, the disappearance of an entity (an expression) from a point in abstract space and its appearance at another point in the same space.
For example, if we have the expressions
x=(a ⟨u⟩ b) y=(c d ⟨v⟩)
and we define the rule
⟨( (u=θ v=t) ←' e=0 → (u=t v=θ)⟩
then, depending on the value of e, the expression t appears in one place or another:
If e=0, x=(a t b) y=(c d).
If e=1, x=(a b) y=(c d t).
This can be generalized. An expression t disappears from one place and appears in multiple places at once. For example, with the same rule as above,
x=(a ⟨u⟩ ⟨u⟩ b ⟨v⟩ ⟨v⟩)
If e=0, x=(a t t b)
If e=1, x=(a b t t).
Abstract space and the laws governing it (the dimensions of semantic primitives) constitute a meeting point with the mental world and the world of quantum physics, where there is no physical space and time, but abstract space and time. In the deep, physical world and mental world are unified.
Bibliography
Gribbin, John. Unveiling the Edge of Time: Black Holes, White Holes, Worm Holes. Three Rivers Press, 1994.
Griffiths, David J. Introduction to Quantum Mechanics. Prentice Hall, 2004.
Hawking, Stephen W. Agujeros negros y pequeños universos. Plaza Janés, 1994.
Hawking, Stephen W. Historia del tiempo. Del big bang a los agujeros negros. Crítica, Barcelona, 1988.
Hawking, Stephen W. El universo en una cáscara de nuez. Crítica, Barcelona, 2002.
Hawking, Stephen W. y Penrose, Roger. La naturaleza del espacio y el tiempo. Debate, 1996.
Liboff, Richard L. Introductory Quantum Mechanics. Addison-Wesley, 2002.
Razavy, Mohsen. Quantum Theory of Tunneling. World Scientific, 2003.
Visser, Matt. Lorentzian Wormholes: From Einstein to Hawking. AIP Press, 1996.
