Non-orientable wormhole
Encyclopedia
In wormhole
theory, a non-orientable wormhole is a wormhole connection that appears to reverse the chirality
of anything passed through it. It is related to the "twisted" connections normally used to construct a Möbius strip
or Klein bottle
.
In topology
, this sort of connection is referred to as an Alice handle.
has described a way of visualising wormhole geometry:
Although this set of instructions seems straightforward, there are two topologically distinct ways in which the two surfaces can be mapped
to one another. If we draw a map of the Earth's surface onto one wormhole mouth, how does this map appear at the second mouth?
For a "conventional" wormhole, the network of points will be seen at the second surface to be inverted, as if one surface was the mirror image of the other—countries will appear back-to-front, as will any text written on the map. This is as it should be, because in a sense, the second mouth is showing us the view of the same map seen "from the other side".
This configuration reverses the "handedness" or "chirality" of any objects passing through. If a spaceship pilot writes the word "IOTA" on the inside of their forward window, then, as the ship's nose passes through the wormhole and the ship's window intersects the surface, an observer at the other mouth looking in through the glass should see the same word, "IOTA", written on the window of the emerging spaceship. Once the spaceship has passed through, the curious onlooker may peek inside the spaceship cockpit and find that what is written on the inside of the glass is actually "ATOI" – the handedness of the writing (and of every other part of the spaceship, including the pilot) has been inverted by its passage through the wormhole.
can be considered as a time-reversed
electron
, it can also be considered as an electron aging conventionally, but with one spatial dimension reversed. The existence of a traversable nonorientable wormhole would seem to allow the conversion of matter to antimatter
, and vice versa.
A universe that includes one of these "non-orientable" connections does not allow a global definition of whether a particle is "really" matter or antimatter, and this sort of universe, with no global definition of charge is referred to in research papers as an "Alice universe."
, an Alice universe is a hypothetical universe with no global definition of charge
. What a Klein bottle
is to a closed two-dimensional surface, an Alice universe is to a closed three-dimensional volume. The name is a reference to the character in Lewis Carroll
's children's book, Alice Through the Looking-Glass
.
An Alice universe can be considered to allow at least two topologically-distinct routes between any two points (it is doubly connected), and if one connection (or "handle") is declared to be a "conventional" spatial connection, at least one other must be deemed to be a non-orientable wormhole connection.
Once these two connections are made, we can no longer define whether a given particle is matter or antimatter
. A particle might appear as an electron
when viewed along one route, and as a positron
when viewed along the other. If we define a reference charge as nominally positive and bring it alongside our "undefined charge" particle, the two particles may attract if brought together along one route, and repel if brought together along another - the Alice universe loses the ability to distinguish between positive and negative charges, except locally.
As with a Möbius strip
, once the two distinct connections have been made, we can no longer identify which connection is "normal" and which is "reversed" — the lack of a global definition for charge becomes a feature of the global geometry. This behaviour is analogous to the way that a small piece of a Möbius strip allows a local distinction between two sides of a piece of paper, but the distinction disappears when the strip is considered globally.
Wormhole
In physics, a wormhole is a hypothetical topological feature of spacetime that would be, fundamentally, a "shortcut" through spacetime. For a simple visual explanation of a wormhole, consider spacetime visualized as a two-dimensional surface. If this surface is folded along a third dimension, it...
theory, a non-orientable wormhole is a wormhole connection that appears to reverse the chirality
Chirality (physics)
A chiral phenomenon is one that is not identical to its mirror image . The spin of a particle may be used to define a handedness for that particle. A symmetry transformation between the two is called parity...
of anything passed through it. It is related to the "twisted" connections normally used to construct a Möbius strip
Möbius strip
The Möbius strip or Möbius band is a surface with only one side and only one boundary component. The Möbius strip has the mathematical property of being non-orientable. It can be realized as a ruled surface...
or Klein bottle
Klein bottle
In mathematics, the Klein bottle is a non-orientable surface, informally, a surface in which notions of left and right cannot be consistently defined. Other related non-orientable objects include the Möbius strip and the real projective plane. Whereas a Möbius strip is a surface with boundary, a...
.
In topology
Topology
Topology is a major area of mathematics concerned with properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing...
, this sort of connection is referred to as an Alice handle.
"Normal" wormhole connection
Matt VisserMatt Visser
Matt Visser is a mathematics Professor at Victoria University of Wellington.Some of his research interests include General Relativity, Quantum Field Theory and Cosmology....
has described a way of visualising wormhole geometry:
- take a "normal" region of space
- "surgically remove" spherical volumes from two regions ("spacetime surgery")
- associate the two spherical bleeding edges, so that a line attempting to enter one "missing" spherical volume encounters one bounding surface and then continues outward from the other.
Although this set of instructions seems straightforward, there are two topologically distinct ways in which the two surfaces can be mapped
Map (mathematics)
In most of mathematics and in some related technical fields, the term mapping, usually shortened to map, is either a synonym for function, or denotes a particular kind of function which is important in that branch, or denotes something conceptually similar to a function.In graph theory, a map is a...
to one another. If we draw a map of the Earth's surface onto one wormhole mouth, how does this map appear at the second mouth?
For a "conventional" wormhole, the network of points will be seen at the second surface to be inverted, as if one surface was the mirror image of the other—countries will appear back-to-front, as will any text written on the map. This is as it should be, because in a sense, the second mouth is showing us the view of the same map seen "from the other side".
"Reversed" wormhole connection
The alternative way of connecting the surfaces makes the "connection map" appear the same at both mouths.This configuration reverses the "handedness" or "chirality" of any objects passing through. If a spaceship pilot writes the word "IOTA" on the inside of their forward window, then, as the ship's nose passes through the wormhole and the ship's window intersects the surface, an observer at the other mouth looking in through the glass should see the same word, "IOTA", written on the window of the emerging spaceship. Once the spaceship has passed through, the curious onlooker may peek inside the spaceship cockpit and find that what is written on the inside of the glass is actually "ATOI" – the handedness of the writing (and of every other part of the spaceship, including the pilot) has been inverted by its passage through the wormhole.
Consequences
As well as turning left-handed screwthreads into right-handed screwthreads, and left-handed gloves into right-handed gloves, reversing the chirality of an object is also usually associated with the idea of reversing the sign of electromagnetic charge – if a positronPositron
The positron or antielectron is the antiparticle or the antimatter counterpart of the electron. The positron has an electric charge of +1e, a spin of ½, and has the same mass as an electron...
can be considered as a time-reversed
Time reversal
Time reversal may refer to:* In physics, T-symmetry - the study of thermodynamics and the symmetry of certain physical laws where the concept of time is reversed — ie...
electron
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...
, it can also be considered as an electron aging conventionally, but with one spatial dimension reversed. The existence of a traversable nonorientable wormhole would seem to allow the conversion of matter to antimatter
Antimatter
In particle physics, antimatter is the extension of the concept of the antiparticle to matter, where antimatter is composed of antiparticles in the same way that normal matter is composed of particles...
, and vice versa.
A universe that includes one of these "non-orientable" connections does not allow a global definition of whether a particle is "really" matter or antimatter, and this sort of universe, with no global definition of charge is referred to in research papers as an "Alice universe."
Alice universe
In theoretical physicsTheoretical physics
Theoretical physics is a branch of physics which employs mathematical models and abstractions of physics to rationalize, explain and predict natural phenomena...
, an Alice universe is a hypothetical universe with no global definition of charge
Charge (physics)
In physics, a charge may refer to one of many different quantities, such as the electric charge in electromagnetism or the color charge in quantum chromodynamics. Charges are associated with conserved quantum numbers.-Formal definition:...
. What a Klein bottle
Klein bottle
In mathematics, the Klein bottle is a non-orientable surface, informally, a surface in which notions of left and right cannot be consistently defined. Other related non-orientable objects include the Möbius strip and the real projective plane. Whereas a Möbius strip is a surface with boundary, a...
is to a closed two-dimensional surface, an Alice universe is to a closed three-dimensional volume. The name is a reference to the character in Lewis Carroll
Lewis Carroll
Charles Lutwidge Dodgson , better known by the pseudonym Lewis Carroll , was an English author, mathematician, logician, Anglican deacon and photographer. His most famous writings are Alice's Adventures in Wonderland and its sequel Through the Looking-Glass, as well as the poems "The Hunting of the...
's children's book, Alice Through the Looking-Glass
Through the Looking-Glass
Through the Looking-Glass, and What Alice Found There is a work of literature by Lewis Carroll . It is the sequel to Alice's Adventures in Wonderland...
.
An Alice universe can be considered to allow at least two topologically-distinct routes between any two points (it is doubly connected), and if one connection (or "handle") is declared to be a "conventional" spatial connection, at least one other must be deemed to be a non-orientable wormhole connection.
Once these two connections are made, we can no longer define whether a given particle is matter or antimatter
Antimatter
In particle physics, antimatter is the extension of the concept of the antiparticle to matter, where antimatter is composed of antiparticles in the same way that normal matter is composed of particles...
. A particle might appear as an electron
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...
when viewed along one route, and as a positron
Positron
The positron or antielectron is the antiparticle or the antimatter counterpart of the electron. The positron has an electric charge of +1e, a spin of ½, and has the same mass as an electron...
when viewed along the other. If we define a reference charge as nominally positive and bring it alongside our "undefined charge" particle, the two particles may attract if brought together along one route, and repel if brought together along another - the Alice universe loses the ability to distinguish between positive and negative charges, except locally.
As with a Möbius strip
Möbius strip
The Möbius strip or Möbius band is a surface with only one side and only one boundary component. The Möbius strip has the mathematical property of being non-orientable. It can be realized as a ruled surface...
, once the two distinct connections have been made, we can no longer identify which connection is "normal" and which is "reversed" — the lack of a global definition for charge becomes a feature of the global geometry. This behaviour is analogous to the way that a small piece of a Möbius strip allows a local distinction between two sides of a piece of paper, but the distinction disappears when the strip is considered globally.