Trespassing on Einstein's Lawn (62 page)

Light cone
The region of spacetime encompassing everything with which a given observer can have a causal relation. If something is in your past light cone, you can see it. If it's outside your past light cone, you can't—light that far away hasn't had enough time since the origin of the universe to reach you. If something lies in your future light cone, your actions can affect it. If it's outside your future light cone, it is forever out of reach.

Local
Within a single light cone, accessible by a single observer.

Loop quantum gravity
A theory of quantum gravity in which spacetime is made up of discrete units of area and volume.

Lorentz symmetry
The symmetry that ensures equivalence between inertial frames that are moving at different uniform velocities or are rotated relative to one another.

Lorentz transformation
A method of translating between two inertial, or uniformly moving, reference frames, usually by trading one
reference frame's time for another's space, and vice versa, while keeping the total spacetime interval the same in both frames. This is the key tool of special relativity and is required to ensure that the speed of light remain constant in all reference frames.

Low quadrupole
The lack of temperature fluctuations at scales larger than 60 degrees in the cosmic microwave background.

M-theory
A candidate for a holy grail theory of quantum gravity, it is the larger theory of which the five versions of string theory and eleven-dimensional supergravity are mere shadows. It describes objects such as particles, strings, and branes, but none is its fundamental ingredient. In fact, it's not clear whether M-theory has any fundamental ingredients at all.

Manifold
A space that is locally flat and Euclidean but may be globally curved and warped. The key rule of general relativity is:
To make a curve match up with a line, bend the paper.
The paper is the manifold.

Mathematical structure
A set of isomorphic elements or equivalent representations of a number.

Measure problem (eternal inflation)
In the infinite multiverse produced by eternal inflation, everything that can happen does happen an infinite number of times. Calculating the probability for observing anything becomes impossible, as all probabilities are infinity divided by infinity.

Measurement problem (quantum mechanics)
Prior to measurement, a quantum system is in many states simultaneously, as evidenced by interference. When we measure it, we find it in a single state. What does it mean to make a measurement? Why should our measurements have any effect on reality?

Multiverse
A global collection of causally disconnected universes.

No-cloning theorem
An unknown quantum state cannot be copied.

Non-Boolean logic
A system of logic that defies the Boolean two-valuedness of true and false, usually by revoking the law of the excluded middle and allowing for values to be both true
and
false.

Non-Euclidean geometry
A system of geometry that tosses out Euclid's fifth axiom, which says that parallel lines will never meet. The curved spacetime of general relativity is described by non-Euclidean geometry.

Observer
A reference frame, or perhaps the origin of a reference frame, which is bounded in space by the finite speed of light.

Observer-dependent
Something that changes when viewed from different reference frames.

Occam's razor
The philosophical criterion that when one is given a host of empirically equivalent alternatives, the simplest theory is usually true.

Ontology
What exists; the furniture of reality.

Particle
An irreducible representation of the Poincaré symmetry group—a definition that only means anything in a spacetime with Poincaré symmetry; that is, a flat spacetime without gravity. In the face of gravity, there's no observer-independent definition of a particle. In all cases, however, it is definitely
not
a tiny ball.

Phase
How far along a wave is in its cycle relative to a given observer. The phase is not inherent to the wave—it defines the frame of reference from which the wave is being viewed.

Planck scale
The incredibly tiny (10
^-33
centimeters) or, equivalently, incredibly high-energy (10
¹⁹
GeV) scale at which quantum effects on spacetime grow extreme. Looking to smaller length scales or higher energies would collapse spacetime into a black hole, so the Planck scale is the border beyond which spacetime loses all meaning.

Poincaré symmetry
The symmetry that ensures equivalence between inertial frames that are moving at different uniform velocities, are rotated relative to one another or are at different locations in spacetime. This is the symmetry of Minkowski spacetime, the flat, gravity-free spacetime of Einstein's special relativity. Particles are only invariant in spacetimes that are Poincaré symmetric.

Proposition
A declarative sentence that can be deemed true or false, such as “The Earth is round” or “2 + 3 = 7.”

QCD
Quantum chromodynamics, the theory that describes how gluons bind quarks together via the strong nuclear force.

Quantum cosmology
A theory of the universe's origin and evolution that takes into account its fundamentally quantum nature. Tends to suffer from an extreme form of the measurement problem, since the universe, by definition, has no outside, and therefore no one can measure it.

Quantum gravity
The holy grail theory of everything that will unite Einstein's theory of gravity, general relativity, with quantum mechanics.

Quark-gluon plasma
A hot gas plasma of free-roaming quarks and gluons, which existed in the earliest moments of the universe.

Redshift
The stretching of a photon's wavelength and the corresponding decrease in its frequency and energy. A Doppler redshift results when a photon source is moving away relative to an observer, like the galaxies that are moving away from us as the universe expands. Light can also be redshifted by the expansion of space or by gravity as it travels from its source toward an observer.

Relational quantum mechanics
Carlo Rovelli's interpretation of quantum mechanics, which emphasizes the observer-dependence of quantum measurement.

Rindler horizon
An event horizon that results from an observer's acceleration. So long as the observer continues to accelerate, light from far regions of the universe will never catch up to him, rendering a portion of the universe dark and causally inaccessible, like a black hole.

S-duality
The duality that equates the strong coupling regime of one string theory with the weak coupling regime of another, revealing what look like very different string theories to be different descriptions of the same theory, M-theory.

S-matrix
A method of calculating the probabilities for various outcomes of particle interactions, which requires the observer to stand outside the system under study.

Singularity
A place where spacetime curvature becomes infinite and the laws of general relativity, along with all notions of space and time, lose their meaning.

Solipsism
The belief that I am the only conscious creature in the universe and the only observer who will ever read this sentence.

Special relativity
Einstein's theory, which puts all inertial reference frames on equal footing by keeping the speed of light invariant in all frames but allowing space and time intervals to change from one frame to the next, so that what one observer views as time another might view as space. All observers will agree on four-dimensional spacetime intervals.

String landscape
The vast collection of some 10
⁵⁰⁰
vacua described by string theory, each with its own values of physical constants, like the cosmological constant.

String theory
A theory of quantum gravity, positing that all the different types of elementary particles are each vibrations of a single entity: a string. Supersymmetric strings vibrate in nine spatial dimensions.

Strong complementarity
Physics only makes sense within the reference frame of a single observer. Quantum mechanically, this means that each observer lives in his or her own Hilbert space.

Structural realism (ontic)
The philosophical position that the world is made not of things but of mathematical relationships or structure.

Supergravity
A theory that combines general relativity with supersymmetry. Because supersymmetry is a local symmetry—what looks like a boson in one reference frame might look like a fermion in another—it requires a gauge force to patch up the misalignments between frames. That gauge force is gravity.

Supernova
An exploding star.

Superposition
A phenomenon in which a quantum system is in multiple, mutually exclusive quantum states, such as “dead cat” and “alive cat,” simultaneously. We can't measure superpositions directly, because upon measurement they conveniently disappear. We can,
however, see evidence of them in interference patterns. Superpositions reflect quantum theory's non-Boolean logic.

Supersymmetry
The theory that bosons and fermions are just two ways of looking at a single, unified object. That ought to mean that every known boson is a known fermion in disguise, and vice versa, cutting the number of elementary particles in half. It doesn't. Instead, every known boson is paired with an unknown fermion and vice versa, doubling the number of elementary particles, half of which have yet to be discovered. On the other hand, supersymmetry elegantly cuts the number of families of particles down to just one and, if you make it a local symmetry, unifies gravity with the other known forces. Sometimes Occam's razor cuts both ways.

Symmetry
Sameness. The symmetries of a system ensure that certain features remain invariant under transformation.

T-duality
A string theory duality that equates a space of radius R with a space of radius 1/R, big with small. It results from the strange way in which strings experience geometry.

Top-down cosmology
Stephen Hawking and Thomas Hertog's conception of cosmology in which measurements an observer makes today select the history of the universe from a superposition of quantum possibilities. It's Wheeler's delayed choice on the grandest scale: observers in the present create a 13.7-billion-year cosmic history.

Uncertainty principle
The more accurately you measure one member of a conjugate pair, such as momentum or energy, the less accurately you can measure another, such as position or time. The uncertainty principle reflects the noncommutativity of quantum operators: the order in which you measure things matters. This suggests that quantum features are radically observer-dependent.

Underdetermination
When a physical situation has multiple, equally valid theoretical explanations and we have no way of deciding the true reality that lies beneath. Structural realism resolves underdetermination because the theoretical alternatives usually share the same mathematical structure, leaving only one true reality, and a knowable one at that.

Universe
“We must be prepared to question the very term ‘universe.' ”—John Archibald Wheeler

Unruh radiation
A hot bath of observer-dependent particles, also known as Rindler particles, that exist relative to an accelerated observer as a result of a Rindler horizon.

Virtual particle
A particle—which comes complete with an antiparticle pair—that arises from the vacuum. Time and energy are related by quantum uncertainty, so the more precise the time, the less precise the energy. In a very short span of time, a large amount of energy can fluctuate out of the vacuum, which, by E = mc
²
, is also mass. The mass takes the form of a particle, but because it is living on borrowed energy, it quickly annihilates with its antiparticle and disappears—unless the two are separated by an event horizon, at which point the virtual particle becomes a real particle and is known as Hawking radiation.

Wave-particle duality
The notion that every particle is also a wave at the same time. When you measure it, it's always a particle. The wave aspect is seen in quantum interference, which results from phase differences. Only waves have a phase, so the particle must be a wave. Then again, phase is not inherent to the particle—it defines the reference frame from which you're viewing the particle.

Wavefunction
A probability distribution for the outcomes of quantum experiments, it encodes everything it is possible to know about a quantum state.

Wigner's friend
Eugene Wigner's thought experiment in which his friend measures the state of an atom in a lab, collapsing its quantum wavefunction from a host of probabilities to a single reality. Wigner, however, is standing outside the lab, so from his perspective the atom's wavefunction hasn't collapsed, but has instead become entangled in a superposition with the wavefunction describing Wigner's friend. Who is right? Did the wavefunction collapse or not?

WMAP
NASA's Wilkinson Microwave Anisotropy Probe, a space-based telescope that mapped temperature variations across the cosmic microwave background radiation.

World line
An observer's trajectory through spacetime.