Predictions of quantum mechanics have been verified experimentally to an
extremely high degree of accuracy.
between classical and quantum mechanics, all objects obey the laws of quantum
mechanics, and classical mechanics is just an approximation for large systems of
objects (or a statistical quantum mechanics of a large collection of particles).
statistical average at the limit of large systems or large quantum numbers.
However, chaotic systems do not have good quantum numbers, and quantum chaos
Quantum coherence is an essential difference between classical and quantum
theories as illustrated by the Einstein–Podolsky–Rosen (EPR) paradox — an attack
on a certain philosophical interpretation of quantum mechanics by an appeal to local
whereas classical "waves" infer that there is an adding together of intensities. For
microscopic bodies, the extension of the system is much smaller than the coherence
length, which gives rise to long-range entanglement and other nonlocal phenomena
characteristic of quantum systems.
macroscopic scales, though an exception to this rule may occur at extremely low
temperatures (i.e. approaching absolute zero) at which quantum behavior may
manifest itself macroscopically.
- Many macroscopic properties of a classical system are a direct consequence
of the quantum behavior of its parts. For example, the stability of bulk matter
(consisting of atoms and molecules which would quickly collapse under electric
forces alone), the rigidity of solids, and the mechanical, thermal, chemical, optical
and magnetic properties of matter are all results of the interaction of electric charges
under the rules of quantum mechanics.
- While the seemingly "exotic" behavior of matter posited by quantum
mechanics and relativity theory become more apparent when dealing with particles of
extremely small size or velocities approaching the speed of light, the laws of
classical, often considered "Newtonian", physics remain accurate in predicting the
behavior of the vast majority of "large" objects (on the order of the size of large
molecules or bigger) at velocities much smaller than the velocity of light.
Copenhagen interpretation of quantum versus classical kinematics
very different kinematic descriptions.
In Niels Bohr's mature view, quantum mechanical phenomena are required to
be experiments, with complete descriptions of all the devices for the system,
preparative, intermediary, and finally measuring. The descriptions are in macroscopic
terms, expressed in ordinary language, supplemented with the concepts of classical
mechanics. The initial condition and the final condition of the system are respectively
described by values in a configuration space, for example a position space, or some
equivalent space such as a momentum space. Quantum mechanics does not admit a
completely precise description, in terms of both position and momentum, of an initial
condition or "state" (in the classical sense of the word) that would support a precisely
deterministic and causal prediction of a final condition.
In this sense, advocated
by Bohr in his mature writings, a quantum phenomenon is a process, a passage from
initial to final condition, not an instantaneous "state" in the classical sense of that
word. Thus there are two kinds of processes in quantum mechanics: stationary and
transitional. For a stationary process, the initial and final condition are the same. For
a transition, they are different. Obviously by definition, if only the initial condition is
given, the process is not determined. Given its initial condition, prediction of its final
condition is possible, causally but only probabilistically, because the Schrödinger
equation is deterministic for wave function evolution, but the wave function describes
the system only probabilistically.
For many experiments, it is possible to think of the initial and final conditions
of the system as being a particle. In some cases it appears that there are potentially
several spatially distinct pathways or trajectories by which a particle might pass from
initial to final condition. It is an important feature of the quantum kinematic
description that it does not permit a unique definite statement of which of those
pathways is actually followed. Only the initial and final conditions are definite, and,
as stated in the foregoing paragraph, they are defined only as precisely as allowed by
the configuration space description or its equivalent. In every case for which a
quantum kinematic description is needed, there is always a compelling reason for this
restriction of kinematic precision. An example of such a reason is that for a particle to
be experimentally found in a definite position, it must be held motionless; for it to be
experimentally found to have a definite momentum, it must have free motion; these
two are logically incompatible.
Classical kinematics does not primarily demand experimental description of its
phenomena. It allows completely precise description of an instantaneous state by a
value in phase space, the Cartesian product of configuration and momentum spaces.
This description simply assumes or imagines a state as a physically existing entity
without concern about its experimental measurability. Such a description of an initial
condition, together with Newton's laws of motion, allows a precise deterministic and
causal prediction of a final condition, with a definite trajectory of passage.
Hamiltonian dynamics can be used for this. Classical kinematics also allows the
description of a process analogous to the initial and final condition description used
by quantum mechanics. Lagrangian mechanics applies to this. For processes that need
account to be taken of actions of a small number of Planck constants, classical
kinematics is not adequate; quantum mechanics is needed.
Even with the defining postulates of both Einstein's theory of general relativity
and quantum theory being indisputably supported by rigorous and repeated empirical
evidence, and while they do not directly contradict each other theoretically (at least
with regard to their primary claims), they have proven extremely difficult to
incorporate into one consistent, cohesive model.
Gravity is negligible in many areas of particle physics, so that unification
between general relativity and quantum mechanics is not an urgent issue in those
particular applications. However, the lack of a correct theory of quantum gravity is an
important issue in cosmology and the search by physicists for an elegant "Theory of
Everything" (TOE). Consequently, resolving the inconsistencies between both
theories has been a major goal of 20th and 21st century physics. Many prominent
physicists, including Stephen Hawking, have labored for many years in the attempt to
discover a theory underlying everything. This TOE would combine not only the
different models of subatomic physics, but also derive the four fundamental forces of
nature - the strong force, electromagnetism, the weak force, and gravity - from a
single force or phenomenon. While Stephen Hawking was initially a believer in the
Theory of Everything, after considering Gödel's Incompleteness Theorem, he has
concluded that one is not obtainable, and has stated so publicly in his lecture "Gödel
and the End of Physics" (2002).
The quest to unify the fundamental forces through quantum mechanics is still
ongoing. Quantum electrodynamics (or "quantum electromagnetism"), which is
currently (in the perturbative regime at least) the most accurately tested physical
theory in competition with general relativity,
the weak nuclear force into the electroweak force and work is currently being done to
merge the electroweak and strong force into the electrostrong force. Current
predictions state that at around 10
GeV the three aforementioned forces are fused
may be possible to merge gravity with the other three gauge symmetries, expected to
occur at roughly 10
GeV. However — and while special relativity is parsimoniously
currently the best theory describing the gravitation force, has not been fully
incorporated into quantum theory. One of those searching for a coherent TOE is
Edward Witten, a theoretical physicist who formulated the M-theory, which is an
attempt at describing the supersymmetrical based string theory. M-theory posits that
our apparent 4-dimensional spacetime is, in reality, actually an 11-dimensional
spacetime containing 10 spatial dimensions and 1 time dimension, although 7 of the
spatial dimensions are - at lower energies - completely "compactified" (or infinitely
curved) and not readily amenable to measurement or probing.
Another popular theory is Loop quantum gravity (LQG), a theory first
proposed by Carlo Rovelli that describes the quantum properties of gravity. It is also
a theory of quantum space and quantum time, because in general relativity the
geometry of spacetime is a manifestation of gravity. LQG is an attempt to merge and
adapt standard quantum mechanics and standard general relativity. The main output
of the theory is a physical picture of space where space is granular. The granularity is
a direct consequence of the quantization. It has the same nature of the granularity of
the photons in the quantum theory of electromagnetism or the discrete levels of the
energy of the atoms. But here it is space itself which is discrete. More precisely,
space can be viewed as an extremely fine fabric or network "woven" of finite loops.
These networks of loops are called spin networks. The evolution of a spin network
over time is called a spin foam. The predicted size of this structure is the Planck
length, which is approximately 1.616×10
m. According to theory, there is no
predicts that not just matter, but also space itself, has an atomic structure.
In 1932 Chadwick realized that radiation that had been observed by Walther
Bothe, Herbert Becker, Irène and Frédéric Joliot-Curie was actually due to a neutral
particle of about the same mass as the proton, that he called the neutron (following a
suggestion from Rutherford about the need for such a particle).
Dmitri Ivanenkosuggested that there were no electrons in the nucleus — only protons
and neutrons — and that neutrons were spin
particles which explained the mass not
due to protons. The neutron spin immediately solved the problem of the spin of
nitrogen-14, as the one unpaired proton and one unpaired neutron in this model each
contributed a spin of
in the same direction, giving a final total spin of 1.
With the discovery of the neutron, scientists could at last calculate what
fraction of binding energy each nucleus had, by comparing the nuclear mass with that
of the protons and neutrons which composed it. Differences between nuclear masses
were calculated in this way. When nuclear reactions were measured, these were
found to agree with Einstein's calculation of the equivalence of mass and energy to
within 1% as of 1934.
A heavy nucleus can contain hundreds of nucleons. This means that with some
approximation it can be treated as a classical system, rather than a quantum-
mechanical one. In the resulting liquid-drop model, the nucleus has an energy which
arises partly from surface tension and partly from electrical repulsion of the protons.
The liquid-drop model is able to reproduce many features of nuclei, including the
general trend of binding energy with respect to mass number, as well as the
phenomenon of nuclear fission.
Superimposed on this classical picture, however, are quantum-mechanical
effects, which can be described using the nuclear shell model, developed in large part
by Maria Goeppert Mayer and J. Hans D. Jensen. Nuclei with certain numbers of
neutrons and protons (the magic numbers 2, 8, 20, 28, 50, 82, 126, ...) are particularly
stable, because their shells are filled.
Other more complicated models for the nucleus have also been proposed, such
as the interacting boson model, in which pairs of neutrons and protons interact as
bosons, analogously to Cooper pairs of electrons.
Much of current research in nuclear physics relates to the study of nuclei under
extreme conditions such as high spin and excitation energy. Nuclei may also have
extreme shapes (similar to that of Rugby balls or even pears) or extreme neutron-to-
proton ratios. Experimenters can create such nuclei using artificially induced fusion
or nucleon transfer reactions, employing ion beams from an accelerator. Beams with
even higher energies can be used to create nuclei at very high temperatures, and there
are signs that these experiments have produced a phase transition from normal
nuclear matter to a new state, the quark–gluon plasma, in which the quarks mingle
with one another, rather than being segregated in triplets as they are in neutrons and
Physical cosmology is the branch of physics and astrophysics that deals with
the study of the physical origins and evolution of the Universe. It also includes the
study of the nature of the Universe on a large scale. In its earliest form, it was what is
now known as "celestial mechanics", the study of the heavens. Greek philosophers
Aristarchus of Samos,Aristotle, and Ptolemy proposed different cosmological
theories. The geocentric Ptolemaic system was the prevailing theory until the 16th
century when Nicolas Copernicus, and subsequently Johannes Kepler and Galileo
Galilee, proposed a heliocentric system. This is one of the most famous examples of
epistemological rupture in physical cosmology.
When Isaac Newton published the Principia Mathematical in 1687, he finally
figured out how the heavens moved. Newton provided a physical mechanism for
Kepler's laws and his law of universal gravitation allowed the anomalies in previous
systems, caused by gravitational interaction between the planets, to be resolved. A
fundamental difference between Newton's cosmology and those preceding it was the
Copernican principle—that the bodies on earth obey the same physical laws as all the
celestial bodies. This was a crucial philosophical advance in physical cosmology.
Evidence of gravitational waves in the infant universe may have been
Modern scientific cosmology is usually considered to have begun in 1917 with
Albert Einstein's publication of his final modification of general relativity in the
paper "Cosmological Considerations of the General Theory of Relativity" (although
this paper was not widely available outside of Germany until the end of World War
I). General relativity prompted cosmogonists such as Willem de Sitter, Karl
Schwarzschild, and Arthur Eddington to explore its astronomical ramifications,
which enhanced the ability of astronomers to study very distant objects. Physicists
began changing the assumption that the Universe was static and unchanging. In 1922
Alexander Friedmann introduced the idea of an expanding universe that contained
In parallel to this dynamic approach to cosmology, one long-standing debate
about the structure of the cosmos was coming to a climax. Mount Wilson astronomer
Harlow Shapley championed the model of a cosmos made up of the Milky Way star
system only; while Heber D. Curtis argued for the idea that spiral nebulae were star
systems in their own right as island universes. This difference of ideas came to a
climax with the organization of the Great Debate on 26 April 1920 at the meeting of
the U.S. National Academy of Sciences in Washington, D.C. The debate was
resolved when Edwin Hubble detected novae in the Andromeda galaxy in 1923 and
1924. Their distance established spiral nebulae well beyond the edge of the Milky
cosmological constant, introduced by Einstein in his 1917 paper, may result in an
expanding universe, depending on its value. Thus the Big Bang model was proposed
by the Belgian priest Georges Lemaître in 1927 which was subsequently corroborated
by Edwin Hubble's discovery of the red shift in 1929 and later by the discovery of the
cosmic microwave background radiation by Arno Penzias and Robert Woodrow
Wilson in 1964. These findings were a first step to rule out some of many alternative
Since around 1990, several dramatic advances in observational cosmology
have transformed cosmology from a largely speculative science into a predictive
science with precise agreement between theory and observation. These advances
include observations of the microwave background from the COBE, WMAP and
Planck satellites, large new galaxyredshift surveys including 2dfGRS and SDSS, and
observations of distant supernovae and gravitational lending. These observations
matched the predictions of the cosmic inflation theory, a modified Big Bang theory,
and the specific version known as the Lambda-CDM model. This has led many to
refer to modern times as the "golden age of cosmology".
On 17 March 2014, astronomers at the Harvard-Smithsonian Center for
Astrophysics announced the detection of gravitational waves, providing strong
evidence for inflation and the Big Bang.
However, on 19 June 2014, lowered
confidence in confirming the cosmic inflation findings was reported.
On 1 December 2014, at the Planck 2014 meeting in Ferrara, Italy,
4.9% atomic matter, 26.6% dark matter and 68.5% dark energy.
Religious or mythological cosmology is a body of beliefs based on
mythological, religious, and esoteric literature and traditions of creation and
Cosmology deals with the world as the totality of space, time and all
phenomena. Historically, it has had quite a broad scope, and in many cases was
founded in religion. The ancient Greeks did not draw a distinction between this use
and their model for the cosmos. However, in modern use metaphysical cosmology
addresses questions about the Universe which are beyond the scope of science. It is
distinguished from religious cosmology in that it approaches these questions using
philosophical methods like dialectics. Modern metaphysical cosmology tries to
address questions such as:
Observational astronomy is a division of the astronomical science that is
mainly concerned with finding out the measurable implications of physical models. It
is the practice of observing celestial objects by using telescopes and other
The majority of astrophysical observations are made using the electromagnetic
- Radio astronomy studies radiation with a wavelength greater than a few
millimeters. Example areas of study are radio waves, usually emitted by cold objects
such as interstellar gas and dust clouds; the cosmic microwave background radiation
which is the redshirted light from the Big Bang; pulsars, which were first detected at
microwave frequencies. The study of these waves requires very large radio
- Infrared astronomy studies radiation with a wavelength that is too long to be
visible to the naked eye but is shorter than radio waves. Infrared observations are
usually made with telescopes similar to the familiar optical telescopes. Objects colder
than stars (such as planets) are normally studied at infrared frequencies.
- Optical astronomy is the oldest kind of astronomy. Telescopes paired with a
charge-coupled device or spectroscopes are the most common instruments used. The
Earth's atmosphere interferes somewhat with optical observations, so adaptive optics
and space telescopes are used to obtain the highest possible image quality. In this
wavelength range, stars are highly visible, and many chemical spectra can be
observed to study the chemical composition of stars, galaxies and nebulae.
- Ultraviolet, X-ray and gamma ray astronomy study very energetic processes
such as binary pulsars, black holes, magentas, and many others. These kinds of
radiation do not penetrate the Earth's atmosphere well. There are two methods in use
to observe this part of the electromagnetic spectrum—space-based telescopes and
ground-based imaging air Cherenkov telescopes (IACT). Examples of Observatories
of the first type are RXTE, the Chandra X-ray Observatory and the Compton Gamma
Ray Observatory. Examples of IACTs are the High Energy Stereoscopic System
(H.E.S.S.) and the MAGIC telescope.
Other than electromagnetic radiation, few things may be observed from the
Earth that originate from great distances. A few gravitational wave observatories
have been constructed, but gravitational waves are extremely difficult to detect.
Neutrino observatories have also been built, primarily to study our Sun. Cosmic rays
consisting of very high energy particles can be observed hitting the Earth's
Observations can also vary in their time scale. Most optical observations take
minutes to hours, so phenomena that change faster than this cannot readily be
observed. However, historical data on some objects is available, spanning centuries
or millennia. On the other hand, radio observations may look at events on a
millisecond timescale (millisecond pulsars) or combine years of data (pulsar
deceleration studies). The information obtained from these different timescales is
The study of our very own Sun has a special place in observational
astrophysics. Due to the tremendous distance of all other stars, the Sun can be
observed in a kind of detail unparalleled by any other star. Our understanding of our
own Sun serves as a guide to our understanding of other stars.
The topic of how stars change, or stellar evolution, is often modeled by placing
the varieties of star types in their respective positions on the Hertz sprung–Russell
diagram, which can be viewed as representing the state of a stellar object, from birth