Absolute time and space

Absolute time and space

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Originally introduced by Sir Isaac Newton in the Philosophiæ Naturalis Principia Mathematica, the concepts of absolute time and space provided a theoretical foundation that facilitated Newtonian mechanics. According to Newton, absolute time and space respectively are independent aspects of objective reality.

Absolute, true and mathematical time, of itself, and from its own nature flows equably without regard to anything external, and by another name is called duration: relative, apparent and common time, is some sensible and external (whether accurate or unequable) measure of duration by the means of motion, which is commonly used instead of true time ...

According to Newton, Absolute time exists independently of any perceiver and progresses at a consistent pace throughout the universe. unlike relative time, Newton believed Absolute time was imperceptible and could only be understood mathematically. According to Newton, humans are only capable of perceiving relative time, which is a measurement of perceivable objects in motion (like the moon or sun). From these movements, we infer the passage of time.

To quote Newton again:

Absolute space, in its own nature, without regard to anything external, remains always similar and immovable. Relative space is some movable dimension or measure of the absolute spaces; which our senses determine by its position to bodies: and which is vulgarly taken for immovable space ...

Absolute motion is the translation of a body from one absolute place into another: and relative motion, the translation from one relative place into another

These notions imply that absolute space and time do not depend upon physical events, but are a backdrop or stage setting within which physical phenomena occur. Thus, every object has an absolute state of motion relative to absolute space, so that an object must be either in a state of absolute rest, or moving at some absolute speed. To support his views, Newton provided some empirical examples: according to Newton, a solitary rotating sphere can be inferred to rotate about its axis relative to absolute space by observing the bulging of its equator, and a solitary pair of spheres tied by a rope can be inferred to be in absolute rotation about their center of gravity (barycenter
Barycentric coordinates (astronomy)
In astronomy, barycentric coordinates are non-rotating coordinates with origin at the center of mass of two or more bodies.The barycenter is the point between two objects where they balance each other. For example, it is the center of mass where two or more celestial bodies orbit each other...

) by observing the tension in the rope.

Absolute time and space continue to be used in classical mechanics
Classical mechanics
In physics, classical mechanics is one of the two major sub-fields of mechanics, which is concerned with the set of physical laws describing the motion of bodies under the action of a system of forces...

, but modern formulations by authors such as Walter Noll
Walter Noll
Walter Noll is a mathematician, and Professor Emeritus at Carnegie Mellon University. He is best known for developing mathematical tools of classical mechanics and thermodynamics....

and Clifford Truesdell
Clifford Truesdell
Clifford Ambrose Truesdell III was an American mathematician, natural philosopher, historian of science, and polemicist.-Life:...

go beyond the linear algebra
Linear algebra
Linear algebra is a branch of mathematics that studies vector spaces, also called linear spaces, along with linear functions that input one vector and output another. Such functions are called linear maps and can be represented by matrices if a basis is given. Thus matrix theory is often...

of elastic moduli to use 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...

and functional analysis
Functional analysis
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure and the linear operators acting upon these spaces and respecting these structures in a suitable sense...

for non-linear field theories.

Historical controversy

The idea of absolute space has proved particularly controversial from Newton's time to the present. For example, Leibniz
Gottfried Leibniz
Gottfried Wilhelm Leibniz was a German philosopher and mathematician. He wrote in different languages, primarily in Latin , French and German ....

was of the opinion that space made no sense except as the relative location of bodies, and time made no sense except as the relative movement of bodies. Bishop Berkeley
George Berkeley
George Berkeley , also known as Bishop Berkeley , was an Irish philosopher whose primary achievement was the advancement of a theory he called "immaterialism"...

suggested that, lacking any point of reference, a sphere in an otherwise empty Universe could not be conceived to rotate, and a pair of spheres could be conceived to rotate relative to one another, but not to rotate about their center of gravity. A more recent form of these objections was made by Mach
Ernst Mach
Ernst Mach was an Austrian physicist and philosopher, noted for his contributions to physics such as the Mach number and the study of shock waves...

. Mach's principle
Mach's principle
In theoretical physics, particularly in discussions of gravitation theories, Mach's principle is the name given by Einstein to an imprecise hypothesis often credited to the physicist and philosopher Ernst Mach....

proposes that mechanics is entirely about relative motion of bodies and, in particular, mass
Mass
Mass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...

is an expression of such relative motion. So, for example, a single particle in a Universe with no other bodies would have zero mass. According to Mach, Newton's examples simply illustrate relative rotation of spheres and the bulk of the Universe.

When, accordingly, we say that a body preserves unchanged its direction and velocity in space, our assertion is nothing more or less than an abbreviated reference to the entire universe.
—Ernst Mach; as quoted by Ciufolini and Wheeler: Gravitation and Inertia, p. 387

These views opposing absolute space and time may be seen from a modern stance as an attempt to introduce operational definition
Operational definition
An operational definition defines something in terms of the specific process or set of validation tests used to determine its presence and quantity. That is, one defines something in terms of the operations that count as measuring it. The term was coined by Percy Williams Bridgman and is a part of...

s for space and time, a perspective made explicit in the special theory of relativity.

Even within the context of Newtonian mechanics, the modern view is that absolute space is unnecessary. Instead, the notion of inertial frame of reference
Inertial frame of reference
In physics, an inertial frame of reference is a frame of reference that describes time homogeneously and space homogeneously, isotropically, and in a time-independent manner.All inertial frames are in a state of constant, rectilinear motion with respect to one another; they are not...

has taken precedence, that is, a preferred set of frames of reference that move uniformly with respect to one another! The laws of physics transform from one inertial frame to another according to Galilean relativity
Galilean invariance
Galilean invariance or Galilean relativity is a principle of relativity which states that the fundamental laws of physics are the same in all inertial frames...

, leading to the following objections to absolute space, as outlined by Milutin Blagojević:

• The existence of absolute space contradicts the internal logic of classical mechanics since, according to Galilean principle of relativity, none of the inertial frames can be singled out.
• Absolute space does not explain inertial forces since they are related to acceleration with respect to any one of the inertial frames.
• Absolute space acts on physical objects by inducing their resistance to acceleration but it cannot be acted upon.

Newton himself recognized the role of inertial frames.

The motions of bodies included in a given space are the same among themselves, whether that space is at rest or moves uniformly forward in a straight line.

As a practical matter, inertial frames often are taken as frames moving uniformly with respect to the fixed stars. See Inertial frame of reference
Inertial frame of reference
In physics, an inertial frame of reference is a frame of reference that describes time homogeneously and space homogeneously, isotropically, and in a time-independent manner.All inertial frames are in a state of constant, rectilinear motion with respect to one another; they are not...

for more discussion on this.

In 1903 Bertrand Russell
Bertrand Russell
Bertrand Arthur William Russell, 3rd Earl Russell, OM, FRS was a British philosopher, logician, mathematician, historian, and social critic. At various points in his life he considered himself a liberal, a socialist, and a pacifist, but he also admitted that he had never been any of these things...

wrote a defense of absolute space and time in Principles of Mathematics, while admitting (page 465) that in the analysis of rational dynamics "non-Newtonian dynamics, like non-Euclidean geometry, must be as interesting to us as the orthodox system."

Impact of special relativity

The concepts of space and time were separate in physical theory prior to the advent of special relativity
Special relativity
Special relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...

theory, which connected the two and showed both to be dependent upon the observer's state of motion. In Einstein's theories, the ideas of absolute time and space were superseded by the notion of spacetime
Spacetime
In physics, spacetime is any mathematical model that combines space and time into a single continuum. Spacetime is usually interpreted with space as being three-dimensional and time playing the role of a fourth dimension that is of a different sort from the spatial dimensions...

in special relativity
Special relativity
Special relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...

, and by dynamically curved spacetime in general relativity
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...

.

The theory of relativity does not allow the existence of absolute time because of nonexistence of absolute simultaneity
Relativity of simultaneity
In physics, the relativity of simultaneity is the concept that simultaneity–whether two events occur at the same time–is not absolute, but depends on the observer's reference frame. According to the special theory of relativity, it is impossible to say in an absolute sense whether two events occur...

. Absolute simultaneity refers to the experimental establishment of coincidence of two or more events in time at different locations in space in a manner agreed upon by all observers in the universe. The theory of relativity
Theory of relativity
The theory of relativity, or simply relativity, encompasses two theories of Albert Einstein: special relativity and general relativity. However, the word relativity is sometimes used in reference to Galilean invariance....

postulates a maximum rate of transmission of information as the speed of light
Speed of light
The speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...

, and one consequence is that simultaneity at separated locations always is relative to the observer.

Einstein's later views

In some of his later paper (especially in 1920 and 1924), Einstein gave a new definition of the aether by identifying it with "properties of space", and this aether can be called absolute, as long its state cannot be influenced by matter. So he argued that Newton's absolute space can be considered as an "absolute aether", and also the four-dimensional spacetime of special relativity
Special relativity
Special relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...

(which replaces the absolute space of Newton) would be some sort of "absolute aether", as its states cannot be influenced by matter as well. However, Einstein also said that in general relativity
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...

the "aether" is not absolute anymore, as the gravitational field and therefore the structure of spacetime depends on the presence of matter. (It also must be said that Einstein's terminology (i.e. aether = properties of space) was not accepted by the scientific community.)

• Absolute rotation
• Free space
• Inertial frame
• Luminiferous aether
Luminiferous aether
In the late 19th century, luminiferous aether or ether, meaning light-bearing aether, was the term used to describe a medium for the propagation of light....

• Mach's principle
Mach's principle
In theoretical physics, particularly in discussions of gravitation theories, Mach's principle is the name given by Einstein to an imprecise hypothesis often credited to the physicist and philosopher Ernst Mach....

• Philosophy of space and time
Philosophy of space and time
Philosophy of space and time is the branch of philosophy concerned with the issues surrounding the ontology, epistemology, and character of space and time. While such ideas have been central to philosophy from its inception, the philosophy of space and time was both an inspiration for and a...