Fundamental physics concepts

A clockwise motion is one that proceeds 'like the clock's hands': from the top to the right, then down and then to the left, and back to the top. In a mathematical sense, a circle defined parametrically by the equations x = r sin t and y = r cos t, where r is the radius of the circle, is traced clockwise as t increases in value. The opposite sense of rota ...

Read more here: » Clockwise and counterclockwise: Encyclopedia - Clockwise and counterclockwise

In physics, spacetime is a model that combines space and time into a single construct called the space-time continuum. In our universe, this continuum has three dimensions of space and one dimension of time. Treating space and time on the same footing and as two aspects of a unified whole was devised by Hermann Minkowski shortly after the theory of special relativity was developed by Albert Einstein. This unification is further exemplified by the common practice of expressing time in the same units as space by multiplyin ...

Including:

• Spacetime - Basic concepts
• Spacetime - Spacetime intervals
• Spacetime - Mathematics of space-times
• Spacetime - Space-time topology
• Spacetime - Space-time continua and symmetry
• Spacetime - Spacetime in special relativity
• Spacetime - Spacetime in general relativity
• Spacetime - Is space-time quantized?
• Spacetime - Other uses of the word 'spacetime'
• Spacetime - History of the concept of space-time

Read more here: » Spacetime: Encyclopedia - Spacetime

An Isolated system, is a physical system that does not interact with its surroundings. It obeys a number of conservation laws: its total energy and mass stay constant. They cannot enter or exit, but can only move around inside. An example is in the study of spacetime, where it is assumed that asymptotically flat spacetimes exist. Truly isolated physical systems do not exist in reality, but real systems may behave nearly this way for finite (possibly very long) times. The concept of an isolated system can serve as a useful model ...

Including:

• Closed system - Closed system

Read more here: » Closed system: Encyclopedia - Closed system

In physics, a physical body is an object which can be described by the theories of classical mechanics, or quantum mechanics, and experimented upon by physical instruments. This includes the determination of position, and in some cases the orientation in space, as well as means to change these, by exerting forces. For instance, the force of gravity will accelerate a body if it is not supported, thus causing ...

Read more here: » Physical body: Encyclopedia - Physical body

Density in terms of the SI base units is expressed in terms of kilograms per cubic metre (kg/m³). Other units fully within the SI include grams per cubic centimetre (g/cm³) and megagrams per cubic metre (Mg/m³). Since both the litre and the tonne or metric ton are also acceptable for use with the SI, a wide variety of units such as kilograms per litre (kg/L) are also used. Imperial units or U.S. customary units, the units of density include pounds per cubic foot (lb/ft³), pounds per cubic yard (lb/yd³), pounds per cubic inch (lb/ ...

See also:

Density, Density - Other units, Density - Measurement of density, Density - Density of substances

Read more here: » Density: Encyclopedia II - Density - Other units

The Schrödinger equation for a free particle is: The solution for a particular momentum is given by a plane wave: with the constraint where r is the position vector, t is time k is the wave vector and ω is the angular frequency. Since the integral of ψψ* over all space must be unity, there will be a problem normalizing this momentum eigenfunction. This will not be a problem for a general free particle which is somewhat localized in ...

See also:

Free particle, Free particle - Classical Free Particle, Free particle - Non-Relativistic Quantum Free Particle, Free particle - Relativistic free particle

Read more here: » Free particle: Encyclopedia II - Free particle - Non-Relativistic Quantum Free Particle

A tensor may be expressed as the sequence of values represented by a function with a vector valued domain and a scalar valued range. These vectors in the domain are vectors of counting numbers, and these numbers are called indexes. For example, a rank 3 tensor might have dimensions 2, 5, and 7. Here, the vectors range from <1, 1, 1> through <2, 5, 7>. Here, the tensor would have one value at <1, 1, 1>, another at <1, 1, 2>, and so on for a total of 70 values. (Likewise, vectors may be expressed as a sequence of values ...

See also:

Tensor, Tensor - Brief overview, Tensor - Importance and usage, Tensor - History, Tensor - The choice of approach, Tensor - Examples, Tensor - Approaches in detail, Tensor - Tensor densities, Tensor - Notation, Tensor - Foundational, Tensor - Applications, Tensor - Reference books, Tensor - Tensor software

Read more here: » Tensor: Encyclopedia II - Tensor - Examples

In 3D, there are 6 degrees of freedom associated to the movement of a mechanical particle, 3 for its position, and 3 for its momentum. For a roughly dumbbell-shaped hydrogen molecule, described by two mechanical particles linked by a spring, 6 such independent directions (or modes) of movement would be translation (hurtling through space, 3 modes), rotation (twirling, 2 modes), and vibration (the two dumbbell "balls" bouncing together and apart, 1 mode). Each mode has associated with it a position variable and a conjugate momentum var ...

See also:

Degrees of freedom physics and chemistry, Degrees of freedom physics and chemistry - Degrees of freedom in mechanics, Degrees of freedom physics and chemistry - A more general definition, Degrees of freedom physics and chemistry - Example: classical ideal diatomic gas, Degrees of freedom physics and chemistry - Independent degrees of freedom, Degrees of freedom physics and chemistry - Definition, Degrees of freedom physics and chemistry - Properties, Degrees of freedom physics and chemistry - Demonstrations, Degrees of freedom physics and chemistry - Quadratic degrees of freedom, Degrees of freedom physics and chemistry - Quadratic degrees of freedom in mechanics, Degrees of freedom physics and chemistry - Quadratic and independent degree of freedom, Degrees of freedom physics and chemistry - Equipartition theorem, Degrees of freedom physics and chemistry - Demonstration

Read more here: » Degrees of freedom physics and chemistry: Encyclopedia II - Degrees of freedom physics and chemistry - Example: classical ideal diatomic gas

For physical reasons, a space-time continuum is mathematically defined as a four-dimensional, smooth, connected pseudo-Riemannian manifold together with a smooth, Lorentz metric of signature . The metric determines the geometry of spacetime, as well as determining the geodesics of particles and light beams. About each point (event) on this manifold, coordinate charts are used to represent observers in ref ...

See also:

Spacetime, Spacetime - Basic concepts, Spacetime - Spacetime intervals, Spacetime - Mathematics of space-times, Spacetime - Space-time topology, Spacetime - Space-time continua and symmetry, Spacetime - Spacetime in special relativity, Spacetime - Spacetime in general relativity, Spacetime - Is space-time quantized?, Spacetime - Other uses of the word 'spacetime', Spacetime - History of the concept of space-time

Read more here: » Spacetime: Encyclopedia II - Spacetime - Mathematics of space-times

For physical reasons, a space-time continuum is mathematically defined as a four-dimensional, smooth, connected pseudo-Riemannian manifold together with a smooth, Lorentz metric of signature . The metric determines the geometry of spacetime, as well as determining the geodesics of particles and light beams. About each point (event) on this manifold, coordinate charts are used to represent observers in ref ...

See also:

Spacetime, Spacetime - Basic concepts, Spacetime - Spacetime intervals, Spacetime - Mathematics of space-times, Spacetime - Space-time topology, Spacetime - Space-time continua and symmetry, Spacetime - Spacetime in special relativity, Spacetime - Spacetime in general relativity, Spacetime - Is space-time quantized?, Spacetime - Other uses of the word 'spacetime', Spacetime - History of the concept of spacetime, Spacetime - Philosophical Interpretation of Spacetime

Read more here: » Spacetime: Encyclopedia II - Spacetime - Mathematics of space-times

Spacetime has taken on meanings different from the 4-dimensional one given above. For example, when drawing a graph of the distance a car has travelled for a certain time, it is natural to draw a 2-dimensional spacetime diagram. As drawing 4-dimensional spacetime diagrams is impossible, physicists often resort to drawing 3-dimensional spacetime diagrams (for example, the Earth orbiting the Sun i ...

See also:

Spacetime, Spacetime - Basic concepts, Spacetime - Spacetime intervals, Spacetime - Mathematics of space-times, Spacetime - Space-time topology, Spacetime - Space-time continua and symmetry, Spacetime - Spacetime in special relativity, Spacetime - Spacetime in general relativity, Spacetime - Is space-time quantized?, Spacetime - Other uses of the word 'spacetime', Spacetime - History of the concept of spacetime, Spacetime - Philosophical Interpretation of Spacetime

Read more here: » Spacetime: Encyclopedia II - Spacetime - Other uses of the word 'spacetime'

The entire concept was presented by Albert Einstein in 1926 in his article on space-time in the 13th edition of the Encyclopedia Britannica. ...

See also:

Spacetime, Spacetime - Basic concepts, Spacetime - Spacetime intervals, Spacetime - Mathematics of space-times, Spacetime - Space-time topology, Spacetime - Space-time continua and symmetry, Spacetime - Spacetime in special relativity, Spacetime - Spacetime in general relativity, Spacetime - Is space-time quantized?, Spacetime - Other uses of the word 'spacetime', Spacetime - History of the concept of spacetime, Spacetime - Philosophical Interpretation of Spacetime

Read more here: » Spacetime: Encyclopedia II - Spacetime - History of the concept of spacetime

The word "tensor" was first introduced by William Rowan Hamilton in 1846, but he used the word for what is now called modulus. The word was used in its current meaning by Woldemar Voigt in 1899. The notation was developed around 1890 by Gregorio Ricci-Curbastro under the title absolute differential geometry, and was made accessible to many mathematicians by the publication of Tullio Levi-Civita's classic text The Absolute Differential Calculus in 1900 (in Italian; translations followed). The tensor calculus achieved broa ...

See also:

Tensor, Tensor - Brief overview, Tensor - Importance and usage, Tensor - History, Tensor - The choice of approach, Tensor - Examples, Tensor - Approaches in detail, Tensor - Tensor densities, Tensor - Notation, Tensor - Foundational, Tensor - Applications, Tensor - Reference books, Tensor - Tensor software

Read more here: » Tensor: Encyclopedia II - Tensor - History

In general relativity, it is assumed that spacetime is curved by the presence of matter (energy), this curvature being represented by the Riemann tensor. In special relativity, the Riemann tensor is identically zero, and so this concept of 'non-curvedness' is sometimes expressed by the statement: 'Minkowski space is flat'. Many space-time continua have physical interpretations which most physicists would consider bizarre or unsettling. For example, a compact spacetime has closed timelike curves, which violate our usual ideas of causal ...

See also:

Spacetime, Spacetime - Basic concepts, Spacetime - Spacetime intervals, Spacetime - Mathematics of space-times, Spacetime - Space-time topology, Spacetime - Space-time continua and symmetry, Spacetime - Spacetime in special relativity, Spacetime - Spacetime in general relativity, Spacetime - Is space-time quantized?, Spacetime - Other uses of the word 'spacetime', Spacetime - History of the concept of spacetime, Spacetime - Philosophical Interpretation of Spacetime

Read more here: » Spacetime: Encyclopedia II - Spacetime - Spacetime in general relativity

The geometry of spacetime in special relativity is described by the Minkowski metric on R4. This spacetime is called Minkowski space. The Minkowski metric is usually denoted by η and can be written as a 4 by 4 matrix: where the Landau-Lifshitz spacelike convention is being used. A basic assumption of relativity is that coordinate transformations must leave spacetime intervals invariant. Intervals are invariant under Lorentz transformations. This invariance property leads to the u ...

See also:

Spacetime, Spacetime - Basic concepts, Spacetime - Spacetime intervals, Spacetime - Mathematics of space-times, Spacetime - Space-time topology, Spacetime - Space-time continua and symmetry, Spacetime - Spacetime in special relativity, Spacetime - Spacetime in general relativity, Spacetime - Is space-time quantized?, Spacetime - Other uses of the word 'spacetime', Spacetime - History of the concept of spacetime, Spacetime - Philosophical Interpretation of Spacetime

Read more here: » Spacetime: Encyclopedia II - Spacetime - Spacetime in special relativity

Tensors are of importance in physics and engineering. In the field of diffusion tensor imaging, for instance, a tensor quantity that expresses the differential permeability of organs to water in varying directions is used to produce scans of the brain. Perhaps the most important engineering examples are the stress tensor and strain tensor, which are both 2nd rank tensors, and are related in a general line ...

See also:

Tensor, Tensor - Brief overview, Tensor - Importance and usage, Tensor - History, Tensor - The choice of approach, Tensor - Examples, Tensor - Approaches in detail, Tensor - Tensor densities, Tensor - Notation, Tensor - Foundational, Tensor - Applications, Tensor - Reference books, Tensor - Tensor software

Read more here: » Tensor: Encyclopedia II - Tensor - Importance and usage

The entire concept was presented by Albert Einstein in 1926 in his article on space-time in the 13th edition of the Encyclopedia Britannica.[1] And there is another argument in philosophy which says "there is nothing called space and time." In order to substantiate it philosophically, let us try thinking in this way: Imagine a situation where there is no change in anything. No leaf moves, no wind blows, nothing is moving or changing. Since time is used to measure change and events, and if the ...

See also:

Spacetime, Spacetime - Basic concepts, Spacetime - Spacetime intervals, Spacetime - Mathematics of space-times, Spacetime - Space-time topology, Spacetime - Space-time continua and symmetry, Spacetime - Spacetime in special relativity, Spacetime - Spacetime in general relativity, Spacetime - Is space-time quantized?, Spacetime - Other uses of the word 'spacetime', Spacetime - History of the concept of space-time

Read more here: » Spacetime: Encyclopedia II - Spacetime - History of the concept of space-time

There are equivalent approaches to visualizing and working with tensors; that the content is actually the same may only become apparent with some familiarity with the material. The classical approach The classical approach views tensors as multidimensional arrays that are n-dimensional generalizations of scalars, 1-dimensional vectors and 2-dimensional matrices. The "components" of the tensor are the values in the array. This idea can then be further generalized to tensor fields, w ...

See also:

Tensor, Tensor - Brief overview, Tensor - Importance and usage, Tensor - History, Tensor - The choice of approach, Tensor - Examples, Tensor - Approaches in detail, Tensor - Tensor densities, Tensor - Notation, Tensor - Foundational, Tensor - Applications, Tensor - Reference books, Tensor - Tensor software

Read more here: » Tensor: Encyclopedia II - Tensor - Approaches in detail

The basic elements of spacetime are events, these being represented by points in the spacetime. Examples of events include the explosion of a star, or the single beat of a drum. A spacetime is independent of any observer. However, in describing physical phenomena (which occur at certain moments of time in a given region of space), each observer chooses a convenient coordinate system. Events are specified by ...

See also:

Spacetime, Spacetime - Basic concepts, Spacetime - Spacetime intervals, Spacetime - Mathematics of space-times, Spacetime - Space-time topology, Spacetime - Space-time continua and symmetry, Spacetime - Spacetime in special relativity, Spacetime - Spacetime in general relativity, Spacetime - Is space-time quantized?, Spacetime - Other uses of the word 'spacetime', Spacetime - History of the concept of spacetime, Spacetime - Philosophical Interpretation of Spacetime

Read more here: » Spacetime: Encyclopedia II - Spacetime - Basic concepts

There are two ways of approaching the definition of tensors: The usual physics way of defining tensors, in terms of objects whose components transform according to certain rules, introducing the ideas of covariant or contravariant transformations. The usual mathematics way, which involves defining certain vector spaces and not fixing any coordinate systems until bases are introduced when needed. Covariant vectors, for instance, can also be described as one-forms, or as the elements of th ...

See also:

Tensor, Tensor - Brief overview, Tensor - Importance and usage, Tensor - History, Tensor - The choice of approach, Tensor - Examples, Tensor - Approaches in detail, Tensor - Tensor densities, Tensor - Notation, Tensor - Foundational, Tensor - Applications, Tensor - Reference books, Tensor - Tensor software

Read more here: » Tensor: Encyclopedia II - Tensor - The choice of approach