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Topic: Spacetime

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www.spacetime.com   (376 words)

  Spacetime - Wikipedia, the free encyclopedia
Events with a spacetime interval of zero are separated by the propagation of a light signal.
Second, for a manifold, the property of connectedness and path-connectedness are equivalent and one requires the existence of paths (in particular, geodesics) in the spacetime to represent the motion of particles and radiation.
In general relativity, it is assumed that spacetime is curved by the presence of matter (energy), this curvature being represented by the Riemann tensor.
en.wikipedia.org /wiki/Spacetime   (1947 words)

 USATODAY.com - Black hole puts dent in spacetime   (Site not responding. Last check: 2007-10-26)
Spacetime can be thought of as an elastic sheet that bends under the weight of objects placed upon it.
The phenomenon can be roughly compared to the movement of a needle on a record player: As the needle moves along an etched groove on a record, it produces a sound, the exact nature of which is determined by physical deformations in the groove itself.
The lower 300 Hz frequency is caused by the gas wobbling slightly due to the spacetime deformations.
www.usatoday.com /tech/science/space/2006-01-24-spacetime-dent_x.htm   (974 words)

 The Hole Argument
Spacetime substantivalism requires that we ascribe such a surfeit of properties to spacetime that neither observation nor even the laws of the relevant spacetime theory itself can determine which are the correct ones.
It is the proposal that spacetime is better represented not by the manifold of events alone but by some richer structure, such as the manifold of events in conjunction with metrical properties.
So Maudlin (1990) urges that each spacetime event carries its metrical properties essentially, that is, it would not be that very event if (after redistribution of the fields) we tried to assign different metrical properties to it.
plato.stanford.edu /entries/spacetime-holearg   (5340 words)

 Static spacetime - Wikipedia, the free encyclopedia
In general relativity, a spacetime is said to be static if it admits a global, nowhere zero, timelike hypersurface orthogonal Killing vector field.
In a static spacetime, the metric components may be chosen so that they are all independent of the time coordinate.
It is in this sense that a static spacetime derives its name, as the geometry of the spacetime does not change.
en.wikipedia.org /wiki/Static_spacetime   (138 words)

 Better Optical Triangulation through Spacetime Analysis
Figure 5 illustrates the principle of spacetime analysis for a laser triangulation scanner with Gaussian illuminant and orthographic sensor as it translates across the edge of an object.
The streaks in the spacetime image of Figure 8b correspond to speckle noise, for the object has uniform reflectance and should result in a spacetime image with uniform peak amplitudes.
These streaks are tilted precisely along the direction of the spacetime analysis, indicating that the speckle noise adheres to the surface of the object and behaves as a noisy reflectance variation.
graphics.stanford.edu /papers/spacetime/paper_1_level/paper.html   (4837 words)

 Spacetime Mediation of Quantum Interactions   (Site not responding. Last check: 2007-10-26)
In general this locus is a quadratic surface in spacetime, and its surface area is inversely proportional to the mass of the transferred particle.
The difference is that the mediating surfaces of a moving particle are skewed in spacetime relative to those of a stationary particle, corresponding to their respective planes of simultaneity.
According to this view, the "unoccupied points" of spacetime are elements of the 6D space, whereas an event or particle is an element of the 4D space (t,x,y,z).
www.mathpages.com /rr/s9-11/9-11.htm   (1833 words)

 Nasty Little Truth About Spacetime Physics
Spacetime is frozen from the infinite past to the infinite future by definition.
Note: the representation of a position in spacetime is conventionally given by (ict, x, y, z) where i is the square root of -1, an imaginary number (the crackpottery never ends).
Spacetime is an abstract mathematical construct, that is all.
www.rebelscience.org /Crackpots/notorious.htm   (8978 words)

 Spacetime - General Relativity, Quantum Gravity, and the Existence of Time
A brief summary of Spacetime Theories at the beginning of the Third Millennium, and of the possibility that we live in an essentially atemporal universe.
Operationally, this background spacetime can be defined by means of physical reference-system objects, but these objects are considered as dynamically decoupled from the physical system that one studies.
In physics there is a general consensus that spacetime does not allow for such a distinction, that all events in spacetime represent physical reality, that which “is”.
www.ws5.com /spacetime   (7269 words)

 Immovable Spacetime
Although the words "relativity" and "relational" share a common root, their meanings are quite different.  The principle of relativity asserts that for any material particle in any state of motion there exists a system of space and time coordinates in terms of which the particle is instantaneously at rest and inertia is homogeneous and isotropic.
Thus the natural (inertial) decomposition of spacetime intervals into temporal and spatial components can be defined only relative to some particular frame of reference.  Of course, the absolute spacetime intervals themselves are invariant, so the "relativity" refers only to the anaytical decomposition of these intervals.
In this context every point in the entire spacetime manifold is a vertex of actual relations between physical entities, a fact which obscures the distinction between absolute and relational premises.
www.mathpages.com /rr/s4-01/4-01.htm   (1154 words)

 Spacetime and branes   (Site not responding. Last check: 2007-10-26)
Spacetime is the Einsteinium expression of the M-Brane in a dynamic sense (movements in time).
The reason is very simple: growth of the D-group USES surface of the spacetime pillow between the group of holons and the single holon.
One of the predictions of Einstein's general theory of relativity is that local spacetime is twisted by the rotation of the Earth.
www.mu6.com /spacetime.html   (879 words)

 SpaceTime Hypersurfing by Michael Szpir (American Scientist V82)
According to Einstein, spacetime (the union of the three dimensions of space with the dimension of time) is not an inert substrate, but rather a dynamical entity that twists and distorts under the influence of concentrations of energy.
This could be done by creating a disturbance in spacetime such that the region directly in front of a spaceship is contracted while the region directly behind the spaceship is expanded.
The reason is that light also travels in spacetime, and is carried along just as the spaceship is. The light beam is still traveling at the speed of light, relative to the spaceship, which itself is not accelerating relative to the spacetime in its immediate vicinity.
www.islandone.org /Propulsion/Alcubierre.html   (1028 words)

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www.spacetimemobile.com /index.php?page=spacetime   (563 words)

 A Spacetime Map of the Universe
The expansion and cooling of spacetime is the result of the intrinsic motion of light, which is the entropy drive of free energy.
All observers are receding from the central spacetime event of the Big Bang with the same velocity in time - all observers in the Universe necessarily exist in a region of spacetime on its expanding edge which is exactly as old as the Universe itself, and all see the Universe as we do.
When we construct a geometrically correct four-dimensional spacetime map, it at once becomes obvious that our common perception that faraway objects lie at the "edge" of the Universe is completely wrong: we are at the "edge" of spacetime, since the present moment is the furthest in time and space from the Big Bang.
www.people.cornell.edu /pages/jag8/spacetxt.html   (10502 words)

 The Light Cone: The Schwarzschild Black Hole
In practical terms, the Schwarzschild spacetime describes the gravitational field of the Sun, or of the Earth.
This spacetime was studied carefully, and it led to a few physical predictions.
The spacetime of a fl hole is curved in such a way as to cause the future light cones to tip inward.
physics.syr.edu /courses/modules/LIGHTCONE/schwarzschild.html   (604 words)

Spacetime depicts relativistic motion in one space dimension using two separate but related displays: the Spacetime Highway and the more traditional Spacetime Diagram.
The diagram shows a corresponding plot of position versus time that displays the locations of events and the trajectories of objects in spacetime.
Spacetime provides an excellent introduction to the study of special relativity.
webassign.net /pasnew/spacetime/spacetime.html   (308 words)

 Five Thoughts Conerning a Rock Thrown in Four Dimensional Spacetime, by Chris Tannlund   (Site not responding. Last check: 2007-10-26)
Modern consciousness researchers consider the device an early precursor of the sensory-deprivation tank, made famous by the movie Altered States, in which one floats in total darkness on the surface of salt-saturated water, allowing the exploration of inner states of consciousness through the complete elimination of outer sensory distractions.
Perhaps we, as a society, should require each individual to pull at one such thread until he or she achieves at least the beginnings of four-dimensional consciousness.
In four-dimensional spacetime, the rock, the catapult, the witch's cradle, the hammock, the reverb now shaking the radio on the desk beside me, the radio and desk themselves are all threads weaving, together, the very same sweater, all letters in the same word, that multi-dimensional call to experience:
www.uforia-research.com /5thoughts.htm   (1330 words)

 Minkowski Spacetime
Minkowski spacetime M is the model of spacetime geometry used in the theory of special relativity.
M is the mathematical model of the spacetime of relativity.
Lorentz transformations are used to relate the spacetime coordinates for an event observed by two observers in their respective frames of reference.
bkocay.cs.umanitoba.ca /Students/Theory.html   (2717 words)

 Spacetime Stereo
In this work, we propose a common framework called spacetime stereo that unifies and generalizes many of these previous methods.
Based on our analysis, we show that methods derived from the spacetime stereo framework can be used to recover depth in situations in which existing methods perform poorly.
Below we see the robot itself with mounted spacetime stereo range capture equipment, the robot in action, and rendered polygon meshes of the captured geometry from both the front and top view.
graphics.stanford.edu /papers/SpacetimeStereo   (452 words)

 Minkowski Diagrams   (Site not responding. Last check: 2007-10-26)
One frequently used method of visualizing spacetime is the Minkowski Diagram.
Such diagrams are a subset of the general spacetime diagrams presented earlier.
One example of the use of Minkowski Daigrams is as follows (refer to Figure 3): A Square conveniently rests at the origin of spacetime.
www.brown.edu /Students/OHJC/ma8/papers/minkowsk.htm   (632 words)

 Spacetime Stereo
This paper extends the traditional binocular stereo problem into the spacetime domain, in which a pair of video streams is matched simultaneously instead of matching pairs of images frame by frame.
First, spacetime stereo serves as a general framework for structured light scanning and generates high quality depth maps for static scenes.
Second, spacetime stereo is effective for a class of natural scenes, such as waving trees and flowing water, which have repetitive textures and chaotic behaviors and are challenging for existing stereo algorithms.
grail.cs.washington.edu /projects/ststereo   (257 words)

 The Spacetime Wheel
As the spacetime wheel boosts, the spacetime coordinates (t, x) of a point on the wheel relative to its centre change, but the spacetime separation s between the point and the centre remains constant
The invariant spacetime separation s between two events is a rock in the sea of relativity, a quantity that remains the same for all observers, whereas time and space themselves differ for different observers.
The spacetime wheel offers a cute way to solve this problem, since the rotating spacetime wheel can be regarded as representing spacetime frames undergoing constant acceleration.
casa.colorado.edu /~ajsh/sr/wheel.html   (924 words)

 Spacetime Pythagorean Theorem
Spacetime is said to have a non-Euclidean geometry -- in other words, the normal rules of geometry that we learn in high school don't always work for spacetime!
Both equation (4.3) and equation (4.5) express the spacetime Pythagorean theorem.
Similarly, for events separated by a timelike interval, the proper time is just the time between two events in a reference frame in which the two events are collocated.
www.physics.nmt.edu /~raymond/classes/ph13xbook/node43.html   (354 words)

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