relativity of simultaneity

Examples of relativity of simultaneity in the following topics:

• Simultaneity

  • The relativity of simultaneity is the concept that simultaneity is not absolute, but depends on the observer's reference frame.
  • 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 frame of reference.
  • If the two events are causally connected ("event A causes event B"), then the relativity of simultaneity preserves the causal order (i.e.
  • In 1905, Albert Einstein abandoned the (classical) aether and emphasized the significance of relativity of simultaneity to our understanding of space and time.
  • He deduced the failure of absolute simultaneity from two stated assumptions: 1) the principle of relativity–the equivalence of inertial frames, such that the laws of physics apply equally in all inertial coordinate systems; 2) the constancy of the speed of light detected in empty space, independent of the relative motion of its source.

• Four-Dimensional Space-Time

  • Let us examine two observers who are moving relative to one another at a constant velocity.
  • (Using the principles of relativity, you can prove this for general separations, not just light rays).
  • This phenomenon is known as the relativity of simultaneity and may be counterintuitive.
  • The question of whether the events are simultaneous is relative: in some reference frames the two accidents may happen at the same time; in other frames (in a different state of motion relative to the events) the crash in London may occur first; and in still other frames the New York crash may occur first.
  • Finally, let's discuss an important result of special relativity -- that the energy $E$ of an object moving with speed $v$ is:

• Shifting the Paradigm of Physics

  • After 1905, however, the Special Theory of Relativity destroyed this old, but intuitive, view.
  • Relativity of Simultaneity (for certain events, the sequence in which they occur is dependent on the observer)
  • In order to examine this we must know the founding principles of relativity.
  • The Principle of Relativity: The laws of physics for observers which are not accelerating relative to one another should be the same.
  • Another radical finding that was made possible by the discovery of special relativity is the equivalence of energy and mass.

• Relativistic Addition of Velocities

  • When both the fly and the ship are moving slowly compared to speed of light, it is accurate enough to use the vector sum $s = u + v$ where $s$ is the velocity of the fly relative to the shore.
  • According to the theory of special relativity, the frame of the ship has a different clock rate and distance measure, and the notion of simultaneity in the direction of motion is altered, so the addition law for velocities is changed.
  • Since special relativity dictates that the speed of light is the same in all frames of reference, light shone from the front of a moving car can't go faster than light from a stationary lamp.
  • For collinear motions, the velocity of the fly relative to the shore is given by the following equation:
  • Composition law for velocities gave the first test of the kinematics of the special theory of relativity.

• Associations

  • Our definition of associations is as follows: An association exists when one person's satisfaction is being changed by the actions of another person.
  • For purposes of our definition, these changes are measured relative to the level of satisfaction at which there would be no association at all between the people in question, point 0 on the diagram.
  • (To diagram the relationship of our individual to yet another person would require an additional diagram: Jones may simultaneously be associated with Smith and not associated with Baker. )
  • All three of the following diagrams are therefore simultaneously true:
  • Obviously, these diagrams express only relative levels of satisfaction rather than absolute satisfaction.

• Effects of Time Dilation: The Twin Paradox and the Decay of the Muon

  • The twin paradox is a thought experiment in special relativity involving identical twins, one of whom makes a journey into space in a high-speed rocket and returns home to find that the twin who remained on Earth has aged more.
  • Blue lines show the planes of simultaneity for the traveling twin during the first leg of the journey; red lines, during the second leg.
  • In a sense, during the U-turn the plane of simultaneity jumps from blue to red and very quickly sweeps over a large segment of the world line of the Earth-based twin.
  • Time is relative, but both twins are not equivalent (the ship experiences additional acceleration to changes the direction of travel).
  • Explain the twin paradox within the standard framework of special relativity

• Summary

  • The actors in the kinds of networks that social scientists study are very frequently connected by more than one type of tie, simultaneously.
  • In this chapter, we've introduced a few of the tools that are commonly used to help to make sense of the complex patterns of embedding that can emerge when there is more than one kind of tie operating simultaneously.
  • With relatively small networks, and relatively small numbers of relations, graphs can be prepared that show the unions and intersections of multiple kinds of relations, or "animate" change over time in network structure.
  • A special set of tools for dealing with the unique features of CSS data was also discussed.
  • Our understanding of kinship structures, and our understanding of the positions of nation-states in the world system have been greatly enhanced by indexing actor's relational positions based on multiple and simultaneous ties.

• Interaction Models

  • In statistics, an interaction may arise when considering the relationship among three or more variables, and describes a situation in which the simultaneous influence of two variables on a third is not additive.
  • The presence of interactions can have important implications for the interpretation of statistical models.
  • An interaction variable is a variable constructed from an original set of variables in order to represent either all of the interaction present or some part of it.
  • Treatment $A$ is helpful on average regardless of whether treatment $B$ is also administered, but it is more helpful in both absolute and relative terms if given alone, rather than in combination with treatment $B$.
  • Outline the problems that can arise when the simultaneous influence of two variables on a third is not additive.

• Cannon–Bard Theory of Emotion

  • The Cannon–Bard theory of emotion argues that physiological arousal and emotional experience occur simultaneously but independently.
  • Researchers have developed several theories of how human emotions arise and are represented in the brain.
  • The Cannon–Bard theory of emotion was developed by researchers who criticized the James–Lange theory for its limited ability to account for the wide variety of emotions experienced by human beings.
  • According to the Cannon–Bard theory, emotional expression results from activation of the subcortical centers of the brain.
  • The Cannon–Bard theory states that physiological arousal and emotional experience occur simultaneously, yet independently.

• Pericyclic Reactions

  • An important body of chemical reactions, differing from ionic or free radical reactions in a number of respects, has been recognized and extensively studied.
  • They are relatively unaffected by solvent changes, the presence of radical initiators or scavenging reagents, or (with some exceptions) by electrophilic or nucleophilic catalysts.
  • They proceed by a simultaneous (concerted) series of bond breaking and bond making events in a single kinetic step, often with high stereospecificity.
  • Since reactions of this kind often proceed by nearly simultaneous reorganization of bonding electron pairs by way of cyclic transition states, they have been termed pericyclic reactions.
  • Although some pericyclic reactions occur spontaneously, most require the introduction of energy in the form of heat or light, with a remarkable product dependence on the source of energy used.