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.

• Length Contraction

  • Length contraction is the physical phenomenon of a decrease in length detected by an observer of objects that travel at any non-zero velocity relative to that observer.
  • Now imagine that the clock is moving in the horizontal direction relative to a stationary observer.
  • We have established that in a frame of reference that is moving relative to the clock (the stationary observer is moving in the clock's frame of reference), the clock appears to run more slowly.
  • where L0 is the proper length (the length of the object in its rest frame); L is the length observed by an observer in relative motion with respect to the object; v is the relative velocity between the observer and the moving object; c is the speed of light; and the Lorentz factor is defined as:
  • For the observer in relative movement, the length of the object is measured by subtracting the simultaneously measured distances of both ends of the object.

• 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

• A General Approach

  • Basic problem-solving techniques can aid in the solution of problems involving motion (i.e., the laws of motion).
  • When dealing with the laws of motion, although knowledge of concepts and equations is important, understanding basic problem solving techniques can simplify the process of solving problems that may appear difficult.
  • If you can judge whether the answer is reasonable, you have a deeper understanding of physics than simply the mechanics of problem solving.
  • When solving problems, we tend to perform these steps in different order, as well as do several steps simultaneously.
  • In time, the basics of problem solving can become relatively automatic.

• Einstein's Postulates

  • Special relativity is based on Einstein's two postulates: the Principle of Relativity and the Principle of Invariant Light Speed.
  • With two deceptively simple postulates and a careful consideration of how measurements are made, Einstein produced the theory of special relativity.
  • The Principle of Relativity: The laws of physics are the same and can be stated in their simplest form in all inertial frames of reference.
  • The Principle of Invariant Light Speed: The speed of light c is a constant, independent of the relative motion of the source and observer.
  • Einstein accepted the result of the experiment and incorporated it in his theory of relativity.

• Photon Interactions and Pair Production

  • Below is an illustration of pair production, which refers to the creation of an elementary particle and its antiparticle, usually when a photon interacts with a nucleus.
  • The energy of this photon can be converted into mass through Einstein's equation $E=mc^2$ where $E$ is energy, $m$ is mass and $c$ is the speed of light.
  • Without a nucleus to absorb momentum, a photon decaying into electron-positron pair (or other pairs for that matter) can never conserve energy and momentum simultaneously.
  • If all three gamma rays, the original with its energy reduced by 1.022 MeV and the two annihilation gamma rays, are detected simultaneously, then a full energy peak is observed.
  • Describe process of pair production as the result of photon interaction with nucleus

• The Heisenberg Uncertainty Principle

  • The uncertainty principle asserts a basic limit to the precision with which some physical properties of a particle can be known simultaneously.
  • The uncertainty principle is any of a variety of mathematical inequalities, asserting a fundamental limit to the precision with which certain pairs of physical properties of a particle, such as position x and momentum p or energy E and time t, can be known simultaneously.
  • If a large aperture is used for the microscope, the electron's location can be well resolved (see Rayleigh criterion); but by the principle of conservation of momentum, the transverse momentum of the incoming photon and hence the new momentum of the electron resolves poorly.
  • One of the most-oft quoted results of quantum physics, this doozie forces us to reconsider what we can know about the universe.
  • Some things cannot be known simultaneously.