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More precisely, the Hartle-Hawking state is a hypothetical vector in the Hilbert space of a theory of quantum gravity that describes the wave function of the universe.. It is a functional of the metric tensor defined at a (D − 1)-dimensional compact surface, the universe, where D is the spacetime dimension.
The Berkeley course was contemporary with The Feynman Lectures on Physics (a college course at a similar mathematical level), and PSSC Physics (a high school introductory course). These physics courses were all developed in the atmosphere of urgency about science education created in the West by Sputnik .
In 2011, MIT OpenCourseWare introduced the first of fifteen OCW Scholar courses, which are designed specifically for the needs of independent learners. While still publications of course materials like the rest of the site content, these courses are more in-depth and the materials are presented in logical sequences that facilitate self-study.
The phase velocity is the rate at which the phase of the wave propagates in space. The group velocity is the rate at which the wave envelope, i.e. the changes in amplitude, propagates. The wave envelope is the profile of the wave amplitudes; all transverse displacements are bound by the envelope profile.
Physics is the scientific study of matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. [1] Physics is one of the most fundamental scientific disciplines. [2] [3] [4] A scientist who specializes in the field of physics is called a physicist.
The observation that these wave solutions had a wave speed exactly equal to the speed of light led Maxwell to hypothesise that light is a form of electromagnetic radiation and to posit that other electromagnetic radiation could exist with different wavelengths. [19]
(Modern physics no longer uses this form of the total energy; the energy–momentum relation has proven more useful.) De Broglie identified the velocity of the particle, v, with the wave group velocity in free space: = (/)
A transverse wave is the form of a wave in which particles of medium vibrate about their mean position perpendicular to the direction of the motion of the wave. To see an example, move an end of a Slinky (whose other end is fixed) to the left-and-right of the Slinky, as opposed to to-and-fro. [ 2 ]