**TIME Presents** is a documentary series from the writers of Time
Magazine that covers different aspects of Celebrities' lives.

Type: Documentary

Languages: English

Status: Running

Runtime: 60 minutes

Premier: 2016-12-21

## TIME Presents - Spacetime - Netflix

In physics, spacetime is any mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum. Spacetime diagrams can be used to visualize relativistic effects such as why different observers perceive where and when events occur. Until the turn of the 20th century, the assumption had been that the three-dimensional geometry of the universe (its spatial expression in terms of coordinates, distances, and directions) was independent of one-dimensional time. However, in 1905, Albert Einstein based his seminal work on special relativity on two postulates: (1) The laws of physics are invariant (i.e., identical) in all inertial systems (i.e., non-accelerating frames of reference); (2) The speed of light in a vacuum is the same for all observers, regardless of the motion of the light source. The logical consequence of taking these postulates together is the inseparable joining together of the four dimensions, hitherto assumed as independent, of space and time. Many counterintuitive consequences emerge: in addition to being independent of the motion of the light source, the speed of light has the same speed regardless of the frame of reference in which it is measured; the distances and even temporal ordering of pairs of events change when measured in different inertial frames of reference (this is the relativity of simultaneity); and the linear additivity of velocities no longer holds true. Einstein framed his theory in terms of kinematics (the study of moving bodies). His theory was a breakthrough advance over Lorentz's 1904 theory of electromagnetic phenomena and Poincaré's electrodynamic theory. Although these theories included equations identical to those that Einstein introduced (i.e. the Lorentz transformation), they were essentially ad hoc models proposed to explain the results of various experiments—including the famous Michelson–Morley interferometer experiment—that were extremely difficult to fit into existing paradigms. In 1908, Hermann Minkowski—once one of the math professors of a young Einstein in Zürich—presented a geometric interpretation of special relativity that fused time and the three spatial dimensions of space into a single four-dimensional continuum now known as Minkowski space. A key feature of this interpretation is the formal definition of the spacetime interval. Although measurements of distance and time between events differ for measurements made in different reference frames, the spacetime interval is independent of the inertial frame of reference in which they are recorded. Minkowski's geometric interpretation of relativity was to prove vital to Einstein's development of his 1915 general theory of relativity, wherein he showed how mass and energy curve this flat spacetime to a Pseudo Riemannian manifold.

## TIME Presents - Relativity of simultaneity - Netflix

All observers will agree that for any given event, an event within the given event's future light cone occurs after the given event. Likewise, for any given event, an event within the given event's past light cone occurs before the given event. The before-after relationship observed for timelike-separated events remains unchanged no matter what the reference frame of the observer, i.e. no matter how the observer may be moving. The situation is quite different for spacelike-separated events. Fig. 2‑4 was drawn from the reference frame of an observer moving at v = 0. From this reference frame, event C is observed to occur after event O, and event B is observed to occur before event O. From a different reference frame, the orderings of these non-causally-related events can be reversed. In particular, one notes that if two events are simultaneous in a particular reference frame, they are necessarily separated by a spacelike interval and thus are noncausally related. The observation that simultaneity is not absolute, but depends on the observer's reference frame, is termed the relativity of simultaneity. Fig. 2-6 illustrates the use of spacetime diagrams in the analysis of the relativity of simultaneity. The events in spacetime are invariant, but the coordinate frames transform as discussed above for Fig. 2‑3. The three events (A, B, C) are simultaneous from the reference frame of an observer moving at v = 0. From the reference frame of an observer moving at v = 0.3 c, the events appear to occur in the order C, B, A. From the reference frame of an observer moving at v = −0.5 c, the events appear to occur in the order A, B, C. The white line represents a plane of simultaneity being moved from the past of the observer to the future of the observer, highlighting events residing on it. The gray area is the light cone of the observer, which remains invariant. A spacelike spacetime interval gives the same distance that an observer would measure if the events being measured were simultaneous to the observer. A spacelike spacetime interval hence provides a measure of proper distance, i.e. the true distance =

− s 2 . {\textstyle {\sqrt {-s^{2}}}.} Likewise, a timelike spacetime interval gives the same measure of time as would be presented by the cumulative ticking of a clock that moves along a given world line. A timelike spacetime interval hence provides a measure of the proper time = s 2 {\textstyle {\sqrt {s^{2}}}} .

## TIME Presents - References - Netflix

- http://arxiv.org/abs/1202.2487
- http://arxiv.org/abs/1701.06474
- http://doi.org/10.1088%2F0031-8949%2F9%2F1%2F014107
- http://arxiv.org/abs/1603.09674
- https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.57.21
- https://www.netflixtvshows.com/shows/time-presents/
- http://einstein.stanford.edu/content/faqs/faqs.html#launch