Physical definition

From the age of Newton up until Einstein's profound reinterpretation of the physical concepts associated with time and space, time was considered to be "absolute" and to flow "equably" (to use the words of Newton) for all observers.^[34] The science of classical mechanics is based on this Newtonian idea of time.

Einstein, in his special theory of relativity,^[35] postulated the constancy and finiteness of the speed of light for all observers. He showed that this postulate, together with a reasonable definition for what it means for two events to be simultaneous, requires that distances appear compressed and time intervals appear lengthened for events associated with objects in motion relative to an inertial observer.

Einstein showed that if time and space is measured using electromagnetic phenomena (like light bouncing between mirrors) then due to the constancy of the speed of light, time and space become mathematically entangled together in a certain way (called Minkowski space) which in turn results in Lorentz transformation and in entanglement of all other important derivative physical quantities (like energy, momentum, mass, force, etc) in a certain 4-vectorial way (see special relativity for more details).

Classical mechanics

Newton's Second Law

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Classical mechanics

In classical mechanics Newton's concept of "relative, apparent, and common time" can be used in the formulation of a prescription for the synchronization of clocks. Events seen by two different observers in motion relative to each other produce a mathematical concept of time that works pretty well for describing the everyday phenomena of most people's experience.

Modern physics

In the late nineteenth century, physicists encountered problems with the classical understanding of time, in connection with the behavior of electricity and magnetism. Einstein resolved these problems by invoking a method of synchronizing clocks using the constant, finite speed of light as the maximum signal velocity. This led directly to the result that time appears to elapse at different rates relative to different observers in motion relative to one another.

Two-dimensional space depicted in three-dimensional spacetime. The past and future light cones are absolute, the "present" is a relative concept different for observers in relative motion.

Spacetime

Main article: Spacetime

Modern physics views the curvature of spacetime around an object as much a feature of that object as are its mass and volume.^{[citation needed]}

Time has historically been closely related with space, the two together comprising spacetime in Einstein's special relativity and general relativity. According to these theories, the concept of time depends on the spatial reference frame of the observer, and the human perception as well as the measurement by instruments such as clocks are different for observers in relative motion. Even the temporal order of events can change, but the past and future are defined by the backward and forward light cones, which never change.^{[citation needed]} The past is the set of events that can send light signals to the observer, the future the events to which the observer can send light signals. All else is non-observable and within that set of events the very time-order differs for different observers.^{[citation needed]}

Time dilation

Relativity of simultaneity: Event B is simultaneous with A in the green reference frame, but it occurred before in the blue frame, and will occur later in the red frame.

Main article: Time dilation

"Time is nature's way of keeping everything from happening at once". This quote, attributed variously to Einstein, John Archibald Wheeler, and Woody Allen, says that time is what separates cause and effect. Einstein showed that people travelling at different speeds, whilst agreeing on cause and effect, will measure different time separations between events and can even observe different chronological orderings between non-causally related events. Though these effects are minute unless one is travelling at a speed close to that of light, the effect becomes pronounced for objects moving at speeds approaching the speed of light. Many subatomic particles exist for only a fixed fraction of a second in a lab relatively at rest, but some that travel close to the speed of light can be measured to travel further and survive much longer than expected (a muon is one example). According to the special theory of relativity, in the high-speed particle's frame of reference, it exists, on the average, for a standard amount of time known as its mean lifetime, and the distance it travels in that time is zero, because its velocity is zero. Relative to a frame of reference at rest, time seems to "slow down" for the particle. Relative to the high-speed particle, distances seems to shorten. Even in Newtonian terms time may be considered the fourth dimension of motion; but Einstein showed how both temporal and spatial dimensions can be altered (or "warped") by high-speed motion.

Einstein (The Meaning of Relativity): "Two events taking place at the points A and B of a system K are simultaneous if they appear at the same instant when observed from the middle point, M, of the interval AB. Time is then defined as the ensemble of the indications of similar clocks, at rest relatively to K, which register the same simultaneously."

Einstein wrote in his book, Relativity, that simultaneity is also relative, i.e., two events that appear simultaneous to an observer in a particular inertial reference frame need not be judged as simultaneous by a second observer in a different inertial frame of reference.