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xem_007
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What exactly the "time" is?
Is it just like other spatial dimension?
It is very confusing for me to understand.
Is it just like other spatial dimension?
It is very confusing for me to understand.
Fredrik said:We could define spacetime to be the set [itex]\mathbb R^4[/itex] and let functions of the form [itex]C:\mathbb R\rightarrow\mathbb R^4[/itex] represent an object's motion, even if we knew nothing about special relativity. It's this definition that turns time into a "dimension". Time is a dimension in that model, for the reasons DaleSpam explained.
In this model of spacetime, "space" is a subset of spacetime such that all the members of it are simultaneous (i.e. have the same time coordinate). The difference between SR and pre-relativistic physics is what atyy said: Each inertial observer would call a different 3-dimensional slice of spacetime "space" (assuming that they assign coordinates to events using a pretty obvious definition of simultaneity involving light, a mirror and a clock).
Fredrik said:Regarding the definition of time...
We can define a coordinate system in Newtonian mechanics, SR and GR as a function [itex]x:M\rightarrow\mathbb R^4[/itex], where M is spacetime, and then define "coordinate time" as a component of that function. In SR and GR it's also necessary to define "proper time", which is the integral of [tex]\sqrt{-g_{\mu\nu}dx^\mu dx^\nu}[/tex] along a curve.
That takes care of the definitions in the mathematical models used in these three theories, but the theories must still include postulates that tell us how these things are related to what clock's measure. In Newtonian mechanics, clocks measure coordinate time. In SR and GR, a clock measures the proper time of the curve that represents its motion.
Maybe this essay will deconfuse you:xem_007 said:Is it just like other spatial dimension?
It is very confusing for me to understand.
xem_007 said:Is it just like other spatial dimension?
It is very confusing for me to understand.
Time is a fundamental concept that is used to measure the duration of events and the intervals between them. It can be defined as the ongoing sequence of events that occur in a continuous manner.
Time is typically measured using units such as seconds, minutes, hours, days, weeks, months, and years. These units are based on the Earth's rotation and orbit around the sun.
Time is important because it allows us to organize and plan our daily lives, understand the past, and predict the future. It also plays a crucial role in scientific research and the development of technology.
According to Einstein's theory of relativity, time is not constant and can be affected by factors such as gravity and velocity. However, for everyday purposes, time is considered constant and is measured at a consistent rate.
While time travel is a popular concept in science fiction, it is currently not possible according to our current understanding of physics. However, some theories suggest that it may be possible to travel through time in certain conditions, such as near the speed of light or in the presence of a black hole.