In special relativity it is said that " Time and space cannot be defined separately from one another. Rather space and time are interwoven into a single continuum known as spacetime. " What is the exact meaning of this statement ? In SR, even though time is relative too but still in classical physics, we still needed time to define an event and what is the meaning of the term continuum ?
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Possible duplicate: http://physics.stackexchange.com/q/96249/2451 – Qmechanic Feb 01 '14 at 15:33
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possible duplicate of What's the difference between space and time? – John Rennie Feb 01 '14 at 15:53
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1"Continuum" in the sense that spacetime is mathematically smooth – Feb 01 '14 at 17:03
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The difference between Einsteinian space-time and Galilean/Newtonian space and time is explored in every introduction to special relativity. Usually right at the beginning, though the authors rarely point it out that early in the presentation. The inability to define simultanaiety for space-like separated points or to define co-location for time-like separated points is exactly the---er, well---point. – dmckee --- ex-moderator kitten Feb 01 '14 at 17:33
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Consider in classical physics we can rotate our coordinate system such that the spatial coordinates become mixed up (e.g. if we start with some coordinates x,y,z we can find new coordinates x',y',z' such that x' may depend not only on x but also on y and z (and similarly for the other "primed" coordinates). However, in classical physics we can never perform a "rotation" (more generally, a "transformation") that mixes the time coordinate with the spatial coordinates.
In SR, we are able to perform a transformation that mixes time coordinates with spatial coordinates. This transformation is known as the Lorentz transformation and it mixes up the time and space coordinates. That's why instead of calling the coordinates "time and space" we note them as one system "spacetime". Furthermore, we also find that the speed of light is the conversion factor between time and space.
Lastly, a "continuum" just means that each coordinate (t,x,y,z) is continuous (not discrete). That is, each coordinate can take on any real number.
mcFreid
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