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Space and Time

# Space and Time - iClicker iClicker Announcements Help room...

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Announcements Help room hours (1248 BPS) Mon 5:30-8:30 PM Tues/Thurs noon-2:50 PM CAPA homework #2 due on Tuesday at 10 AM Final exam Friday Dec 12 10 AM - noon

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Reference systems Can imagine a coordinate system with a system of clocks and meter sticks such that it is possible to describe an event with the spacetime coordinates (x,y,z,t) Question: is time the same in every reference frame? For the moment, yes Once we discuss special relativity, we’ll find the answer is no The clocks for separate observers may run differently, depending on their frames of reference moving clocks tick more slowly than stationary clocks We can move in either direction along the x, y and z directions What about t? Through wormholes?
Cartesian coordinate systems Rectilinear coordinate axes (axes are perpendicular to each other)

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Can expand to 3 dimensions
What other kind of coordinate systems are there? Polar coordinate system where you can represent a 2D position by the coordinates r and θ

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Other coordinate systems Cylindrical ( ρ , φ ,z) Spherical (r, θ , φ )
Scalars, vectors and tensors Physical quantities can have characteristics Scalars-a quantity without direction the mass of an object the magnitude of a vector Vectors-a quantity that has both a length and a direction Tensors-generalized versions of vectors in multiple directions the number of dimensions of a tensor is called its rank rank 0 tensor is a scalar rank 1 tensor is a vector

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Tensors Einstein’s field equations (from General Theory of Relativity) Einstein tensor (describes how space is curved) energy-momentum tensor cosmological constant (“my biggest blunder”) (=T μ ν )
Another example: stress tensor

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Motion Position
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