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http://www.eng.fsu.edu/~mpf. EEL 5930 sec. 5, Spring ‘05 Physical Limits of Computing. Slides for a course taught by Michael P. Frank in the Department of Electrical & Computer Engineering. Review of Basic Physics Background. (Module 2). Basic physical quantities & units. Unit prefixes
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Slides for a course taught byMichael P. Frankin the Department of Electrical & Computer Engineering
(Module 2)
M. Frank, "Physical Limits of Computing"
M. Frank, "Physical Limits of Computing"
M. Frank, "Physical Limits of Computing"
M. Frank, "Physical Limits of Computing"
M. Frank, "Physical Limits of Computing"
M. Frank, "Physical Limits of Computing"
M. Frank, "Physical Limits of Computing"
M. Frank, "Physical Limits of Computing"
M. Frank, "Physical Limits of Computing"
M. Frank, "Physical Limits of Computing"
Note the over-dot!
Where:
or just
M. Frank, "Physical Limits of Computing"
M. Frank, "Physical Limits of Computing"
A.k.a.Hamilton’sprinciple
M. Frank, "Physical Limits of Computing"
Implicitsummationover i here.
M. Frank, "Physical Limits of Computing"
ℒ(x) = ℒ[φ(x), (∂φ/∂xi)(x), (x)]
M. Frank, "Physical Limits of Computing"
M. Frank, "Physical Limits of Computing"
M. Frank, "Physical Limits of Computing"
M. Frank, "Physical Limits of Computing"
M. Frank, "Physical Limits of Computing"
M. Frank, "Physical Limits of Computing"
M. Frank, "Physical Limits of Computing"
Actually it was written down earlier; e.g., one form by Voigt in 1887
Where:
Note: our γ here is the reciprocal of the quantity denoted γ by other authors.
M. Frank, "Physical Limits of Computing"
M. Frank, "Physical Limits of Computing"
increasing t′
increasing t
increasing x′
increasing x
x=0
x′=0
Original x,t(“rest”) frame
Line colors:
Isochrones(space-like)
t′=0
Isospatials(time-like)
New x′,t′(“moving”) frame
Light-like
In this example:
v = Δx/Δt = 3/5γ = Δt′/Δt = 4/5vT = v/γ = Δx/Δt′ = 3/4
t = 0
The “tourist’s velocity.”
M. Frank, "Physical Limits of Computing"
(Where θ = arctan vT)
M. Frank, "Physical Limits of Computing"
t′
t
t′
StandardFrame #1
MixedFrame #1
t
x
x
In this example:
v = Δx/Δt = 3/5
vT = Δx/Δt′ = 3/4γ = Δt′ /Δt = 4/5
Note that (Δt)2 = (Δx)2 + (Δt′)2by the PythagoreanTheorem!
Rememberthe slogan:
“My space isperpendicularto your time.”
x
t′
t
x′
StandardFrame #2
MixedFrame #2
x′
x′
Note the obvious complete symmetryin the relation between the two mixed frames.
M. Frank, "Physical Limits of Computing"
Higher-orderrelativistic corrections
Pre-relativistic kinetic energy ½ m0v2
M. Frank, "Physical Limits of Computing"
s2 = (ct)2− xi2
s2 > 0 - Events are timelike separated (s is real)May be causally connected.
s2 = 0 - Events are lightlike separated (s is 0) Only 0-rest-mass signals may connect them.
s2 < 0 - Events are spacelike separated (s is imaginary)Not causally connected at all.
M. Frank, "Physical Limits of Computing"
m02 = E2 − p2
M. Frank, "Physical Limits of Computing"