Now find t', the t coordinate of the event in frame S! Express your answer in seconds to three significant figures. ΜΕ ΑΣΦ ? t' = 10 S Learning Goal: To be able to perform Lorentz transformations between inertial reference frames. Suppose that an inertial reference frame S'moves in the positive x direction at speed with respect to another inertial reference frame S. In classical physics, the Galilean transformations relate the coordinates measured for an event in frame S to the coordinates measured for the same event in frame S'. Assuming that both frames have the same origin (i.e., at t = t' = 0, x = x' = 0), the Galilean transformations take the following simple form: t'=t, x'x vt, y' = y, z' = z. The Galilean transformations are not valid at very large speeds. To transform between inertial frames when v is close to the speed of light c, we need to use the Lorentz transformations of special relativity. Again, assuming that both frames have the same origin, the Lorentz transformations take the following form: ť' = x' = x-vt y' = y, z' = z. These equations become more manageable with the introduction of the quantity 2= (1 - v²/c²)-1/2 so that the Lorentz transformations become - t' = √(t − x), x' = √(x — vt), - y' = y, z' = z. Often, the space-time coordinates for an event will be given in the form (t, x, y, z), or just (t, x) when the y and z coordinates are not important.
Now find t', the t coordinate of the event in frame S! Express your answer in seconds to three significant figures. ΜΕ ΑΣΦ ? t' = 10 S Learning Goal: To be able to perform Lorentz transformations between inertial reference frames. Suppose that an inertial reference frame S'moves in the positive x direction at speed with respect to another inertial reference frame S. In classical physics, the Galilean transformations relate the coordinates measured for an event in frame S to the coordinates measured for the same event in frame S'. Assuming that both frames have the same origin (i.e., at t = t' = 0, x = x' = 0), the Galilean transformations take the following simple form: t'=t, x'x vt, y' = y, z' = z. The Galilean transformations are not valid at very large speeds. To transform between inertial frames when v is close to the speed of light c, we need to use the Lorentz transformations of special relativity. Again, assuming that both frames have the same origin, the Lorentz transformations take the following form: ť' = x' = x-vt y' = y, z' = z. These equations become more manageable with the introduction of the quantity 2= (1 - v²/c²)-1/2 so that the Lorentz transformations become - t' = √(t − x), x' = √(x — vt), - y' = y, z' = z. Often, the space-time coordinates for an event will be given in the form (t, x, y, z), or just (t, x) when the y and z coordinates are not important.
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Chapter1: Units, Trigonometry. And Vectors
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Transcribed Image Text:Now find t', the t coordinate of the event in frame S!
Express your answer in seconds to three significant figures.
ΜΕ ΑΣΦ
?
t' =
10
S
Transcribed Image Text:Learning Goal:
To be able to perform Lorentz transformations between inertial reference frames.
Suppose that an inertial reference frame S'moves in the positive x direction at speed with respect to another inertial
reference frame S. In classical physics, the Galilean transformations relate the coordinates measured for an event in frame
S to the coordinates measured for the same event in frame S'. Assuming that both frames have the same origin (i.e., at
t = t' = 0, x = x' = 0), the Galilean transformations take the following simple form:
t'=t, x'x vt,
y' = y, z' = z.
The Galilean transformations are not valid at very large speeds. To transform between inertial frames when v is close to the
speed of light c, we need to use the Lorentz transformations of special relativity. Again, assuming that both frames have the
same origin, the Lorentz transformations take the following form:
ť'
=
x' =
x-vt
y' = y, z' = z.
These equations become more manageable with the introduction of the quantity
2=
(1 - v²/c²)-1/2
so that the Lorentz transformations become
-
t' = √(t − x), x' = √(x — vt),
-
y' = y, z' = z.
Often, the space-time coordinates for an event will be given in the form (t, x, y, z), or just (t, x) when the y and z
coordinates are not important.
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