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How do observers in different reference frames describe events in terms of space and time?
How do observers in different reference frames describe events in terms of space and time?
In Galilean relativity, observers in different inertial frames use Galilean transformations assuming time is absolute.
In special relativity, Lorentz transformations replace Galilean ones, accounting for time dilation and length contraction at high speeds.
Observers disagree on measurements of time, length, and simultaneity, but agree on the space-time interval (s), an invariant.
How does special relativity change our understanding of motion compared to Galilean relativity?
How does special relativity change our understanding of motion compared to Galilean relativity?
Special relativity introduces two postulates: the laws of physics are the same in all inertial frames, and the speed of light (c) is constant for all observers.
At speeds close to c, time slows down (time dilation) and lengths contract (length contraction) compared to Galilean predictions.
Relativity of simultaneity means different observers may disagree about whether two events happen at the same time.
How are space-time diagrams used to represent relativistic motion?
How are space-time diagrams used to represent relativistic motion?
Space-time diagrams plot events with time on the vertical axis and space on the horizontal axis.
The world line of a moving particle is angled relative to the time axis, and the slope is related to the particle’s speed.
Light rays are shown at 45°, and relativistic effects like time dilation and simultaneity shifts are visualized through the geometry of the diagram.
Understandings
Understandings
reference frames
that Newton's laws of motion are the same in all inertial reference frames and this is known as Galilean relativity
that in Galilean relativity the position x' and time t' of an event are given by x'=x-vt and t'=t
that Galilean transformation equations lead to the velocity addition equation
the two postulates of special relativity
that the postulates of special relativity lead to the Lorentz transformation equations for the coordinates of an event in two inertial reference frames
that Lorentz transformation equations lead to the relativistic velocity addition equation
that the space-time interval s between two events is an invariant quantity
proper time interval and proper length
time dilation
length contraction
the relativity of simultaneity
space-time diagrams
that the angle between the world line of a moving particle and the time axis on a space-time diagram is related to the particle's speed
that muon decay experiments provide experimental evidence for time dilation and length contraction.
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