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Consider a spacetime diagram in which for simplicity, we will omit the space coordinate z. That is, only take into account three axes, two axes that define the xy plane characterized by the spatial coordinates x and y, and a third axis perpendicular to the xy plane that corresponds to the temporal coordinate t (ct so that the three axes have the same dimensions ). This coordinate system S is in which an observer O describes the events that occur in the Universe from his point of view
a) Draw the world line of a particle moving in the xy plane describing a circle with constant speed.
b) Draw the world line of a particle that is accelerating from rest until it reaches a certain speed, which already remains constant.
c) Now drop the spatial coordinate y. On the plane (x, ct) that describes the events seen by the observer O in his system S and considering the Lorentz transformations, draw the axes for a system S' in which an observer O' would describe the events that occur in the universe.
d) Use the scheme that you generated in part c) to represent two events A and B that for the observer O are simultaneous. Describe how to “observe” O' the events A and B, that is, discuss the concept of “simultaneity” in the context of relativity
special.
Dear student as per the guidelines I will answer the first 3 subparts. Please repost the remaining subpart again thankyou.
Given in the problem we need to construct a space-time diagram for the given situation. We need to take only the x, y, and ct-axis into account. Hence we have our 3 dimensions (ct, x, y).
For the units, we will stick to the relativistic units where c which is the velocity of light, c=1.
Hence we can keep our coordinates as (t, x, y).
Now let's consider an observer O whose coordinate system is described by the set of coordinates we chose.
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