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 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. We must create a space-time diagram for the scenario presented in the problem. Only the x, y, and ct-axis must be taken into consideration. Thus, we have our three dimensions (ct, x, y). We'll remain with relativistic units for the units, where c is the speed of light and c=1. so that we can maintain our coordinates as (t, x, y). Let's now take a look at an observer O whose coordinate system is defined by the set of coordinates we selected. (c) To describes the events seen by the observer O in his system S and considering the Lorentz transformations.To draw the axes for a system S' in which an observer O' would describe the events that occur in the universe. Solution: (c) Now that the y spatial coordinate is gone, we only take the x and t axes into account. Assume the Observer O has the coordinates and is at rest in his frame S. (x,t). Let O' represent the observer in frame S', moving with a constant relative velocity v to frame S. The coordinates are S'. (x',t') Both observers were at rest at time t=0. At that point, O' starts to move continuously. If the frame S' travels with v in reference to the S frame, it will appear to the observer that the frame S' has moved by a distance of vt. the world line for the observer O in his frame will therefore be x=vt however, in O's context, it will be x'=0 that produces the t' axis Here is the x' axis. It will be provided by Since t'=t-vx1-v2 (c=1 in relativistic units) produces ust=vx in the S' frame, t'=0. t=vx (relativistic units) t=vc2x.. (general unit) that which is x' axis Blue lines represent the observer O's axis. According to the relativity principle, the speed of light won't change for either observer. please answer part d) 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.
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
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.
We must create a space-time diagram for the scenario presented in the problem. Only the x, y, and ct-axis must be taken into consideration. Thus, we have our three dimensions (ct, x, y).
We'll remain with relativistic units for the units, where c is the speed of light and c=1.
so that we can maintain our coordinates as (t, x, y).
Let's now take a look at an observer O whose coordinate system is defined by the set of coordinates we selected.
(c) To describes the events seen by the observer O in his system S and considering the Lorentz transformations.To draw the axes for a system S' in which an observer O' would describe the events that occur in the universe.
Solution:
(c) Now that the y spatial coordinate is gone, we only take the x and t axes into account.
Assume the Observer O has the coordinates and is at rest in his frame S.
(x,t).
Let O' represent the observer in frame S', moving with a constant relative velocity v to frame S.
The coordinates are S'.
(x',t')
Both observers were at rest at time t=0. At that point, O' starts to move continuously.
If the frame S' travels with v in reference to the S frame, it will appear to the observer that the frame S' has moved by a distance of vt.
the world line for the observer O in his frame will therefore be
x=vt
however, in O's context, it will be
x'=0 that produces the t' axis
Here is the x' axis.
It will be provided by
Since t'=t-vx1-v2 (c=1 in relativistic units) produces ust=vx in the S' frame, t'=0.
t=vx (relativistic units)
t=vc2x.. (general unit)
that which is
x' axis
Blue lines represent the observer O's axis.
According to the relativity principle, the speed of light won't change for either observer.
please answer part d)
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.
Given
the Observer O has the coordinates and is at rest in his frame S.
(x,t).
Let O' represent the observer in frame S', moving with a constant relative velocity v to frame S.
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