Notes on Relativity and Cosmology - Physics Department, UCSB

40 CHAPTER 1. SPACE, TIME, AND NEWTONIAN PHYSICS
1-6. Describe at least one way in which some law of Newtonian physics uses
each of the Newtonian assumptions T and S about the nature of time and
space.
1-7. In section 1.6 we used Newton’s first law and the Newtonian rules for space
and time to conclude that the following three statements are equivalent:
i) An object is in an inertial frame of reference.
ii) The net force on that object is zero.
iii) The object moves in a straight line at constant speed in any inertial
frame. (Note that this means that the worldline of our object is drawn
as a straight line on any spacetime diagram that corresponds to an
inertial frame.)
Give the argument for this, filling in any holes that you may have missed
in lecture or in reading the text. Please do this in your own words. (Hint:
The easiest way to prove that all three are equivalent is to prove that
1 implies 2, that 2 implies 3, and that 3 implies 1. That will make a
complete cycle and show that any one of the above statements implies the
other two).
1-8. It is always good to get more practice working with different reference
frames and spacetime diagrams. This problem will provide you with some
of that practice before we get to (Einstein) relativity itself.
Suppose that you are in a room in a rocket in deep space. When they
are on, the rocket engines cause the rocket to be pushed ‘upwards,’ in the
direction of the ‘ceiling.’ Draw spacetime diagrams showing the worldlines
of the ceiling of the room, the floor of the room, and your head, and your
feet in the following situations, using the reference frames specified.
Be sure to start your diagrams a short time before t = 0. You need only
worry about where things are located in the direction marked x below (in
other words, you only need to worry about the ‘vertical’ positions of the
ceiling, floor, etc.). By the way, following our conventions you should draw
this position coordinate along the horizontal axis, since time should run
up the vertical axis.