GeoGebra

When Left Alone

Author:Timo Budarz
[url=https://pixabay.com/en/background-wallpaper-blue-1430009/]"Asteroid in Space"[/url] by Frantisek_Krejci, [url=http://pixabay.com/]pixabay is in the [/url][url=http://creativecommons.org/publicdomain/zero/1.0/]Public Domain, CC0[/url]
"Asteroid in Space" by Frantisek_Krejci, pixabay is in the Public Domain, CC0
I gave this chapter a somewhat silly title for a good reason. I want to start our physics discussions with a discussion of what an object's behavior looks like when nothing else is around. The object can be anything you'd like it to be, except that I don't want you to think of moving parts. Picture something like a rock or a ball or a planet seen from space.. We don't want to think of a complex object with movable parts because the added complexity will draw focus away from the point I want to make right now. Let's say our object is a rock - maybe the asteroid in the picture above. The question I want to pose is this: What will the rock's motion look like if the rock is all alone in the universe? Of course nothing can ever be truly alone, so what I mean by this is that the rock is far away from anything with which it would interact. The reason this is a question that's worth asking is that if we understand its answer, we will more clearly recognize and be able to describe the rock's motion when other things are around and the rock is not alone. So picture a rock (asteroid) floating in interstellar space that is far from any planet or star. Consider these questions for a moment:
  • Do you suppose the rock could speed up or slow down on its own?  
  • Do you suppose it could turn?  
  • If the rock is at first observed to be in motion, what do we expect the properties of this motion to be? Pause and consider these questions before reading on.
The laws of nature tell us that the motion of the rock will be constant. That is to say that the motion will not change. Whatever the rock's speed is right now will be the same later on. Whatever the rock's direction of travel is, it will have the same direction of travel later on. You might have guessed as much - perhaps by having seen some random movie scene with a rock floating in space. So what we know is that the speed and direction of travel are constant when an object is not being affected by its surroundings. But is the rock's position constant? Not if it's moving! So it is certainly incorrect to just say that according to the laws of nature that nothing about the rock changes. Rather, we find that its position may constantly be changing, but only in such a way that the speed and direction are constant. Keep in mind that a stationary rock still has a constant speed of zero. In only this case of zero speed is the direction of travel undefinable. AN ASIDE: Earth itself is almost like our rock floating through interstellar space. There are obviously other rocks (planets + moon) and the sun out there as well, but they are rather distant. If you look at the details of earth's orbit, it orbits at a very nearly constant speed of around 67,000 miles per hour, and the gravitational pull of the very large sun only manages to change the direction of earth's path through space by less than one degree each day! That is very nearly inertial motion, and yet the difference between true inertial motion and earth's orbit is a matter of life and death for all of us living here on earth. Whether obvious to you or not, it took humanity a rather long time to document this understanding that we refer to as the inertia of an object. Ancient Greeks like Aristotle believed that the natural state of objects was rest. Others opposed this notion through the centuries, but never quite correctly. It was Galileo Galilei of Italy who came close to the principle of inertia in the early 1600s, but his notion was still flawed. I don't want to dwell on any historical misconceptions. It was on the foundation of bits and pieces of understanding and, I should say, despite millennia of misconceptions, that Isaac Newton published his three laws of motion in July of 1687. Newton is famously quoted as writing "If I have seen further, it is by standing on the shoulders of giants", in which he is believed to have been thinking of intellectual giants such as Galileo Galilei, Robert Hooke, Descartes and others. A history of science professor I once had for a course suggested that Newton said those words facetiously, but I prefer to side with others who suggested he was genuine even if he didn't have much admiration or affection for all those individuals. Newton's first law of motion is simply a statement indicating what we discussed above: To the extent that objects are unaffected by external influences, objects at rest remain at rest, and objects in motion remain in constant-speed, straight-line motion. Today we equate Newton's first law of motion with the modern definition of inertia. In other words, if asked to define inertia, the correct response is to state Newton's first law of motion using words similar to the bold text above. So this idea that objects unaffected by anything else will travel at constant speed and direction is generally referred to as either The law of inertia or as Newton's first law of motion. They may be used interchangeably.

Deeper Implications

Having had this brief discussion about inertia, even without getting into any equations we can make a profound statement about nature and physics. The law of intertia was instrumental for Einstein's relativity theories 250 years later. One deeper implication about the law of interia is that there is no difference in the behavior of an object at rest from that of one in motion. What I mean is that whether going what we call quickly or slowly, the behavior is identical.  Both continue moving at constant speed in a straight line.  There is nothing about going faster that makes the behavior different.   At first glance this argument may seemed flawed.  After all, sticking your head or hand out a car window while traveling 30mph versus 120mph is a very different experience.  But what you are doing is moving your head or hand relative to the air.  Relative velocities are easy to measure and often have real effects associated with them as in the example above.  But what if there was no atmosphere?  Now could you feel or measure anything different in the car at 30mph versus 120mph when you stick your head out?  No! It is not possible to define a state of absolute rest, only relative rest. We can only ever say that an object is at rest with respect to some other object. You might be thinking that you are at rest right now, but you're only at rest with respect to earth while earth is traveling very rapidly through space in a galaxy that also is moving with respect to other neighboring galaxies. Yet we don't feel like we're moving at hundreds of kilometers per second. That's precisely because there is no difference in how it feels to move rapidly than to not move at all.  Motion can only be defined relative to another object. There is no experiment that can be performed to determine whether you are moving or are at rest in an absolute sense.  So how quickly is earth moving right now?  It depends on who is measuring!  The fact that the answer is relative to the observer is at the core of Einstein's relativity theory.   In order to get more sophisticated in discussions of motion we will need to develop some definitions and as you'll see, mathematics will enter our discussions, since it is a much more elegant language than English to discuss natural laws. A more careful discussion of motion will be the focus of the next section.

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