It probably goes without saying: Trying to understand the entire universe is nearly impossible. Fortunately, it’s also really simple. We’ll try to find some middle ground, honoring both the simplicity and the impossibility.
First, there’s only one universe1. That’s good news and bad news. Only having one thing to study means there’s less to be looking for, but it also means we can’t compare this universe to others. There’s no “control” group when you study the universe. It’s all or nothing.
Well, actually, it’s “all.” It contains everything. This is a good definition of the universe: the container of all space and the backdrop for all of time. Within that time and space you have a kind of gameboard, and all of the rules of the game and all of the pieces are played within.
For us, the question is, Where did that everything come from and what does that everything look like and how does that tell us anything at all about the beginnings? Oh, and also, where is it all going?
To get a sense of what we’re talking about, I like to show an image produced by the Hubble Space Telescope early in its career. But first, imagine holding a pencil, and then holding that pencil in your hand at arm’s length away from you, and then hold that pencil up to the sky and consider the amount of sky that is blocked by the very tip of the pencil. Got it? Just a little point in the sky. Oh, and make sure the part of the sky you’re looking at is a dark part, not with any stars in the way.
Take a moment to consider that penciltip of dark sky.
Okay.
So, that dark, minute fraction of a sliver of our view of the universe actually looks like this:
Each one of those blobs of light (remember, in this pencil tip of space) is a galaxy, an entire island of stars. Each of these islands holds on order of 100 billion stars, and there’s on order of 100 billion galaxies in the universe.2 You can go ahead and multiply these together to get an idea of how many stars (each with possibilities of planets orbiting about) there are in the universe. I don’t know what to say about this number, actually. I write it out and stare at it but I don’t really understand it in any real way.3
So, this gives you a sense for the stuff out there, but we also want to consider the space that allows for all the stuff to exist. For us to start to get a handle on this, all we do is look in all directions and we see pretty much the same thing everywhere we look: galaxies. We say the galaxies are distributed homogeneously and isotropically, which is just to say that every direction and every place has the same distribution of galaxies. You might think this is obvious, but it didn’t have to be this way. And yet, we’re pretty happy that it’s this way because it tells us that space is all equivalent. There’s no place that’s any more specialized than any other.
Also, the space goes on forever and ever. But it also has a finite amount of stuff in it, distributed uniformly. Okay, sure, that sounds obvious, too. Until you sit with that just a little longer. How can something go on forever, have a finite amount of stuff in it, and be uniform throughout?
I’ll wait.
Okay, here’s how I picture this. I’ve invented a universe that I actually can step outside of. In fact, I can actually draw it on the page. I call it Circleland.4 Imagine that you can live on the line of the circle, but you can’t understand any space beyond that inked, one-dimensional curve. In fact, you can’t even tell that it’s curved or that it’s a circle. You just know that the line you can travel and see goes forward and backward, or left and right—I’m not sure how a Circlelander thinks about direction since there’s only two of them. At any rate, your only sense of space is along the one dimension that just keeps going, and you can only go two different directions. We, here outside of that page, might feel sorry for Circlelanders, but they don’t know any different, just as you don’t know anything other than three dimensions of space. After all, what else could there be? Your imagination might be a little bit limited simply based on your existence.
I bring this up because it gives us a useful way to picture space from the outside. We don’t normally get a chance to do this with the space we’re already in, so I like looking at other simpler spaces so I can imagine what extra dimensions look like.
Hold this picture for a moment.
Back in our own universe where we move around in three spacial dimensions as time moves us forward in another, we can observe distance galaxies that HST slurps up with such aplomb. In the early 1900s, Edwin Hubble observed that all distant galaxies were getting farther away from our own, and the farther away they are the more quickly they seem to be moving5. A rough sketch of this might look something like this, with arrows representing the perceived recession of galaxies from our own location:
To me, at first glance, this looks like we’re at some center and everything is flying out away from us; and it even looks as though the stuff that’s farthest has had a chance to move more and is now going faster, as if it had seen us coming. But this doesn’t make sense for a few reasons. First, we’ve realized that every time we think we’re at the center of the universe—or at the center of anything, actually—it becomes clear that we’re wrong. So we should have learned to inhibit that reaction by now, though that’s hard for us humans. We like to be at the center of lots of things.
Maybe more convincing is the overwhelming evidence that the universe is the same everywhere and in all directions. If that’s the case, then we can’t be at the center. In fact, an infinite and smooth universe doesn’t have a center that you can exist at. This is hard to picture, but having Circleland as an analogy helps.
The center of Circleland can’t be visited or even seen or even pointed to by its residents. They only point along the surface of the circle. But if their circle gets bigger, expanding from that center they can’t see, look at what happens:
Your Circleland neighbors all are getting farther away from you; but if they are looking back at you they will claim that you are the one becoming more distant. In a sense you’re both right, and you’re both wrong. Not one of you is moving, it’s just that the space between is getting greater6. Everyone will agree on the observation that you are all getting farther away from one another. More interesting still: There’s more space between you and your more distant neighbor, so as the circle gets bigger that recession is faster. In other words, the farther apart two points are to begin with, the faster they’ll separate. Again, everyone will observe the same features of this expansion, feeling as though they’re staying in place (which is basically true) while everything else is getting more distant (also true, but not for the reasons we might naturally assume).
Spend a little time with the idea of living on Circleland, and then think about the similarities to our own sense of space. I can’t point to the center of our own universe, but our expansion is such that we must be limited by our existence in the wretched prison of only three dimensions of space. There could be an expansion from some central point in another dimension, even if that point doesn’t exist in our standard three dimensions.
Chew on this for a second. Maybe go get a snack. Take a deep breath.
Once you’re ready, consider this: If everything is expanding, then where did it all come from?
To me, this is the easier problem to solve. You just take the current pattern of expansion and you rewind7 it back as far as you can. Then you can answer the question, Where does it all start?
In Circleland, it’s pretty clear that the start—and this would be the start of some kind of clock for the entirety of space’s existence—would be when the space itself was all condensed into a single point. You could say that it’s really really small, although at the same time it’s the entirety of an infinite universe. Ah, the paradox. I’d like to suggest it’s like some kind of poem or song, but the idea isn’t that it’s metaphorically small and big at the same time. It truly is both of these things at the same time.
This start from a what’s known as a singularity that holds all of our physical existence and marks the beginning of time is referred to as the Big Bang. This was originally supposed to be a sarcastic description of the ridiculousness of the whole idea, but the name stuck. To call it “Big Bang” is both an understatement and a ridiculous embellishment. It’s not just a “bang” or “big.” It’s everything’s beginning. But it’s also not an explosion into space, but the breath that inflates the very structure of space itself. As with so many things, I don’t really know what to tell you to make of this. It’s big and subtle and everything and very little all at the same time.
To be sarcastic about a “big bang” feels merited in so many ways. It’s a ridiculous idea, audacious to claim that we know the beginning of the universe and the ability to rewind 13 billion years to describe the very moment in which the existence of all things began. You should very definitely be asking, How do we know that?
One piece of evidence is the very simple idea of taking the expansion we currently witness and rewinding it. While the process and details here are not simple, the basic idea is. When you look for patterns in motion you can extrapolate to see where the simple rolling ball has come from and where it’s going. The idea here isn’t much different. We see a certain pattern and we understand the basic rules. We can re-create the scene from those basic principles, and it’s easy to go back to a beginning point from that.
But this certainly shouldn’t be all that we use to make the claim. There should be more evidence to search out. So, we think about what an early, dense universe would feel like. Lots of subatomic particles in very close confines with lots of energy. Unlike our current regime in which particles are spread out and generally repulsive, these charges particles would be forced together in nuclear fusion. This produces two things: New forms of matter and the resulting energy from these reactions.
The most basic and prevalent element in the universe is (and should be) hydrogen. It has a single particle at its center (a proton) that is completely uncomplicated by anything else. To make an element with anything else at the center you need to form these from smaller pieces. This happens in the center of our Sun right now, but it would also happen in a dense early universe. The net result would be a big production of the next most complicated element, helium, with its two protons and (typically) two neutrons. So, you would predict that if the big bang were a real occurrence, you should see higher amounts of helium than other elements besides hydrogen, and sure enough we do: about a quarter of the known matter in the universe is helium, way more than what stars could have produced on their own.
And also, there’s that energy. The cosmic microwave background, a radiated energy that would be everywhere throughout the universe, even as it has continued to expand, is a predicted indicator of this. You “see” some of this background energy in static on a television channel connected to an antenna but picking up no programming8. We can also study this and see that the energy is really smoothly distributed everywhere in the universe, though it’s just lumpy enough that you can imagine how the first seeds of galaxies formed from clumps of matter accumulating.
So all of this helps us to understand the really big picture of the universe. It’s a simple picture, but there are big implications and big questions, like what makes the expansion? If gravity structures space itself and there’s all this stuff, why isn’t there enough to pull it all back? You might think about scenarios where the universe had so much stuff that gravity was more dominant; or the case in which the universe expanded more quickly early on so that gravity’s hold on space was much less. In either case you wouldn’t be here to be conscious of these very questions. It’s likely that there’s no other universe that you could exist in. On the other hand, there’s no other there must be multitudes of other universe possibilities, none of which could have had the right conditions for self awareness, not to mention scientific study.
But it’s more than simply the right universe. To be you, there has to be a galaxy with the right about of space and time, sure. But also you have to have more elements than simply hydrogen and helium. Carbon, nitrogen, oxygen, and so much else doesn’t come pre-fabricated in the universe we’re describing. You need more time and you need some kind of factory to produce the elements that make chocolate, Doritos, kittens, beer, and us.
In truth, there’s quite a bit more to contend with here. Based on the overall proportions of the universe, you’d think we should have more hydrogen and helium, but it’s not as pervasive on Earth as on other, cooler planets. There are some interesting dynamics going on there, but for now let’s focus on the elements we deem essential to Earth and our existence.
We organize the elements on this periodic table. Essentially, this should be your ingredients label. This codes elements according to when they were discovered by humans:
It’s interesting to see that when things were discovered isn’t necessarily in any kind of order. There are some surprises, like the fact that helium eluded us for so long even though it’s the second most abundant element in the entire universe. Part of the reason is that helium doesn’t interact with other elements very often. The other reason is that it isn’t as abundant on Earth as it is on other planets or the Sun.
Anyway. I just thought you should know that or stick it somewhere in the back of your psyche for some other time when you’re wondering what to think about. The real task at hand right now is to question why we have anything beyond hydrogen in the first place. All the rest of it has to have evolved in some other fashion. It turns out that the energy factories of stars have to convert one form of matter to another, and the generalization of this process (known as nuclear fusion) is that you end up with elements—waste products, really—that are higher up on the periodic table. This other version of the periodic chart shows the various origins, as far as we know, of these more complicated and essential (to us) elements:
In a nutshell, the materials that you are assembled from have to have come from really energetic reactions that combined lighter elements together. Carbon, for example, would in most cases be formed by three subsequent collisions and fusings of helium. But that isn’t very likely unless the helium is really close together, moving very fast (we’ll see later this means high temperatures), and there’s a whole bunch of it really concentrated. This is exactly the kind of environment you’d expect in the core of a star.
The trick is that if we’re made of stuff that was sourced in other stars, then those stars would have had to have already cycled through their entire existences and then shed all their materials for us to re-form in the creation of another star. Our Sun, then, is a recycled collection of parts from which we get to rebuild. You are star stuff, as they say. What you are created from and what you continue to build from and what you continually interact with (breathing, eating, touching, etc.) has all been on the insides of another distant, long forgotten star.
I can say with great confidence that I know this isn’t all there is to it. You aren’t simply the byproduct of a universe with just the right conditions, nor are you the simple amalgamation of elements that happen to have been recycled in long dead stars. Of course there’s more to figure out. The nature of life itself is way more than the sum of these elements or the final outcome of all these events. But this story—a universe that gives time and space for the development of elements that can then be use in the creation of compounds that can be stirred together in the right conditions and temperatures and stewing to allow for Doritos and kittens—still has more to it. Physics is a big part of this, and we’ll keep working out those pieces.
Yesterday in class we talked about what it means to be the day of the “equinox.” We related this to the “equator” and to “equal” amounts of sunlight and darkness in our day. But I also remembered that this meant something about where you could expect to see a sunrise or sunset. That made me want to go watch the sun going down that evening.
Where I live, the streets are lined up in a grid lining up north-south and east-west. We also live up on the side of mountains where we can get a good view of the setting sun. So I went out that evening for a walk as the sun was setting into the really smokey horizon, sinking behind some distant mountains.
I really like our east-west streets, especially at this time of year and its counterpart six months from now. (I also liked that no one was driving on this stretch of road while I was in the middle of it.) This helped me get my bearings as I watched the sun continue to sink lower and slightly to the right–exactly where the street points. And, on other days, before and after the equinox and closer to the solstice, I can use these streets to show me where the sunset drifts as the seasons ebb and flow. It’s fun to watch this change through the year, and even to take photos of the different locations of a sunset over time.
I also posted a cropped version of this photo here on Instagram, but I think I like this long, tall perspective better.
A few years later, here’s a couple more examples of images taken on these east-west streets. These are taken a week apart from one another:
I like to send people into elevators with scales that they can stand on while traveling up and down. It’s a great exercise because they get to see some physics that they are actively a part of. At the same time, it becomes a nice conversation piece as different, surprised observers come in and out of the elevator we’ve turned into a laboratory.
I spent some time myself on the scale on an elevator, and I made a point of recording a round trip from the bottom floor to the top and back again.
I think it’s really important for you to know that this scale, like many, is a little sticky and is probably only trustworthy within a pound or so. That is, I think anything that between 158 to 162 pounds is really the same. Keep that in mind as you watch.
You can watch the video as many times as you’d like and look for connections between the motions of the elevator and the readings on the scale. What patterns do you see? What do you think the cause and effect relationships are? In other words, what makes the scale reading change; and what does not cause the scale to change from its normal reading?
This might inspire other experiments you can do on elevators. Does it matter if the person is bigger or smaller? If the elevator is faster or slower? What if you were on a roller coaster or other ride that might move you in more drastic ways? Can you model how the pushes and pulls on the rider would change?
I made a new video, this one without captions but a smoother responding scale. I think it could be useful for another round of observations, or even as a place to start:
I love to do this lab or one similar to it in person, but you can also conduct an investigation about motion on your own. I’ve created some videos that you can use to collect data (and maybe these will inspire you to setup a situation from which to collect your own data) and I’ve also given you a little bit of video instruction to help out.
Here’s the basic idea: You want to figure out how to characterize motion, but all we can really measure directly is a position (“where”) and a time (“when”). We look for changes in these two things to describe motion.
I’ve just found a pool ball and a smooth table that the ball will roll on. (Like I said, you could do this as well, but it turns out I have a really nice setup for this.) You will want to compile some data about when (time) the ball is in different locations (positions). By getting this motion of the ball on video, you have the ability to repeat the same motion over and over and collect whatever data you need. In this case, I’m suggesting that you collect data for the time it takes to go from the start position of 0cm to another given position. I’ve marked increments of 10cm, so you can get the time it takes to get to the 10cm mark, the 20cm mark, the 30cm mark, and so on. The biggest distance I have marked on the video is 120cm. By replaying the video and running your stopwatch 12 different times, you can get 12 different data pairs of position and time.
I explain this here:
Then, you can jump into collecting data. Start with this video of the pool ball on a flat table. There’s two different versions of the motion, one in real time and the other in slow motion. Just pick one of these.
Like I said, you can pause and go back over and over, each time finding the time it takes the ball to go from 0cm to another mark on the table. Record those times with their corresponding positions in your notebook.
Then, you can do the same with this video of a ball rolling on a sloped table:
Once you’ve made all your measurements, your data can go into a spreadsheet or another table, and then from this you can create a graph. By tradition, and so that we can all compare our graphs to one another, your graph should have the positions on the vertical axis (“y-axis”) and the times on the horizontal axis (“x-axis”). So, a blank version might look like this:
But you’ll be filling this in with your own data. You can do this by hand, of course, but it’s also straightforward to have a spreadsheet (Excel, Google Sheets, etc.) make the graph for you as you input your data. To give you an idea of what I mean and to get you started, here’s a template for a spreadsheet that you can copy or download. You can then edit your own version to your heart’s content. I’ve set this up so that as you input data in the appropriate columns you should see the graphs form magically, all by themselves. You’re also welcome to change the settings for the graph, although I’ve tried to make it so you don’t have to.
Enjoy! I’m excited to see your data and the patterns your data create. You’ll be thinking about why it looks this way and we’ll talk about what this all means. Your assignment will tell you what I’m looking for in your report.
In class, we worked together to make sense of data. We usually think of “data” as something that comes in numbers and graphs, like it did with pendulums and with motion data collected in lab. But it can take many forms, like this example we imagined of indentations on some sandstone:
(This is taken from a lesson often referred to as “Tricky Tracks.” An example is here, though the idea goes back a long time. This version comes from the National Research Council1.)
The fun thing about revealing this bit by bit is that we can start to imagine the possibilities and where this collection of observations is going to lead us. We made some points in our discussion that, even though I asked “what do you see?” many times we start to go straight to what we interpret. We have to be careful about this distinction. At the same time, there’s a lot of power that our sense-making adds to the observations. We start to see patterns and possibilities, and the way that we connect these observations to other things we’ve seen (other big and small organisms, predator-prey relationships, parent-child relationships, not to mention the idea of dinosaur tracks or bird tracks in general). How we find meaning in these data is important. We have to rely on the data and be ready to change our ideas if we find new, contradictory observations; but we also get to construct a new idea that the observations don’t tell us directly.
That was the point of where I took you next, suggesting that you look at the following set of words as if they had been spilled on a parking lot and you had to reconstruct their origin:
This isn’t a real scientific situation, but it’s something that’s a lot like our Tricky Tracks scenario or the way that we figure out the Earth goes around the Sun or how we figure out how matter is made out of lots of small particles we can’t see directly. We take all this evidence and put it together into patterns, knowing about other patterns and using our knowledge of the data at hand. For example, we know that words often come from stories, and we can start to imagine how these ideas could have been strung together. We might have something out of order before we get more information; and we might even have something really backwards at some point. For example, “crane” is a piece of equipment but it’s also a bird, and it’s also a verb, something we might do with our neck and head. But in the context of movers and dangles, we start to put together a possible use of a tall crane dangling a piano. Oh, and the “stories” seem to fit well with this, as long as they’re referring to levels of a building rather than narratives and tales. Though it could be both.
We also had to know a little bit to make more sense of this. “Steinway” is a famous line of pianos, but that isn’t necessarily familiar to you. “April” could be a month or a name of a person, though we start to imagine it’s about the calendar and season when we combine it with snow—something that might be surprising and story-worthy, but still possible.
There are lots of other examples of how different meanings and interpretations can get pulled into this. We’d always want to be able to look for more data and see if those fit as well. We’d also want to be able to compare this data set to others and see if there are similar patterns. When Venus was first observed with a telescope, for example, Galileo was able to see that it went through phases, like the Moon. But the pattern of apparent sizes and phases it goes through is different than the Moon’s, and this tells us something really important about orbits and positions of planets.
One of the most interesting things about this exercise (to me, at least) is how we all come up with very similar stories based on these words, for the most part. (There’s always a new, creative solution to this puzzle, I’ve noticed. That happens in science, too; and it’s really important that we allow for these when the data support them.) Nature will never directly reveal to us the answers to all our questions—we can’t go back in time and really see what happened between the two creators of the footprints we observed—even though we get really consistent, testable explanations. In this case, though, I’m happy to reveal to you where these words came from. It’s one of my very favorite poems, written by Taylor Mali, an advocate for teachers and teaching. It’s called Undivided Attention.
I like this exercise a lot as a way to help us understand how we create explanations from observations, and how that is more interesting than you might first imagine. But I’ll admit that I love doing this in class so that I have a chance to read this poem. It’s hanging over my desk and it’s often the last thing I see before I step into a class.
For your lab, you’ll be investigating what’s known as the “hot chocolate effect.” You don’t need to know anything about this effect and you certainly don’t need to try to look it up or read about it. (This usually just makes things worse.) Instead, take a look at my intro and then use this as a starting point for your own investigation:
Truly, I hope you always tap the bottom of your mug from now on when you stir hot chocolate.
(I created this other post for the general public about this effect, too. I think the effect worked better in this video.)
One of our first tasks has been to collect some data on an object known as a “simple pendulum.” There’s no perfect simple pendulum, but instead this term is used to describe something that swings back and forth with all of its mass stuck to the end that’s swinging. A yo-yo swinging back and forth is a good example, or maybe a tetherball at the end of its cord; but lots of things are really close to a perfect simple pendulum. In fact, I was counting on the fact that you could find something that would work, likely right there in front of you.
Here are the instructions I gave for setting this up:
Then, you each collected data from your own objects: keys at the end of a lanyard, the adapter at the end of an electrical cord, a weight at tied to the end of a string, etc. These all work — though you might wonder if it’s okay to all be using different things if we’re going to share the data with one another. That’s a good question, and we’ll get to this.
After everyone reported data for the length of their pendulum and the time it took to swing 10 times, I took all of that and made a graph. Here’s an example:
I love this graph for a few reasons. First and foremost, you each collected ONE piece of data, and that single piece of information didn’t tell you very much. But now we have it in the context of all the other data. You can see how yours compared to others. More important, you can see if there are any patterns in these data. To me, it looks like there are. I tried to sketch some of what I’m seeing right on the graph:
MOST of the data show that the shorter strings take the least amount of time to swing, and the longest strings take the greatest amount of time. In addition, it looks like those times change most drastically when we change the shortest strings, and they change less for the longer strings. This makes a kind of curve that seems to be getting flatter and flatter as you go from left to right (shorter to longer strings). There’s a pattern here, and your data likely fits right into it. But we needed lots of these experiments in order to see the bigger picture. In fact, now we can even imagine that this curve could be described mathematically. Nature actually abides by this mathematical relationship — or maybe it even invents the mathematical relationship for which we needed to invent the mathematics!
For now, I’ll leave you with a few questions:
Whenever two objects collide or interact in any way, we might start to talk about “Newton’s 3rd Law.” I should say from the outset that I don’t like starting with this label, because I think we have to assemble a bunch of experiences before we really have a feel for what we’re talking about. At the end of these notes, I finally get to some experiences we can look at in class (or socially distanced across the internet). If you’re reading these notes, that’s very likely where you started. This is just meant to circle back.
Newton’s 3rd Law really bothers me. Here’s why: It’s so easy to give it a quick definition, something like “equal and opposite” or “action and reaction” or “forces come in pairs.” But because these quick descriptions are so, well, quick, it’s hard to really see the significance of them. Newton’s 3rd law tells us that there are always two bodies responsible for forces, and so there are always two forces, one on each of the objects. These forces are the “equal and opposite” forces.
Let’s consider this in more detail and test more situations.
First, let’s think about a collision, since this is the most obvious place where two bodies interact. A collision never happens with just one object. One thing has to run into the other. As that happens, both bodies are “feeling” something. It’s easy to imagine this when to two objects are comparable: two ice skaters collide, or a car runs into a tree, or one curling stone runs into another. In other cases, we didn’t think of the two bodies as colliding so much as they were just in contact with one another, but it’s the same kind of situation: I sit on a chair, or two stationary ice skaters push one another, or the tires of a car push backwards on the road. And, it could be that the forces aren’t pushes, but pulls: two tug-of-war teams are pulling on the same rope, or a child is sitting in a swing, or, even, the Earth and Moon pull one another using the force of gravity.
As we think about each of these situations, what is our model for how these interactions take place? That is, what are the pushes and pulls? We’ll start with a rope that two people hold, thinking about how the pull on one person compare to the pull on another. We can also think about the details of pushing forces, such as Adam pushing on the wall. What about other cases?
It’s hard to really collect evidence for how forces compare. What if we had some kind of spring-bumper in between colliding objects? What would we expect of these as they experienced different forces? What would you expect spring-bumper cars to exhibit as they were colliding in different situations?
In class, we consider a lot of different situations where we vary the masses of the two objects colliding (same masses or a big vs. little mass) and we also vary the speeds of the two objects (both moving towards one another or one running into another that’s originally at rest). We can predict what we think the relative forces will be.
The “spring-bumper” mechanism that I imagine is exactly what this physics teacher has setup in his own classroom. For his students’ benefit, as well as the rest of us, he’s compiled slow motion video footage into one file, and he’s also supplied some background info and access to the original data, if you so desire. This is all available here in his class notes. You can also catch the video right from the YouTubes.
There’s some amazing revelations, and I think that seeing the footage like this is just really hard to believe on a gut, instinctual level — even though Newton’s 3rd law is so easy to state! Why is this hard for us? I think it’s because we forget about the fact that we are observing both forces and changes in motion (which is described by Newton’s 2nd Law) at the same time, and we confuse these. Two paired forces in a collision can be exactly the same size, but they’ll produce very very different accelerations — changes in motion — depending on the mass of the objects experiencing the forces. We observe most directly the changes in motion, and we erroneously equate this with force. So, the mosquito that hits your windshield and the car both experience the same amount of force, but they go through much different changes in their respective motions, much to the chagrin of the mosquito.
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* For more information or for fun, you could view a classic episode from Dr. Julius Sumner Miller on Newton’s 3rd Law. Or, take a look at this PhET simulation.
The concepts of force, matter, and energy get mixed together and confounded. For example, it’s easy to say that forces, matter, and energy are all in the following photos. But these are all distinct from one another, even though they’re related. Where and how do you see forces, matter, and energy in these?
Generally, I don’t like to define words up front. In this case, I just want us to start painting edges around these terms, not so much to define them as to make sure we recognize that they’re all playing in different but complementary fields.
A force is an action. It’s the push or pull between two objects. These always come in pairs exerted between two objects, one on the other and the other on the one.
Matter is stuff. You can put it a container and close the lid. Sometimes that container will need to be really, really big, but if it’s a thing or a collection of things and takes up space, you have some matter.
Energy — oh, energy. This, to me, is the hardest because it feels so obvious but also isn’t either a piece of something nor something I push against. It’s a property of matter that describes what the stuff is doing or what it could do. Energy is transferred or changed in matter by forces (even though not all forces do this).
Clear? No, I didn’t think so. For now, let’s be content but confused with the idea that these three categories are completely different, like Doritos are different from love is different from sound. You know that one might have relevance to the other, but you can’t compare Doritos to love to sound. They aren’t even on the same plane.
Collectively, our class recorded positions and times of a bowling ball. This sounds like a funny thing to say unless you were there to witness it. The bowling ball got rolled down a long hallway, and groups were able to synchronize their timing devices and associate a time with a given position of the bowling ball as it passed by. After a few different trials of this, we collected back into the room to share data. After all, the data are all only interesting once we see them all together. That’s an important point of the exercise.
We didn’t have time to compile all of our data from all four trials of the bowling ball rolling, so I left it as “an exercise for the reader,” as they say. (Sometimes in physics it seems like this is what we call the really hard problems, as though the textbook author or teacher doesn’t actually know how to finish the problem. I’m guessing that sometimes there’s some truth to that.) So, we set up a place where everyone could contribute their data online, and as those points were entered in a graph was created to display what the data look like. Right now, as I’m writing this, students are contributing their data points, and, so far, here’s what a graph looks like:
Almost everyone has put in their contributions, but two of our research groups haven’t yet submitted their data. (Don’t worry, it wasn’t due yet and I was getting ahead of myself.) You can see these points in their default positions on the left side. I’d just entered false numbers in for these at first, so the points show up, but not in the right place.
But we know where they’re going to go, don’t we? There’s a pattern here that the rest of the data is describing for us really clearly. If graphs could talk, this one would be screaming at us about the trend that’s taking place. If those last two data points come in and are not fitting into the line that’s inferred from the rest of the collection, we’re going to be really surprised and we’d probably even question what went wrong.
In fact, not only do we know about where these next two points are supposed to go, but we know an infinite amount of information from this graph already. The bowling ball was in all of the places in between all of these data points, all of the positions and times represented in this pattern. But we didn’t need to get an infinite number of stopwatches and recorders of the bowling ball. By knowing about only ten points in time and space, we could construct all of the information about all of the travel of this bowling ball. This is incredibly powerful. When was the last time you figured out an infinite amount of information and were able to represent it in one picture? In science, this is just what we do.
First, this exercise — the collection and organization of data, the analysis and pattern-finding via the graph — tells us about patterns and how we use them to make sense of data. No single point of data was important. And, really, even though the collection of the data was essential, it wasn’t this assembly of ten points that was important. It was the overall trend that the collection showed to us. It shows us clearly what would happen in between all of our recorded observations; and it also shows us what happened even before we were collecting data. (Look closely: Can you describe where the bowling ball was when the time was at “zero?” What does that mean?)
Second, it tells us that Nature plays fair. Nature is understandable, predictable, and consistent. If it didn’t play fair and play by the same predictable rules all the time, we couldn’t do science. In fact, we couldn’t have even imagined the existence of anything scientific. Never would we have even thought to invent science if we didn’t have a universe that is operating in a consistent way. We probably can’t even imagine a universe that wouldn’t behave that way. We take it for granted that it plays fair because we’ve never known a universe that does not. (Okay, once in a while “life isn’t fair,” but that generally has more to do with the whims of people, and they’re really complicated bundles of nature, making it hard to get all of the right data to predict what they might do, not to mention why.) If Nature did not play fair and consistently, we would now have only ten or twelve bits of information that have no connection to anything bigger. Instead, we know everything.
Finally, that pattern and the interpolation of what nature is doing tells us something very specific. This is a bowling ball rolling down a hallway — to be sure, a questionable practice, but one that pays scientific dividends. That ratio of how far (position change) to how long (time change) is constant. We see this by virtue of the fact that the slope is always the same. What’s remarkable is that no one is doing anything to the bowling ball except for making sure it doesn’t run into anyone. And yet, it keeps going in exactly the same way throughout the trip. This is remarkable and miraculous, at least to my common sensibilities. How does the ball know to keep going, and especially to keep moving at exactly the same pace? Also, to be clear about our amazement, we don’t know why this is. It just happens. It’s not something that we could logic for ourselves without having rolled the bowling ball or some other object — maybe a hockey puck on ice or a craft through space, for example. We trace this kind of finding and this kind of data collection back to Galileo in the early 1600s; and, Newton used this to build the same physics that we use to run NASA’s space programs. We call this particular rule, “Newton’s 1st law,” but it’s more appropriate to say it’s the wonderful nature of motion. Motion is natural and consistent, not because we are doing anything to make it so, but because we are not doing anything to the bowling ball while it’s rolling. We’ll be trying to make sense of this.