physics1

I’m Walter Lewin. I will be your lecturer this term.  In physics we explore the very small to the very large. The very small is a small fraction of a proton, and the very large is the universe itself. They span 45 quarters of magnitude.  The one with 45 zeros.  To express measurements quantitatively we have to introduce units. And we introduce for the unit of length: the metre (m), and for the unit of time: second (sec), and for the unit of mass: the kilogram (kg). You can read in your book how these are defined and how these definitions evolved historically. There are many derived units which we use in our daily lives for convenience, and some are tailored towards specific fields: we have centimetres (cm), we have millimetres (mm), kilometres (km), inches, feet, miles. Astronomers even use the astronomical unit, which is the mean distance between the earth and the sun. And they use light years, which is the distance that light travels in one year. We have milliseconds, we have microseconds, we have days, weeks, hours, centuries, months. All derived units. For the mass we have milligrams, pounds, we have metric tons. So lots of derived units exist. Not all of them are very easy to work with- I find it extremely difficult to work with inches and feet. It’s an extremely uncivilised system. I don’t mean to insult you.  But think about it – 12 inches in a foot, 3 feet in a yard.. it drives you nuts!! I work almost exclusively with decimal, and I hope you will do the same during this course, but we may make some exceptions. I will now first show you a movie which is called ‘the powers of ten’. It covers forty orders of magnitude, it was originally conceived by a Dutchman named Kaiz Hooker in the early 50’s. It is the second generation movie and you will hear the voice of professor Morson, who is a professor at MIT. ‘The Powers Of Ten’ - Forty orders of magnitude. Here we go.. [the clip was removed from the video]
I already introduced, as you see, there are lengths, time and mass; and we call these the three fundamental quantities in physics. I will give this the symbol capital ‘L’, for lengths, capital ‘T’ for time, and capital ‘M’ for mass. All other quantities in physics can be derived from these fundamental quantities. I give you an example: I put brackets around here, and I said‘speed’ ([speed]), which means the dimensions of speed. The dimensions of speed is the dimension of length divided by the dimension of time. So I can write for that [speed] = [L] / [T]. Whether it is metres per second, or inches per year, that’s not what matters – it has the dimension length per time . Volume would have the dimension of length to the power 3. ([volume] = [L]^3). Density would have the dimension of mass per unit volume. So that means length to the power 3. ([density] = [M]/ [L]^3). All important in our course is acceleration. We will deal a lot with acceleration. Acceleration, as you will see, is length per time squared – the unit is metres per second squared. ([acceleration] = [L] / [T]^2). So all other quantities can be derived from these three fundamentals. So now that we have agreed on the units – we have the metres per second, and the kilogram – we can start making measurements. Now all important in making measurements, which is always ignored in every college book, is the uncertainty in your measurement. Any measurement that you make, without any knowledge of the uncertainty, is meaningless! I will repeat this. I want you to hear it tonight at 3 o’clock when you wake up. Any measurement that you make, without the knowledge of its uncertainty, is completely meaningless. My grandmother used to tell me that, at least she believed it!.. that someone who is lying in bed is longer than someone who stands up. And in honour of my grandmother, I’m going to bring this today to a test. I have here a set up where I can measure the person standing up, and a person lying down. It’s not the greatest bed, but lying down. I have to convince you about the uncertainty in my measurement because measurement without the knowledge of uncertainty is meaningless. And therefore what I will do is the following: I have here an aluminium bar, and I make the reasonable, plausible assumption that when this aluminium bar is sleeping- when it is horizontal- that it is NOT longer than when it is standing up. If you accept that, we can compare the length of this aluminium bar with this set up (vertical) and with this set up (horizontal). At least we have some sort of calibration to start with. I will measure it -you have to trust me. During these 3 months we have to trust each other.

So, I measure here 149.9 cm. However, i would think that, so this is the aluminium bar in vertical position, 149.9, but I would think that the uncertainty of my measurement is probabily 1 mm.  I can't really guarantee you that I did it actually any better.  So that's the vertical one.  Now, we're going to measure the bar horizontally, for which we have a setup here.  Opps, put the scales aside, so now I measure the length of this bar.  150.0, horizontally. 150.0, again, plus or minus 0.1 cm.  So you would agree with me that I'm capable of measuring plus or minus 1 mm.  That's t he uncertainty of my measurement.

Now if, the difference in length between lying down and standing up instead were 1 ft, we would all know it, wouldn't we? You get out of bed in the morning, you lie down, you get up and you go *clunk*, and you are 1 ft shorter.  We know that's not the case. If the difference were only 1 mm, we would never know. Therefore, I suspect that if my grandmother was right, that's it's probably only a few cm, maybe an inch. And so I would argue that if I can measure a length of a student to 1 mm accuracy; that should settle the issue.  So, I need a volunteer. You want to volunteer! It looks like you're very tall, I hope that we don't run out of...you're not taller than 7'8" or so?  What is your name?  Rick, Rick Rider.  Man~ sit down. I can't have tall guys here, come'on!  We need someone who is modestly in size - don't take it personal, Rick.  Ok, what is your name? Zack. Nice day today, Zack? Yeah? You feel alright? First lecture in MIT? I don't. Ok, man, stand there. Yeah. Okay, 183.2, stay there, don't move. Zack, at his vertical, what did I say? 180...? Only one person. 3? Come'on. .2? Okay. 183.2, yeah. And the uncertainty is off about, 1, oh, this is cm, 0.1 cm.  And now, I'm going to measure him horizontally.  Zack, I don't want you to break your bones, so we have a little step for you here.  Put your feet there, woo, let me remove the aluminium bar.  Don't, watch out for these scales, don't break that, cause then it's all over.  Okay, I'll come on to your side, I'll have to do that. Yeah, yeah, relax.  Think of this as a small sacrifice for the sake of science, alright? It's not, ok, you're good? You're comfortable? You're really comfortable, right? Okay, you ready? OKay. 185.7. Stay where you are. [10:30]