The main news is that Israel invaded Lebanon after a few preliminary forays, but for a day or two we’ll have lighter stuff. That includes this contest submitted by mirandaga. His challenge is indented:
Here’s a little game you might share with the troops to lighten things up a bit. Think of a movie actor and movie character that are so inseparably linked that you can’t imagine anyone else playing that role. Here are five that come to mind (I can’t think of any female actors/roles, but perhaps others can): Clark Gable as Rhett Butler in “Gone with the Wind” Gregory Peck as Atticus Finch in “To Kill A Mockingbird” Anthony Hopkins as Hannibal Lecter in “The Silence of the Lambs” Jimmy Stewart as George Bailey in “It’s A Wonderful Life” Gary Cooper as Will Kane in “High Noon” Dan Akroyd and John Belushi in “Blues Brothers” (And yes, my age is showing.)I’ll add these as my own choices. I’ll show a scene from each:
Marlon Brando in “The Godfather” series. The opening scene:
Sean Connery as James Bond (none of the other six actors who played Bond held a candle to him; they hadn’t the suavité).
Jack Nicholson in “One Flew Over the Cuckoo’s Nest. I can’t imagine another actor doing that part.
Humphrey Bogart in “Casablanca”. No comment needed.
Woody Allen in “Annie Hall” (I love this scene!)
James Cagney in “Yankee Doodle Dandy” (when I was a kid I used to watch this every Fourth of July, and this was my favorite scene). Cagney was a great dancer. Sadly, it’s no longer shown:
Another great scene from that movie: Cagney dances down the White House stairs after getting a medal from Franklin Roosevelt and then joins a war parade playing a song he wrote: “Over There”.
George C. Scott in “Patton”. Who can forget this scene?:
I previously put up pictures by Rik Gern showing his front yard (see here); now we get to see his backyard in Austin, TX. The captions are indented, and you can enlarge Rik’s photos by clicking on them.
The last batch of pictures I sent you was from my front yard, which I try to keep nice and trim for the neighbors. The back yard is a more casual place and I generally don’t like to mow or remove anything that grows there until I can see what it’s flowers look like.
This delicate looking little flower (first photo) is Common Hedge Parsley (Trills arvensis). I had a hard time determining whether it was Hedge Parsley or Poison Hemlock until I found a website that showed the difference in the appearance of the seed pods (second photo). It’s also home to a spider of some sort. Spiders and their webs are all over the back yard!
Prostrate Spurge (Euphorbia prostrata) sounds like something you should consult your urologist about, but it’s just a common weed that thrives in sunshine and dry soil. It grows rapidly, but is really easy to remove. It’s got a woody stem, like a miniature tree branch.
Summer rains brought a bunch of Boletus mushrooms. As for the species, your guess is as good as mine. There’s something about the underside that has a spooky but elegant look.
Speaking of spooky, now we come to the rough part of town, or at least of the back yard.
This Saw Greenbriar (Smilax bona-nox) (6) looks like it’s armed with knives—don’t mess with it or it’ll cut you!!
Also looking rough is this aged Common Sunflower (Helianthus annus). It’s youth and beauty gone, it now looks like a cranky senior citizen—with hairy legs!!!
This detail of the stalk makes it look like a menacing plant, but you can actually grip them with your hands without discomfort when it’s time to pull them, though you’d get itchy if you did it for a long time. If you look closely you can see tiny spider webs all up and down the sides of the stalks.
These front-and-back pictures formed the basis for the following two images which were made by combining them and putting them through the photoshop blender.
This Seussadelic image might be from Dr. Seuss’ unconceived, unwritten, and therefore unpublished book, “If I Ran The Botany Lab”.
The last one, “The Cosmic Cowboy Rides Again” is sort of a tribute to Texas music legend Doug Sahm*.
I’m often asked two very natural and related questions.
It’s true that the speed of light does seem fast — light can travel from your cell phone to your eyes in a billionth of a second, and in a full second and a half it can travel from the Earth to the Moon.
And indeed the energy stored in your body is comparable to the Earth’s most explosive volcanic eruptions and to the most violent nuclear bombs ever tested — enormously greater than the energy you use to walk across the room or even to lift a heavy suitcase.
What in the name of physics — and chemistry and biology — is responsible for these bewildering features of reality? The answer is fascinating, and originates in particle physics and the resulting structure of matter. It is surprisingly intricate, though, so I’m going to approach this step-by-step over three blog posts. Here’s the first.
Refining and Rephrasing the QuestionsWe should start by recognizing that the second question has two sub-questions, one qualitative, and one precise:
We’ll see that questions 1 and 2a are almost the same question, and have largely the same answer. But as we’ll see, they aren’t phrased well yet.
The problem is that “fast” and “gargantuan” are relative terms. I can run much faster than a slug but much slower than a cheetah. I am huge compared to a bacterium, but not compared to a star. So we ought to start by restating these questions in relative terms; that will help us think them through.
To get us warmed up, I’ll start with a brief quote from my book, chapter 2.
“It’s well-known that light has a characteristic speed, which scientists call c ; this is the speed at which each individual photon travels, too. As scientists discovered centuries ago, c is about 186,000 miles per second. That’s fast, in a way. Our fastest spaceships don’t come anywhere close to that speed. Though my last car was with me for fifteen years, I drove it less than 186,000 miles. At the speed c , you could circle the Earth in a blink of an eye (literally) and travel from my head to my toe in a few billionths of a second.
“And yet c is also slow. It takes light more than one second to travel to the Moon, over eight minutes to reach the Sun, and over four years to reach the next-nearest star. If we sent off a robot spaceship at nearly c to explore the Milky Way, it could visit only a few dozen nearby stars during our lifetimes.
“You and I are small, so we think light runs like a rabbit. But the universe is vast, and from its perspective, light creeps like a turtle.”
The point of this quote is to remind us that we’re not the center of the universe. We are not annointed creatures relative to whom all cosmic facts should be measured. There’s nothing unique or special about the Earth or its size, mass or temperature — nothing materially unique about animals, about mammals more specifically, or about us. The way the cosmos works is not influenced by the objects of our ordinary lives. So our own perspectives are not privileged, and we should be aware that there are other perspectives, ones from which light’s speed is slow and/or from which the energy stored in a human is tiny.
To make our questions really meaningful, then, we ought to step back and ask not just how we view the cosmos but how the cosmos views us. From the universe’s perspective, the questions really are these:
For us to understand how the universe would answer these questions, we have to understand what “natural speed” and “natural energy” might mean from a cosmic perspective. So let’s start there.
The Natural SpeedThe quantity c is not just the speed of light, and so “speed of light” is not the best name for it. For instance, it is also the speed of gravitational waves. Even more important, it is the limit on the relative speed of all physical objects. That’s why I and many others often call it “the cosmic speed limit” — because that makes it clear that rather than being a property of light, it is a property of the universe. (Caution; there are lots of conceptual traps and subtleties here, some of which I’ve written about.)
This cosmic speed limit seems to be the same everywhere across the universe (based on our observations of almost unimaginably distant and ancient objects), and so every living intelligent creature in the cosmos can measure it. No other speeds are fixed and reliable in the same way. Compare it, for instance, with the speed of sound. Sound speed varies with temperature and with the material through which it travels, and so this speed is completely different in other planets’ atmospheres and oceans. It could never be used as a cosmic measure of speed that all intelligent species could agree on.
Nor should we think of human speeds of about 1 meter per second (about one yard per second) as “normal speed”. First, if we were peregrine falcons or sloths, we’d view human speed very differently. Second, the now-standard choice of “meter” to measure length and “second” to measure time is arbitrary. A blue whale is many meters long, very big in this sense. But a sufficiently intelligent species of whale wouldn’t use “meter” as their yardstick, and would instead likely define length using a “whaler”, comparable in size to a whale. We’d be a fraction of a whaler tall, and thus seem diminutive by that measure. Similarly, a sequoia tree would probably not want to use “second” as a time-frame; “hour” would be more characteristic.
So the precise way one defines distances and times and speeds, and what makes a length or a duration or a velocity large or small, are all species-dependent, planet-dependent, and perspective-dependent unless you use facts about the cosmos that everyone can agree on. And when it comes to speed, the cosmos has a view on this matter. It says:
“c is normal speed, because that’s the maximum rate at which information can travel from one place to another. No two objects can move relative to each other faster than that. No knowledge can be sent faster than that. There’s no other speed of comparable stability or of comparable importance. So typical objects should always pass each other at a speed that is a reasonable fraction of c.
“But, uhhh… WOW… you Earth-creatures are absurdly, ridiculously slow! Look at how you crawl around your planet!”
The Appearance of c2Setting aside the issue of whether c should be viewed as large, small or normal, why is it “natural” that the energy E stored inside an object should be related to its mass m by c2? My answer follows the logic of this post, which goes into more detail about the methods of “dimensional analysis”, one of physicists’ most important tools. You may want to read it if my explanation here seems too sketchy to you.
Einstein’s basic claim was that even a stationary object has energy stored inside it. The amount of that energy, he suggested, is reflected in its mass — specifically its “rest mass” m, which is the mass as measured by an observer who is stationary relative to the object. (For more details on rest mass and on various forms of energy, see chapters 5-8 of my book.)
Any relation between energy and mass must involve the square of a speed (or the product of two speeds.) We find this already in first-year physics. In pre-Einsteinian days, the motion energy (i.e. “kinetic energy”) of a moving object was understood to be equal to an object’s mass m times its speed v squared:
If you tried to replace v2 with v3 or v99 , the equation would become nonsensical. (As a physicist would say it: the units on the two sides of the equation don’t match.) It would be like claiming that the height of a tree is equal to the color of its leaves — two things of completely different character can’t generally be equal.
But back to Einstein’s claim that a stationary object has energy too. The corresponding formula can’t contain v, since a stationary object has v=0. Some other speed or speeds must appear instead.
Why should that speed be c? Well, it wouldn’t make much sense for an object’s energy/mass relation to depend on the speed of some other object. Imagine if the energy in my body were my mass times the square of the speed of some ultra-distant star. Not only would this be bizarre (and inconsistent even with Galileo’s relativity), what would the formula have meant before the star was born?
No, the relationship between energy and mass for stationary objects must be universal — cosmic — and so it can only depend on speeds that are properties of the universe itself. As far as we know, the universe has only one inherent speed: c. (In fact you can prove that Einstein’s conception of relativity would be inconsistent if there were more than one basic speed.) Therefore any relation between energy and mass must be of the form E = #mc2, where # is a fixed number that someone has to figure out. There’s no other equation that could logically make any sense.
Einstein knew this, of course, even before he wrote his relativity papers. So did all his colleagues.
The fact that the # is equal to 1 is partly a historical accident of definitions, and partly, given this accident, a matter of brilliant deduction and imagination. Click here for some details.Regarding the question as to whether E = 1/2 mc2 or E = 2 mc2 or E = 4/3 mc2, here physicists got a little lucky historically. The definition of mass was given in Newton’s day, and energy was defined later in just such as a way that, for pre-Einsteinian physics, the motion energy of a moving object is 1/2 mv2. There are sensible reasons for that definition. It is directly related to the definition of momentum as mv, mass times velocity, with no 1/2 or 2 in front. The definition of momentum was in turn was motivated by Newton’s equation F=ma, which defines what we mean by mass. If Newton had put a 1/2 in that equation, defining mass differently, then there’d be a 1/2 in Einstein’s formula too. But with the definitions that Newton and his followers used, the correct equation that matches nature is E=mc2 , with no numerical factor. That’s a nice historical accident; any change in the definition of energy or mass would have affected the sleek appearance of Einstein’s formula.
Now, why was Einstein the one to figure out that, with these definitions, the correct number in the equation is 1, when his colleagues had been trying so hard and getting so close for a couple of decades? He asked the right question, while his colleagues did not. More about that here.
So 2b is answered: in our universe, the only possible relation between E and m for a stationary object is E=#mc2, where # may depend on how one’s culture exactly defines energy and mass, but which happens, with our historical definitions of energy and mass, to be 1.
The Natural EnergyAnd so, from the universe’s perspective,
“The natural energy for an object with a rest mass m is something like mc2 . When the object is stationary, that’s exactly how much energy it has, and when it’s moving, it has more. And if it’s moving at a natural speed — some moderate fraction of c — then we already know from pre-Einstein physics that its motion energy will be something like 1/2 mv2 , which will be a substantial fraction of mc2 . In short, typical objects in the universe will be seen to carry internal energy mc2 and motion energy which is not so far from mc2.
“But you Earth-creatures … you are like frightened mice, keeping all your activities down to a tiptoe and a whisper! Are you trying to avoid being noticed? Are you cowards, afraid of any drama?”
The answer to the last question is “yes, absolutely”. But more on that in the next post.
Why the Energy Question is a Speed QuestionI’ve already now hinted at why the energy question 2a is the same as the speed question 1. The reason the energy stored in ordinary objects seems so large in human terms is that the speed of light seems so fast in human terms.
Again,
This means that the ratio of an object’s motion energy, which is easily observed in ordinary life, to its internal energy, which is hidden in ordinary life, is
This is extremely tiny if (v/c) itself is very small. And therefore, if we understand why v is so much less than c in daily life, then we will simultaneously understand why the energies of ordinary human affairs are so small compared to the internal energies of typical objects around us.
So when I return to this topic in an upcoming blog post, we’ll explore why particle physics itself assures that the speeds of daily life must be slow.
Stay tuned for the next post in this series!