Feeds:
Posts
Comments

Posts Tagged ‘Physics’

Anyone can launch something into orbit!

Posted in Physics, tagged , , on August 18, 2015| 1 Comment »

You probably learned about projectile motion in introductory physics class. If you throw something (a baseball, say) then its horizontal motion will remain constant, whereas its vertical motion will change under the influence of Earth’s gravitational pull. The result is a parabolic arc, right?

Well, no. Saying that projectile motion is parabolic is only an approximation.

In class, I “prove” that the motion of the baseball is a parabola, but in order to do so, I make the (reasonable) assumption that the effect of gravity is a constant. That is, I assume that the vector g (the acceleration due to gravity) always points in the same direction all along the trajectory.

This is actually not quite true, however. I’ve neglected the curvature of the Earth.

Now, this isn’t really a big deal when throwing baseballs. Suppose you toss a ball to your friend 50 m away. The vector g for you does point in a slightly different direction then g for your friend, but the angular difference is miniscule…it’s about 50/637,000,000 radians, or 0.00045 degrees. This is so small that I am comfortable pretending that the two g’s are actually parallel, and the derivation thereby leads to a parabolic arc.

But what if you don’t make that approximation? What answer do you get?

You get an ellipse. You get an orbit. And here’s the point of my post:

Every time you throw an object, the object is (temporarily) in orbit until it hits the ground.

Here’s the orbit of a thrown baseball (not to scale):

orbit1

Now suppose the Earth had the same mass, but was the size of the Little Prince’s home asteroid B-612, which is as big as a house. The orbit is the same, but this time the baseball doesn’t strike the surface:

orbit2

The takeaway is that all projectile motion is really orbital motion. I find this fascinating: you don’t need a fancy rocket to launch something into orbit. Your arm will suffice. It’s just that you need the Earth to not be in the way.

Advertisement

Read Full Post »

The dumbest person at the 1927 Solvay conference

Posted in Uncategorized, tagged , , , on April 29, 2015| 22 Comments »

I suspect there are hundreds of physics classrooms across the country that have the following poster:

10314603This is the CENCO (Central Scientific Company) poster of the famous 1927 Solvay Conference. I’ve been to at least three universities that have this thing on the wall, including my own institution, Western Carolina University, and my alma mater, Wake Forest University. Strangely, I can’t date the poster, although if you read the descriptions of the 1927 Solvay attendees, the poster lists Dirac as being dead and De Broglie as being alive. Ergo, the posters were printed some time between 1984 and 1987. I suppose CENCO gave the posters away for free as a promotional during the Reagan administration, and I’d guess most of those freebies are still hanging on the wall today. (Physicists don’t update their décor very often.)

I’ve spent a fair amount of time looking at this poster (sometimes, the life of a lab instructor is dreary). And, in all my time staring at these giants of modern physics, I’ve formulated one burning question:

Which of these people was the dumbest?

[Note: I used this site for a listing of the attendees in the famous photo]

Don’t get me wrong; I’m not claiming anyone in the poster is dumb per se. And I would never compare myself to anyone on the list. But logic dictates that one of the people here was literally the dumbest attendee; I feel a moral obligation to identify this person for posterity.

Most of the names on the poster are familiar to physicists, and most of the attendees are therefore out of the running. No one would ever seriously consider Einstein, Curie, Dirac, Bohr, etc. as being the “dumbest.” On the other hand, some of the physicists aren’t so familiar, but they were obviously talented: Guye wrote over 200 papers; Knudsen had a bunch of crap named after him (Knudsen cell, Knudsen flow, Knudsen number, Knudsen layer and Knudsen gases). Piccard and Langmuir fall into this category as well.

And then there are the scrubs flanking Ehrenfest,

Picture1

Henriot, Ehrenfest, and Herzen

and the scrubs flanking Schrödinger,

Picture2

de Donder, Schrödinger, and Verschaffelt

These scrubs are so scrubby that the CENCO poster doesn’t even talk about them.

Surely one of these fools was the dumbest?

Let’s take them in order. Henriot was a chemist, so that’s a strike against him; he discovered that potassium is naturally radioactive, which is cool I guess, and figured out a way to make tops spin at high speeds. Woop-de-do. Herzen was a friend of Ernest Solvay, but didn’t really do anything else of note; I think we know how Herzen got an invite to the conference, don’t we?

Being a mathematician, de Donder probably gets a pass: he also wrote a shitload of books. The final scrub, Verschaffelt, is notable as having the shortest Wikipedia article of any Solvay attendee. Basically, all I can find out about him was that he was a physicist. Period.

Before we decide between Herzen and Verschaffelt, we should mention two other physicists in the poster. Compton once said, “the supernatural is as real as the natural world of Science,” so I’m tempted to list Compton amongst the scrubs. Anyone with so much woo in his veins can’t be listed amongst the top tier of physicists. Compton did win a Nobel prize though, and he was American…we have to disqualify him, then. America, fuck yeah! That leaves Ehrenfest, who was by all accounts a clever guy. But come on, the guy shot his own son and then killed himself. That’s hard to get past. I guess we’ll chalk that up to mental illness, not stupidity, but no one is ever going to make an Ehrenfest action figure.

Parents snub traditional action figures in favour of such as historical icons as Einstein and Van Gogh

None of these for Ehrenfest.

So who was dumber, Herzen or Verschaffelt?

Herzen wrote a book or two, and supposedly played a “leading role” in physics and chemistry. So I’ll give him the nod over Verschaffelt. Thus we can tentatively say:

Verschaffelt was the dumbest attendee of the 1927 Solvay Conference.

Scrub

“I’m still smarter than you.”

You’re welcome.

Read Full Post »

Physicist or not a physicist?

Posted in Uncategorized, tagged on March 31, 2015| 6 Comments »

In the film Amadeus, Salieri wonders what Mozart looks like.  He knows Mozart by reputation, but has never met the man.  He says:

“As I went through the salon, I played a game with myself. This man had written his first concerto at the age of four; his first symphony at seven; a full-scale opera at twelve. Did it show? Is talent like that written on the face?”

Good question. Decide for yourself:

Is this genius?

Which brings me to a game we can play: Physicist or not a physicist?

Look at the following portraits, and see if you can see the spark of genius in them.  Which ones are as smart as Einstein?  And which ones are merely composers, economists, or chess players?  [Answers follow at the end of the post.]

Picture2

#1

Picture3

#2

Picture4

#3

Picture5

#4

Picture6

#5

Picture7

#6

Picture8

#7

Picture9

#8

Picture10

#9

Picture11

#10

Picture12

#11

Picture13

#12

[A quick note on the formatting of this post.  Yes, I know it sucks.  And it took me 2.5 hours to get to this level of suckiness.  Thanks, WordPress, for forcing the broken Beep Boop Boop editor on me, and disabling classic mode!  In the Beep Boop mode, not only is everything slower, but (1) you can’t center text in picture captions, (2) the visual editor doesn’t accurately display what’s in the HTML editor, (3) the visual editor doesn’t accurately display what’s in preview mode, (4) if text is left justified, then it wraps around automatically, even if you didn’t choose this option, (5) you can’t change font size of the text, or caption, (6) you can’t even change the fucking FONT, (7) tags are now buried under several levels of drop-down menus, slowing things down immensely, and (8) there’s an annoying pop-up asking me after every edit if Hey! Do I want to Preview?  No, I don’t want a preview, WordPress, and your removing the “switch to classic mode” button was frankly just malicious.]

Answers [highlight to reveal]: #1 Physicist Emmy Noether.  #2 Composer Bela Bartok.  #3 Chess champion Mikhail Tal.  #4 Economist John Maynard Keynes.  #5 Physicist Shirley Jackson.  #6 Physicist Lise Meitner. #7 President John Tyler.  #8 Physicist Chen Ning Yang.  #9 Physicist Michael Faraday.  #10 Physicist Emilie du Chatelet.  #11 Swordsman Miyamoto Musashi.  #12 Physicist Michael Binger.

Read Full Post »

Seven units of radioactivity

Posted in Physics, tagged , , , , , on December 18, 2014| 7 Comments »

I’ll start with a limerick:

The Becquerel has me morose;

These units I can’t diagnose.

The rads and the Grays

Don’t measure decays—

But what of equivalent dose?

becquerel_postcard

1 Becquerel = 1 decay/s

There are at least seven units of radioactivity floating around out there, measuring at least three different kinds of things; a veritable zoo of scientific terms. Unfortunately, most people don’t know a rad from a Gray from a Becquerel. Here, then, is my attempt to sort out the confusion.

You’re welcome.

First, let me just say that most people (to my dismay) equate the terms “radioactivity” and “radiation”. There’s some disagreement on the meanings of these terms; I find myself in the conservative camp on this issue. To me, “radioactivity” refers to junk flying out of an unstable nucleus: alpha particles, gamma rays, and the like. “Radiation”, on the other hand, refers exclusively to electromagnetic radiation (anything from long-wavelength radio waves to ultra-short-wavelength gamma rays). By my fuddy-duddy standards, “radiation” is just light; it may or may not be biologically dangerous. Radiation is just one of the possible kinds of radioactivity.

Unfortunately, through the inevitable process of “language creep” (the same process by which the original four “collie” birds became four “calling” birds in the Twelve Days of Christmas, because people are just ignorant) the term “radiation” has come to encompass any ionizing junk from a nucleus.  So some people now call alpha particles and beta particles “particle radiation” to distinguish them from gamma rays, which is “electromagnetic radiation”. This usage bothers me, but I’ll get over it. Just note that I won’t use this terminology here.

So: unstable nuclei exist. They occasionally spit out things—a phenomenon I call radioactivity. These things can often knock electrons free from atoms (i.e. they can ionize atoms). Such ionization events can be detected by a Geiger-Müller tube (among other devices).

Activity. The first way to measure radioactivity is to measure these ionization events in a given amount of time, which in turn tells you how often decays are occurring. So we measure R, the “activity” of a nuclear sample. The metric system unit of activity is the Becquerel (Bq), which is defined to be one decay/second. (Note that 1 Bq is essentially equivalent to 1 Hz = 1 s–1.)

Unfortunately, the Becquerel is a small unit—if we’re talking about radioisotopes used in medicine, for example, we might have to speak of billions of Becquerels. So there’s another unit of activity: the Curie (Ci). One Curie is defined to be the activity of 1 gram of 226Ra. If you want to convert, 1 Ci = 3.7 x 1010 Bq.

There is a problem with measuring activity: it doesn’t really tell you how dangerous a particular sample is. Not all radioactivity particles are the same. Getting hit with millions of weak particles might be preferable to being hit by only a few high velocity ones. One bullet is more dangerous than 500 rapidly-fired marshmallows.

Absorbed dose. To get a feel for the dangerousness of a sample, we talk about absorbed dose: a measure of energy absorbed per kilogram of target material. In metric units, the applicable unit is the Gray (Gy): 1 Gy = 1 Joule/kg. Other people use the rad, with the conversion 1 rad = 1 erg/g = 0.01 Gy. Use of the rad is discouraged by the international scientific community but is still common in (surprise surprise!) the United States.

There’s still a problem. Suppose I’m exposed to 1 Gy of radioactivity (meaning that I expect to absorb a joule of energy per kilogram of my mass). It matters whether I’m absorbing beta particles (say) or alpha particles, because the damage done by alpha particles is worse, pound-for-pound. That is, different kinds of radioactivity are more or less dangerous, depending on the predilection of the given particle(s) for causing genetic damage and possibly causing cancer. This leads us to introduce…

Equivalent dose. Equivalent dose is basically just absorbed dose, times a “fudge factor” that depends upon the kind of radioactivity involved. The unit we use is the Sievert (Sv) = 1 J/kg (weighted). X-rays, gamma rays, and beta particles are all in a sense “equally” dangerous and have a weight factor of 1. So for those kinds of particles, 1 Gy → 1 Sv. Alpha particles, though, are around 20 times as “dangerous”, so if we’re dealing with alpha particles then 1 Gy → 20 Sv.

Of course Americans are contrary when it comes to units, and so the rem is still in common use; 1 rem = 100 erg/g (weighted) = 0.01 Sv. If you’re a science writer, you’d be best served by eliminating rad’s and rem’s altogether; why perpetuate archaic units? You don’t use furlongs/fortnight to measure speed, do you?

I can’t help but mention a seventh unit of radioactivity: the Banana Equivalent Dose, or BED; 1 BED = 0.1 μSv, and so represents an equivalent dose. It (roughly) equates to the amount of radioactive exposure you would get if you ate a banana. (Bananas are naturally radioactive, as they contain significant amount of radioactive potassium, 40K.) This kind of unit helps people put the hobgoblin of “radioactivity” into perspective. “Oh my God! The nuclear plant let off some radioactive steam! Am I doomed?” “Well, your exposure was about 10 BED’s. So basically eat 10 bananas for the same effect.” (There are some issues with the BED as a unit; see this for more information.)

tumblr_ndk1altiWI1r3kmkso3_400

In summary:

Unit                                                     Symbol            Note

Activity

Becquerel: one decay/s                     Bq                   Same as 1 Hz

Curie: activity of 1g of 226Ra              Ci                    Not SI unit, 1 Ci = 3.7×1010 Bq

Absorbed dose

Gray: 1 J/kg                                         Gy

rad: 100 erg/g                                     rad                  Not SI unit; 1 rad = 0.01 Gy

Equivalent dose

Sievert: 1 J/kg                                     Sv

rem: 100 erg/g rem                             rem                 Not SI unit; 1 rem = 0.01 Sv

Banana equivalent dose                      BED                Not SI unit; 1 BED = 0.1 mSv

Read Full Post »

Lagrange, Laplace, and Legendre: which one is which?

Posted in Physics, tagged , on November 24, 2014| 13 Comments »

Anyone who studies physics and/or mathematics has often encountered the following conundrum:

How do you distinguish 18th-century French mathematicians with surnames beginning with an “L”? (I call these E.C.F.M.W.S.B.W.A.L.’s)

For example, you might recall that an E.C.F.M.W.S.B.W.A.L. invented the calculus of variations, some time around 1760.  Was it Legendre?  Lagrange? Laplace?  Or maybe you remember that an E.C.F.M.W.S.B.W.A.L. was the father of probability theory, and worked on the Buffon needle problem.  Was that Laplace?  Legendre? Lagrange?

So as a public service, I’ve sorted this out for you.  I henceforth talk about these three great mathematicians, and hope to distinguish them in your mind.

Lagrange: perhaps the best mathematician of the 1700’s.

Lagrange is the oldest of the E.C.F.M.W.S.B.W.A.L.’s, born in 1736.  Some call him the greatest mathematician of the century, although I might give that title to Euler.  In any case, he’s responsible for a host of discoveries: he pretty much invented an entire branch of mathematics, the calculus of variations; he used this tool to reformulate classical mechanics (think L = T – V) making it suitable for non-Cartesian coordinates, such as polar; he invented Lagrange multipliers, an elegant way to deal with constraints in differential equations; and he introduced the f(x),f'(x),f”(x)…notation for derivatives.

His greatest work was Mécanique analytique; all of the above achievements are found in this book.  Hamilton described the work as a “a scientific poem,” for its elegance is astounding.

lagrange

Lagrange

Lagrange was rigorous and abstract: he bragged that the Mécanique analytique did not have a single diagram.  To Lagrange, math was an art; the aesthetics of a theory took precedence over utility.

Laplace: the “applied” mathematician

Laplace was seven years younger than Lagrange, born in 1749.  He also is associated with classical mechanics, but unlike Lagrange, he did not reformulate the field per se.  Rather, he took Newtonian mechanics to its “apex” with his work Mécanique céleste.  This work is brilliant, but it’s also clunky and difficult.  It analyzes the orbits of all known bodies in the solar system, and concludes that there is no need of God to keep the whole mess going.  In fact, Napoleon supposedly asked why Laplace didn’t mention God in the Mécanique céleste.  He reportedly said “I have no need for that hypothesis.”

ban-laplace

Laplace

Laplace didn’t place as much emphasis on “beauty” in mathematics.  To him, math was just a tool.  Not surprisingly, he contributed to the “applied” field of probability theory; in fact, he’s arguably the founder of probability theory as we know it today.

Legendre: the elliptic integral guy

Although highly regarded in his day, Legendre (b. 1752) is really a tier below the first two guys.  Basically, he worked out how to do some elliptic integrals, and he introduced the Legendre transformation, which is used in many branches of physics.  For example, you can go back and forth between the Hamilton and Lagrange approaches of classical mechanics by means of Legendre transformation.  Also, such transformations are ubiquitous in thermodynamics (think U → H → A → G).

Legendre is also know for the portrait debacle.  Only a single known image of Legendre exists, and that image is not flattering:

Legendre

Legendre

Every other supposed portrait of Legendre is actually the picture of some obscure politician, because of a mistake which has propagated forward for 200 years.

In summary:

Lagrange: the beauty of math; reformulated mechanics in the Mécanique analytique

Laplace: math as a tool; Newtonian mechanics reaches its zenith in Mécanique céleste; probability theory

Legendre: the creepy looking elliptic integral guy

Note: I have not mentioned Lavoisier (b. 1743) because he was a chemist.  But if you really need him:

Lavoisier: a chemist who was guillotined in the French Revolution.

[Note added Dec. 4, 2014]  I could have included L’Hopital (French, died 1704) but all he did was write a textbook.  Laguerre was French, but he was born in 1834;  Lebesgue was French, but he was born in 1875.

Read Full Post »

Many Worlds Puzzle #3, Solutions

Posted in Puzzle, tagged , , , on October 22, 2014| 6 Comments »

As promised, the solutions…

1.   681472 [Um, Didn’t we answer this one earlier?]

2.   3927.27272… seconds This represents the amount of time it takes the minute hand of a clock to lap the hour hand.  For example, the hands coincide at midnight; they next coincide 3927.27272 seconds later, or at about 1:05:27 AM.

3.   23.14069… This is just e^π.

4.   2.1656 x 10^185 This is how many cubic planck lengths fit in the observable universe…basically, if our universe were a 3D computer, this is how many pixels you’d need.

5.   1.03 light year/year^2 This is the acceleration due to gravity g, in non-standard units.  It has the following interpretation: if you ignored relativity and accelerated at a rate of 1 g (reasonable for a starship), after a year you’d have reached the speed of light.

6.   133956 This is the number of possible combinations of two birthdays, since 133956 = 366^2.  If everyone on Earth had a significant other, there would be over 26,000 couples with the exact same two birthdays as you and your other.

7.   About 19.5 million people The number of people on Earth who share your birthday.

8.   0.739085… This is called the “Dottie number”…an irrational number that solves the equation cos x = x.

9.   1.72048 m^2 The area of a pentagon with sides of 1 m.

10.   0.004295 % This is what percent of Earth’s history homo sapiens has been around.

Read Full Post »

Many Worlds Puzzle #3

Posted in Puzzle, Uncategorized, tagged , , on October 10, 2014| 1 Comment »

Today there are really 10 puzzles. Can you figure out the significance of each number below? I’ve answered the first to get you started.

1.   681472

This number has a prime factorization of 2^9 x 11^3, which indicates that it equals 88^3. There are 88 keys on a piano…so one obvious interpretation is that the number 681472 is the number of possible three-note permutations that could start any piece on a piano (not counting rests, and ignoring duration). I wonder how many of the permutations have actually ever been played over the years?

2.   3927.27272… seconds

3.   23.14069…

4.   2.1656 x 10^185

5.   1.03 light year/year^2

6.   133956

7.   About 19.5 million people

8.   0.739085…

9.   1.72048 m^2

10.   0.004295 %

Because many of these problems are challenging, I will post hints in a week or so.

Read Full Post »

Everyone can be a world champion at SOMETHING

Posted in Physics, tagged , , , , , on August 18, 2014| 9 Comments »

Magnus Carlsen is the current world chess champion. He’s the best in the world at something. Not that many people can make that claim, can they?

Magnus Carlsen at FIDE World Chess Championship

Then again, there are lots of things in the world that you could be best at. Whistling, lemur training, lemon-pie-making, juggling, lying, rock climbing, sleepwalking. Somewhere in the world, there is “the best in the world” at each of these pursuits. Maybe my chances of being best at something are not so bad, after all? Maybe I just have to find the right thing…

Consider the modern pentathlon. In this sport, athletes compete in five events—fencing, shooting, swimming, running, and horse jumping—to achieve the overall best combined score. The winner need not be the best at any one specific event, but must have proficiency in all five.

Let’s say I am in the 99th percentile in all five events: very good, but not world class. [Here I am assuming that I’m in the 99th percentile of all humans, not just people who fence.] Taken individually, I wouldn’t have a prayer of making the Olympics. For example, the 99th percentile in épée fencing would still mean that there are

(0.01)^1 * 7,000,000,000 = 70,000,000

people with a similar proficiency around the world. Doesn’t seem that impressive, does yet? But I’m in the 99th percentile in all five events, right? So in reality there are only

(0.01)^5 * 7,000,000,000 = 0.7

people like me. That is, there’s just me. I’m probably the best at this combination of events. I should medal in the modern pentathlon.

And this brings me to my broader point. If you can think of five events in which you are in the 99th percentile individually, then in all likelihood you would be world champion if these events were combined into a single composite event. For those scoring at home, here’s where the number five comes from:

(0.01)^N * 7,000,000,000 = 1 (a single champion)

N ln (0.01) = ln [1/(7 x 10^9)]

N = [–ln (7 x 10^9)] / [ln (0.01)] = 4.9 ≈ 5

Let’s take my own skill set and see how I would do. I am certainly in the 99th percentile when it comes to physics. (Remember, I am comparing myself to the general population, not just physicists. I would never claim to be in the 99th percentile of people with physics PhD’s.) I am probably in the 99th percentile when it comes to chess (considering that I am in the 85th percentile for tournament players based on an 1800 rating). But am I good, really good, at anything else?

I will claim without proof that I am also in the 99th percentile (among the general population) in the following additional skills:

  • Knowledge of classical music
  • Playing the recorder
  • Geometry

Remember, I am not claiming any particularly high proficiency in any of these things. I just claim a 99th percentile rank in the general population. And individually, any one of these skills would only put me in the company of some 70 million others.

But now: make a hybrid event, where competitors have to take a battery of tests on physics, geometry, and classical music, then perform on the recorder, and then play chess… I believe I may do well in such an event. I might even be world champion.

Of course, nothing is that simple. I have ignored the fact that some of these skills may be correlated. Anyone who can play the recorder will probably also know about classical music. And many physicists will also be good at geometry. This means that my competition will be stiffer than I suppose, since if the events aren’t mutually exclusive then I’ve calculated the probabilities incorrectly. But I can improve my chances by making the five events as disparate as possible. I might change “Geometry” to “Movie Trivia”, for example.  My chances of becoming world champion would thereby be increased.

If you think that “99th percentile” is too high a bar, we could lower it to 90th percentile. Most people are in the top 10% at several things. Redoing our calculation, we get N = 9.8 in this case. So if you can find ten things you’re fairly good at and combine them, you too can be a world champion.

Of course, you also have to convince the Olympic governing body that that particular concatenation of events is worthy of a medal. But hey, that’s your problem.

I have some geometry to do.

Read Full Post »

Black hole misconceptions or: Why Dr. Who is not science fiction

Posted in Physics, tagged , , , , on February 5, 2014| 6 Comments »

I was watching Dr. Who the other day and came across a physics mistake so common I thought I’d address it here.  The mistake is this:

Black holes suck you in like a vacuum cleaner!

The setup: in Dr. Who [2.8] “The Impossible Planet”, the good Doctor and Rose meet the crew of a ship who are on “an expedition [to] the mysterious planet Krop Tor, impossibly in orbit around a black hole.” [Wikipedia]  That phrase “impossibly in orbit” made me almost spit out my drink while watching the show.

Black holes have event horizons.  I get it.  Even light cannot escape.  I get that, too.  But why does that mean I cannot orbit a black hole?

OK, time for a little general relativity.  Einstein figured out, between 1905 and 1915, that gravity is “just” a warping of space-time.  Matter causes the space-time around it to curve; the curvature of space-time determines how matter moves (insofar as objects in the absence of gravitational forces follow geodesics).  The formulas that link the distribution of matter to the curvature of space are Einstein’s equations:

einstein_equation

This expression is compact and might seem relatively simple, but it’s not.  Gαβ and Tαβ are components of tensors, which are like vectors, but worse; they’re really 4×4 matrices.  So this equation is not one equation, but 16 different equations, since α and β can take on any of four values each.

What do all those letters stand for?  Gαβ is a component of the Einstein tensor, which tells you about how space-time is curved; the indices α and β can be any of four values in a 4D space-time.  (If you’re mathematically inclined, the Einstein tensor can be related to the Ricci scalar, the Ricci tensor, and the Riemann tensor.)  Tαβ is a component of the stress-energy tensor, which basically describes how matter/momentum/energy/stress/strain is distributed in a region of space-time.  So here’s another way to visualize Einstein’s equations:

einstein_explained

The cause (mass) is on the right; the effect (the curvature of space-time) is on the left.

So what does this have to do with black holes?

One of the first solutions discovered to the Einstein equations is called the Schwarzschild solution, which applies to a spherically symmetric gravitational source.  The solution gives you a “metric” (essentially, a geometry) that is almost the same as “flat” space-time, except for a pesky (1–2GM/c2r) term.  But that pesky term has a strange implication: when that term equals zero, the solution “blows up” (i.e. becomes infinite).  Space becomes so curved that you essentially have a hole in the fabric of space-time itself.

When does this happen?  It happens when R = 2GM/c2, as one line of algebra will show.  This is called the Schwarzschild radius.  The Einstein equations predict that something weird and horrifying happens when a mass is squeezed down to the size of its Schwarzschild radius.  Current understanding is that the mass would then keep going, and squeeze itself into a point of zero radius.  Literally, zero.  (I did say it was weird and horrifying).

Incidentally, the Schwarzschild radius is exactly the radius you’d get if you set the escape speed for an object equal to the speed of light.  So this means that not even light can escape this super-squeezed object.

And here’s where various misconceptions start to creep in.

Another name for the Schwarzschild radius is the event horizon.  It’s a boundary of no return:  if you cross it, you can never go back.  But that’s all it is: a boundary.  There is not necessarily anything physical at the event horizon.  You might never know that you had crossed it.  Remember, all the mass is at the center.

Here’s how I “picture” a black hole:

black hole

Now, if I am outside the event horizon, what would I see?  Well, nothing from inside the event horizon could reach me (hence the term “black”) but I might see Hawking radiation.  I would certainly see gravitational lensing: the bending of distant light around a black hole.  Here’s a cool picture of gravitational lensing in action (artists conception only!) from Wikipedia:

225px-Black_hole_lensing_web

Let’s say the Sun were a black hole.  Its event horizon would be around 3 km.  As long as we never got closer than 3km, we could do what we like.  We could fly in, fly out, orbit the black hole as we please.

Would the black hole “suck us in”?  Sure, in the same way that the Sun sucks us in already.  There is a strong pull of the Sun on the Earth.  And there would be a strong pull on our hypothetical spaceship.  But change the Sun to a black hole, and the pull would not get any stronger.  That is the key point that most people miss: black hole gravity is not somehow “stronger” than ordinary gravity.  There is just gravity; that’s it.  Change the Sun to a black hole, and the Earth would continue in its orbit, and nothing would be any different.  Except for, maybe, the lack of light.

Why was the planet Krop Tor’s orbit impossible?  Astronomical black holes (created by stellar collapse) have a lot of mass; when there’s a lot of mass hanging around, things tend to orbit them.  That’s what you’d expect.  It would only be impossible if somehow the orbit crossed the event horizon multiple times during its trajectory.  But of course, the show didn’t mention this.

I want to end my rant on GR with a suggestion: that there are two kinds of sci-fi: science fiction, and “sciency” fiction.  The first kind tries to get the science right, and makes an effort to be possible (if not plausible).  The second kind throws sciency words around in an effort to appeal to a certain demographic.  Basically, “sciency” fiction is fantasy, set in outer space.  When seen in this light, Dr. Who has more in common with Lord of the Rings than it does with 2001.

Don’t get me wrong: I love Lord of the Rings, and I love Dr. Who.  Just don’t call it science fiction.

Read Full Post »

Don’t cut yourself on Occam’s razor

Posted in Many-worlds Interpretation, tagged , on January 13, 2014| 66 Comments »

One of the most common criticisms of the many-worlds interpretation (MWI) of quantum mechanics is that it is absurdly complicated, and therefore violates Occam’s razor.  Most people’s first reaction, on hearing of MWI, think that the theory is (to quote Martin Gardner) “bizarre”, “monstrous”, “fantastic”, “radical”, “appalling”, “nonsense”, “frivolous”, and “low”.  And many people seem to think that theorists who ascribe to MWI have their heads in the clouds to believe such nonsense.  MWI seems to be taken, in fact, as evidence that physics has lost its way—as if (supposedly) blind belief in such frivolity is indicative of a philosophical rot that pervades theorists like me.

rotten-apple

Theoretical physics today, to some

There are so many refutations of such criticisms that I don’t know where to start.  First of all, although MWI is popular, it is by no means canon, and I daresay that a majority of physicists reject it still.  So there!  We’re not all sheep.  Still, MWI has become almost mainstream (especially with cosmologists) so maybe it’s the cosmologists and the ivory-tower theorists who should be singled out for criticism?

People who think this have probably never met a theoretical physicist before in their life.  Getting such people to agree is like herding cats; every theory one puts forth (in a journal article or in a conference talk) is debated, criticized—dare I say, attacked.  And that is as it should be.  There is not, contrary to popular belief, some holy scripture that every theorist quotes verbatim.  We are all different, and have basically come to interpret quantum mechanics in our own personal way…not at the behest of some lord on high.

How do I know this?  Because I was never taught about interpretations of quantum mechanics.  Ever.  Everything I know about such things, I learned on my own since graduation.  Thinking of taking a quantum mechanics class at your local university?  Guess what: they will probably not talk about MWI, or the Copenhagen interpretation, or Schrodinger’s f***ing cat.  Why not?  Because those are philosophy topics, not physics.  You can do quantum mechanics without ever interpreting a single thing.  There’s no crying in baseball, and there’s no philosophy in quantum mechanics.  It is a purely mathematical theory, that undeniably works, and most people just leave it at that.  The idea that thousands of physicists subscribe to one particular world-view just because they constitute a single monolithic conformist society is ludicrous.  Invite a physicist to lunch if you don’t believe me.

But I still haven’t addressed the idea that MWI is obviously absurd.  It is absurd, right?  I mean, come on!

But wait.  Let’s think back to the Copernican revolution.  It’s obvious that the Earth is stationary, no?  I bet people thought that Copernicus and Galileo and their ilk were bizarre, monstrous, fantastic, radical, appalling, nonsensical, frivolous, and low.

And what about the idea that there are billions and billions of galaxies, each with billions and billions of stars?  We forget now, but this idea was radical when first presented and wasn’t settled until the 1920’s.  Why are we OK with a multiplicity of stars, but not a multiplicity of universes?  Why aren’t people complaining about the absurd notion (fact) that there are more stars in the observable universe than there are grains of sand on Earth’s beaches?

PerseusCluster_041008_041214_2000

Whoa.

So, Occam’s razor.  MWI just seems to have too much baggage, right?  For a lot of people MWI is too high a cost to bear to have a mathematically simple interpretation of quantum mechanics.  And let’s be clear: MWI is a simpler theory than (say) the Copenhagen interpretation (CI).  For you can start with three postulates, and add a fourth about wave-function collapse, and you get CI.  Or you can start with just three, and say nothing of wave-function collapse, and you get MWI.  Which interpretation seems simpler now?  MWI is a consequence of accepting the three basic postulates of quantum mechanics.  If you don’t like that, then you must introduce a fourth postulate ex nihilo to make yourself feel better.

But wait! you say.  10100 universes doesn’t seem simpler.  It’s a huge number!  It’s ridiculous!

OK.  You wanna go there?  I’ll turn the argument around.  By that rationale, you probably believe that there are only a finite number of integers, because any finite number is simpler than infinity.  There.  That makes sense, right?

The truth is that an infinite set is often simpler than a single member of that set.  Take the natural numbers.  I can write a computer program in BASIC that writes every natural number.  Here it is:

10           x=1

20           PRINT x

30           x=x+1

40           GOTO 20

On the other hand, if I want to print out the number

5679200359662711389685023885761799

then my computer program is longer:

10           PRINT “5679200359662711389685023885761799”

Count the keystrokes.  The second program requires more typing.  And note that the first (simpler) program will eventually print this number—the long arbitrary program is “contained” within the first.

In information theory, the information “content” of something is related to its algorithmic complexity—roughly speaking, how easy it is to write a computer program that “specifies” the object.  By that measure, “all the natural numbers” is a simpler concept than the number

5679200359662711389685023885761799

Similarly, “all possible universes” is a much simpler concept than one specific arbitrary universe.  You want to recreate this universe?  Good luck…you’ll have to specify the position and momentum of every particle in the universe.  That’s a long computer program.  However, if you just say “create all possible universes” then eventually this one will pop up…

Do I believe in the MWI?  Yes.  Why?  It’s not because I was indoctrinated into such belief; I don’t think a single professor in graduate school ever mentioned MWI.  It’s because I’ve looked at the evidence over a number of years, and (tentatively) decided that it fits the data best.  That is the only reason to ever believe something, ever.  It fits the data best.  But I stress that my conclusion is tentative because, hey, it’s science.  There is no dogma.  There is just stuff that we are 99.44% sure of.

Like evolution by natural selection, or heliocentrism, or the existence of ghosts.  I mean, seeing’s believing, right?

               [Note: more Americans believe in ghosts than evolution.  Sigh.]

If you enjoyed this post, you may also enjoy my book Why Is There Anything? which is available for the Kindle on Amazon.com.

sargasso

I am also currently collaborating on a multi-volume novel of speculative hard science fiction and futuristic deep-space horror called Sargasso Nova.  Publication of the first installment will be January 2015; further details will be released on Facebook, Twitter, or via email: SargassoNova (at) gmail.com.

Read Full Post »

Older Posts »