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## 10 physics misconceptions, explained poorly

[This blog post was written by a guest columnist, a D-student in freshman physics who will remain anonymous]

10.         It’s winter because we’re far from the Sun

Everyone knows that it’s cold in January because, well, we’re farther from the Sun that usual.  The orbit of the Earth is elliptical, so in the Summer we’re closer to the Sun, like Mercury.  I have no idea why the seasons are reversed in Australia…maybe it’s because they’re upside-down?

9.            Force is non-reciprocal

I tug on a rope with a force of 100 N.  On the other end of the rope is a football player; let’s say Greg Olsen (TE for the Carolina Panthers, of course, but you knew that I’m sure).  With what force is Greg Olsen pulling on the rope?  It must be much more than 100 N, because a football player is stronger than me.

8.            Areas and volumes have the same conversion factors as linear units

If 100 cm = 1 m, then 100 cm2 = 1 m2.  This is so obvious it doesn’t merit comment.  Another way to look at it is that a meter and a square meter are, basically, the same thing.

7.            Acceleration is the same as speed

Acceleration is, like, how fast you’re going.  So if I throw a ball straight up, at the top of its arc, its speed is zero, so its acceleration must be zero.  Can I have some of those Cheetos?

Best comic ever?

6.            Weight and mass are the same

I was asked in lab the other day to find the weight of a brass cylinder.  So I did:  I weighed it, and got that its weight was 250 g.  I was then asked to find the force due to gravity on the object, but I don’t know how to do that.  Oh, I have to go; I’m rushing Phi Upsilon.

5.            There’s a magical force that appears whenever you move in a circle

So, I was driving the Tail of the Dragon on my scooter the other day, and almost got pulled off the road because of centrifugal force.  That’s another kind of force; you know, like gravity, friction, drag, spring force…centrifugal force.  It appears whenever you move in a circle.  It’s directed outward.  It is a repulsive force, the opposite of gravity.

4.            Objects have a memory of circular motion

If you spin a circle with a ball in your hand, then let go, the ball will spiral outward (obviously) because by the 1st Law objects in motion stay in the same kind of motion that they had before: circularly moving objects keep moving in a circle, etc.  I might then wonder why my scooter didn’t keep going in a circle in spite of centrifugal force, but luckily I don’t ever experience cognitive dissonance.

3.            There’s no gravity in space

Here’s a spoiler in case you didn’t see Gravity with Sandra Bullock and George Clooney.  In the scene where Sandra Bullock is knotted up in some ropes, she tries to hold on to George Clooney, but lets go.  Of course then George Clooney plummets towards the Earth, because of gravity.  They must have been right at the invisible border between space and not-space, where gravity suddenly drops to zero.

2.            g stands for “gravity”

The formula for weight is w = mg, which stands for mass times gravity.  g is gravity.  It’s like a force or something.  I have no idea why my instructor winces every time I say this.

1.            No net force means no movement

This is the most obvious one of all.  On one of our homework problems, there were only two forces acting on a box: 50 N up, and 50 N down.  The net force is clearly zero.  So the box cannot be moving!  Therefore v = 0 (duh!)  But my professor marked this wrong.  She said that v might be 50,000 m/s for all we know.  That makes no sense!  Physics is too hard.

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

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.

## Why many worlds?

I thought I would re-post this excellent discussion of the many-worlds interpretation by David Yerle:

Why I Believe in the Many-Worlds Interpretation

I agree with him 100%, and he says it better than I ever could.  The crux of the argument is this: it depends on the book you’re reading, but as a practical matter there are typically 4 postulates of quantum mechanics (about the primacy of the wavefunction, Schrödinger’s equation, measurements being Hermitian operators, and wave function collapse).  Many worlds is what you get when you reject the unmotivated “wave function collapse” postulate.  It is a simpler theory in terms of axioms, so obeys Occam’s razor.  If multiple universes bother you, think of how much it bothered people in the 1600’s to contemplate multiple suns (much less multiple galaxies!)

## An H-R diagram for the 9 kinds of physics undergrad

In my continuing effort to present cutting-edge research, I present here my findings on the 9 kinds of physics undergrad.

First, let’s look at a scatter plot of Ability vs. Effort for a little more than 100 students.  (This data was taken over a span of five years at a major university which will remain unnamed.  Even though it’s Wake Forest University.)

Student ability is normalized so that 1 is equivalent to the 100th percentile, 0 is the 50th percentile, and –1 is the 0th percentile.  [This matches the work of I. Emlion and A. Prilfül, 2007]  Ability scores below –0.5 are not shown (such students more properly belong on the Business Major H-R diagram).

On the x-axis is student effort, given as a spectral effort class [this follows B. Ess, 2010]:

O-class: Obscene

B-class: Beyond awful

A-class: Awful

F-class: Faulty

G-class: Good

K-class: Killer

M-class: Maximal

As you can see, most students fall onto the Main Sequence.

The Typical student (effort class G, 50th percentile) has a good amount of effort, and is about average in ability.  They will graduate with a physics degree and eventually end up in sales or marketing with a tech firm somewhere in California.

The Giant student (effort class K, 75th percentile) has a killer amount of effort and is above average in ability.  Expect them to switch to engineering for graduate school.

The Smug Know-it-all student (effort class O, 100th percentile) is of genius-level intellect but puts forth an obscenely small amount of effort.  They will either win the Nobel prize or end up homeless in Corpus Christi.

The Headed to grad school student (effort class B, 75th percentile) is beyond awful when it comes to work, and spends most of his/her time playing MMORPG’s.  However, they score well on GRE’s and typically go to physics graduate schools, where to survive they will travel to the right (off the main sequence).

The Headed to industry student (effort class F, 55th percentile) is slightly above average but has a faulty work ethic.  This will change once they start putting in 60-hour weeks at that job in Durham, NC.

The Hard working math-phobe student (effort class M, 30th percentile) is earnest in their desire to do well in physics.  However, their math skills are sub-par.  For example, they say “derivatize” instead of “take the derivative”.  Destination: a local school board near you.

The Supergiant student (effort class K, 100th percentile) is only rumored to exist.  I think she now teaches at MIT.

The Frat boy student (effort class O, 50th percentile) is about average, but skips almost every class.  Their half-life as a physics student is less than one semester.  They will eventually make three times the salary that you do.

The White dwarf student (effort class B, 30th percentile) is below average in ability and beyond awful when it comes to putting forth even a modicum of effort.  Why they don’t switch to being another major is anyone’s guess.

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If you enjoyed this post, you may also enjoy my book Why Is There Anything? which is available for the Kindle on Amazon.com.  The book is weighty and philosophical, but my sense of humor is still there!

***********************************************************************************

I am also currently collaborating on a multi-volume novel of speculative hard science fiction and futuristic deep-space horror called Sargasso Nova.  My partner in this project is Craig Varian – an incredibly talented visual artist (panthan.com) and musician whose dark ambient / experimental musical project 400 Lonely Things released Tonight of the Living Dead to modest critical acclaim a few years back.  Publication of the first installment will be January 2015; further details will be released on our Facebook page, Twitter feed, or via email: SargassoNova (at) gmail.com.

## The 9 kinds of physics seminar

As a public service, I hereby present my findings on physics seminars in convenient graph form.  In each case, you will see the Understanding of an Audience Member (assumed to be a run-of-the-mill PhD physicist) graphed as a function of Time Elapsed during the seminar.  All talks are normalized to be of length 1 hour, although this might not be the case in reality.

The “Typical” starts innocently enough: there are a few slides introducing the topic, and the speaker will talk clearly and generally about a field of physics you’re not really familiar with.  Somewhere around the 15 minute mark, though, the wheels will come off the bus.  Without you realizing it, the speaker will have crossed an invisible threshold and you will lose the thread entirely.  Your understanding by the end of the talk will rarely ever recover past 10%.

The “Ideal” is what physicists strive for in a seminar talk.  You have to start off easy, and only gradually ramp up the difficulty level.  Never let any PhD in the audience fall below 50%.  You do want their understanding to fall below 100%, though, since that makes you look smarter and justifies the work you’ve done.  It’s always good to end with a few easy slides, bringing the audience up to 80%, say, since this tricks the audience into thinking they’ve learned something.

The “Unprepared Theorist” is a talk to avoid if you can.  The theorist starts on slide 1 with a mass of jumbled equations, and the audience never climbs over 10% the entire time.  There may very well be another theorist who understands the whole talk, but interestingly their understanding never climbs above 10% either because they’re not paying attention to the speaker’s mumbling.

The “Unprepared Experimentalist” is only superficially better.  Baseline understanding is often a little higher (because it’s experimental physics) but still rarely exceeds 25%.  Also, the standard deviation is much higher, and so (unlike the theorist) the experimentalist will quite often take you into 0% territory.  The flip side is that there is often a slide or two that make perfect sense, such as “Here’s a picture of our laboratory facilities in Tennessee.”

You have to root for undergraduates who are willing to give a seminar in front of the faculty and grad student sharks.  That’s why the “Well-meaning Undergrad” isn’t a bad talk to attend.  Because the material is so easy, a PhD physicist in the audience will stay near 100% for most of the talk.  However, there is most always a 10-20 minute stretch in the middle somewhere when the poor undergrad is in over his/her head.  For example, their adviser may have told them to “briefly discuss renormalization group theory as it applies to your project” and gosh darn it, they try.  This is a typical case of what Gary Larson referred to as “physics floundering”.  In any case, if they’re a good student (and they usually are) they will press on and regain the thread before the end.

The “Guest From Another Department” is an unusual talk.  Let’s say a mathematician from one building over decides to talk to the physics department about manifold theory.  Invariably, an audience member will gradually lose understanding and, before reaching 0%, will start to daydream or doodle.  Technically, the understanding variable U has entered the complex plane.  Most of the time, the imaginary part of U goes back to zero right before the end and the guest speaker ends on a high note.

The “Nobel Prize Winner” is a talk to attend only for name-dropping purposes.  For example, you might want to be able to say (as I do) that “I saw Hans Bethe give a talk a year before he died.”  The talk itself is mostly forgettable; it starts off well but approaches 0% almost linearly.  By the end you’ll wonder why you didn’t just go to the Aquarium instead.

The “Poetry” physics seminar is a rare beast.  Only Feynman is known to have given such talks regularly.  The talks starts off confusingly, and you may only understand 10% of what is being said, but gradually the light will come on in your head and you’ll “get it” more and more.  By the end, you’ll understand everything, and you’ll get the sense that the speaker has solved a difficult Sudoku problem before your eyes.  Good poetry often works this way; hence the name.

The less said about “The Politician”, the better.  The hallmark of such a talk is that the relationship between understanding and time isn’t even a function.  After the talk, no one will even agree about what the talk was about, or how good the talk was.  Administrators specialize in this.

If you enjoyed this post, you may also enjoy my book Why Is There Anything? which is available for the Kindle on Amazon.com.  The book is weighty and philosophical, but my sense of humor is still there!

I am also currently collaborating on a multi-volume novel of speculative hard science fiction and futuristic deep-space horror called Sargasso Nova.  My partner in this project is Craig Varian – an incredibly talented visual artist (panthan.com) and musician whose dark ambient / experimental musical project 400 Lonely Things released Tonight of the Living Dead to modest critical acclaim a few years back.  Publication of the first installment will be January 2015; further details will be released on our Facebook page, Twitter feed, or via email: SargassoNova (at) gmail.com.

## Formula snobs

I am a formula snob.

We all know about grammar snobs: the ones who complain bitterly about people using who instead of whom.  Many people know how to use whom correctly; only grammar snobs care about it.  I gave up the whom fight long ago (let’s just let whom die) but I am a grammar snob when it comes to certain words.  For example, ‘til is not a word, as I have discussed before.

However, I am almost always a formula snob.

Consider this formula from the text I’m currently using in freshman physics:

x = v0 t + ½ a t2.

Robin Thicke, c. 2012

To me, looking at this equation is like watching Miley Cyrus twerk with Beetlejuice.  I would much, much rather the equation looked like this:

Δx = v0 Δt + ½ a Δt2.

The difference between these two formulas is profound.  To understand the difference, we need to talk about positions, clock readings, and intervals.

A position is just a number associated with some “distance” reference point.  We use the variable x to denote positions.  For example, I can place a meter stick in front of me, and an ant crawling in front of the meter stick can be at the position x=5 cm, x=17 cm, and so on.

A clock reading is just a number associated with some “time” reference point.  We use the variable t to denote clock readings.  For example, I can start my stopwatch, and events can happen at clock readings t=0 s, t=15 s, and so on.

Here’s the thing: physics doesn’t care about positions and clock readings.  Positions and clock readings are, basically, arbitrary.  A football run from the 10 yard line to the 15 yard line is a 5 yard run; going from the 25 to the 30 is also a 5 yard run.  The physics is the same…I’ve just shifted the coordinate axes.  If I watch a movie from 8pm to 10pm (say, a Matt Damon movie) then I’ve used up 2 hours; the same thing goes for a movie from 9:30pm to 11:30pm.  Because a position x and a clock reading t ultimately depend on a choice for coordinate axes, the actual values of x and t are of little (physical) importance.

Suppose someone asks me how far I can throw a football.  My reply is “I threw a football and it landed on the 40 yard line!”  That’s obviously not very helpful.  A single x value is about as useful as Kim Kardashian at a barn raising.

Can you pass that hammer, Kim?

Or suppose someone asks, “How long was that movie?” and my response is “it started at 8pm.”  Again, this doesn’t say much.  Physics, like honey badger, doesn’t care about clock readings.

Most physical problems require two positions, or two clock readings, to say anything useful about the world.  This is where the concept of interval comes in.  Let’s suppose we have a variable Ω.  This variable can stand for anything: space, time, energy, momentum, or the ratio of the number of bad Keanu Reeves movies to the number of good (in this last case, Ω is precisely 18.)  We define an interval this way:

ΔΩ = Ωf – Ωi

So defined, ΔΩ represents the change in quantity Ω.  It is the difference between two numbers.  So Δx = xf – xi is the displacement (how far an object has traveled) and Δt = tf – ti  is the duration (how long something takes to happen).

When evaluating how good a football rush was, you need to know where the player started and where he stopped.  You need two positions.  You need Δx.  Similarly, to evaluate how long a movie is, you need the starting and the stopping times.  You need two clock readings.  You need Δt.

I’ll say it again: most kinematics problems are concerned with Δx and Δt, not x and t.  So it’s natural for a physicist to prefer formulas in terms of intervals (Δx = v0 Δt + ½ a Δt2) instead of positions/clock readings (x = v0 t + ½ a t2).

But, you may ask, is the latter formula wrong?

Technically, no.  But the author of the textbook has made a choice of coordinate systems without telling the reader.  To see this, consider my (preferred) formula again:

Δx = v0 Δt + ½ a Δt2.

The formula says, in English, that if you want to calculate how far something travels Δx, you need to know the object’s initial speed v0, its acceleration a, and the duration of its travel Δt.

From the definition of an interval, this can be rewritten as

xf  – xi = v0 (t– ti) + ½ a (t– ti) 2.

This formula explicitly shows that two positions and two clock readings are required.

At this point, you can simplify the formula if you make two arbitrary choices: let xi = 0, and let ti = 0.  Then, of course, you get the (horrid) expression

x = v0 t + ½ a t2.

I find this horrid because (1) it hides the fact that a particular choice of coordinate system was made; (2) it over-emphasizes the importance of positions/clock readings and undervalues intervals, and (3) it ignores common sense.  Not every run in football starts at the end-zone (i.e. x = 0).  Not every movie starts at noon (i.e. t = 0).  The world is messier than that, and we should strive to have formulas that are as general as possible.  My formula is always true (as long as a is constant).  The horrid formula is only true some of the time.  That is enough of a reason, in my mind, to be a formula snob.

A formula snob?

Bonus exercise: show that the product

ΩKeanu Reeves  x  ΩMatt Damon  ≈  3.0

has stayed roughly constant for the past 15 years.

From a recent blog post, high on hyperbole and low on science:

[Fukushima: At the Very Least, Your Days of Eating Pacific Ocean Fish Are Over  We’re writing this post becasue [sic] we feel that it is extremely important for everyone to be aware of this crisis, and it’s not being sufficiently reported on. In our entire month in the US, we did not see this in the mainstream media and hardly anyone knew about it…In a nutshell, Japan’s nuclear watchdog has now declared the leak of radioactive water from Fukushima a “state of emergency.” Each day, 300 tons of radioactive water seeps into the ocean…]

Ok.  Time out.  We need a reality check.  First of all, what’s “radioactive water”?  If I take a Geiger-Müller tube and wave it over any seawater, I will detect radioactivity.  I will also detect radioactivity in any banana (from 40K), and in my dog Banjo (from 14C).

Banjo

In fact, just going outside in the open air I will detect radioactivity; in fact, over the course of a day I will absorb something like 10 μSv.  Why?  Because radioactivity is everywhere.  Radioactive isotopes aren’t like some nefarious pixie dust that is sprinkled here and there, giving us rare cancers and making us sprout third eyes.  Radioactive isotopes are everywhere.  So when you say the water is “radioactive” you’d better define what that means.

I assume that the author is just parroting what he or she read in some other blog, and doesn’t even know what “radioactive water” means (much less understand the difference between units such as Bequerels, Sieverts, Curies, Grays, rads, rems, and BED’s).  But let’s try to understand: what might “radioactive water” actually mean?  Some frustrated Google searching yielded little real science, until I stumbled upon a National Geographic article.  “…radiation levels in its groundwater observation hole on the east side of the turbine buildings had reached 310 becquerels per liter for cesium-134 and 650 becquerels per liter for cesium-137.”  Finally something we can work with!  I don’t know if this contaminated groundwater is leaking directly into the ocean, but let’s assume that it is…we might as well give in to some of the hyperbole.

650 Bq.  Is that a lot?  Well, it’s hard to say; Bq is a unit of activity (meaning decays per second) but it doesn’t tell you how much energy a person would be exposed to (for that, use the Gray; 1 Gy = 1 Joule/kg).  It also doesn’t take into account the type of radioactivity in question and how such radioactivity affects biological tissue (for that, use the Sievert, which includes a human-centric biological fudge factor).  But, as a physicist I have the right to make an educated guess, and (conservatively) say that drinking a liter of the water contaminated with 137Cs represents an exposure approximately equivalent to the EPA’s recommended limit on exposure for one year; that is, 1 mSv (one millisievert).

(It’s funny: the EPA recommends no more than 1 mSv per year, but the average person is exposed to 4 mSv per year, mostly from the air around us.  I suppose they mean to warn us not to expose ourselves to more than 1 mSv/yr beyond the 4 mSv/yr we normally get…but I digress.)

Don’t get me wrong; it’s quite a bit of radioactivity all at once, like getting 50 chest x-rays all at the same time.  But it’s still only half the dose you’d get if you got a single head CT scan.

And to get that dose, you’d have to drink the water.

But still.  The water’s “radioactive”, right?  And 300 tons of the stuff are being pumped into the Pacific every single day!

Here’s another good opportunity to practice unit conversion.  Go get a pencil.  I’ll wait.  Ready?  300 tons of water is 272,155 kg.  So that water has a volume of 272.155 m3, which is 272,155 liters.  OK so far?

272,155 x 1 mSv = 272 Sv.  A fatal dose is around 8 Sv, so this is a lot.  But you’d have to drink all 300 tons of water.

And the Pacific ocean is kinda big: maybe 6.4 x 1020 kg, or a volume of 6.4 x 1020 liters.  Imagine: each day, 300 tons of “radioactive water” enter the Pacific; but this water gets diluted (surely, it has mixed thoroughly before reaching California?)  272,155 kg / 6.4 x 1020 kg is a very, very, very small number: 4.25 x 10-16 .

This means that your initial dangerous level of radioactivity, 272 Sv, is diluted by a factor of 4.25 x 10-16, giving you 1.16 x 10-13 Sv, per day.  That is, if you drank 300 tons of water on the California coast.  If you’re numerically challenged, here’s a hint as to what this means.  1.16 x 10-13 is basically zero.  Go ahead.  Drink those 300 tons.

The hyperbolic blog continues:

[The contamination has made it’s [sic] way to the USA. A Stanford University study…]

Wait…what study?  Citation please!  Otherwise you’re just making stuff up!

[…just showed that every bluefin tuna tested in the waters off California has shown to be contaminated with radiation that originated in Fukushima. Every single one. Our FDA assures us that our food supply is safe. They LIE. Don’t trust the government testing. They are covering up the magnitude of this situation. The only safe level is zero.]

This is breathtaking.  For one thing, even if I take a Geiger counter and detect radioactivity from a fish—which I don’t doubt in the slightest; fish contain 14C, after all—how could I possibly know that the individual radioactivity events “came” from Japan?  And that final sentence…“The only safe level is zero.”  Wow.  Just, wow.  Doesn’t the author know that a “zero level of radioactivity” does not exist on this Earth?  Should we give up breathing, and eating bananas, and having basements, and walking out into the open air?

Imagine Frankenstein’s monster saying “Fire bad!”  Now imagine sciencephobes saying “Radioactivity bad!”  It amounts to the same thing.  People don’t like what they don’t understand.  And there are too many science illiterates in the world.

Here’s one more gem:

[In the wake of Fukushima, The White House has given final approval for dramatically raising permissible radioactive levels in drinking water and soil. The EPA says the new levels are within the “safe” range, but they keep moving those safe levels higher as things unfold. In soil, the PAGs allow long-term public exposure to radiation in amounts as high as 2,000 millirems. Welcome to the new normal.]

2000 millrems = 20 mSv, which is equivalent to getting 3 chest CT scans, but spread out over a whole year (which is a good thing).  This is still less than the maximum permitted yearly dose for radiation workers, which is 50 mSv.

Here’s a summary of what I’m saying.  Fukushima was a disaster, sure.  But no one in America should worry in the slightest.  You get way, way, way more radiation exposure from the person you’re sleeping next to, than you do from some water in the western Pacific.

Don’t blame the blog author.  I mean, the blog is called “Sprinter Life”.  Enough said.

[For help with radioactivity units, see this excellent graphic.]

## Why your kids’ model of the atom is completely wrong

When I was in elementary school, at some indeterminate age, I made a model of the atom with pipe cleaners and Styrofoam balls.  It probably looked something like this:

These models are about as accurate as depicting the Taj Mahal as a decrepit hovel:

The Taj Mahal, built from 1632–1653.

Sure, the atom has a nucleus; this nucleus has protons and (usually) neutrons.  And electrons “orbit” the atom (although quantum mechanics tells us that this “orbit” is a much more nebulous concept than Bohr would have us believe).  But—and here’s the main problem with 5th grade Styrofoam ball models—the scale is completely, totally, massively wrong.

Let’s do a simple calculation.  A typical atomic radius is one the order of 0.1 nm.  A typical nucleus, about 10 fm.  What is the ratio of these two lengths?

This bears repeating.  A nucleus is something like 10,000 times smaller than an atom, by length.  By volume, it’s even more dramatic:

A nucleus is 1,000,000,000,000 times smaller than an atom, by volume.

You don’t really get that impression from the Styrofoam ball model, do you?

A typical football stadium has a radius of maybe 120 m.  One ten-thousandth of this is 1.2 cm, about the size of a pea.  To get a sense of what an atom really looks like,  place a pea at the center of a field in the middle of a football stadium.  Then imagine, at the outskirts of the stadium, there are a few no-see-um gnats (biting midges, of the family Ceratopogonidae).  These bugs represent the electrons.  The atoms are the bugs and the pea.  That’s it.  The rest of the atom is empty space.

Another way to think about it is this:

In terms of volume, a nucleus is only 0.0000000001% of the volume of the atom.

That means, for those of you scoring at home, that 99.9999999999% of an atom is nothing.

That is, you are mostly nothing.  So am I.  So is Matt Damon.

So the next time you’d like to help your kids make a model of the atom, just forget it.  Whatever model you make will be about as accurate as the physics in The Core.  I’d recommend instead getting some nice casu marzu, having a strong red wine, and watching True Grit.  You’ll thank me for it.

There’s flies in this, too.