Q: Why does wind make you colder, but re-entry makes you hotter?

March 13th, 2010

The original question was:

Why is it that, when you are outdoors and the atmosphere is moving past you at a moderate rate (wind), you get colder; but when the atmosphere is moving past a space shuttle during re-entry, it gets hotter?

Things falling from space get crazy hot. Unless they're designed specifically to survive the onslaught of air, they tend to aerosolize. That doesn't seem to be the case on the ground.

Physicist: The air right on a surface stays effectively fixed to that surface, an effect that the fluid dynamicists call “the no-slip boundary condition”.  You can imagine this like a deck of cards being spread out on a table, the bottom card barely moves, the card above that moves a little more and so on.  By the time you get to the top card there’s plenty of movement, but the first couple of cards would seem to be effectively “stuck”.

The top card moves a lot, the bottom card barely moves, and the distance each card moves with respect to its neighbors is about the same.

We experience this as a “bubble” of air around our bodies.  The air right next to our skin is almost stationary, while the air a foot or two away barely notices us at all.  The greater the air speed, the more shearing the air near our bodies is, and the thinner the layer of roughly-stationary-air.  The boundary layer (since it’s near us) is warmer than the surrounding air, and acts as insulation.  So more wind means less insulation, which makes you colder.

Unless you live somewhere terrible like Florida or Morocco.  Then the wind just blows away the air that was keeping you cool.  Terrible places to live.  If you want to know what Florida is like, get a dozen humidifiers and hairdryers, and lock yourself in a tiny, air-tight room.

When you wave a piece of cardboard, or something, through the air the resistance you feel is (mostly) a build up of pressure on one side, and a drop of pressure on the back.  Increasing the pressure on a region of air compacts it and causes it to heat up.  When you walk down the street your front should actually be a little warmer than your back, but if you really think you can feel it, then you’re probably walking with the Sun in your face.

The space shuttle does the exact same thing.  It’s just better at compressing the air in front of it, since it’s moving at about Mach 23.  The rush of air moving past the shuttle does cool it off, but the effect is completely overwhelmed by the effect of the compression.  The effect is most pronounced above the speed of sound (Mach 1).  Below Mach 1 air will just get out of the way rather than compress much, but above Mach 1 you can basically “sneak up” on the air.  It doesn’t know you’re coming until it gets hit.

Posted in -- By the Physicist, Physics | No Comments »

Q: Are explosions more or less powerful in space?

March 12th, 2010

Physicist: Brace yourself for a mess of guesses:

I’ve heard (anecdotally, and on Mythbusters) that explosions in water are more dangerous that than explosions in the air.  I don’t know if that has more to do with the specific properties of the medium, or merely with the presence of the medium itself, but (with a reasonable guess) it seems that having material around should help transmit the energy.

For an explosion in space, the only thing that carries the energy to you is light (which you would have gotten anyway) and material from the explosive itself.  So the explosion itself should do less damage, while the shrapnel should actually be more dangerous (in air it would get slowed down, and even somewhat cushioned on impact).

Also, in a medium energy tends to travel at specific speeds (the speed of sound generally) which means that most of the energy will hit you all at once (Shock waves can travel faster than the speed of sound, but they burn up a lot of energy doing it)  An explosion in space will cause material to fly out with a broad distribution of velocities, so you’ll experience the explosion over a more drawn-out time.

That’s all guess work.  If anyone knows anything for certain, please post a comment.

Interesting aside: The famous EMP (electro-magnetic pulse) that follows soon after an atmospheric nuclear detonation would be absent in space (deep space anyway).  The bulk of the pulse is actually generated by the explosion moving the ionosphere (it moves… the ionosphere).

Deep seated pet peev: The kick-ass billowing explosions of Vin-Diesel movies will also be missing from explosions in space.  Instead, the explosion would appear as a “star burst” of material all flying outward in straight lines.

A billowing explosion and a star burst explosion.

Posted in -- By the Physicist, Physics | 2 Comments »

Q: What is infinity? (A brief introduction to infinite sets, infinite limits, and infinite numbers)

March 11th, 2010

Mathematician: To mathematicians, infinity is not a single entity, but rather a label given to a variety of related mathematical objects. What unites these “infinities” is that they are all, in some sense, larger than anything that can be obtained or enumerated in the real physical world. Below, I will discuss a few of the infinities that crop up most frequently. One common feature they share is that our intuition about how things should behave often break down in these cases and the math requires some subtlety. Hang onto your hat.

1. Infinite Sets

Whereas sets like {1,2,3} and {dog, cat, apple, bat} clearly are finite in size (with size 3 and 4 respectively), it is natural to say that the set of all integers and the set of real numbers have infinite size. What is particularly interesting though is that while both infinite sets, the integers have an infinite size that’s smaller (in a precise sense) than that of the real numbers.

To observe this, we begin by noting that we can relabel the elements of {dog, cat, apple, bat} to be {1,2,3,4} by assigning dog=1, cat=2, apple=3, bat=4, which does not alter the size of our set (since the size of a set is independent of the names given to its items). However, {1,2,3} is obviously a subset of {1,2,3,4}, so {1,2,3} cannot be larger in size than {1,2,3,4}, and therefore {1,2,3} cannot be larger than {dog, cat, apple, bat} since this set was constructed from {1,2,3,4} just by renaming elements. More generally, if one (finite) set is larger than another, then we can always relabel the larger set so that the smaller one becomes a subset of it. Let’s now assume that this property continues to hold for infinite sets (or, if you like, we can use this very natural property as part of the foundation for the definition of the sizes of infinite sets).

Now, we apply this reasoning about relabeling to the real numbers and integers. First, we observe that the integers are a subset of the real numbers, and hence cannot have size larger than the real numbers. On the other hand though (and this is subtle requiring proof, which can be found here and here) it is impossible to relabel the integers in such a way that the real numbers become a subset of them. Hence, the real numbers are indeed larger than the integers in some important sense.

It may seem obvious that the size of the set of real numbers is in some sense a larger infinity than that of the size of the integers. What may come as a greater surprise however, is that the set of integers {…, -2, -1, 0, 1, 2, …}, the set of positive integers {1, 2, 3, 4, …}, and the set of all rational numbers {p/q where p and q are integers and q > 0} are all infinite but have exactly the same infinite size. The reason is simply because relabelings of these sets exist that make them all into the same set. For example, note that the assignment 1=0, 2=1, 3=-1, 4=2, 5=-2, 6=3, 7=-3, etc. will turn the positive integers into the set of all integers.

As it turns out, there is an infinite “chain” of infinities that measure the size of sets, including \aleph_{0}, the size of the integers, \aleph_{1}, the size of the real numbers, \aleph_{2}, the size of the set of all functions from the real numbers to binary values, and so on. In fact, for every set of size \aleph_{n} one can form a set of size \aleph_{n+1} by taking the set of all subsets of the original set. A disturbing questions with an even more disturbing answer can then be posed: “does there exist a set whose size is greater than \aleph_{0} but less than \aleph_{1}?” Bizarrely, this question turns out to be independent from the standard axioms of mathematics. That leaves us with just three options:

(a) Accept the fact that this mathematical question in unanswerable or “outside of math”.

(b) Reject the existence of sets that are larger than the integers and smaller than the real numbers which would be confirming what is known as the Continuum Hypothesis and amounts to adding a new axiom to math.

(c) Accept the existence of sets with this in between size, which implies adding the existence of such sets as a new mathematical axiom.

2. Limits

Infinities often arise when using “limits”, mathematical constructions which provide a rigorous backbone for calculus. When we have a function f(x) and write

\lim_{x \rightarrow \infty} f(x)

what we mean is the value (if one exists) that the function f(x) approaches as x gets larger and larger. So, for example, we have

\lim_{x \rightarrow \infty} \frac{1}{x} = 0

since by making x large enough, we can make \frac{1}{x} as close to 0 as we like. We would also write that

\lim_{x \rightarrow \infty} x^{2} = \infty

since as x gets larger and larger, x^{2} grows bigger without end (for any real number r there exists an x large enough so that x^{2} exceeds r) . We note though that there is a “rate” at which x^{2} approaches infinity. To see this, we can consider taking limits of the ratio of x^{2} to other functions which also grow without bound as x grows. If these ratios “go to infinity”, then x^{2} goes to infinity faster than these other functions. For example, we have:

\lim_{x \rightarrow \infty} \frac{x^{2}}{x} = \infty

and

\lim_{x \rightarrow \infty} \frac{x^{2}}{\log(x)} = \infty

whereas

\lim_{x \rightarrow \infty} \frac{x^{2}}{x^{2}-1} = 1

so x^{2} goes to infinity faster than x and \log(x) but at the same rate as x^{2}-1.

3. Algebra

Yet another way to think about infinity, is to introduce it as a special “number” with certain properties. For example, we can define \infty so that it satisfies (for all real numbers x):

\infty > x

\infty + x = \infty

\infty \times x = \infty when x > 0

\frac{x}{\infty} = 0

Similar rules could be used to define -\infty.  Some tricky cases arise though, for which no sensible definition of \infty seems possible. For example

\infty \times 0 = ?

\frac{\infty}{\infty} = ?

\infty - \infty = ?

Defining each of these latter statements is problematic. However, as long as we never need to multiply infinity by zero, or divide infinities, or do any other “undefinable” operations in whatever context we happen to be working, we can introduce \infty as if it were just a special new type of number.

4. Topology

Topology is the study of surfaces (actually, topological spaces, but surfaces are very similar and easier to think about) and the properties they have that are independent of angles and distances. If two surfaces can be made the same through stretching or pulling without requiring any cutting or gluing (more technically, if they can be mapped onto each other by a continuous function with a continuous inverse) then they are considered identical from a topological perspective. Hence, a disc and rectangular surface are topologically equivalent, as are a rubber band shaped surface and a disc with one hole punched in it (imagine stretching the hole until you get a band like object). You may begin to see why it has been said that a topologist is a person who can’t tell a teacup from a doughnut.

When topologists work with the real number line (i.e. the set of real numbers together with the usual notion of distance which induces topological structure), they sometimes introduce a “point at infinity”. This point, denoted \infty can be thought of as the point that you would always be heading towards if you started at 0 and traveled in either direction at any speed for as long as you liked. Strangely, when this infinite point is added to the real number line, it makes it topologically equivalent to a circle (think about the two ends of the number lining both joining up to this single infinite point, which closes a loop of sorts). This same procedure can also be carried out for the plane (which is the two dimensional surface consisting of points (x,y) where x and y are any real numbers). By adding a point at infinity we compactify the plane, turning it into something topologically equivalent to a sphere (imagine, if you can, the edges of the infinite plane being folded up until they all join together at a single infinity point).

In some sense these “points at infinity” that are introduced are not special in any way (they behave just like all other points from a topological perspective). However, if measures of distance are thrown back into the mix, it seems fair to say that these points at infinity are infinitely far away from all the others.

Conclusion

Ultimately, the question “what is infinity?” is not one that really can be answered, as it assumes that infinite things have a unique identity. It makes more sense to ask “how do infinite things arise in mathematics”, and the answer is that they arise in many, very important ways.

Posted in -- By the Mathematician, Math, Philosophical | No Comments »

Q: Are there physical limits in the universe other than the speed of light?

March 10th, 2010

Physicist: Hells yeah.

Fastest fast: This is worth commenting on since you often hear “nothing can travel faster then light”, but the justification is almost always missing.  The universe seems to be pretty happy thinking of the speed of light as being the same to everybody first (Maxwell’s Laws give you the speed of light, but Maxwell’s laws are the same to everybody so the speed of light is the same to everybody), and as a speed limit second.  Since you always see light moving at the same speed, then no matter how much you speed up, it will always pass you by.  So catching up to it isn’t an option, and everyone will always see you traveling slower than the speed of light.

Densest dense: The harder you compress something, the denser it becomes.  Normally this is reflected in the distance between atoms shrinking.  However, if the pressure is great enough, the atoms will find that it’s easier to have their electrons merge with their protons which then turn into neutrons (and also spit out neutrinos, but whatever).  Without battling electron shells, the once mostly-empty atoms can be packed nucleus-to-nucleus.  Pressures and densities this high only seem to show up in neutron stars (guess where the name comes from).  By way of comparison, here are some densities (in kilograms per liter): Air = 0.0012, People = 1, the Sun = 1.4, Iron = 7.8, Gold = 19.3, Neutron Star = 500,000,000,000,000.

You can also cheat a little.  If a neutron star has a mass of more than about 5 Suns it will collapse into a blackhole, which is technically more dense.

Coldest cold: You might have guessed: zero.  Specifically 0°K = -273°C = -460°F.  However, this is more of an “asymptotic limit” and can never quite be reached.  An object with a temperature of absolute zero will have no atomic movement (heat) whatsoever, but that’s not possible.  One way of thinking about it is in terms of the Heisenberg uncertainty principle which, in a paraphrased nutshell, states: “You can’t have both a perfectly certain position and a perfectly certain momentum”.  Where \Delta x and \Delta p are the position and momentum errors respectively, the uncertainty principle can be written: \Delta x \Delta p \ge \frac{\hbar}{2}.

So if you’ve got a substance and you have any idea where it is (\Delta x < \infty), then you can’t be sure that the momentum is zero, and the object will always have at least a little atomic movement.  Most people who have heard of Heisenberg’s uncertainty principle are under the impression that it’s a limit on how well we can know about an object.  In fact, it’s far better to think of it as a description of how well the universe can know about an object.

Despite the difficulties imposed by the uncertainty principle, we can still get things crazy cold.  The world record for lowest temperature now stands at 0.0000000001°K = 0.1 nK.

Hottest hot: There are actually two limits here, depending on how you phrase the question.  The first is the theoretical upper limit, which depends on which theory you’re working with, but is often quoted around 1030 °K.  These limits have to do with “the graininess” of space, and how much energy can be forced into a particular region.

The second kind of limit is more practical.  As a gas is heated its atoms move faster and faster.  When they collide they bounce of each other and often create photons (light), which generally just go on to push other atoms around.  However, as the temperature approaches about 4 billion °C, the atoms of the gas will often have enough energy to create electron/positron pairs (“E=mc2“, where “E” is the kinetic energy of the gas atoms, and “m” is the total mass of the electron/positron pair).  Normally these newly created particles will almost immediately find other electrons and positrons and annihilate, creating light.  But sometimes they’ll create neutrinos instead of light.  Neutrinos are “weakly interacting” (which is science speak for “goes through walls, no problem”), so the energy used to create them just flies into space, never to be seen again (or just about never).  This has the effect that a gas with a temperature above around 4,000,000,000°C will cool off on its own (without seeming to radiate any energy).  For comparison, the core temperature of the Sun is about 15.7 million °C.

The Sudbury neutrino detector: 40 feet across, and among the more evil looking things every built. Image stolen without remorse from "http://zuserver2.star.ucl.ac.uk/~idh/apod/ap990623.html"

This is sometimes important during stellar collapse.  If a star needs to have a core temperature above the cut-off point to hold itself up, then it’s not going to hold itself up.

Smallest small: Again, for “uncertainty principle type reasons” it doesn’t make sense to talk about objects or events smaller than the Planck scale, which is about 10-35m.  So far, nobody can think of anything in the universe, at any scale, that would really care, or be able to tell the difference between two points separated by 10-35m.

Emptiest empty: One version of the Heisenberg uncertainty principle can be written “\Delta E \Delta t \ge \frac{\hbar}{2}”, which means that the time and energy of something can’t both be perfectly well known (not even by the universe, the quantities themselves are uncertain).  If you apply this principle to empty space you’ll notice that over short enough time scales there will be measurable, non-zero energy, and over really short time scales you’ll find particle popping in and out of existence.  These particles are called “virtual particles”, and this phenomena is sometimes described as a “particle foam”.

So even with a perfect vacuum, you’ll still have crap around.  This crap is often called the “vacuum energy” or “zero point energy”.

One of the few examples of a device that can harness the vacuum energy of the universe to charge your chrystals or whatever. This illustration of "pyramid power" stolen from "http://www.merlinsrealm.com/pyramid-power.htm"

Sadly, harvesting the vacuum energy is physically impossible (it would violate the uncertainty principle).  The vacuum energy amounts to about 10-13J/m3, or about “the energy a baseball has falling off a table per volume of Lake Superior“.

Posted in -- By the Physicist, Astronomy, Physics, Quantum Theory, Relativity | 2 Comments »

Q: Is it of any coincidence that mathematics is able to describe physical reality – given that both are inventions of the human mind?

March 5th, 2010

Physicist: There’s a lot of math that doesn’t describe physical reality at all, and even some (few) mathematicians who feel that
“applicability” is just another word for “impurity”.  The ability of math to describe reality is just a consequence of the fact that reality is nice and consistent.

The fact that the math we use (addition, subtraction, geometry, calculus, whathaveyou) works is no coincidence at all.  Mathematics literally evolves in the sense that, if something doesn’t work, then people will ignore it.  So if you have a theory that \pi = 7, great, but no one will use it because it’s patently, provably false.  It doesn’t describe reality (in this case the reality that the ratio of the circumference to the diameter of a circle is \pi), so it goes the way of the Woolly Mammoth.

π=7

I assume that this question is about perceived reality (colors only exist in the brain, whereas in reality there is no “blueness” or “redness”), and not physical reality.  The fact that we can only describe (mathematically and otherwise) the reality we perceive does guide the direction of mathematical research, and as we perceive more we find that the field of math expands accordingly.  For example; number theory wasn’t much more than a hobby before digital communication and RSA encryption, and differential geometry was mostly a nuisance (and anal-retentive over-generalization) until general relativity cropped up.  Now these are both thriving fields of research (in computer science and physics, respectively).

However, just because something works in your head has absolutely no bearing on whether or not it will work in reality (which you would expect if the physical world were created by our minds).  Very good, very reasonable ideas get shot down by experiment every day, and we are constantly surprised.

Philosopher: If we assume the external world exists (independent of our minds), Math’s correspondence to reality is no more coincidental than the correspondence to reality of theories stated in any other language.  This isn’t dependent on the existence of mathematical objects, and it’s not dependent on Mathematical truths existing independently of humans (though I think they do).  If we assume the external world is merely an “invention of the human mind”, then the correspondence of Math to the world is even less coincidental, since the same thing is the author of both.

Posted in -- By the Physicist, Evolution, Math, Paranoia, Philosophical | No Comments »

Q: If you were to break down an average human body into its individual atoms, and then laid the atoms out in a single straight line, how far would it stretch?

March 3rd, 2010

Physicist: Atoms are a little “fuzzy”, so there exact size is a little tricky to define.  So taking their size in terms of bond length, and looking at the most common elements in the human body (by mass: 65% oxygen, 18% carbon, and 10% hydrogen), you’ll find that 1kg of person will stretch about 7 trillion km.  So an average (80kg) human would extend about 550 trillion km, or about 14 billion loops around the equator, or 1.4 billion trips to the moon, or about 58 light years.

So you can fit a rich man through the eye of a needle, but be sure to coil him up after you string him out.  Otherwise the process will take at least 58 years.

Posted in -- By the Physicist, Biology, Brain Teaser | No Comments »

Q: What’s it like when you travel at the speed of light?

March 3rd, 2010

Physicist: From a classical (Newtonian) view point this is a completely solid question.  However, in the context of special relativity the question itself is (unfortunately) non-sense.  For many practical purposes, the speed of light (hereafter I’ll call it “C”) is “infinitely fast”.  If you define infinitely fast as the speed you’ll be going if you accelerate forever, then C is exactly that.

Normally when you want to figure out “the behavior at infinity” you can “take a limit”.  For example; the limit as x goes to infinity of 1/x is 0.  This statement just means that as x gets bigger and bigger 1/x gets closer and closer to zero.  So by looking at the behavior at larger and larger finite values you can talk about what happens at infinity.  C, on the other hand, is fundamentally different from all other speeds.

At a basic level, speed is just distance traveled over time taken (as in “miles per hour”).  Due to the laws of special relativity, movement affects both the relative distances and relative time between two reference frames.

As a quick aside, a “reference frame” is just the set of all things that are moving at the same speed or, equivalently, are stationary with respect to each other.  So if you’re traveling down the highway you’re in the same frame as all the other cars around you (if everyone’s going the same speed), while the repair teams and clean-up crews on the shoulder are in a different reference frame.

It may seem silly to say it, but no matter how fast you move you still see things passing by, and it still takes at least a little time to get where you’re going.  At C however, the distance to your destination is always zero due to length contraction, while the time it takes to get there is also zero due to time dilation.  If you were to calculate your own speed you would say v= \frac{d}{t} = \frac{0}{0} = ?, which makes no damn sense.  I mean, what is that?

The universe: As seen by something traveling slower than C, and something traveling at C.

Also, consider this: at any other speed you can speed up or slow down, but at C you genuinely don’t have time to step on the brakes or the gas.  Literally, “time” and “distance” are phenomena that only make sense if you’re talking about them at speeds slower than C.  Stuff in the universe is divided into two categories: “massive” and “massless”.  Massive objects (anything with mass) always travel slower than C, while massless things must travel at C.

All that being said, you can wave your hands and talk about what life is like for a photon, that can’t exist at sub-light speeds (after all, what speed would you expect light to move at?).  When a photon is generated it immediately takes off at C, and never slows down until it runs into something.  Photons never experience time or distance.  As far as they’re concerned they are emitted and absorbed at the same place and time.  Many of the radio photons hitting you right now (about a third of them), have been traveling for around 15 billion years, but they think that the beginning of the universe just happened (or would, if they could think).

Posted in -- By the Physicist, Physics, Relativity | No Comments »

Q: Is there a real life example where two negatives make a positive?

March 3rd, 2010

Physicist: Although the laws of the universe are very absolute, the equations and terms we use are generally easy to rewrite and rephrase.  For example: it seems natural to describe the motion of a ball in terms of its altitude.  In this case gravity is negative (it decreases altitude).  But if instead you describe the motion of the ball in terms of “distance fallen”, then gravity becomes positive.

The classic example of the “arbitrarity of sign” is Ben Franklin’s horrifying mistake.  At the time that he was working it was impossible to tell where charge came from (in terms of electrons and protons), so he arbitrarily chose negative to be what we now know is the charge on electrons, and positive to be the charge on protons.  It makes no difference to the physical laws, which only care that the charges are different.  But it is annoying to electrical engineers who are haunted by the fact that “current”, which is defined as the flow of positive charge, actually points in the opposite direction in which the electrons move.

The point is this: I can’t think of any example of putting together two negative things and getting a positive thing, that couldn’t equally well be thought of as putting together to negative things and getting another negative thing.  For example: the force between two negative charges is repulsive.  So if you want to define “apart” as positive then two negatives (charges) makes a positive (force).  But if you define “together” as positive then two negatives make a negative.

Feynman summed up the general feeling in physics toward sign error (flipping positive/negative) when he said “If the sign is wrong, change it.”  So if, after lengthy calculation, you find that the moon is  – 238857 miles away, don’t stress about it.

Posted in -- By the Physicist, Philosophical, Physics | No Comments »

Q: Do the “laws” of physics and math exist? If so, where? Are they discovered or invented/created by humans?

March 1st, 2010

The original question was:

Mathematicians sometimes say, “There exists a number such that . . .”  Which provokes me to ask, Where does it exist? For how long has it existed? Did numbers exist before people did? Or did people somehow create (instead of discover) them?

In her “Incompleteness” quasi-biography of Godel (not a bad mathematician), Rebecca Goldstein emphasizes that he was a Platonist about math. What’s the current state of Platonism in math?

And such questions can be extended to the “laws” of physics: Do they exist?  If so, where? And for how long? Are they discovered (implying prior existence) or invented/created by humans?

Some comments relating to such issues would be interesting!

Physicist: Discovered.  Although most of the laws that can be re-arranged and expressed in different ways.  For example you can express “conservation of total momentum” as “the velocity of the center of mass never changes”.

A good physicist (one who pick their words carefully) will avoid saying that one thing or another is “true”.  Physics, and the laws we come up with, don’t exist “out there somewhere”.  Boiled down to its most basic, what we study is “what has worked before, and still seems to work” as opposed to “what is true”.

For example: Einstein showed that Newtonian physics is wrong (so wrong), but it still “works”.  If you learn Newton’s stuff you’ll notice that it’s fairly intuitive (compared to some other sciences at least), and seems to be true.  It was taught as fact for over 200 years, but again: wrong.  Taking this, and dozens of other similar stories as a warning, physicists try to talk only about what works and not what’s true.

That being said, some of the laws that have been found may actually be true, written into the nature of the universe.  I’d like to say that we know at least a few of them for sure, and that if what we know is wrong then the universe is entirely fucked.  However, that has been exactly the case before (I’m looking at you wave-particle duality), so who knows?

I like the hat best.

The pitiable population of "Monopoly". Are the rules they perceive the same as the rules written on the box? They could pass Go forever, and never know.

The laws we have could easily be special cases of the true laws (like Newtonian mechanics in relativistic mechanics), or could be merely the descriptions of the behavior created by those laws.

As far as the physical laws of the universe actually, physically existing in some form somewhere (this is the total extent of my understanding of Platonism): no, I don’t think there are very many scientists who think that.

Posted in -- By the Physicist, Philosophical | No Comments »

Q: Do we have free will?

February 27th, 2010

Physicist: If you want to get into an argument that drags on forever, you can frame a question like this in terms of consciousness, and the nature of choice, or any number of other ill-defined ill-understood ideas.  So consider only the question in terms of determinism;

Q: “does the state of the universe now (and in the past) completely determine the future of the universe and, by inclusion, the future of me?”

Back in the day (classical physics day) the answer could rightly be “yes” or “I don’t know”.  However, with the advent of modern quantum mech we’ve managed to make great strides on questions like this.  Now we can answer: “yes, no, and kinda”!  It’s progress like this that almost makes going back to clipper ships and horse carts worth it.

One of the biggest weirdnesses to come out of quantum mechanics is the idea of “super-position”, which is that a single thing (a particle or whatever) can be in multiple states at the same time (the state of a thing can involve position, speed, orientation, and even how the thing is related to other things).  QM allows us to see how all of those states change in time and interact each other.  However, any direct interaction with an “undetermined state” will reveal it to be in only one (of its many) state(s).  In what follows I’ll use “universe” to mean the universe with just one state (things did happen this way), and multiverse to mean all the states involved simultaneously (with all the interference and what-have-you).

The two ways of looking at this are the “Copenhagen interpretation” (wrong) and the “many worlds interpretation” (right).

“Yes!”: Given complete knowledge of the multiverse’s quantum wave function you can determine the future of that function forever.  Unfortunately, this isn’t particularly useful for those of us who live inside the universe.  The wave function in question encompasses all possibilities simultaneously and involves plenty of self-interference.  For example: when you do the double slit experiment you can calculate exactly what the fringes will look like on the screen, by doing a calculation that assumes that the photons involved go through both slits.  However, if you were to instead look a one of the slits, this doesn’t tell you anything about whether or not you will see the photon go through that slit.

(Just a quick note about the link above.  “The Secret”, and its creepy brainchild “What the bleep”, are both symptoms of a greater douchiness, but despite their culty bent they explain the double slit pretty well.)

In fact what happens is it goes through both slits, but in turn there are different versions of you that see both outcomes.  If you look at the multiverse as a whole (seeing every state) then everything is completely deterministic.  If you look at just one tiny piece at a time (like we seem to), then everything seems random.

Essentially, for every choice you can make, there are a whole mess of versions of you (identical up to the moment of choice) that do make that choice.  In fact, if your wave function is known completely, then how much (many?) of you goes down any road can be derived.  I don’t want to hear anyone saying “but I chose to do that!”, because some (part?) of you had to.  But then, some of you had to do every available choice.

“No!”: Part of the Copenhagen interpretation is fundamental, true randomness.  There’s no multiverse in Copenhagen (so don’t go flying there to look), so any choice you make is unpredictable (or at least, not completely predictable, there are some pretty reliable people out there) in the sense that no matter how good your fore-knowledge of someone’s wave function, you still can’t make perfect predictions.

It’s seems like there’s enough wiggle room in there to fit some free will.

“Kinda!”: Even if you subscribe to the many world hypothesis you could argue that “dude, who cares?”.  You’ll never meet (can’t meet) those other versions of yourself, so what does it matter that, in theory, all of your simultaneous actions are determined in a multiverse-kind-of-way?  Doesn’t.

Posted in -- By the Physicist, Paranoia, Philosophical, Physics, Quantum Theory | 1 Comment »

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