Q: Do aliens exist?

Posted on January 30, 2010 by The Physicist

Physicist: Yuppers.  In as much as the probability that they don’t is effectively zero.

The statistics on this are a little weak, since we only have one real data point.  If you define intelligent life as tool-using, then (based on the age of the oldest tools and the oldest fossils, and the progress of the Earth to date):  Intelligent life has existed 0.06% of Earth’s history, and animal life has existed for about 16% of Earth’s history.  Moreover, the vast majority of life on Earth (and the toughest) is microbial.  So by “yuppers”, I mean that space bacteria almost certainly exists.

As far as the fancy aliens (with their lasers and tentacles) that I assume the question is really about: probably.  The universe is crazy big.  However, stars are far apart (especially around here), and the likelihood of finding intelligent life is really low.

In the last decade there have been some surprising results from the panspermia people.  It seems to be entirely possible, even likely, for life to get kicked from planet to planet and even from star to star.  The three difficulties are getting off a planet, surviving in space, and landing somewhere else.  During a major impact the material immediately around the impact is vaporized.  A little farther out and things are pulverized.  Just beyond the “automatically dead zone” is a thin ring where material from the planet’s surface can be thrown into space smoothly (no more than a couple hundred G’s) and without excessive heating.  Although no animals could survive the shock, massive G forces have very little impact on single celled life (too small to slosh).

There’s a wide variety of life from Earth that does fine in space.  Things like Water Bears, and some bacteria can put up with the cold and radiation, and are more than happy to drop into a state of suspended animation for the trip (forever if they have to).  The classic example is a few cells of Streptococcus that survived on the moon (on Surveyor 3’s camera) between 1967 to 1969.

Something you may notice, if you collect large meteorites, is that although the surface tends to be pretty messed up, the interior is frequently quite intact.  Although the fall looks pretty impressive, the heat and fireball don’t have time to cook the meteors all the way.  In fact the hottest parts of the meteor vaporize during the fall, which serves to keep it cool (like sweat, but like… a rock version).  Although it’s unlikely for living things on any one rock to make it through all three stages intact, keep in mind that there are actually many rocks flying around that have been knocked off of planets in the past.  There are so many, that one of the cheapest ways to collect samples from Mars or Venus is to go to Antarctica.  (If you find a rock sitting on top of a 3 miles of ice, where do you think it came from?)  One of the biggest “life is out there” stories came from exactly this source.

Here’s the point: If there’s life anywhere it’s likely to spread everywhere, like… well, like life.  Panspermists think that life may have started on some other planet around some other star, and that this life then infected the Earth.  This would help explain why the Earth was covered with sophisticated (microbial) life almost immediately after it was capable of supporting life at all.  Or to spin it around, if there’s life here (check) it’s had over 3 billion years to get blasted out into the nearby universe.

Mathematician: There are compelling reasons to think that life exists on other planets (perhaps even on a huge number of other planets). If life spontaneously arose on earth from a soup of molecules through an evolutionary process, then all you need for life to be created is the right planetary conditions, the proper raw materials, and a sufficient amount of time. The right conditions may include things like being close enough to a sun that the planet is reasonably warm, but far enough from that sun so that it isn’t  burnt to a crisp. The right materials probably include carbon and water among other things. In any event, once you get these things right, you just add time (a billion years probably would suffice) and viola, life is born. That means that for earth to house the only living organisms in the universe, these requirements would have to have been met one time and one time only in all the billions of galaxies that have formed during the 14 billion year history of our universe. That sure sounds pretty unlikely.

Here’s another way to think about it: there is some probability p that a randomly selected planet will form life on it within a billion years. If p is sufficiently small, then there would be almost no chance of any life forming, including our own, and hence we should not exist. If p is sufficiently large, then life would exist almost everywhere in the universe. The only way that we should expect to be the one and only planet with life is if p is just right to produce about one planet with life over all the years and on all the planets that have ever existed. But we have no evidence whatsoever indicating that p should be perfectly balanced in this way, indicating that the chance of alien life is a good one.

But does technologically advanced alien life exist? Well, if life occurs on many other planets, then we should expect technologically advanced life to occur on at least some of them. Whatever caused natural or sexual selection to select for high levels of mammalian intelligence on earth could lead to intelligent aliens as well. On the other hand though, if technologically advanced civilizations tend to wipe themselves out fairly quickly (say, within a hundred thousand years) or if the process that creates highly intelligent life requires sufficiently rare conditions, then advanced aliens could certainly be the exception rather than the rule.

Posted in -- By the Mathematician, -- By the Physicist, Astronomy, Biology, Evolution, Physics | 11 Comments

Q: Is it true that all matter is simply condensed energy?

Posted on January 29, 2010 by The Physicist

The complete question was: Is it true that all matter is simply condensed energy? Does that mean that the Big Bang was pure energy and coalesced into matter?

Physicist: Pretty much.  If you can get enough energy into one place (generally light or kinetic energy), then you’ll get a (mostly random) variety of particles popping out. The conversion between mass and energy is so ubiquitous in physics, that most physicists only know the mass of particles in the context of their equivalent energy.  If you ask a physicist “what is the mass of an electron?” they’ll say “0.5 MeV” (which is a unit of energy).  Frankly, it’s more important to know than the actual mass.  I mean, how hard is it to pick up an electron?  If you answered “I don’t care” or “zero”, you’re right.

The only thing that keeps particles from turning back into energy (again, usually light and kinetic) are “conserved quantities”.  If you’ve taken an intro physics course you should be familiar with conservation of energy and momentum.  In particle physics you also need things like: charge, Lepton flavor (which covers things like electrons and neutrinos), and Baryon number (which covers things like protons and neutrons).

The classic example is neutron decay:

Neutron decay: Tricky business.

A neutron is heavier than a proton, so you’d think it would decay into a proton and some extra energy (conserving energy and baryon number).  But that would violate conservation of charge (protons have 1, neutrons have zero).  So maybe it could decay into a proton and electron?  Now you’ve balanced charge, but violated lepton flavor (electrons have “electron flavor 1”).  To balance everything you need to add an anti-electron neutrino (electron flavor -1) to the mix.

The very early universe was a “particle soup”.  The mean energy of the photons flying about was more than enough to generate new particles.  These would pop into existence in balanced quantities and then cancel out again.  The big difference between now and then (why we don’t see particles being spawned off all the time) is that the average energy of photons today is closer to 660 meV (about 1 billionth of the energy needed to create electrons, the smallest particle).

Posted in -- By the Physicist, Particle Physics, Physics, Quantum Theory | 33 Comments

Q: Which is better: Math or Physics?

Posted on January 28, 2010 by The Physicist

Physicist: Physics.

Mathematician: Math, of course. Can physics do this?

1 = \sum_{k=0}^{\infty} \frac{(2 \pi)^{2 k}}{(2 k)!} (-1)^{k}

Physicist: Lasers, dude.

Mathematician: Lasers, shmasers.

Posted in -- By the Mathematician, -- By the Physicist, Math, Philosophical, Physics | 65 Comments

Q: Why is the number 1 not considered a prime number?

Posted on January 27, 2010 by The Mathematician

Mathematician: Note that when we say that a number is “prime”, all that we are doing is applying a definition that was devised by mathematicians. A prime number is generally defined to be any positive number that has exactly two distinct positive integer divisors (the divisors being 1 and the number itself). So 13 is prime, because it is divisible only by 1 and 13, whereas 14 is not prime because it is divisible by 1, 2, 7 and 14. Note that this excludes the number 1 from being prime. The biggest reason this definition of primality is used, as opposed to a slightly different one, is merely a matter of convenience. Mathematicians like to choose definitions in such a way that important theorems are simple and easy to state. Probably the most important theorem involving prime numbers is the Fundamental Theorem of Arithmetic, which says that all integers greater than 1 can be expressed as a unique product of prime numbers up to reordering of the factors. So, for example, 54 can be written as 54 = 3*3*3*2 which is a unique factorization assuming that we list the factors in decreasing order. Now, notice that if we counted 1 as a prime number, then this theorem would no longer hold as stated, since we would then be able to write

54 = 3*3*3*2*1 = 3*3*3*2*1*1 = 3*3*3*2*1*1*1

so there would not be a single, unique representation for 54 as the theorem requires. Hence, if we count 1 as a prime number, then the Fundamental Theorem ofArithmetic would have to be restated as something like, “all integers greater than 1 can be expressed as a unique product of prime numbers (not including 1) up to reordering of the factors.” This is a tiny bit more cumbersome, but not horrible. If you have to work with prime numbers day in and day out though, simplifying theorems just a little bit (by choosing your definitions carefully) may well be worth it. Nonetheless, if mathematicians chose a slightly different definition for primality that included the number one, while they would then be forced to modify many of their theorems involving primes, the world wouldn’t come crashing down on its head.

Posted in -- By the Mathematician, Math, Number Theory | 41 Comments

Q: If the universe is expanding and all the galaxies are moving away from one another, how is it possible for galaxies to collide?

Posted on January 26, 2010 by The Physicist

Physicist: Because the universe isn’t expanding fast enough.  On average all the galaxies are moving apart, but often a given pair will be moving together.

Hubble observed that the farther things are away, the faster they’re receding.  Specifically, in the universe today, v = H_0 d where v is the relative velocity of two objects, d is the distance between them, and H_0 = 22 \pm 2 \, mm/s/Lyr (millimeters per second per light year).  Now this is an averaging thing, since galaxies are free to move however they like.

So for example, this equation says that the Andromeda galaxy which is 2.5 MLyr (million light years) away should be moving away at around 55km/s.  Instead it’s flying at the Milky Way at about 120 km/s.

As a side note: when Andromeda gets here (or we get there, or whatever) the collision of our gas clouds should set off a huge spike in star formations resulting in a liberal peppering of supernovas (bad for everyone).  But we’ve still got another 2.5 billion years, so don’t pack your bags just yet.

Posted in -- By the Physicist, Astronomy | 6 Comments

Q: What happens when you fall into a blackhole?

Posted on January 24, 2010 by The Physicist

Physicist: Terrible, terrible things.

The first thing you’ll be likely to notice as you approach the hole is the tidal forces.  Tidal forces are nothing more than the difference in gravitational force between the near and far side of an object, and they aren’t particular to blackholes.  For example, the tidal force of the moon on the Earth causes tides (hence the name).  For any reasonable sized blackhole (less than thousands of suns), the tidal force between different parts of your body will be greater than your body’s ability to stay intact, so you’ll be pulled apart in the up-down direction.  For much more obscure reasons, you’ll also be crushed from the sides.  These two effects combined are called “spagettification”.  Seriously.  Assuming that you somehow survive spagettification, or that you’re falling into an super-massive blackhole (which is ironically much more gentle than a smaller blackhole) then you can look forward to some bizarre time effects.

It’s been established for decades that “time moves slower the lower”.  For example, GPS satellites have to deal with an additional 45 microseconds every day due to their altitude (they move through time faster).  Also, one way to think about gravity is as a “bending” of the time direction downward.  In this way anything that moves forward in time will also naturally move downward.  At the event horizon of a blackhole (the outer boundary) time literally points straight down.  As a result, escaping from a blackhole is no more difficult than going back in time.  Once you’re inside all directions literally point toward the singularity in the center (since no matter what direction you move in will be toward the future).

We don’t experience time moving at different rates or being position dependent, so when we start talking about messed up spacetime it’s useful to look at things from more than one point of view.

From an outsider’s perspective (far from the blackhole): As someone falls in they will move slower and slower through time.  They will appear redder, colder, and dimmer.  As they approach the event horizon their movement through time will halt, as they fade completely from view.  Technically, you’ll never actually see someone fall into a blackhole, you’ll just see them get really close.

From an insider’s perspective (falling into the blackhole): First, torn apart and crushed.  Things farther from the blackhole move through time faster, so the rest of the universe will speed up from your point of view.  As a result the rest of the universe becomes bluer, hotter, and brighter.  The blue shift of the incoming light turns it into gamma rays.  So, right before you pass through the event horizon, you’ll get nuked with a universe’s lifetime worth of starlight and microwave background radiation turned into nuking nastiness.  The event horizon itself is only special from an outside perspective.  If you fall in you should pass right through it.  However, what you see in the moment that you pass through the horizon is dependent on things we don’t know yet.

-If the blackhole lasts until the universe ends (assuming that the universe ends), then you’ll see the entire history of the universe whip by (bluely).  You’ll then find yourself face to face with the singularity.  At that point you go away, according to the math.  However, the universe is slippery like a greased up eel fresh from the bar exam.  It always finds a way to not have singularities where the math predicts it.  So, to be safe, I’ll say “no one knows what happens then”.

-If the blackhole evaporates, then all the matter that (almost) gets to the horizon will be torn apart and reappropriated as Hawking radiation.  If you were to survive, then you would find yourself as close to the horizon as (for uncertainty reasons) it is possible to be, and you would ride it in as it shrinks.  In a blink you’d suddenly find yourself floating around right next to an amazing explosion, as the last of the blackhole evaporates.

Posted in -- By the Physicist, Astronomy, Physics | 89 Comments