Q: Can things really be in two places at the same time?

Posted on December 6, 2009 by The Physicist

Physicist: Yuppers.

The classic example is Young’s Double Slit experiment.

Experimental set up for Young's Double Slit experiment. Image stolen from http://psi.phys.wits.ac.za/teaching/Connell/phys284/2005/lecture-02/lecture_02/node3.html

a) Experimental set up for Young's Double Slit experiment. b) The astounding results. Image stolen from here.

When coherent light is shined on two slits, then the image that’s projected on the final screen exhibits interference patterns (because light is a wave, of course).  Back in the day, Mr. T. Young got his coherent light by only allowing light to come through a single tiny hole, thus preventing any interference from other sources (as in light from the left side of a window interfering with light from the right side of a window).  It was very dark and, I suspect, lonely.  These days we have kick-ass lasers, well lit labs, and occasionally married scientists.

Einstein demonstrated that photons are particles (of course) with the “photo-electric effect”.  Now, here’s what makes Young’s experiment such an excellent argument for why the universe hates scientists: The interference fringes continue to persist no matter how much you turn down the intensity of the light source.  Even when the source is so low that only one photon is being released at time, you can still see interference.  The conclusion is that a single photon can interfere with itself.

WTF! you may say.  And rightly so.  If it goes through the lower slit, then obviously it didn’t go through the upper slit, so obviously it shouldn’t have any idea that the upper slit is even there, and visa versa.  However, the pattern on the screen is exactly consistent with the (single) photon acting like a wave: interfering with itself, being in many places, and all that.

Here’s something even worse: A particle can actually interfere with itself across time as well.  In the double slit experiment the photon self-interferes between two uncertain sources in space (which slit did the photon go through?).  Experiments, such as the “Franson Experiment”, have been done to demonstrate self-interference where the source of light is uncertain in time (when was the photon emitted?).  The exact details of the experiment are subtle and surprisingly boring, so just go with it.

Set up for the Franson Experiment

Set up for the Franson Experiment

As an aside, the Franson experiment also shows that not only do things have multiple futures (Young: the photon will go through both slits), but also that things have multiple pasts (Franson: the photon you observe was emitted at several different times).  Please send all complaints to: The Universe, et al.

Posted in -- By the Physicist, Quantum Theory | 17 Comments

Q: Why do weird things happen so much?

Posted on December 5, 2009 by The Physicist

Physicist: First, “normal” things don’t catch the eye.  There’s a natural bias toward noticing the out-of-the-ordinary.

Where did you look?

Where did you look?

Also (mathematically speaking), although the chance of any one particular unlikely event is unlikely (because it’s unlikely), there are a very large number of unlikely events that could happen.  It’s this huge number of possible events that forces the probabilities to favor the “unusual happenstance camp”.  Feynman summed it up pretty well:

“You know, the most amazing thing happened to me tonight. I was coming here, on the way to the lecture, and I came in through the parking lot. And you won’t believe what happened. I saw a car with the license plate ARW 357. Can you imagine? Of all the millions of license plates in the state, what was the chance that I would see that particular one tonight? Amazing!”

Everyday you’re exposed to billions of Weird things (I’m defining “Weird” as 1 in a million) that could happen.  Substantially less if you don’t leave the house.  Substantially more if you live outside of Kansas (that’s right, Kansas).  The probability that something extremely Weird happens around you in any given moment is 100%.  For example; if you get change for any transaction, the probability that you get that particular set of coins (those exact coins) is much less than 1 in a million.  However the probability that you’ll notice a Weird event is fairly small.  Luckily, this is something you can control.

Say you notice N things everyday that have the potential to be Weird.  Every piece of toast hiding the Virgin Mary™, every pair of snowflakes that might be identical, every bird that may drop gold doubloons on you, etc.  Then the chance of noticing something Weird is P = 1 - \left( \frac{999,999}{1,000,000} \right)^N.  Which means that every time you look at about 700,000 things you’ll have a 50% chance of seeing something Weird (which isn’t that bad, can you see 1,000 things now?).  If you restrict you attention only to “big” Weird things, then you’ll find yourself pretty disappointed, and it’s because there aren’t a lot of big things that happen day-to-day.

Now most people would consider 1 in a million a little strict, so if you keep your eyes open you’ll see Strange things almost continuously.

Also, consider this: “close calls” are substantially more likely than “hits”.  For example; you’re 8 times more likely to hit the bull (50 points ring) on a dart board than you are to hit the bull’s eye.  Unless you’re like crazy good, in which case: keep it to yourself.

The "Bull" and the "Bull's Eye"

The "Bull" and the "Bull's Eye"

Posted in -- By the Physicist, Math, Philosophical | 3 Comments

Q: Why?

Posted on December 2, 2009 by The Mathematician

Mathematician: From time to time, people like asking us questions such as “Why?”, while steadfastly refusing to explain what the heck they are talking about. The best example of this was a naked guy who approached our “Ask a Mathematician / Ask a Physicist” booth at Burning Man. In an attempt to respect everyone’s right to not explain themselves, we’ll make a series of guesses about what those folks might be trying to get at, and briefly respond to each of these possible questions.

1. “Why do we exist?”

Mathematician: We exist because our ancestors were at least slightly better at passing down their genetic material than other people. If the environment of earth happened to be just a tad bit different, then other genes besides our own would have been favored, and we would not be here today. If the environment had been a little more different still, then not only would we not be here, but the human species would not even be here. Some other creatures (possibly of great intelligence) would now be romping around this planet. In conclusion, we exist because the process of evolution works, because our planet happened to have the right conditions for evolution to begin, and because conditions changed over time such that human genes (and more specifically, our ancestor’s genes) happened to be favored for survival. We all got very, very lucky.

Physicist: If the many-worlds hypothesis holds (it totally does), then everything that’s possible happens in some version of the universe.  If you can ask the question “Why do we exist?”, then you’ve already restricted your attention to the (possibly very small) set of universes where intelligent life exists.  This argument is called the “anthropic principle“.  So the reason we exist is because there is at least some vanishingly small chance that we could.

2. “Why does existence exist?”

Mathematician: Nobody knows. A related question that nobody knows the answer to is “why does consciousness exist?”  For example, why aren’t we like computers, going about our business without ever “feeling” anything or having any “internal, personal experience”? There are a few possible answers to this question. Perhaps we don’t really have consciousness and we just think we do (though this answer strikes me as bullshit). Another possibility is that consciousness is something that emerges automatically (call this a property of the universe) when you have a sufficiently complicated system with the right components, and that we have consciousness merely because evolution happened to produce those special components in our brain (so in that case consciousness is a side effect of some useful brain parts). A third option is that consciousness was created by the process of evolution because it has a specific survival use (perhaps it is a handy way to get creatures to spread their genes).

Physicist: What else is existence going to do?

3. “Why is the universe the way it is?”

Mathematician: I consider this to be a deep mystery. According to an old Finnish creation story, the sky is a piece of an egg and the sun is its yolk, but this strikes me as unlikely. Perhaps physicists will one day be able to shed light on this question.

Physicist: If there’s some kind of rhyme or reason behind the beginning, then go figure out who was doing the reasoning and ask them.  If, however, the universe was randomly generated, then it may follow the same rules for random generation that everything else in the universe does.  The probability that a particle is generated is proportional to the number of states it can be in.  So if an electron can be in two states and a pion can be in three, then the pion is 3/2 times more likely to be created than an electron.  More states means more entropy.  The universe may be the way it is because our particular set of physical constants (speed of light, gravitational constant, planck’s constant, etc.) cause the universe to have tremendous complexity (many many states). If the constants were different, then everything might have already fallen into black holes, or complex molecules may not form, or there may be no stars or solar systems, etc.  Each of these circumstances have a much lower entropy than the universe we see today. So (perhaps) the universe is the way it is so that it can maximize it’s own entropy.

4. “Why are we the way we are?”

Mathematician: We have eyes because there is a Sun near our planet that is bouncing light off of everything, and it is mighty useful (for survival) to be aware of this radiation. It is so useful, in fact, that eyes have been created (from scratch) multiple times on the evolutionary tree. But why do we have two eyes, rather than one? In part, it probably serves as a back up system: since vision is so critical to survival on this planet, and since eyes can easily be pierced or go faulty, it’s much safer to have two. Another reason to have two eyes is because it allows us to have true 3D vision (which again, likely increases a creatures chance of survival). Why do we have arms and hands? Because our ancestors walked on four legs (which is useful for fast running, and our arms developed from these front legs) and manipulating the world around us is damn useful (thank you fingers!). Why do we have legs? Well, because that’s one of the best mechanisms that evolution found for getting around. These arguments can be repeated for most body parts. The point is that we are the way we are because the environment of earth during our evolution made the traits that we have useful for survival. We could have been very different had conditions been a little different, but things like eyes and legs are so incredibly useful that it is very likely we would have at least had those.

Physicist: Evolution favors what works.  Things that work, and have thus evolved over and over in different places here on Earth, include: limbs, blood, eyeballs, nervous systems, sex, socializing, fighting and fleeing, eating and pooing, smelling, breathing, moving, not looking at the sun, … As for why we’re bipedal, hairless, and whatnot: sometimes these things happen.  If you’ll notice, there aren’t a lot of other creatures that share these traits.  If we were something else we’d wonder about that too.

5. “Why am I me and not someone else?”

Mathematician: Just chance, mostly, but you are also changing into a new person every moment, with new cells, new memories, new ideas and new behaviors.

Physicist: You’re no one at all before you’re born.  Who you are now is who you’ve become.

Posted in -- By the Mathematician, -- By the Physicist, Evolution, Philosophical, Quantum Theory | 7 Comments

Q: Will CERN create a black hole?

Posted on November 26, 2009 by The Physicist

Physicist: Unfortunately, ultra small black holes straddle the line between quantum mechanics and general relativity, which makes it difficult to make useful predictions.  The answer is: a solid maybe.  If your conCERN is that the black hole thus created will destroy the world, you can relax.

First, the hole will be so small that you couldn’t force-feed it an electron.

Second, the TeV (the energy an electron has after being pushed through 1,000,000,000,000 volts) collisions that CERN is aiming for happen in nature.  Statistically, they should happen in the upper atmosphere somewhere in the world a couple times a day.  The record is held by the OhMyGod particle detected in 1991, which had an energy of around 300 million TeV.  So if we can form tiny black holes, then nature’s already beaten us to the punch.  The evidence of these ridiculously high energy collisions come in the form of a “shotgun” wave of intense radiation, that only affect small areas on the ground a couple hundred yards across.  You’ve been hit by several of these events in your lifetime, and been none the wiser.

Do to the effects of Hawking radiation (which makes small black holes fizzle out and disappear), the scientists at CERN are working on methods to detect the secondary effects of a fresh black hole evaporating, instead of detecting the hole itself.  They don’t expect it to last long enough to get from the collision point all the way to the detectors, which are only inches away.

CERN: The last thing James Bond will ever see.

CERN: The last thing James Bond will ever see.

Posted in -- By the Physicist, Paranoia, Physics | 11 Comments

Q: What’s the highest population growth rate that the Earth can support?

Posted on November 24, 2009 by The Physicist

Physicist: Zero.

Populations tend to grow exponentially, which is why the growth rate is defined as R in P = AeRt, where A is the population at time t=0, and P is the population at any other time t.  If the average growth rate is greater than zero, then the population will grow exponentially forever, which is sadly impossible.  Here’s why:

If the population could grow forever, then eventually the total mass of Humans would be greater than the mass of the Earth, which makes no damn sense.  What were we eating?

The population could grow forever if we found a way to colonize other star systems.  However, even with speed-of-light ships we could only colonize something like \frac{4}{3} \pi (Ct)^3 planets in time t, since we can’t travel faster than light (this is the volume of a sphere that expands at the speed of light, C).  The population density in the colonized area of the universe would then look like \frac{\textrm{Population}}{\textrm{Volume}} = \frac{3A e^{Rt}}{4 \pi (Ct)^3} \propto \frac{e^{Rt}}{t^3}, where “\propto” means “proportional to”.  You’ll notice that if R is greater than 0, then as time increases the population density goes up forever, which makes no damn sense.  If you don’t notice, then just graph it.

What this ultimately means is that the average, over all time, of the number of children that a person has is 2 or less.  No way around it.

We’ve had a lot of visits from reddit.com with a little confusion over the line “populations tend to grow exponentially” (my bad).  What I should have written is “populations tend to grow exponentially under the assumption that they have not yet begun to saturate the available resources”, but I figured that might be pushing the discussion.  The less that resources are available, the more the population will tend to level off.  Both the exponential growth and leveling off can be modeled using various scalings of the logistic function.  Try graphing: \frac{1}{1+e^{-t}}, and e^t.  You’ll find that they line up almost exactly until near t=0, where resources begin to dwindle.

Posted in -- By the Physicist, Biology, Math | 5 Comments

Q: What is time?

Posted on November 23, 2009 by The Physicist

Physicist: All philosophy aside, the best answer is due to Einstein, who said (after lots of thought) that “Time is what clocks measure”.

The term “spacetime” gets bandied about a lot.  And you may have been lead to (correctly) suspect that time and space are closely related, and even a little interchangeable.  Time is still not exactly like another spacial dimension (like the usual 3).  Which is why physicists will tend to say that we live in “3+1 dimensions”, for 3 spacial dimensions, and 1 time dimension.  If someone says that time is “the 4th dimension”, keep in mind that there’s an asterisk attached.

If you’re trying to measure a distance D between two events x_1 and x_2 in 1 dimension you’ll find that D = \sqrt{(x_1-x_2)^2}, which is just another way of writing “the absolute value of x_1 - x_2“.  In 2 dimensions D = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}, which is the Pythagorean theorem.  And in 3 dimensions D = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2 + (z_1 - z_2)^2}.  Notice a pattern?  The kick-ass thing about each of these equations is that no matter how you shift or spin around the coordinates, D will always stay the same, which is exactly what you’d expect.  If you measure a yard stick at any angle, anywhere in the world, you’ll always measure the same length.  “D” is the only equation that makes that happen.

In 3+1 dimensions (the standard spacetime) L = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2 + (z_1 - z_2)^2 - C^2(t_1 - t_2)^2}.  Here the x’s, y’s, and z’s are the coordinates in space of event 1 and event 2, the t’s are the time coordinates of those events, and C is the speed of light.  “L” is the measure of distance in spacetime, but to keep everything straight it’s called the “spacetime interval”.  You may have noticed that sometimes when you use this equation that you’ll be taking the square root of a negative number.  Don’t worry about it.  The power of the Interval, L,  is that, like the D above, L remains unchanged by changing location, rotating, and even movement (holy crap), and it is the only equation that does all that.  So hidden away in all that wordiness is the big difference between space and time:

The time term in L has a minus sign.  As far as physics goes, that’s about it.  All of the horror and weirdness of special relativity (all the time dilation, length contraction, ruined simultaneity, all of it) can be tracked back to that minus sign.  If you wanted to, you could define time to be the direction in spacetime that has a minus in front of it in L.  I don’t think many people do that (not many grounded people at least), but they could if they really wanted.

Posted in -- By the Physicist, Philosophical, Physics, Relativity | 11 Comments