Q: If you were on a space station, would you be able to tell the difference between centrifugal force and normal gravity?

Posted on November 10, 2009 by The Physicist

Physicist: Normal gravity on Earth, G, never changes.  However, the acceleration, C, due to centrifugal force on the station is given by C = \frac{V^2}{R}, where V is how fast the station is spinning, and R is the radius of the station.  If you’re sitting still or walking slowly on a space station, then you’d probably never notice the difference, but if you run either with or against the direction of spin you can change the value of V (for yourself), and thus change the amount of centrifugal force you experience.  Whether or not you notice a difference now depends on how big the station is.

What I'm picturing right now

Kick-ass, spinning space station (from "2001")

The acceleration, due to gravity on the surface of the Earth is about G = 9.8 m/s^2, and I would guess that a 5 \% change in your weight is generally detectable.  Given this 5 \% estimate, a running speed of around 4.5 m/s (10 mph), and assuming that the station is spinning exactly fast enough to have C=G, then, after some math happens, you’ll find that when the radius of the station is less than around 3.25 km that you can detect the difference.  So, you could tell the difference on any ship or station likely to be made in this solar system at least.

If you don’t feel like running back and forth you can try playing catch.  You’ll find that when you throw a ball spinward that it curves down, and that when you throw the ball anti-spinward it curves up.  In fact, if you can throw the ball as fast as the station spins, then you can make the ball fly at the same height forever (assuming no air resistance).  In this case the ball is actually sitting still while the station spins around it.

Throwing a ball spinward causes it to fall short

Throwing a ball spinward causes it to fall short

Throwing a ball anti-spinward causes it to go farther

Throwing a ball anti-spinward causes it to go farther

Posted in -- By the Physicist, Physics | 10 Comments

Q: Is teleportation possible?

Posted on November 9, 2009 by The Physicist

Physicist: Nope.

The best you could hope for is a machine that reads the exact location of every atom in your body, as well as it’s chemical relationship to every nearby atom, then sends that blue print to another machine that builds a new body one atom at a time. Not only is every step of this a horrifying technical problem, but for “Uncertainty Principle” reasons is almost certainly impossible. Also, it doesn’t seem to be what they do on Star Trek.

Back in the 90’s it was shown that if two people share a pair of entangled particles, then they can use them to send 1 qbit instead of 2 bits, or they can send 2 bits instead of 1 qbit.  The former is called “superdense coding” and the latter is called “quantum teleportation“.  The guy who named it “quantum teleportation” and not the “2 bits = 1 qbit theorem” is a jerk.

The discovery, and more importantly the subsequent naming, of quantum teleportation lead to a new (false) hope that entire objects might be teleported.  In fact the only thing being “teleported” is information about the particle involved (not the particle itself).

What follows is answer gravy (more complex):

For example: the polarization of a photon is a combination of both vertical and horizontal polarization.  If you were to measure the polarization you would get a result of “vertical” or “horizontal”, but never the true combination of both.  So in the process of measurement you lose some (quantum) information.  Quantum teleportation (stupid name) allows you to get around this problem.

The exact technique is a little confusing, so if you intend to read the wikipedia article it might help to understand “classical teleportation” first.  This is an experiment that also doubles as a party trick (nerd parties).  The following technique will teleport the (classical) state of Alice’s coin A to Bob’s coin C.

1) Get 3 coins, A, B, and C.

2) Get B and C to be the same (heads or tails) without knowing which they both are.  Maybe paper-clip them together, then flip them both without looking, or just get some one else to do this set up.  B and C are now entangled.

3) Alice keeps coins A and B, and Bob takes coin C as far away as he likes.

4) Flip A and B together (like in step 2) and look at them.  There is no way of telling what the original states of either A or B were, but you can tell if they were the same or different.

5) If A and B were not the same, then Alice tells Bob to flip C over.  If A and B were the same, then Alice tells Bob to leave his coin alone.  The idea is, since B=C: if A=B then A=C, and if A≠B, then A≠C (so C should be turned over to match A).

Without ever determining the exact state of any coin, but only comparing two of them, Alice and Bob have teleported the state of A to C.  If A has a 77% chance of being heads and 23% chance of being tails (weird coin), then C will now also have a 77% chance of being heads and 23% chance of being tails.  The information about A, including the probabilies on A, have been transfered to C.  You’ll notice that the actual coin was never teleported, distance is irrelevant, the original state of A is destroyed, and the entire process is not even a little mysterious.

Posted in -- By the Physicist, Entropy/Information, Physics, Quantum Theory | 7 Comments

Q: If black holes are “rips” in the fabric of our universe, does it mean they lead to other universes? If so, then did time begin in that universe at the inception of the black hole? Could we be in a black hole?

Posted on November 8, 2009 by The Physicist

Physicist: Before answering your question, I’ll waste your time with two quick asides.

First: The place where the “ripping” might occur would be at the singularity.  “Singularity” is actually a very general term that roughly means “something goes to infinity in finite time or distance”.  Singularities are surprisingly common in nature and math.  For example, if you look at the flow of water around a drain, you’ll find that the math predicts that the water will spin faster the closer to the center it is.  In fact, the water should spin infinitely fast exactly at the center.  However, if you actually try this experiment you’ll find that there is no water at the exact center.  Either you’ll have a whirlpool (so there’s air at the center), or the water will flash into steam (from a drop in pressure).  The universe truly is a slippery eel.  Every time the math predicts a singularity, the universe finds someway to cheat and get around it.  The math of General Relativity predicts that the stretching of space will be infinite at the center of a black hole.  But my inner cynic says that the universe probably does something duplicitous and clever, and we need to do an experiment to figure out what that is.  Sadly, we’ll never do that experiment (can’t get out of a black hole), so the inside of black holes will be ready fodder for sci-fi authors for a long time yet.

Second: The source of the idea that black holes might go somewhere is what might be called “mathematically based paranoia”. Often in physics simple experiments will lead to simple math, that in turn makes very bizarre predictions.  Relativistic time dilation, quantum tunneling, and anti-particles are all examples of this.  Anti-particles were literally discovered because of a simple x^2 term, that had both a positive and negative solution.  Experiences like these make physicists very careful about throwing out solutions to equations, just because they’re “unreasonable”.  In the case of black holes the equations are the “Kruskal-Szekeres coordinates“, which are used to make the behavior of light and matter in, and around, black holes more intuitive.

Radial Direction vs. Time near a blackhole

Radial Direction vs. Time near a blackhole

The dotted lines are sample light paths going inward and outward.  All matter must travel between these lines (matter can’t travel faster than light).  Notice that the lines are really messed up near the event horizon.

U vs. V (the Kruskal-Szekeres coordinates)

U vs. V (the Kruskal-Szekeres coordinates)

In these coordinates the graph is cleaned up. Time points roughly “up” on this graph, light always travels the same way, and the lightcones are thus “unbent”.  Everything outside of the blackhole is now in the rightmost triangle.  But the space in the leftmost triangle seems to work the same as the space on the right.  Could it exist?  Physicists wouldn’t want to rule it out immediately.  Since light travels at 45º on this graph, you would have to travel faster than light to find out for sure however.  So this is where the idea that blackholes could lead to “somewhere else” comes from.

Finally, to actually answer the original question:

Maybe?  It may happen that as matter gathers in one place the space around it “pinches off”.  To the outside this would look like the formation of a blackhole.  You can picture this like water drops forming, and then falling off of the bottom of a flat surface.  Time in the new universe would be independent of time in our universe.  Not just “flowing at different rates”, but completely apart.  There would be no way to talk about “what’s happening right now in the other universe”.

wide01

Could our universe be a pinched off blackhole?  Sure?  There’s no good reason (that I’m aware of) to doubt conservation of matter and energy, so it would have had to be a really (really) big one.

It’s worth mentioning that whether or not blackholes go anywhere is fundamentally unimportant, since: 1) You can’t actually pass the event horizon (time from an outside perspective slows to zero on approach).  2) On approach you’ll be torn down to your atoms by the tidal forces.  3) You’d never get back out to tell the tale.

Both of the above graphs were happily stolen from “Gravity”, by James Hartle.

The water drop photo is from “Drop Shots!, Reflections on the Waterdrop“.

Posted in -- By the Physicist, Astronomy, Philosophical, Physics, Relativity | 22 Comments

Q: Since pi is infinite, do its digits contain all finite sequences of numbers?

Posted on November 8, 2009 by The Mathematician

Mathematician: As it turns out, mathematicians do not yet know whether the digits of pi contains every single finite sequence of numbers. That being said, many mathematicians suspect that this is the case, which would imply not only that the digits of pi contain any number that you can think of, but also that they contains a binary representation of britney spears’ DNA, as well as a jpeg encoded image of you making out with a polar bear. Unfortunately, to this day it has not even been proven whether every single digit from 0 to 9 occurs an unlimited number of times in pi’s decimal representation (so, after some point, pi might only contain the digits 0 and 1, for example). On the other hand, since pi is an irrational number, we do know that its digits never terminate, and it does not contain an infinitely repeating sequence (like 12341234123412341234…).

One thing to note is that when mathematicians study the first trillion or so digits of pi on a computer, they find that the digits appear to be statistically random in the sense that the probability of each digit occurring appears to be independent of what digits came just before it. Furthermore, each digit (0 through 9) appears to occur essentially one tenth of the time, as would be expected if the digits had been generated uniformly at random.

While tests performed on samples can never unequivocally prove that a sequence is random (in fact, we know the digits of pi are not random, since we know formulas to generate them) the apparent randomness in pi is consistent with the idea that it contains all finite sequences (or, at least, all fairly short ones). In particular, if we generate a number from an infinite stream of digits selected uniformly at random, then there is a probability of 100% that such a number contains each and every finite sequences of digits, and pi has the appearance of being statistically random.

The following rather remarkable website allows you to search the digits of pi for specific integer sequences:

http://www.angio.net/pi/piquery

As it turns out, my social security number occurs near digit 100 million.

Posted in -- By the Mathematician, Math | 115 Comments

Q: What is the connection between quantum physics and consciousness?

Posted on November 3, 2009 by The Physicist

Physicist: No connection.

The idea that consciousness, or observation, can affect the physical world around us is called the “Copenhagen Interpretation”.  According to the Copenhagen interpretation, as long as there is no consciousness observing a system (a system of particles, planets, light, chairs, etc.), then the system will evolve in time according to the rules of quantum mechanics (waves and super-positions and whatnot).  However, the moment that a conscious observer observes the system it suddenly stops obeying the laws of QM and, rather than being in a superposition of states, snaps to one state.  Essentially, the act of observation creates a definite reality.

You’ll notice that at no time does the Observer have any control over what state they’ll observe (I’m looking at you, The Secret).  This has been shown experimentally (so many times).

Just to be clear, the Copenhagen interpretation is wrong.

The Copenhagen interpretation leaves a lot of questions unanswered:

What’s consciousness?

If there’s more than one conscious observer, then who’s observation determines reality?

If you fall asleep or die, and no one observes you, is your body now in a superposition of states?

How does consciousness affect the physical world (what is the mechanism)?

How fast does the effect of the observation move?  This is a good one.  If you say “instant” or “faster than light”, then (for relativity based reasons) the effect can move backwards through time.  If you say “at the speed of light or slower”, then different observers of the same event can create different realities.

Among quantum physicists, the best theory is the “Many Worlds Hypothesis”.  Here’s the basic idea:

Light was the first thing that clearly demonstrated super-position (being in more than one state at once).  After that we saw super-position in electrons, protons and neutrons, alpha particles (helium), and even Buckyballs (also called “Buckminsterfullerene”, a molecule with 60 carbon atoms).  The larger a thing is, the harder it is to do an experiment that shows super-position, but so far everything seems to be capable of being in a super-position of states.

So, extend this from “everything we’ve ever been able to measure can be in a super-position of states” to “everything can be in a super-position of states”.  Where “everything” includes people.  Now the QM laws apply at all times, without awkward questions, exceptions, and explanations.  And, even better, the relationship between quantum physics and consciousness is revealed to be: nothing.

For example: Schrodinger’s Cat.

Copenhagen: Before the box is opened the cat is in a combination of alive and dead.  When the box is opened the cat is exposed to a conscious observer and the act of observing the cat forces it into only one state or the other.  This one reality then goes along it’s merry way.

Many Worlds: Before the box is opened the cat is in a combination of alive and dead.  When the box is opened the cat and the observer are allowed to interact and the larger system is now in a combination of cat-dead / observer-horrified and cat-alive / observer-hugcat.  These two realities then go along their merry ways.

I can’t give you a good definition for consciousness, but I can say that it doesn’t apply here.

Posted in -- By the Physicist, Philosophical, Quantum Theory | 45 Comments

Q: What is the probability that in a group of 31 people, none of them have birthdays in February or August?

Posted on November 3, 2009 by The Physicist

Physicist: There are 365.25 days per year (on average), there are 31 days in August, and 28.25 days in February (on average).  The “.25” isn’t exact, but the last time that the “leap year every four years” rule wasn’t used was 1900.

The chance that one person’s birthday is not in February or August is P = \frac{365.25 - 31 - 28.25}{365.25} = \frac{306}{365.25} = 83.78 \%.  The chance that all 31 people in a group don’t have birthdays in February and August (assuming there are no correlations between those people), is P^{31} = 0.41 \%.

All of this assumes that the probability of being born on any one day of the year is equal to any other, which is nearly true.

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