Musings on the Speed of Light

Friends,
There's a really good chance that you're not as nerdy as I am.  I'm neither bemoaning the fact nor bragging (is nerdiness even braggable; is braggable even a word?).  I'm just stating a probabilistic [Exhibit A] fact.  Two nights ago I played a strategy game that featured cards called "King's Court", "Duchy", "Nobles", and "Steward" [Exhibit B].  Yesterday as I watched Moneyball, some of my favorite moments were the glimpses of the equations used to evaluate players' values [Exhibit C]. 

And now I'm blogging about thoughts I've picked up while reading Einstein and science fiction [Exhibit D].


The speed of light is finite, but faster than you
The former isn't obvious; the latter is routinely discarded in sci-fi

Since you're probably less nerdy than I [see Exhibits A-D above], you may not have ever thought about the speed of light.  No one would blame you for this, unless you studied physics.  But it's time to start thinking about it. 

Because I don't know enough about relativity to actually explain it to you, I'm just going to give you a few cool things to think about.  At least, I think they're cool.  And as we've determined, that might not mean anything.

1. The basis of every cool sci-fi thing: the speed of light is constant
Everything else I'll say hinges on this-- light travels at a fixed, finite speed.  This doesn't quite line up with our experience.  It travels so fast that we sort of assume it's instantaneously everywhere.  But no, when you turn on a flashlight, that light actually has to travel to the far end of the room. 

2. No events are truly simultaneous
To say that two things happen at exactly the same time, what do we mean?  We might imagine syncing up wristwatches or something, but the actual meaning of this must mean that an observer would 'see' (i.e. receive the light particles of) Event A and Event B without any passage of time in between.  But because light has a finite, constant speed-- it matters where the observer is standing!

Consider this example from baseball: a runner tags up from third on an attempted sacrifice fly to left field.  Now, suppose there are two observers: the centerfielder next to the left fielder, and the umpire next to third base.  When the ball hits the glove, the light has only a tiny distance to travel to reach the CF's eyes; but when the runner's foot leaves the bag, there is a much longer distance for the light to traverse.  So he sees the catch with virtually no delay, but a slight lag occurs before he sees the runner leave the bag.  Thus, if he sees the two events as truly 'simultaneous', then the umpire-- with the opposite vantage point-- would fairly call out the runner for leaving early!

[Two points: I realize there would be "virtually no delay" for all events in a baseball park, but over incredibly large distances, this sort of delay for light would be extremely relevant.  You might think there could still be simultaneity if you just plopped the observer at a place equidistant from the two events; but if you just altered the speed the observer is moving, the whole concept would fall apart again.]

3. Looking into the past
If you read the bracketed note above-- and I totally understand if you didn't-- you know that this only creates interesting scenarios if we have super long distances for light to travel across.  And nowhere on our planet do we have a distance long enough for this fact to really play out.  But if you've looked up lately, you might have noticed this thing we call "outer space".

Over the vast reaches of space, light's finite speed becomes incredibly interesting (to me).  The most interesting thing, maybe, is that when we look up at the night sky, we're looking into the past.

In our baseball example, the point was that the umpire might see the runner leaving third just after it happens, but (if the baseball field were enormous) he might not see the ball hit the left fielder's glove until a few seconds after it happens.  This is because the light takes a little time to travel the distance to where he's standing.

Well, space actually is enormous, so we don't have to imagine a pretend baseball game anymore.  We can consider actual facts!  The brightest star in our sky is Sirius.  Its distance from Earth is 8.6 lightyears.  What this means is that it takes light 8.6 years to travel from Sirius to us (or vice versa).  So, if something crazy happens to Sirius (e.g. it explodes), we will see the event eight and a half years later!  To put it another way, when you spot Sirius in the night sky, you are seeing Sirius from 8.6 years ago!  What's up, Past-Sirius?


That's all my brain can handle right now
Kudos to you if you made it this far through my nerdy ramblings

There are so many other cool (to me) consequences of relativity.  If objects were to travel at speeds close to the speed of light, so many crazy things would happen, including a slowing down of the passage of time for that object!  Maybe I can ramble about these things another time.  Now I need to go stare at a TV for a while.

What's your nerdiest pastime?

Any, um, cool physics thoughts?

Jon

To infinity and beyond

The nerd inside me was clamoring for a chance to write.  And while we'll certainly be flying over Nerd Mountain, I'll try to keep us at a safe enough distance that everyone can understand the topic and take part in a hopefully fun discussion.

Infinity in mathematics

This will be the trickiest part to talk about in a way that can hold the attention of the moderately cool person.  I'll do my best.

The concept of infinity is so intuitive that I don't think I need to say anything about it.  It's actually kind of hard to give it a good definition without specifiying what type of thing we're calling infinite (i.e., an infinitely long span of time and infinitely many Blu-Rays of LOST season 6 are two different beasts -- though related, since the show is so addicting you could probably watch it for eternity).  So I'm just going to assume that when I say "infinity," you roughly know what I'm talking about.

But I will point out that in mathematics, the concept of infinity is extremely important.  In grad school, we literally talked about infinity every single day in class.  It played many different roles -- the limit of a function, the number of elements (e.g. numbers) in a set, etc.  I sense I'm losing most of you, so just suffice it to say that literally every day as a math grad student, you use infinite things to understand mathematics.

A few examples of infinity:

• The set of all natural (or "counting") numbers is infinite in size: {0, 1, 2, 3,...}
• The set of all real numbers is infinite in size, and in fact is more infinite.  I won't go into this, but it's really interesting to you if you're legendary in your nerdiness.
• One of the first proofs you learn as an undergrad math major is how to show that there are infinitely many prime numbers.
• The limit of the graph of f(x)=1/x as x approaches 0 from the right is positive infinity:

Infinity in our imaginations

Furthermore, as I mentioned before, we have this intuition about infinite things.  The author of Tuck Everlasting didn't have to explain what eternal life is -- we can all imagine living forever.  Most of us naturally assume the universe is infinitely large, that space just "goes on forever."  Science fiction (and many an actual scientist) posits that there are infinitely many universes.

But the crazy thing is -- and this will serve as our punchline --

We haven't discovered anything infinite in nature.

Yeah, that's right. 

The number of atoms in the universe:  less than 4 x 10^81

The age of the universe:  less than 14 billion years

The number of mudslinging Senator commercials:  somehow less than 70% of all Senate commercials, which is itself (surprisingly) a finite number

The three things you would most naturally guess to be infinite turn out to be finite.  Part of the reason we don't find actual infinites anywhere is that it would be impossible to measure one.  Think about it: if something had infinite weight, it would exceed the capacity of any scale we could build.  We'd just keep building bigger scales, and it would break every one.  And the same is true for length, age, etc. -- our ability to observe/measure will always be finite, so we could never conclusively say that anything is actually infinite.

But it's more than just a measurement problem.  We know the age of the universe and number of total atoms are finite. 

There are two possibilities for infinitude in our natural universe, I think -- black holes' density and the overall volume of the universe.  The latter is still an "open question" in cosmology, and we don't know yet the overall structure or size of the universe.  And the thing about density is that it's sort of a pretend quality -- you take two measurable things (mass and volume) and divide them.  So a black hole gets its infinite density since its volume is zero, and when you divide by zero you (sort of) get infinity.  If the only way to get an infinite thing in reality is to divide by zero, I think the point still stands.

Why is this true?

Recap: we all intuitively understand and can easily call upon the idea of infinity, and yet we don't know of any actual instances of infinity in the natural world.

Why?  What does this tell us about the world?  About ourselves?

I don't know.  That's why it's written in question form.  Please tell me what you think.

I'll give you my one initial thought on this mystery -- we're a bunch of beings who are finite in every way, surrounded by finitely many things that are each finitely sized and finitely old, and yet we think and dream of infinity.  To me, it seems like it could be an innate comprehension of and yearning for something or someone infinite, outside our universe and its finiteness.

Abraham Lincoln thought the same thing: “Surely God would not have created such a being as man, with an ability to grasp the infinite, to exist only for a day! No, no, man was made for immortality.”

Sorry this was so long.  But imagine if it had been infinitely long...

Please feel free to take a stab at the above questions or any other thoughts, comments, questions, or ideas you have.  Thanks!

Jon

Stephen Hawking vs. God

Well-known physicist Stephen Hawking just co-wrote a book called The Grand Design.  In this pop-science best-seller, he and his pal make the argument that we need not call upon God to explain the origins of the universe, because the theory of multiple universes is satisfactory.  I will now attempt to summarize and criticize/debunk this brilliant scientist's work, which I've never read.

You might be thinking, "Jon, you're pretty smart, but you're no Stephen Hawking."  Agreed.  Your next thought might amount to, "You haven't even read the book."  Correct.  But what I have done is pretty significant -- my friend scanned a couple chapters and summarized them for me, and I read the book's wikipedia page.  I rest my case.

No, no, I'm not qualified to talk about cosmology or physics.  But I have a brain, and it usually works, so I'm qualified to talk about my thoughts.

My first thought is that this argument is ooooold, but by leaking to the press that the book would denounce God and using the ethos of Hawking's name, Bantam Books and Hawking were able to recycle it and make tons of money.

Secondly, I'm thinking his argument doesn't give us any more explanatory power than a creation hypothesis.  One classical argument for God's existence is as follows:

1. Everything that has a beginning has a cause (or complex series of causes).
2. The great host of physicists agrees there was a "Big Bang," an actual event that occurred a certain number of years ago, at which point matter and time first came into being.  In other words, our universe  had a beginning.
3. Therefore, our universe had a cause outside of our universe -- something or someone that made matter and time emerge from nothing.

Hawking basically agrees with this argument, but says that "m-theory" (the latest version of string theory that identifies 11 dimensions in our universe) with an understanding that our universe is just one of many, provides a valid alternate hypothesis to the idea that God is the universe's cause.  Hawking specifically states that the properties of gravity would make the spontaneous generation of our universe possible.

But what gravity does he mean?  It can't be the gravity of our universe and its 11 dimensions.  That property didn't exist until after the Big Bang, like all other physical properties in our universe.  So Hawking must be referring to a "supernatural" (i.e. "outside of our nature or universe") gravity.  This is a gravity in one of those other many universes that we've never seen, felt, or experimented on.  Sounds pretty... unscientific.

My third thought is an attempt to understand the idea fully.  We can study our gravity.  We learn its properties and infer how a gravitational force might operate in a completely different universe.  We make some prediction, and (this is the point in the book at which Hawking humorously says there is ample scientific evidence to support the theory) we find that yes siree, if the gravity of another universe were such-and-such a force, it could cause an entirely new universe to form.

Fourthly, I ask myself the many, many questions that stem from this line of reasoning:

• Why is it more reasonable/scientific to assume there is some other universe out there completely separate from ours that somehow -- via pure gravitation -- gave birth to ours (but remained completely separate from us), than to believe there is intelligence outside our universe that caused it to exist?
• What caused that universe to exist?  Another universe with the same sort of gravity?  What about that one?  If we never trace back to an uncaused cause, we eventually have an infinitely old chain of infinitely many universes.  But since all of these apparently have different sets of natural laws (and Hawking admits only a very few could conceivably support life, let alone intelligent life), what laws dictate which universes will have which properties?  Wouldn't you need some over-arching "meta-laws" that are unchanging and eternal that determine this infinite chain of universe-spawning?  And -- hammerstroke -- where do these meta-laws come from?
• How is any of this testable?  Provable?  It's nice that you predicted that a parent universe would have a certain gravity, and then coincidentally those properties theoretically would allow the generation of a new cosmos.  But it sounds, to me, a lot like the natural theologian's exercise of predicting (from nature, human experience) what a Parent Deity would be like, and then coincidentally it's precisely that kind of Deity who would create a universe that supports intelligent life.

The fifth thing going through my mind is how many critics of The Grand Design -- including many who are in no way sympathetic to creation hypotheses -- have shared my first four thoughts (you can make the case that this is no surprise, since I already read their thoughts before writing this post.  Touche.).

One Columbia physics professor said a few weeks ago, "I'm in favor of naturalism and leaving God out of physics as much as the next person, but if you're the sort who wants to go to battle in the science/religion wars, why you would choose to take up such a dubious weapon as M-theory mystifies me."

The Economist -- deciding to review a pop physics book? -- slammed it as well, pointing out that "the authors’ interpretations and extrapolations of [m-theory] have not been subjected to any decisive tests, and it is not clear that they ever could be. Once upon a time it was the province of philosophy to propose ambitious and outlandish theories in advance of any concrete evidence for them. Perhaps science, as Professor Hawking and Mr. Mlodinow practice it in their airier moments, has indeed changed places with philosophy, though probably not quite in the way that they think."

Renowned scientific journalist John Horgan said that if we believe the book's claims that we've reached a trustworthy explanation of the universe's origins, "the joke's on us."

Sixthly (<-- nice), I'm realizing how tired I am.  I really need to get some sleep.  So I'll move on to thought seven:

Stephen Hawking is a brilliant man.  Maybe the most brilliant man in the world when it comes to physics and math.  I'm sure I couldn't ever grasp the full breadth of most ideas in his book, and that what I've done above is almost certainly attacking a straw man.  But I can't help but wonder about his motives -- or others', like Dawkins -- for coming out with a public attack on God's existence.

Of course there are the typical reasons you could imagine.  They simply don't believe, and they want others to see the world the way they do.  Sure.  Maybe they see a lot of hypocrisy, or even evil, done in God's name, and since they don't even believe in Him, it seems like the world would be better if no one else did.  Okay.  Or the grandest of them all -- perhaps they are so convinced of atheism that, in the spirit of the world being educated and knowledgeable, it would only be right for the world to be enlightened and atheistic as well.

But why, then, are their attacks so full of anger and based on bad logic?  Dawkins is almost unreadable to me because he is so full of condescension and underlying rage toward anyone who's a theist.  Even Hawking is willing to imagine this multi-verse universe-popping scheme and then claim that it's supported by empirical evidence!

I guess I just suspect that in many cases, the crusade to refute God is not an educational or purely intellectual one, but a deeply personal and emotional one.  Or possibly a greedy one (the book in question hit #1 on Amazon the day it was released).

I don't know how to best generate conversation about this, except that I would love to hear any and all thoughts regarding the book (if you've read it... or skimmed wikipedia), the existence of God, and the above arguments for and against God's existence.