TDDE 131 Week 7: Space, Time, Echo & Dimensionality

[Crit of Proposals and Pairing]
[Space, Time, Echo & Dimensionality]

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The Space of Now

space-of-now-varies-by-perceptual-modeThe other night I was having dinner with my wife and my neighbor, discussing the concept of “living in the now”. Bah! My cold physicist brain immediately dismissed such new age nonsense.  We cannot possibly live in the “now” because all of the sensory input of our surroundings comes from the past, not the present. Information travels at a finite speed, be it via light (300,000 kilometers per second, or roughly 1 foot per nanosecond1), sound (340 meters per second, or about 1 foot per millisecond 1), or someone’s very strong perfume (about 3 millimeters in an hour if it is simply diffusion, but nearly instantaneous if you are on a plane). Looking at my wife, I was seeing her as she appeared 3 nanoseconds in the past; listening to my neighbor, I heard a story she told 3 milliseconds ago; and the full moon bearing down on us was merely a mirage from the distant past – all of 1 second ago. My experience at that dinner table was a hodge-podge of the asynchronous past.

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Little Gold Star

The Sun’s mini-doppleganger on asphalt

The Sun’s mini-doppleganger on asphalt

I’ve gotten to thinking about scales of the Universe, which are so vast as to be unimaginable to our tiny little human bodies.  Consider our own home star, the Sun.  At a whopping 1.4 million kilometers across, the Great Golden Orb is just an average-sized star, an insignificant dwarf in comparison to super gas bags like VY Canis Majoris. And while that nice warm Sun hanging up in the sky might seem as close as we’d like it, it’s still 150 million kilometers away. By the way, this distance is called the Astronomical Unit, or AU, perhaps the least concise unit ever created.  With gas prices remaining high, the Sun won’t be a vacation destination for our family anytime soon.

In science, we have all sorts of tricks in dealing with big numbers.  One way is to use scientific notation.  For example, 1.4 million converts into the ambiguously pronounced 1.4 x 106 – is that thing in the middle a “times”, a “cross” or a “here be the gold matey, arrrrr”? We can also invent a new unit that’s really big, so that you don’t have to deal with as many of them.  For example, 6 million dollars might sound like a lot of money, but if it’s all in 1 million bills, it’s only 6 (“alas, noone seems to be able to break this million dollar bill”).

None of these options makes cosmic scales any more approachable.  So we can instead just take these big numbers and force them to be small, scaling our vast universe into something tangible, something we can hold in our hand. Something like a little gold sticky star (image above).

That’s right, welcome back to grade 2.  Did you do well on your spelling test?  Very good, here’s a Sun for you.  All one glorious inch of it. On asphalt (I happened to be at a bus stop when I thought of this post). You know, you’re the best student in class, but just don’t tell anyone else, ok?


Measuring distance

We humans can certainly contemplate one inch, so how does the rest of our cosmos scale in comparison?  All we need to do is apply a ratio of 1.4 million kilometers : 1 inch to all of our distances, and we can go to town. Here’s some examples:

Distance between the Sun and the Earth: 1 AU –> 107 inches, or about 9 feet. This seems like an appropriate amount of personal space between the Sun and the Earth, but with traffic going by I’m having a hard time making conversation. Perhaps it’s for the best.

Distance between the Sun and the edge of the Solar System: that’s about 100 AU, which converts to 900 feet – 1/6th of a mile – in gold star universe.  That’s roughly the distance from my house to the bus stop. I have to cross a train track to get to and from my bus stop, but I can professionally assert that there is no train running across the Solar System, so I think we’re safe.

Distance to the nearest star, Proxima Centauri: that’s about 4.3 light-years, where a light-year is the distance light travels in a year.  This works out to be a gargantuan number, about 10 trillion kilometers.  Light has the highest frequent flyer status on every airline.  Come to think about it, this is about the same number as our national debt.  Perhaps we should start measuring our debt in light-dollars?  I digress.  In any case, in our little gold star cosmos, the nearest star is 480 miles away.  Yup, that’s right, Proxima Centauri is in Stockton.  That’s a pretty long bus ride.  I hope we stop for lunch.

Distance to the other side of the Galaxy. Let’s take a real trip!  Only 100,000 light-years to go!  What’s that you say? Even in our mini-verse we’ll have to travel 3 million miles, which is to the Moon and back 5 times? Can I get upgraded?

So our little gold star-i-verse does bring some things down to a scale that’s at least contemplatible.  But perhaps we’ve gone too far, because our humble little planet Earth on this scale is only 0.01 inches across, about 0.2 mm – this is a grain of fine sand.  Not terribly impressive of a planet anymore.  The city of San Diego? 1/2 of a micrometer, about the size of a virus (let the metaphors commence).  And me?  I’m a whopping 30 picometers head to tail, about the size of a single atom.  Maybe that’s why my name is, in fact, Adam?

Even more weirdness persists if we think about how we move in our mini-cosmos.  Remember that light travels at the easily-remembered “speed of light”, which is about 300,000 kilometers every second.  If time doesn’t change in our new universe, that means that light travels a whopping 1/2 centimeter every second, or about a foot a minute. To go from our mini-Sun to the Earth (9 feet away remember), it would take a thrill-pumping 9 minutes to make it.  Wow, that would be an exciting video! [note to collaborators: do not give Adam a video camera].  In fact, in the real Universe, it really does take sunlight somewhere between 8 and 9 minutes to reach us here on Earth, giving the Universe plenty of time to edit out swear words and “wardrobe malfunctions”.

Which leads us to the illuminating revelation of this blog post: if you want to walk from San Diego to Stockton taking one step every minute, it would take you about 4.3 years to do it.

Best just to take the bus.

Photo credits: Adam Burgasser, Amelia Christensen 
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