# The Warping of SpaceTime

One moment you are there, hanging out calmly on the fringes of a remote star system, minding your own business in the near-interstellar vacuum, and in the next there is a vast disturbance of space-time all around you. There is no matter here more dense than a handful of atoms of hydrogen per square meter of space, yet space itself folds at a quantum level.

Rather, space and time alike are unfolding around you, flattening back into normality. You aren’t aware of it having been folded, because you were folded along with it, but there is a definite sign that something dramatic has changed in the local volume.

A starship has arrived.

The starship has traveled a long way, twelve-hundred light-years from its home, yet it has done so over the relatively short time of only three years. That sounds suspiciously like faster-than-light travel, yet it can’t be, because that’s impossible, right? Einstein’s theory of special relativity tells us so.

Yet, Einstein’s theory of general relativity tells us something else. We still cannot travel faster than light in flat space, but space (and time) can be curved.

Indeed, space-time is always curved, regularly distorted by the mass of any objects within it, and we all experience that curvature regularly in our daily life. We experience it as gravity.

Per special relativity, an object with mass cannot move at the speed of light without requiring infinite energy, and at the same time becoming zero mass.

In general relativity, however, in a curved space-time, the equations allow for a warping or folding of space in such a way that a bubble is formed, and as the bubble moves, space in front of it is highly compressed while space behind it is highly expanded.

The bubble appears to an outside observer as if it has moved faster than light, but really it has just warped space around itself. No matter how much warping occurs, anything inside the bubble experiences no acceleration, and what’s more, no funny time dilation effects (more on this in a later post, I think).

This is not to say that there are no inherent problems with warping space to this dramatic extent. For one thing, in the original equations demonstrating this as a possibility, developed by Miguel Alcubierre in 1994, it appeared that a massive negative mass-energy state is required to generate the bubble. Negative energy implies exotic matter, but more troubling is that the amount of mass-energy required to transport a very small ship across the galaxy would be greater than the mass of the observable universe.

That’s a problem. We can’t have starships destroying the entire universe every time they fire up their warp drive.

In 1999, Chris Van den Broeck modified the equations to require the equivalent of just three solar masses. A great improvement! Now firing up the engine just destroys three star systems. With about 250 billion stars in our galaxy, who’s going to notice a few of them disappearing now and then?

Well, presumably the inhabitants of any planets around those stars will notice, and if we assume that the starship consumes the nearest three stars whenever it starts up the drive, then we could extrapolate that our own Sun (and us along with it) would be the first to go. Perhaps ok if we’re fleeing a Sun going nova about five billion years from now, but in the meantime we’d like to keep our home, thank you very much.

There are other problems with the Van den Broeck solution, and also with Serguei Krasnikov’s modification, despite the latter’s reduction of the mass requirement to mere milligrams. Basically, they require keeping the surface area of the warp bubble microscopically small while expanding the interior volume, which seems contradictory at first glance, and even so, they are only able to transport a few atoms of matter in this way. These are interesting modifications of the equation, but not truly useful.

In 2012, all that changed. Harold White showed (on paper) that modifying the shape of the bubble into a torus, or a rounded doughnut, dramatically reduces the mass-energy requirement into the hundreds of kilograms range, and with this the drive could propel a starship of useful (macroscopic) size… more than just a few atoms. No longer do we need to dismantle a gas giant planet — or a sun — for every voyage. White’s equations excited serious physicists enough that NASA is funding lab experiments to prove the concept.

This is where I would love to insert the beautiful image of IXS Enterprise developed by Mark Rademaker and then used in Harold White’s presentation materials as a concept design for how such an Alcubierre-White starship might look. However, all such images are copyrighted with all rights reserved, and at this time I cannot justify the expense of purchasing rights to display them here. Nevertheless, I encourage you to go view the originals.

So, we’ve solved the energy requirement (ignoring for the moment that we’re talking about negative energy and exotic matter), but issues still remain. Stefano Finazzi, Stefano Liberati, and Carlos Barcelo argued in 2009 that a classic Alcubierre warp bubble might be just fine if it is eternally moving at a stable superluminal speed — which makes it rather difficult for travelers to “hop on the bus,” so to speak — but the switching on of quantum effects to spin up such a bubble from flat space (a more realistic and usable scenario) would create enough Hawking radiation inside itself to completely fry any occupants.

Hawking radiation is strange stuff, and so far remains theoretical in nature. Then again, so does pretty much everything we’re discussing here.

Engineers love a good challenge, however, and we shall assume for the moment that the problem of internal radiation is solvable. After all, you’ve just observed an Alcubierre-White starship arriving in your immediate vicinity.

Luckily for you, you were not in the starship’s direct path when it unfolded space-time around itself and allowed the warp bubble to dissolve. Why?

During the ship’s three-year voyage to arrive here, it has folded up and compressed a great deal of space ahead of itself. While the ship’s navigator carefully plotted a course to avoid any significant obstacles along the way, the vacuum of interstellar space is not completely void of matter. Free hydrogen atoms exist between the stars, and while estimates vary, they average anywhere from one-quarter (0.25) to one-thousand per cubic meter of space (though more likely on the lower end of that range). As our warp bubble transited the Sagittarius Arm, it collected all those atoms on its leading edge, folding them into the highly energetic bubble wall itself.

If the torus has a cross-section of about two-hundred meters, then on the low end of the estimate our starship has pushed about fifty atoms for every meter it traveled. Over three years, the starship traveled twelve-hundred light-years; how far is that in meters?

The speed of light is a hair under 300,000 kilometers per second (you may be more familiar with the number 186,000 miles/second). A light-year is the distance it travels in one year, which is about 31,500,000 seconds, and thus roughly 9.46 trillion kilometers (that’s 9,460,000,000,000 in case you are counting the zeroes). Multiply that by 1200 light-years, and our starship traveled 11.35 quadrillion kilometers.

A long distance indeed.

We gathered 50 hydrogen atoms per meter, or 50,000 per kilometer. I think you see where I’m going with this.

Upon arrival at its destination and deceleration to subluminal (please, autocorrect, stop making that subliminal) velocities, the warp bubble has compressed about 568 quintillion hydrogen atoms.

That’s a lot of atoms.

Of course, atoms are very small. It takes 602,000,000,000,000,000,000,000 (602 sextillion) hydrogen atoms to make up one gram of matter. So, all those quintillions of atoms gathered over the course of three years still only amount to about a milligram of matter.

Surely that’s not enough matter to, well, matter, right? Let’s find out.

It’s only a milligram, but it is moving very, very fast. We know the basic equation:

$E=mc^2$

Where:
E = energy
m = mass
c = speed of light

One milligram moving right at the speed of light should be pretty simple to solve for. That is 0.001 g x 300,000 kps squared, or 90 million grams… er, hold on, something funny is happening here. Before we go through all that math, we’ll just approximate a few things. If the milligram of hydrogen atoms are moving at 99.9999% of the speed of light — very, very close, but not quite there — then anything they hit will experience the force equivalent to several kilotons worth of a nuclear bomb. It could definitely ruin your day if your spaceship happened to be right there, but it’s not going to pulverize a planet.

But our atoms aren’t moving at 99.9999% of c. They are moving at c. In our equation, when c = 1, we can simplify it to E = m. Put another way, energy and mass are equivalent, and at the speed of light, our mass becomes pure energy.

When the warp bubble suddenly decelerates, the atoms are ejected off the leading edge as extremely short-wavelength, high-frequency, and thus high-energy radiation, rather than as regular but fast-moving matter. In other words, our decelerating starship emits a gamma ray burst in its forward direction of travel, gamma rays which will easily penetrate almost any shielding and wreak havoc upon anything biological.

For the mathematically- and physics-inclined, I recommend perusing The Alcubierre Warp Drive: On the Matter of Matter by Brendan McMonigal, Geraint Lewis, and Philip O’Byrne.

The starship has a crack navigator, however, and she knows her theoretical physics. A little less theoretical in her case, since she is living it. So, she plots her course not only to avoid large obstacles along the way, but to decelerate far out on the edge of the destination star system. She doesn’t want to pulverize anyone or anything there. So, you survive the starship’s arrival.

There is another minor issue which the starship’s designers had to overcome before sending it on its long voyage. Michael John Pfenning demonstrated in 1998 that for a classic Alcubierre warp bubble there is an inverse relationship between bubble wall thickness and maximum superluminal velocity. At ten times c, the bubble wall can be no thicker than $10^{-32}$ meters. As the Planck length is $1.6x10^{-35}$ meters, our bubble wall is almost as thin as the thinnest possible measurement.

As a quick aside, the Planck length in quantum mechanics is the smallest size at which gravitational effects behave rationally. Below this scale, Euclidean geometry ceases to have any meaning, and spacetime becomes quantum foam. That’s a colorful term for saying it is no longer continuous, but has holes in it. So, in effect, the Planck length is the smallest size that anything can be and still effectively be part of our universe.

Our bubble wall is approaching the smallest possible size, and we’re moving at 10 c. That seems pretty fast, and indeed it is pretty fast, but for a voyage of 1200 light-years, and without any time dilation effects, that means… yep. 120 years to complete the voyage.

10 c may be sufficient for the nearest stars, but if our starship is to visit Kepler 62f, either our astronauts must be very patient (and long-lived), or be willing to risk cold sleep, or our ship is somehow going to have to go faster.

Pfenning made his observations during his doctoral thesis only two years after Miguel Alcubierre first published his equations. We’ve already explored how others have built upon the original equations in the intervening time, refining them in many ways so as to reduce the huge amounts of energy required, so it remains plausible that by employing the methods of Harold White and reshaping the bubble into a torus we may also find that we can effectively increase the speed of our starship. Can we do it enough so as to travel a light-year per day, as would be required to reach Kepler 62 in just three years?

I don’t know.

Can we effectively shield the interior of the bubble so that the astronauts are not fried by Hawking radiation or extremely blueshifted high-energy particles?

I don’t know.

So this, my friends, is what in hard science fiction terms we call a McGuffin.

I’ve rambled on far too long about the Alcubierre drive now, and doubtless put many of you to sleep, without ever getting on to the rest of the technology utilized by the crew of Aniara in The Silence of Ancient Light. I’ve also certainly made some significant technical or scientific errors in my attempts to explain (or simply understand) the complex physics and mathematics behind the idea of warping spacetime. For those, I apologize, and indeed, I invite discussion in the comments. Educate me!

If you enjoy these pseudo-scientific ramblings of mine, you may enjoy my previous similar posts of this nature:

header image credit: Les Bossinas / NASA under public domain

# A Tense Point of View

Do you prefer reading first-person or third-person narratives? Does it make a difference when the story is in a particular genre? Does the narrative point of view give the story a different feel for you?

I know I don’t need to detail for you what I mean here, but just in case:

• First-person: I dashed into the alleyway, gun drawn, and confronted the assassin.
• Third-person: He dashed into the alleyway, gun drawn, and confronted the assassin.

#### First-Person PoV

For a long time the general advice to novelists was to stick with third-person narration, and past tense only, please. First-person narration was for autobiographies and hard-boiled detective stories only, though I think you could find a number of examples in 19th- and early 20th-century literature (think H.G. Wells, for instance). However, a common narrative form of the age was to have a first-person narrator who was not in fact the main character of the story, or even very important to the story. This may seem strange to us today, but it allowed the author to slip into the role of fireside storyteller, relating events of some character he or she had met (if only in his or her imagination).

W. Somerset Maugham’s 1944 novel, The Razor’s Edge, was written in this manner: the author himself is the narrator, but is only barely tangential to the story of Larry Darrell and his friends. Writing in this manner gives the story a hint of “This is something that really happened,” while nevertheless remaining entirely fictional. On the other hand, it would seem to have the drawback of not allowing the storyteller (and thus the reader) to be present when the action occurs far away. In Maugham’s novel, Darrell travels to India and spends years searching for the meaning of life, yet we as the readers only learn of it when he returns to Europe and relates his tale to his friends — one of whom is the author/narrator. Perhaps Maugham didn’t want to emphasize the mysticism of Darrell’s eastern travels, instead keeping the focus on personal relationships more familiar to a western audience, but it was a disappointment for me to not be there when Larry sits on a mountaintop meditating.

Past advice notwithstanding, many great novels — and not just detective stories — are written in first-person. Such a style can make the action much more personal, as we are definitely inside the head of the narrator-protagonist. It can also allow for an unreliable narrator, a main character who relates events to us as they perceive them, or perhaps even as they wish to be perceived, and only later in the novel do we find out that the story’s “inner reality” is different.

But first-person narration also has its drawbacks. Classically, it restricts the author to telling the story from only a single point of view, though in modern times this “rule” has been broken quite successfully (see My Sister’s Keeper by Jodi Picoult for an example). It also classically has been taken as an indicator that the narrator survives to the end of the story, in order to be able to tell the tale, but again — spoiler alert! — see Picoult’s afore-mentioned tale.

#### Third-Person Deep PoV

It is possible to obtain that same “inside the protagonist’s head” feel with third-person narrative, using a technique usually called Deep Point of View (or Deep PoV). For example:

He raised the heavy gun, shakily pointing it at the assassin, who loomed large in the alley. The assassin laughed.

vs

He raised the gun — how did it get so heavy? — and pointed it at the assassin. The man was huge! To make matters worse, the assassin merely laughed at his feeble effort.

Deep PoV attempts to have the reader identify with the character as much as first-person narration does, but still retain some of the detachment of third-person.

#### Second-Person PoV

What about second-person narration? Is there such a thing? Indeed there is! Though I’m not sure I’ve ever seen it with past tense, so:

You dash into the alleyway, gun drawn, and confront the assassin.

As a writer, you will likely be told, over and over, never to write this way, that such a book will never sell.

Jay McInerney laughed all the way to bank after his debut novel, Bright Lights, Big City went bestseller. Yep, all second-person. Same for N.K. Jemison with her Hugo-award-winning novel, The Fifth Season. For a science fiction example, see Charles Stross and Halting State, plus its sequel, Rule 34.

Second-person narration is very hard to pull off, however. If not done exceptionally well, its very strangeness can be off-putting.

#### Past vs Present Tense

Having now mentioned tense, let’s dive into that. Again, traditionally, stories have been told in past tense — He dashed into the alleyway — giving it that feel of an oral tradition, related by elders around the campfire, of mythic deeds by mythic heroes of an ancient age. But in the past few decades, present tense novels have come into vogue. Granted, such writing has existed for some time: Ulysses by James Joyce, published in 1918, employs present-tense narration. Going back even farther, Charles Dickens used present tense for his 1852 serial, The Bleak House.

Still, throughout most of the 20th century, most novels were written in past tense. Lately, however, that seems to be changing. While still true — I think, as I don’t have a statistic on this handy — that while most novels today are in past tense, clearly an increasing number of them are coming out in present tense. This certainly seems prevalent with YA novels — The Hunger Games (Suzanne Collins), Divergent (Veronica Roth) — but is definitely not restricted to that genre. The second-person novels I mentioned earlier, for instance, are also present-tense novels. The Girl on the Train (Paula Hawkins), The 5th Wave (Rick Yancey), and, yes, infamously, Fifty Shades of Grey (E.L. James), are also present-tense novels. The list is quite long, really.

You will probably notice that many of these are also first-person narration. Certainly this isn’t universally true, but it feels more natural — to me, anyway — to couple present tense with first-person.

#### Future Tense and Stranger Things

I admit, I’m not aware of any examples of novels written in future tense, and I have a hard time imagining flowing prose in such a style, at least in English.

He will dash into the alleyway, gun drawn…

Sounds more like a prophecy than a story.

Of course, we could go crazy with future perfect (He will have dashed…), future perfect progressive (He will have been dashing…), and so on, but you can see how cumbersome this quickly gets. Perfect, progressive, and perfect progressive modifiers can be applied to past and present tense as well, of course, but in all cases this starts to add a lot of words to describe an action.

#### Putting It All Together

So that was a long ramble, but why do I bring this up? If you’ve been following my work-in-progress, The Silence of Ancient Light, you’ll note that I’ve been writing (oh, there’s past perfect progressive!) in third-person past tense. However, you’ll also note that there is, so far, only one point-of-view character, Anna Laukkonnen. I think in the early scenes I managed to achieve some deep PoV with Anna, but as I look back on the later scenes, I sense that I’ve drifted a bit from this, which is something I’ll need to correct in the next draft.

But, if the story is entirely from Anna’s point of view, would it make more sense to change it to first-person narrative? I admit, I’m currently undecided on this point. I have written other stories in first-person, and I’ve generally found it to be a comfortable style for me. I am striving for that deep personal perspective, and for me that’s perhaps a little easier in first-person, but it doesn’t have to be that way.

As a reader, I enjoy books in both first- and third-person — and yes, I enjoyed The Fifth Season in second-person as well, though with Halting State I admit it took me a while to get used to it. So, I don’t have a strong preference one way or the other, but instead want to use the style that best lends itself to the tale I have to tell.

The vast majority of my writing has been traditional past tense, as well, but recently I’ve tried my hand at some present-tense writing, and I’ve found it can set a certain mood to a story that is sometimes appropriate, though not always. I’m not against it, though I’m not sure it’s what I want for Silence.

What do you think? What is your preference? What do you think would work best for Anna and Silence? If you’re a writer, what feels most natural to you?

It’s an admission of defeat, I suppose. Even the giants know when to cut their losses, let someone else own the field, and move on to other arenas where they can be successful.

No, I am not talking about myself, although this does impact me in a minor way. It impacts some few of you, too, perhaps, though it would seem to be very few of you, which is why this is happening.

To date, anytime I’ve posted something here, I have (either automatically or manually) linked to it on these four platforms, on each of which I have a related page or feed. I have modestly lively interactions on Twitter, fairly quiet but occasional interactions on Facebook, practically none on Google+, and absolutely zero on Tumblr.

Apparently Google has decided that they, too, have very little going on with their social media platform, and thus their decision. The layout of the platform was actually rather nice; it just never seemed to gain any traction.

So, the disappearance of my Google+ page, and those links from this site, will pass with nearly no one noticing.

I’m tempted to stop publishing to Tumblr as well, as that medium appears to not be very well suited to text; I think it’s more about sharing photos and visual artwork. What do you think?

Should I replace these social sharing platforms with others? Pinterest, perhaps, or LinkedIn? Where do you find it easiest to consume content, or to receive notifications of new publications? Where would you most like to share such content, assuming you’re so inclined?

Let me know what you think!

# In the Year of ’39

In the year of ’39 assembled here the volunteers,
In the days when lands were few;
Here the ship sailed out into the blue and sunny morn,
The sweetest sight ever seen.

Lately I’ve had this song running through my head, pretty much on constant repeat. It’s an old song, first released in 1975 on the album A Night at the Opera by Queen.

And the night followed day,
And the storytellers say
That the score brave souls inside
For many a lonely day sailed across the milky seas,
Ne’er looked back, never feared, never cried.

At first it seems to be telling a relatively ordinary story. Volunteers set sail in a ship for a dangerous journey. Is it 1939? Is this something to do with World War II? It’s not really clear yet.

Don’t you hear my call though you’re many years away,
Don’t you hear me calling you;
Write your letters in the sand
For the day I take your hand
In the land that our grandchildren knew.

Wait, what? The land that our grandchildren knew? Ok, there is something odd going on here. And what’s this about being many years away? The song seems to be playing around with time.

In the year of ’39 came a ship in from the blue,
The volunteers came home that day,
And they bring good news of a world so newly born,
Though their hearts so heavily weigh;

For the Earth is old and grey,
Little darling went away,
But my love this cannot be,
For so many years have gone though I’m older but a year,

Right, this is definitely not an ordinary ship sailing ordinary seas, and time is certainly being twisted. The volunteers bring news of a new world, while the Earth is old and grey? We’re talking about space travel, aren’t we? In fact, we’re talking about interstellar travel.

It’s definitely not 1939.

Many music lovers might have been confused by this song, but by now it should be obvious to readers of this blog what’s going on here. For astronauts to travel far enough to discover another world (“so newly born”), one capable of replacing the “old and grey” Earth as humanity’s home, and return back with the news “older but a year,” they must have traveled very fast indeed. Perhaps even approaching the speed of light?

At speeds this fast, the theory of special relativity tells us (and experimental research has shown) that odd things happen with time. Time appears to slow down for the traveler, at least relative to the stationary observer, so that by journey’s end the traveler will have aged far less than those who stayed home.

In the year of ’39 assembled here the volunteers

2139, perhaps? 2239? It’s not completely clear.

In the year of ’39 came a ship in from the blue,
The volunteers came home that day

Not the same ’39, but 100 years later. 2239? 2339?

For so many years have gone though I’m older but a year

As it happens, given the parameters of the song, we can calculate how fast the ship was traveling, and thus how far away they went, and perhaps even speculate what star they visited! This is because, despite being such a non-intuitive phenomenon, time dilation due to relativistic effects is well understood, and there is an equation to calculate it.

$t'=t\sqrt{1-\frac{v^2}{c^2}}$

Where:

t’ = dilated time
t = stationary time
v = velocity
c = speed of light

We want to know the ship’s velocity, so let’s parse this out (like traveling back in time to algebra class!):

$t'^2=t^2\times({1-\frac{v^2}{c^2}})$

$\frac{t'^2}{t^2}=1-\frac{v^2}{c^2}$

$\frac{t'^2}{t^2}+\frac{v^2}{c^2}=1$

$\frac{v^2}{c^2}=1-\frac{t'^2}{t^2}$

$v^2=(1-\frac{t'^2}{t^2})\times c^2$

$v=\sqrt{(1-\frac{t'^2}{t^2})}\times c$

Ok, let’s plug in some numbers! To keep things simple, we’ll express velocity as a percentage of the speed of light, and time in years, even though normally in physics equations velocities would be meters per second and time in seconds. But at this scale, those would be some big numbers, so we’re going to assume that c=1, and that v therefore is a percent of c.

$v=\sqrt{(1-\frac{1^2}{100^2})}\times 1$

$v=\sqrt{1-\frac{1}{10000}}$

$v=\sqrt{1-0.0001}$

$v=\sqrt{0.9999}$

$v=0.99995$

In order for 100 years to have passed on Earth while only 1 year passed for the astronauts, the ship had to be traveling approximately 99.995% of the speed of light. That is some extreme time dilation, and so that is some extreme speed. Quite the starship!

Time isn’t the only thing dilating here, as traveling at these speeds does some interesting things to the fabric of space as well. Distances ahead of the travelers will appear to shrink somewhat, though even at this high fraction of the speed of light, it’s a minimal effect. Add a few more 9s to the significant digits, however, and it gets very strange indeed.

Meanwhile, though, our travelers have spent a year journeying at very close to the speed of light. How far have they gone? One light-year?

Oh no. They’ve gone much farther than that. The distance traveled is at a speed relative to time for the stationary observers waiting patiently back on Earth, so our starship has traveled a hundred light-years, though it seems to the astronauts to take only one year to do so.

So, what star might they have visited to find a “world so newly born” to which humanity could relocate? First off, this was a round-trip, so with half the time spent journeying out and half spent returning, that would imply they went no more than fifty light-years away (“no more than,” I say, as if this is no big deal, but fifty light-years is a very big deal). Gliese 163 is 49 light-years away and has one potentially habitable world, but it’s not considered an absolutely prime candidate.

Let’s assume, for a moment, that our starship took a little bit of time to accelerate and then decelerate on its journey, so that instead of 50 light-years, perhaps it really only traveled about 40 light-years away.

They went to Trappist-1.

Trappist-1 is a cool red dwarf star 39.6 light-years away, and it has seven temperate and terrestrial planets, four of which are considered potentially habitable even by conservative estimates. Trappist-1 is obviously a prime candidate for finding life, or at least worlds on which humans could live, and being at about the right distance, is also a prime candidate for our volunteers on their desperate and lonely journey.

Not that this provided much consolation to our narrator, who returns to Earth to find his wife long dead, and only a memory of her in the eyes of his (presumably centenarian) daughter (or granddaughter?).

’39 was written by Brian May, lead guitarist for Queen, in 1975. May, as some of you may know, is also an accomplished astrophysicist, and while the planets of Trappist-1 had not yet been discovered in 1975, he certainly understood the effects and impacts of time dilation on travel at relativistic speeds. May studied physics and mathematics up through the time when his music career began to skyrocket to success, though due to focusing on music after that point, it took him 37 years to complete his doctoral thesis (A Survey of Radial Velocities in the Zodiacal Dust Cloud), finally earning his PhD in 2008. He was Chancellor of Liverpool John Moores University from then until 2013, and he was a science team collaborator for the NASA New Horizons mission to Pluto.

Not just a fantastic guitarist and songwriter, but a serious scientist!

Don’t you hear my call though you’re many years away,
Don’t you hear me calling you;
All your letters in the sand cannot heal me like your hand,
For my life
Pity me.

Final note: Although Freddie Mercury is far more well-known as lead vocalist, it was Brian May who sang the lyrics for the studio version of ’39 (though Mercury sang for most of their live performances).

’39 from the album A Night at the Opera by Queen, 1975
Songwriter Brian May, copyright EMI Music Publishing, Sony/ATV Music Publishing LLC

Special thanks to E=mc2 Explained for breaking down the physics of time dilation for us laypeople.

Header image credit: user:Les Chatfield / flickr.com under CC-BY 2.0

# Writing for the Holidays

Merry Christmas, everyone! Although you may not have heard much from me lately, rest assured that I have indeed been busy, plotting character arcs and so forth, and hopefully soon I’ll be able to share some material with you. Indeed, here it is Christmas morning, and I #amwriting (as we say on Twitter!). And in between all that writing, I’ve been getting in a little cross-country skiing.

How are you spending your holidays?

–image credit: nasa.gov