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Several episodes of Star Trek have dealt with situations in which some person or group of people have been living at a highly accelerated rate. Various excuses have been trotted out for this, only a few of which make any sense at all. The idea of this article is to explore the episodes a little and point out the flaws inherent in them. I won't be trying to suggest some grand idea of how such acceleration could work because, frankly, there isn't one.

Lest the title makes this seem like an overly harsh attack on the writers, please accept my assurances that this is not so. Many Trek "science ideas of the week" are impossible, or contain inherent contradictions. Indeed, much of the basic technical premise of the show contains such problems. This doesn't stop me from being a loyal and dedicated fan of the show who will be the very first in front of the TV when the next episode comes along. Even fundamentally illogical episodes like these ones can be entertaining - TNG's "The Next Phase" is a great episode even though it has perhaps the silliest basic premise ever seen in Trek. It's just that finding and thinking through stuff like this is one of the things that I enjoy about Trek, and I simply wanted to share some of the conclusions I've come to with you guys.

The first even Trek "acceleration" episode was "Wink of an Eye". The Enterprise responds to a distress call only to find the planet which sent it deserted - yet though there is no sign of life, they hear a strange insect-like buzzing sound. After beaming back aboard the ship strange incidents indicate intruders aboard. Something is put in Kirk's coffee, and he promptly vanishes after drinking it. Spock concludes that the intruders are living at a hyper-accelerated pace, and eventually manages to accelerate himself also. Meanwhile Kirk has been dealing with the accelerated folk. He threatens to use his phaser, but the slow beam it produces is easily sidestepped - a problem that does not befall the alien weapons, of course. Kirk and Spock eventually overcome the aliens and get things back to normal.

One interesting thing about this episode is that it makes absolutely no attempt to explain how the acceleration works. After Kirk has been accelerated the alien Queen, Deela, tells him that there is indeed an explanation, but really the only thing that matters is that they see and talk to one another. This was a very wise decision by the writers, because any explanation they attempted would certainly have created more problems than it solved. By leaving things blank they leave open the possibility of some sort of answer that does make sense, though as I said I certainly can't think of one.

One of the most interesting features of the episode is the scene where Kirk tries to use his phaser against Deela. The weapon produces the normal beam effect, but at a vastly lower speed than normal - Kirk and Deela stand maybe five or ten feet apart, and it takes the beam at least as many seconds to cross the gap. Deela, naturally, simply steps out of the way before it reaches her.

Phaser beams are generally assumed to be traveling at the speed of light, some 300,000,000 metres per second. Kirk's beam was traveling at a visible speed of about 0.3 metres per second - indicating that he has been sped up by a factor of roughly one billion.

This is clearly nonsense. For instance, although we get many scenes of the non-accelerated crewmembers standing in a "frozen" state from the point of view of the accelerated people, we also see some scenes in the normal timeframe which make it clear that some hours have passed on the ship during this episode. It's not clear just how long passes, but let's assume that it is one hour from the time Kirk is accelerated to the time he comes back again. At a billion-fold ratio, this would mean that, from Kirk's point of view, one billion hours would have passed - well over one hundred thousand years! Even if we say that only a single minute passed in the normal world, it would still seem like nearly two thousand years to Kirk.

So, a billion-fold ratio is impossible. We can get a better idea of the ratio by thinking about why Kirk and the others became invisible when speeded up. There is a phenomenon concerning the Human eye called "persistence of vision"; basically when something vanishes, you keep seeing it for a small fraction of a second (roughly 1/15th) afterwards because it takes the cells in your eyes some time to react to the change. This is absolutely vital the the television and cinema industries, because it is this effect which makes the many slightly different images that are projected onto a screen blur into a moving image in your eye.

Presumably Kirk and the others cannot be seen because they come and go in less than this small fraction of a second - moving literally in the wink of an eye. Yet we see scenes where Kirk is standing around for several minutes with "frozen" crewmembers in the background. So this several minutes must equate to much less than a second if Kirk is to remain invisible.

This implies a ratio of around 3,000 to 1, which is still quite high if some hours have passed on the Enterprise, but certainly much more sensible than before. If we want to rule out the idea of having Kirk make his presence felt by standing directly in front of somebody for ten or fifteen minutes, we should probably regard a ratio of about 15,000 to 1 as being a sensible minimum.

Of course, at this ratio Kirk's phaser beam would still move at more than 20 kilometres per second. Vastly faster than any present day rifle bullet, and easily enough for it to retain its lethality. Unless phaser beams move at well below light speed, of course.

Even a 15,000 to 1 ratio presents other problems, though. For instance, Kirk walks around perfectly normally whilst accelerated. Yet if his normal walking speed is 1 metre per second, then he would be doing 15,000 metres per second - over 40 times the speed of sound! You wouldn't need to see the intruders, they'd be leaving sonic booms whenever they moved! And the friction of their motion would heat them so much that they would burst into flames instantly!

Worse, how would Kirk ever get up to 15,000 m/s in the first place? So far as we know the laws of physics are the same for him as for everyone else, after all. According to Newton the acceleration you can produce is given by the force you can generate divided by your mass. Kirk seems to mass just as much as before, he seems no stronger than before, so it should take him 15,000 times longer than normal to get up to speed. We're left with an image of Kirk frantically running in place like some demented cartoon character, trying to get enough speed up to actually move himself visibly.

Actually, even this wouldn't work. Gravity is an important part of the walking process - indeed walking has been referred to as a continual controlled fall. Yet gravity would be practically nonexistent for Kirk, as it would take him 15,000 times longer to fall through a given distance. So he in fact couldn't walk at all.

Even if Kirk could manage to reach these immense speeds, he would look pretty funny. The ship's air hasn't been accelerated, after all, so he would have the mother of all winds blasting into his face. More than enough to blow the clothes off his body (calm down ladies!), the hair off his head, probably enough to suffocate him, perhaps even enough to blast the flesh clean off his body.

As a final insult, if he survived all this then Kirk would certainly have no chance of stopping or turning - he'd turn himself into a great big red smear on the first wall or door he came to.

Then there is the lighting. A lamp produces energy at a given rate, no matter how futuristic it might be. Say the Enterprise has 450 watts of lighting on the bridge (pretty bright - your living room probably has no more than half of this). The 450 joules of light being put out in one second by the lights would equate to 450 joules in 15,000 seconds for Kirk. The lighting would look like 0.03 watts - almost total darkness.

And that's without considering frequency. Each light wave is taking a given amount of time to pass a given point, but to Kirk they are going past 15,000 times slower than normal. The effect would be to reduce the frequency of the light by 15,000 times, which would make the tiny amount of light that was produced completely invisible to the Human eye. As far as Kirk was concerned, the lamps would be putting out very small amounts of radio waves. Yet all illumination levels look perfectly normal.

TNG left the "accelerated people" thing alone throughout most of its run, but went there with "Timescape". In this episode Picard, Troi and Data come across pockets of altered time - areas where time passes very quickly, or very slowly. When they find the Enterprise-D frozen in the midst of a battle with the Romulans within such a pocket, they are able to use technobabble devices to let them move around, and board the Enterprise-D for some of those "everybody stand really still" scenes.

Problems abound, of course. For instance, Picard at one point accidentally puts his hand into one of these time pockets. He screams and pulls it back to find that the nails have grown much longer - an inch or so. Presumably time passed faster for his hand than the rest of him.

But this means that the hand wasn't getting supplied with new blood... and the nail growth indicates that it was in there for at least a few months. He would have drawn back a dead, shriveled lump rather than a functioning hand.

Once on board the Enterprise, the same movement problems that Kirk faced would probably apply. We don't really know how the devices they are wearing work, but there is no reasonable way that they could overcome these issues. For instance, you might just about say that the effect of the devices extends to the floor somehow, allowing a person to walk normally. But if the effect extended all the way up and out to the lighting fixtures, it would also include other people standing nearby.

Voyager dipped into the accelerated people well not once but twice. The first was in the episode "Gravity". In this episode Paris and Tuvok's ship falls into a "subspace sinkhole", some sort of anomaly. Within is a G2 star and three planets, which are experiencing accelerated time.

Somewhat amazingly, this solves virtually all of the problems that Kirk and Picard would have had. Kirk was an accelerated man moving within a non-accelerated framework, but here a whole solar system is accelerated. That means that all the motion problems are gone, even the lighting problems vanish since the sun is also accelerated. Coolness!

"Gravity" works so well because it avoids the obvious "I can move around whilst everybody else is like a statue" scenes. In fact, the only way in which there is any interaction at all between the fast and slow worlds is via communications systems or transporters - and even these are treated well.

Unfortunately, the writers fall down on their basic maths. Janeway suggests that for every hour on Voyager weeks or even months pass on the planet. This indicates a ratio of around 1,000 to 1. Yet later on Paris declares that thirty minutes on the outside is more than eight hours on the planet, indicating a ratio of only 16 to 1.

Later Janeway gives what seems like a definitive figure in a message to Paris, stating that the distortion is "point four seven four four seconds per minute." This would give a ratio of 126.476 to 1. Tuvok whips out his tricorder and declares that "According to that formula, 30 minutes would translate to two days, 11 hours and 47 seconds." Which is wrong, it would be two days, 15 hours, 14 minutes and 16 seconds. So it seems that whilst the episode does manage to treat the concept of accelerated time very sensibly, a few minutes with a calculator would not have come amiss.

Having done very well with "Gravity", the writers do less well with their next foray into acceleration. The episode is "Blink of an Eye" - presumably a reference to the TOS title. In this Voyager finds a planet which is experiencing accelerated time because it has a tachyon core. Tachyons are imaginary particles that move faster than light, and the use of the term is presumably meant to imply that some sort of Einstein-type time distortion is going on here.

The planet is spinning at 58 revolutions per minute. This is great, because it gives us a fast way to work out a rough ratio between the planet and the rest of the universe - 1 revolution in 24 hours for Earth compared to 58 per minute for the planet gives a ratio of 83,520 to 1. Of course this may be off because the planet may not have 24 hour days, but 80,000 to 1 should be in the ballpark. This means that one hour on Voyager is the same as nearly ten years on the planet.

Voyager gets caught in the effect, becoming a "third pole" in the core's subspace particle field and causing earthquakes on the planet below. We get this dialogue :

Janeway : "The tachyon core has created a space-time differential between the planet and the surrounding space. We're watching the seasons change in a matter of seconds."
Seven : "For each second that passes on Voyager, nearly a day goes by on the planet."

Since an Earth day is 86,400 seconds, this fits well with the 83,520 to 1 ratio previously established. If a season was three months, we would expect it to pass in about 93 seconds - again in the right ballpark for the previous ratio.

Some of the problems Kirk should have experienced would fall by the wayside here. Kirk was an accelerated person living within a non-accelerated environment. But like "Gravity", here the whole planet is accelerated. Since time itself has been speeded up for these aliens, all the problems with moving, turning, stopping, etc go neatly out the window. One big problem does remain, however - the sun.

In "Gravity" there was a sun within the anomaly which was also sped up. But if Voyager itself is not experiencing the time distortions up in orbit of the planet in this episode, then it is highly unlikely that the sun is experiencing them umpty-million miles beyond. Which means that the aliens should experience some of the same problems that Kirk would have had with being able to see.

The frequency shifting thing wouldn't be as much of an issue. Unlike artificial lights, stars put out energy over a very wide frequency band. So whilst the star's visible output would be shifted off somewhere into the radio waveband, there is all kinds of ultraviolet, X-rays, gamma rays and suchlike that would be shifted towards the visible band. This wouldn't necessarily mean that the sun would look the same, because stars don't put out equal amounts of light in all wavelengths, but it could at least mean that there was some visible light.

The dimming problem would remain, though, and in spades. With a ratio of 80,000 to 1 the sun would appear virtually invisible in the sky. With no heat from the sun the planet's atmosphere would lie on the surface as a solid. We might argue that the planet is just much closer to its sun than is normal for a class M world, but it would have to be practically sitting on the surface to make up for the difference.

Late in the episode the locals travel to Voyager, staying in their own timeframe until after they are aboard. It seems incredible that this could be the case - the planet is accelerated because time is passing at a different rate there than it is on Voyager. Yet these people have come to Voyager, whilst still operating on planetary time. It's as if the writers are suggesting that time is a property of the object rather than an objective reality - that two things sitting within the same inertial reference frame can have different time rates much as they might have different weight or colour.

Even if this were so, we would still then have all the same problems Kirk should have endured - no lighting, impossible to move, sonic booms if you could, etc.

Eventually Voyager is able to escape, with the assistance of the locals who by now have developed highly advanced technology. One has to wonder whatever happened to this planet. After all, one year later for everybody else they would have advanced by at least 80,000 years. These people could quite easily end up being the most advanced beings in the galaxy in short order.


There's no real conclusion here, as such. I rather enjoyed all three of these episodes, and "Gravity" in particular was a very credible stab at dealing with this kind of thing. As much as anything, I guess I'm saying that if you are going to write one of these types of episode, it would be best to be very, very careful about it...

Yellow text = Canon source Green text = Backstage source Cyan text = Novel White text = DITL speculation

Copyright Graham Kennedy Page views : 18,283 Last updated : 1 Jan 1970