Time Dilation

[Butters]

Did it ever come up, why, relativistic effects of travelling in excess of the speed of light aren’t experienced with a warp engine?

Why the time/distance/velocity is the same for all observers?

So, at the speed of light, travelling to Alpha Centauri four light years away. You would arrive there in four years to an external observer, but as the traveller, thanks to relativity, you’d get there in no time at all, and by the time you got home, everyone else would be eight years older.

But with warp drive, the time frame is the same for everyone, and Warp One is the equivalent of light speed. 1 light year, per year. So the same trip to alpha centauri would take four years to get there, four years to get back, and everyone would be eight years older.

I don’t remember it ever coming up, being mentioned in the Tech Manual. I suppose I always imagined that the warp field somehow negated the issue with subspace, but is it addressed on screen?

 

[Christopher]

Did it ever come up, why, relativistic effects of travelling in excess of the speed of light aren’t experienced with a warp engine?

Because there are none. Time dilation arises from the equations of Special Relativity, which apply to unaccelerated motion. Warp drive is an outgrowth of the broader General Theory of Relativity, which covers cases of accelerated motion (including acceleration due to gravity/spacetime distortion) that Special Relativity doesn't address.

Indeed, a ship at warp technically isn't moving at all. Rather, it's altering the geometry of spacetime around it in order to change its spatial relationship to the rest of the universe. Basically it's creating a bubble of spacetime that "surfs" on the surrounding distortion in spacetime, compressing the space ahead of it and expanding the space behind it. Miguel Alcubierre showed mathematically in his 1994 "warp drive" solution to General Relativity that the observed time flow inside and outside the warp field would be the same, i.e. there'd be no time dilation. You can read more here: http://www.if.ufrj.br/~mbr/warp/

 

[Maurice]

The warp drive supposedly gets around the issue because the ship at warp is relatively stationary inside its warp field. The warp field bends space around the ship, but the ship is not moving inside its bubble, hence no relativistic effects.

 

[Christopher]

The one time I can think of that the makers of Star Trek ever acknowledged relativistic non-simultaneity was in the passage in The Making of Star Trek where Roddenberry described how he answered fan letters complaining about the episode stardates being out of order by explaining that the measurement of time was different for observers on different ships and planets depending on how they moved, so presumably the log entries were giving stardates in whatever the local time was. But no show or movie ever made that canonical, and it was always presumed for simplicity that everyone experienced the same time interval between events.

 

[Spot261]

Given that relativity as we know it pretty much precludes FTL, it's fair to say our fictional tech has bypassed it somehow

 

[Christopher]

Given that relativity as we know it pretty much precludes FTL, it's fair to say our fictional tech has bypassed it somehow

As I said, that's incorrect. Special Relativity says that an object accelerating toward the speed of light can never reach it because it would take infinite energy. But General Relativity goes far beyond those equations, as should be evident from the name. Basically, Special Relativity only applies locally. You can't reach or exceed lightspeed relative to the spacetime around you. But General Relativity shows that the topology of spacetime can be changed by mass and energy, so it's theoretically possible to warp (distort) that topology in an extreme enough way to create a cosmic shortcut that lets you effectively move faster than light relative to the universe as a whole, while still moving slower than light relative to local space. Einstein himself and his colleague Nathan Rosen discovered that the equations of General Relativity allowed for the type of spacetime distortion that we now call a wormhole. The idea of a warp drive is also a direct outgrowth of General Relativity and its concept of warping space, hence the name. The link I gave above includes Miguel Alcubierre's 1994 letter in which he proves mathematically that a Star Trek-like warp field is a valid solution of General Relativity's equations.

The idea of time as a fourth dimension and the ability to distort space through it also implies the existence of higher dimensions, i.e. hyperspace. A lot of fictional FTL drives are based on the idea of accessing a hyperspace dimension that allows for FTL shortcuts -- again, not violating Special Relativity, but bypassing it by using concepts from General Relativity and related physics. And these stories generally assume that some form of space warp or wormhole-like portal would be needed to access hyperspace.

So far from contradicting relativity, the concepts behind most fictional FTL drives come from relativity in the first place -- just General rather than Special. Special Relativity is called that because it's not the whole picture, just the starting point. Einstein solved for the simplest case of constant, unaccelerated motion before he extended his efforts to a more comprehensive understanding that accounted for acceleration and gravitation as well.

 

[Spot261]

As I said, that's incorrect. Special Relativity says that an object accelerating toward the speed of light can never reach it because it would take infinite energy. But General Relativity goes far beyond those equations, as should be evident from the name. Basically, Special Relativity only applies locally. You can't reach or exceed lightspeed relative to the spacetime around you. But General Relativity shows that the topology of spacetime can be changed by mass and energy, so it's theoretically possible to warp (distort) that topology in an extreme enough way to create a cosmic shortcut that lets you effectively move faster than light relative to the universe as a whole, while still moving slower than light relative to local space

I'm pretty sure most of us are aware of the distinction, we have educations of our own and don't actually need you to explain it to us. General Relativity is a way to incorporate gravity into Special Relativity and in so far as certain predictions (in particular gravitational time dilation) do hold up under empirical observation it seems to hold up. However in so far as it allows FTL by any means including a black hole we can only speculate. Apodicticity, no matter how thoroughly considered, does not equate to scientific truth, especially if the framework on which it is based is demonstratably incomplete, which General Relativity remains.

The link I gave above includes Miguel Alcubierre's 1994 letter in which he proves mathematically that a Star Trek-like warp field is a valid solution of General Relativity's equations.

Provided one disregards much of quantum physics and posits certain assumptions which we have no reason to believe have any basis in reality. Alcubierre himself has frequently drawn attention to these shortcomings when people have overestimated the reach of his work beyond being an interesting way of making reality look like it might allow for FTL, but more likely not.

We have no real idea how a warp drive works because it isn't real and any extension of known physical frameworks is speculation at best.

The most we can really say is it clearly does work in universe and we don't really know for sure how, which is what I said.

 

[Christopher]

We have no real idea how a warp drive works because it isn't real and any extension of known physical frameworks is speculation at best.

This is a specious objection. Of course it isn't real -- we're talking about fiction. Nobody expects it to be real; it's just an exploration of ideas. The question is where the ideas come from in the first place. No science fiction writer was able to postulate a "space warp" or "warp drive" until Albert Einstein defined space as something that could be warped. No science fiction writer could have their characters fall through a wormhole until Einstein and Rosen produced the concept of a wormhole -- and, indeed, few writers made any use of the concept at all until Kip Thorne worked out the math of wormhole travel for Carl Sagan's Contact. Of course the ideas are conjectural and unlikely to be achievable in real life, but that's academic because we're talking about fiction. The point is that the hypotheses originated in relativistic physics and were then adopted by fiction writers, rather than being invented by fiction writers as an ignorant or deliberate contradiction of relativity.

 

[Spot261]

The question is where the ideas come from in the first place.

Considering the sequence of events with regards to Alcubierre was the opposite way around, his work in many ways was inspired by watching star trek which already had warp drives, sorry but that doesn't hold.

Nobody expects it to be real; it's just an exploration of ideas

No, trek really doesn't explore those ideas, warp drive works just fine and gets people from a to b, anything else is simply projecting something onto the show that isn't there. Warp drive as initially envisioned may have included references to "the time barrier" but it was only ever a means to an end without going into the details. That real scientific ideas get periodically mentioned on trek is pretty slap dash and superficial, it is a way of lending a passing vague credibility to the imaginary technology employed, not a hard science exploration of those ideas. To think it could be stated to make sense on the basis of using google scholar to look up theoretical physics sufficiently to give definitive answers to questions such as the OP is simply not true. Trek doesn't really explore those ideas, you do.

 

[Christopher]

Considering the sequence of events with regards to Alcubierre was the opposite way around, his work in many ways was inspired by watching star trek which already had warp drives, sorry but that doesn't hold.

Alcubierre was the first to do the actual detailed math for that specific type of space warp, but he was hardly the first person to conceive of the idea. Dr. Jesco von Puttkamer's technical memos written for Star Trek: The Motion Picture's producers in 1978 explain warp drive in essentially the same terms Alcubierre did, as a "bubble" of spacetime surfing on a progressive distortion of surrounding spacetime moving it effectively faster than light, just without the formal mathematics. And obviously the very concept of a "space warp drive" -- which goes back to 1930s prose science fiction -- is called that because it involves the warping of spacetime, a concept that comes directly from General Relativity in the first place. The writers who introduced the term, including John W. Campbell and Jack Williamson, knew their physics. They weren't operating from ignorance. They extrapolated from Einstein's work to produce a fictional application of the idea of space warping.

No, trek really doesn't explore those ideas, warp drive works just fine and gets people from a to b, anything else is simply projecting something onto the show that isn't there.

What makes you think I'm talking about Star Trek? As I said, the concept of space warp propulsion was introduced in science fiction in the 1930s. The specific term "warp drive" was in use by the 1950s. And there are many FTL drives throughout science fiction that employ various forms of space warps, space folds, wormholes, hyperdimensional transits, and the like, many of which are extrapolated directly from the theoretical papers of Einstein, Rosen, Schwartzchild, Wheeler, Tipler, and other physicists. I thought I'd made it clear that I was speaking about the use of the concept throughout SF.

To think it could be stated to make sense on the basis of using google scholar to look up theoretical physics sufficiently to give definitive answers to questions such as the OP is simply not true.

Actually it's on the basis of my 1993 BS in Physics from the University of Cincinnati, my lifelong interest in space science and physics before that, and my 20-plus years as a professional hard science fiction writer. I don't even know what Google Scholar is. That's after my time, I guess. I had to learn this stuff the old-fashioned way, by actually reading books and taking classes.

 

[Spot261]

Alcubierre was the first to do the actual detailed math for that specific type of space warp, but he was hardly the first person to conceive of the idea. Dr. Jesco von Puttkamer's technical memos written for Star Trek: The Motion Picture's producers in 1978 explain warp drive in essentially the same terms Alcubierre did, as a "bubble" of spacetime surfing on a progressive distortion of surrounding spacetime moving it effectively faster than light, just without the formal mathematics. And obviously the very concept of a "space warp drive" -- which goes back to 1930s prose science fiction -- is called that because it involves the warping of spacetime, a concept that comes directly from General Relativity in the first place. The writers who introduced the term, including John W. Campbell and Jack Williamson, knew their physics. They weren't operating from ignorance. They extrapolated from Einstein's work to produce a fictional application of the idea of space warping.

Exactly, which is what I said, it was a term loosely applied to something to give it a veneer of science, not something that was applied in a hard mathematical sense such that anything occurring onscreen could be said to follow the predictions of the theory. Once in a while some vague reference was made to warping space or the time barrier to make it sound like there was some sort of science going on if people didn't look too hard into it. They could equally have referred to pixie dust for all the predictive power of those statements in relation to what happened in any given episode. The episodes would play out just the same because they aren't about how the ship works, they are about what happens when it gets there.

We don't know how warp drive really works or how it affects reality around it except that which we are shown on screen. It is a plot device given a surface skim of sounding like it might have something to do with real science and no amount of parallels with real world models will change that.

What makes you think I'm talking about Star Trek?

You might not be, everyone else is.

Actually it's on the basis of my 1993 BS in Physics from the University of Cincinnati, my lifelong interest in space science and physics before that, and my 20-plus years as a professional hard science fiction writer.

And to be honest given the way you tend to present yourself and your self declared expertise I was assuming you were at the very least a PhD. All you have told me is you have an educational level approximately average for the people in this forum and are a sci fi fan. Writing novels makes not one jot of difference to whether you have anything remotely approaching the authority implied when you respond to this glib passing comment, which wasn't even aimed at you:

Given that relativity as we know it pretty much precludes FTL, it's fair to say our fictional tech has bypassed it somehow

With this self satisfied debacle masquerading as definitive scientific expertise which actually explains something none of us could have figured out for ourselves:

As I said, that's incorrect. Special Relativity says that an object accelerating toward the speed of light can never reach it because it would take infinite energy. But General Relativity goes far beyond those equations, as should be evident from the name. Basically, Special Relativity only applies locally. You can't reach or exceed lightspeed relative to the spacetime around you. But General Relativity shows that the topology of spacetime can be changed by mass and energy, so it's theoretically possible to warp (distort) that topology in an extreme enough way to create a cosmic shortcut that lets you effectively move faster than light relative to the universe as a whole, while still moving slower than light relative to local space. Einstein himself and his colleague Nathan Rosen discovered that the equations of General Relativity allowed for the type of spacetime distortion that we now call a wormhole. The idea of a warp drive is also a direct outgrowth of General Relativity and its concept of warping space, hence the name. The link I gave above includes Miguel Alcubierre's 1994 letter in which he proves mathematically that a Star Trek-like warp field is a valid solution of General Relativity's equations.

The idea of time as a fourth dimension and the ability to distort space through it also implies the existence of higher dimensions, i.e. hyperspace. A lot of fictional FTL drives are based on the idea of accessing a hyperspace dimension that allows for FTL shortcuts -- again, not violating Special Relativity, but bypassing it by using concepts from General Relativity and related physics. And these stories generally assume that some form of space warp or wormhole-like portal would be needed to access hyperspace.

So far from contradicting relativity, the concepts behind most fictional FTL drives come from relativity in the first place -- just General rather than Special. Special Relativity is called that because it's not the whole picture, just the starting point. Einstein solved for the simplest case of constant, unaccelerated motion before he extended his efforts to a more comprehensive understanding that accounted for acceleration and gravitation as well.

 

[CorporalCaptain]

so it's theoretically possible to warp (distort) that topology in an extreme enough way to create a cosmic shortcut that lets you effectively move faster than light

That's a technically incorrect usage of the term "topology."

The topology of a manifold embodies those characteristics of it that are invariant under bicontinuous (in other words, topological) transformations. One doesn't, as you say, warp topology. Manifolds have geometry, curvature, metric tensors and so forth. Intuitively, they are warped, but that property is static. Indeed (can I use that word in this way without sounding arrogant?), one of the key ideas of general relativity is that space and time are fused into spacetime, and any solution of Einstein's equation defines spacetime everywhere and at all times. The presence of matter may be said to warp spacetime, but the theoretical manifold is not exactly acted on by the matter; it simply exists in a way that obeys the system of differential equations, everywhere and always.

The point here is, such a manifold has a topology, or a set of topological properties. Sufficiently small variations in the metric tensor, or equivalently in the energy tensor, do not alter its topology at all, because topology embodies by definition properties that remain invariant under bicontinuous transformations. However, great enough changes in the metric tensor, or equivalently in the energy tensor, might require topological modification of the spacetime manifold, but that transition from one set of topological properties to another will occur discretely, and by a non-topological (non-bicontinuous) transformation, and the topology itself will (again by definition) not survive that sort of transformation.

In summary, discussing the warping of topology as you are doing is technically incorrect. Honestly, it sounds like someone using a technical term without really knowing what they are talking about. This will get you started: https://en.wikipedia.org/wiki/Topology

so it's theoretically possible to warp (distort) that topology spacetime in an extreme enough way to create a cosmic shortcut that lets you effectively move faster than light

This would be decidedly better.

The idea of time as a fourth dimension and the ability to distort space through it also implies the existence of higher dimensions, i.e. hyperspace.

That's flat-out incorrect (if you'll pardon the pun). I'm not sure where you get that at all. If you happen to be getting it from the fact that any Riemannian surface can be embedded in a Euclidean space of sufficiently high dimension, then I would say the following. One of the motivations in the development of general relativity was the postulate that inertial frames of reference have no special role to play in the formulation of natural laws. Supposing that there is an embedding space for our universe that is in some sense "flat" would be a violation of that principle. Indeed (again, can I use that word in this way without sounding arrogant?), flatness is just a special kind of metric. So, the situation of embedding the universe in a flat space of higher dimension is really logically the same as embedding the universe in a curved space of higher dimension, which raises the question, "Why bother?"

Or, in other words and scientifically, what is the reason to suppose that such an embedding space exists in the first place? The four dimensional spacetime manifold extrapolated (at least theoretically) from what we observe does not need to be embedded in anything, in the sense that none of the properties that the theory postulates depend upon the manifold being embedded in a higher dimensional space. The boldfaced is the critical point.

Of course, the manifold's properties are compatible with the manifold being embedded in a higher dimensional space, but embedding is not necessary. So, nothing about embedding into higher dimensional spaces is implied.

Not to mention, why stop with one with superspace, when it in turn might be embedded in another of even higher dimension? There's no limit to the number of dimensions that can be postulated, but there is a definite limit to the number that are emperically required.

a Star Trek-like warp field

What makes you think I'm talking about Star Trek?

 

[Skipper]

Did they ever discuss time dilation while using impulse drive?

 

[Christopher]

Did they ever discuss time dilation while using impulse drive?

Nope, it's never come up. The only time that Trek canon has ever mentioned time dilation is on the fine print of a graphic of the Bajoran wormhole in Keiko's classroom.

The TNG Tech Manual says that impulse operations are normally limited to 0.25c to avoid relativistic effects, which has led some people to draw the erroneous conclusion that that's the maximum speed impulse drive is capable of. Of course, in space there's no friction to slow you down, so as long as you can keep applying thrust, you can continue to accelerate arbitrarily close to the speed of light. Starfleet vessels just normally don't have a reason to, since it's easier just to use warp drive if you're in that much of a hurry. And really, you'd have to get up to 70 or 80 percent of lightspeed before time dilation becomes significant. At about 0.85c you'd have time slowed down aboard ship by a factor of 2; at 0.95c it'd be a factor of 3; and even at 0.99c you'd only be slowed down by a factor of 7, with a day passing aboard ship for every week outside. And you'd rarely need to be at impulse speed for that long.

 

[Destructor]

But, and this is a genuine question here, does outpacing light, no matter how you do it, lead to relativistic effects? We're talking about 'avoiding' time dilation as if there is some sense of simultaneity or common frame of reference when we refer to time 'slowing down' in relation to other things, but is there? Isn't that the key to the theory of relativity, that true simultaneity is an illusion, and if I was suddenly 8.3 light minutes away, I've already 'gone back in time' relative to my previous position? I genuinely do not understand this, but I thought part of the reason light speed was the galactic speed limit wasn't just because you couldn't accelerate to light, but also that there would be wacky effects if you somehow outpaced light through other means.

 

[Christopher]

But, and this is a genuine question here, does outpacing light, no matter how you do it, lead to relativistic effects? We're talking about 'avoiding' time dilation as if there is some sense of simultaneity or common frame of reference when we refer to time 'slowing down' in relation to other things, but is there? Isn't that the key to the theory of relativity, that true simultaneity is an illusion, and if I was suddenly 8.3 light minutes away, I've already 'gone back in time' relative to my previous position? I genuinely do not understand this, but I thought part of the reason light speed was the galactic speed limit wasn't just because you couldn't accelerate to light, but also that there would be wacky effects if you somehow outpaced light through other means.

Mathematically speaking, as you plug numbers closer and closer to c into the equations of Special Relativity, your mass increases toward infinity and your observed time decreases toward zero. If you could reach the speed of light, you'd be totally frozen in time and your mass would be infinite. If you plug numbers larger than c into those equations, those values become imaginary numbers -- the square root of a negative number, which is physically meaningless. Some theorists interpret that imaginary time flow as going backward in time, but I've never understood how that math is supposed to work. The equations show how time is measured on the moving object itself, so you'd think that if its time were going backward, then it wouldn't be going back in time per se; rather, outside observers would still see the ship moving forward in time, but the people on board would just get younger. Of course, an imaginary number is not a negative number, so it wouldn't just be time going backward, but I've never been able to figure out what it would be instead.

Using a warp drive or a wormhole or a spatial fold or whatever means, again, that you're not actually accelerating to or beyond the speed of light; you're just following a shortcut through hugely distorted spacetime that lets you reach a destination far away by covering a much shorter effective distance, so that you get there before a beam of light could even though your velocity through local space remains below the speed of light. Now, yes, you're right that that would potentially create a time paradox, due to the causality violation. But that's a different kind of physics from time dilation, which specifically means time slowing down relative to an outside observer.

When we talk about time slowing down aboard a relativistic spaceship, that's not in reference to a universal frame of reference, just to a specific observer's frame of reference, e.g. someone watching the ship from Earth. But as long as the ship's velocity is constant and unaccelerated, then the situation is symmetrical and there's no preferred frame of reference. If Alice is standing on an asteroid in space and sees Bob fly by on a ship at 85% of lightspeed, then Alice will see Bob's clocks slowed down to half speed -- but Bob will also see Alice's clocks slowed down to half speed. As far as Bob can measure, he's standing still and Alice's asteroid is moving at 0.85c. (Well, assuming that they're in a universe where nothing else exists or is visible to them, or they're just too lazy to measure. Bob and Alice like to keep things simple.)

What breaks the symmetry is if the ship accelerates -- if it slows down, turns around, and comes back so that Bob and Alice can compare their clocks again. In that case, it's no longer a symmetrical situation, and there is no frame of reference in which Bob can be defined as stationary (i.e. unaccelerated). When that happens, both Bob and Alice will agree that Bob has aged less in the interim than Alice did (though Bob might be too polite to mention it in Alice's hearing).

 

[Skipper]

The TNG Tech Manual says that impulse operations are normally limited to 0.25c to avoid relativistic effects, which has led some people to draw the erroneous conclusion that that's the maximum speed impulse drive is capable of.

Indeed I struggle to remember an episode where impulse speed/acceleration was a relevant plot point. I suppose if I escape my pursuers thanks to my superior impulse acceleration, then they will reach me later with the warp speed.

 

[Deks]

Indeed I struggle to remember an episode where impulse speed/acceleration was a relevant plot point. I suppose if I escape my pursuers thanks to my superior impulse acceleration, then they will reach me later with the warp speed.

Unless of course you can't use Warp drive for whatever reason.
I don't think Trek ships are limited to 0.25c though (the technical manuals aren't canon for one thing).... they might be able to accelerate even more without experiencing relativistic effects.
Remember that ships still project a subspace field around themselves, and can also project a low level warp field while using sublight (which wouldn't necessarily need the ability to be able to go to warp and might be projected when Warp is damaged)... so these things (and/or something else) might be used to negate relativistic effects at say 0.5 and 0.6c (levels at which relativistic effects are still relatively minimal).

In TNG, the Enterprise-D was chasing a Borg cube to Earth across the solar system at sublight and they had to drop out of warp outside SOL (as did the Borg cube).
It was mentioned it would have taken the Enterprise 23 minutes to intercept the cube when it broke through the Mars orbital perimeter... or basically, to cross something along the lines of about 98.6 astronomical units... given that the cube was at Mars at that point, and the Enterprise just outside SOL).
If I calculated the distance properly (although admittedly, I could be HORRIBLY wrong), crossing that distance in 23 mins would mean a velocity of what... approximately over 10.7 million km per second?
These speeds go way beyond speed of light (about 35 times faster than c)... and could probably only be achieved through use of warp technology to gain warp like velocities without actually entering warp inside SOL... though this kind of feat seems... improbable?

I can concede speeds in the range of 0.5 - 0.6c for impulse without relativistic effects through use of say subspace fields, but I doubt you could get 35 c on impulse alone.
Then again, who knows what goes on when subspace fields interact with the hull to drop the mass... never-mind adding a warp field into the mix.
Ds9 had nothing but maneuvering thrusters and used subspace fields to lower its mass to get to the wormhole the next day.
On a starship with fully equipped impulse engines... I suppose you could further increase this effect.

 

[Christopher]

I don't think Trek ships are limited to 0.25c though (the technical manuals aren't canon for one thing)....

As I said in post #14 above, the tech manuals never said ships are limited to 0.25c. That's a common misapprehension based on a misunderstanding of the term "full impulse" as used in the Star Trek Encyclopedia. "Full speed" is a naval term that means the maximum standard speed at which a ship normally operates. The term for its maximum possible speed is "flank speed."

What the TNG Tech Manual actually says (on pp. 75-8) is that normal impulse operations are kept below 0.25c by convention in order to minimize relativistic effects, but that the main impulse engine can drive the ship up to 0.75c before needing to draw on additional thrust from the Saucer Module engines -- although impulse engines are most efficiently below 0.5c.

In TNG, the Enterprise-D was chasing a Borg cube to Earth across the solar system at sublight and they had to drop out of warp outside SOL (as did the Borg cube).
It was mentioned it would have taken the Enterprise 23 minutes to intercept the cube when it broke through the Mars orbital perimeter... or basically, to cross something along the lines of about 98.6 astronomical units... given that the cube was at Mars at that point, and the Enterprise just outside SOL).
If I calculated the distance properly (although admittedly, I could be HORRIBLY wrong), crossing that distance in 23 mins would mean a velocity of what... approximately over 10.7 million km per second?
These speeds go way beyond speed of light (about 35 times faster than c)... and could probably only be achieved through use of warp technology to gain warp like velocities without actually entering warp inside SOL... though this kind of feat seems... improbable?

I learned long ago that trying to get any sense or consistency out of numbers in Star Trek is a futile effort. It's generally best just to treat the numbers spoken onscreen as placeholders. The writers and filmmakers aren't trying to solve math problems, they're trying to entertain people, and the numbers are just a bit of texture meant to create a fleeting impression. So they're rarely thought through carefully enough by the writers to have any real consistency.

 

[Deks]

As I said in post #14 above, the tech manuals never said ships are limited to 0.25c. That's a common misapprehension based on a misunderstanding of the term "full impulse" as used in the Star Trek Encyclopedia. "Full speed" is a naval term that means the maximum standard speed at which a ship normally operates. The term for its maximum possible speed is "flank speed."

What the TNG Tech Manual actually says (on pp. 75-8) is that normal impulse operations are kept below 0.25c by convention in order to minimize relativistic effects, but that the main impulse engine can drive the ship up to 0.75c before needing to draw on additional thrust from the Saucer Module engines -- although impulse engines are most efficiently below 0.5c.

Oh, I'm aware of the premise that most people misunderstand that Trek impulse speeds are limited to 0.25c... and besides, these limitations make little to no sense with subspace technology in place which manipulates spacetime.

I learned long ago that trying to get any sense or consistency out of numbers in Star Trek is a futile effort. It's generally best just to treat the numbers spoken onscreen as placeholders. The writers and filmmakers aren't trying to solve math problems, they're trying to entertain people, and the numbers are just a bit of texture meant to create a fleeting impression. So they're rarely thought through carefully enough by the writers to have any real consistency.

Yeah... see, the writers could have used a simple calculator to make accurate statements.
Establish certain rules around the technology and then just write within the confines of that technology.
But, 24th century technology in the Federation would simply be too advanced for most dumbing down (which end up making little to 0 sense). A better approach is to then devise a plot/story element that surpasses the technology just enough to impair its normal operations (and just pulling arbitrary anomalies out of a writers end to make the tech inoperative in just about any condition is equally stupid).
The existing stories could easily be adjusted in a small manner to make numbers consistent.