This thread is for discussion of warp speed paraxoes in Star Trek, and the various solutions proposed for them.
Most of us have done math problems in school where we had to calculate how long a train will take to travel a specfied distance at a specifed speed, or if a train travels 150 miles in 2.5 hours what is its average speed, and so on.
And I suspect that most Star Trek writers, producers, and other creators hated doing those problems in school, because it seems like they never bothered with them ihen creating various productions, and the evidence about warp speeds is highly conradictory.
There have been separate "official' warp speed scales for TOS and for TNG era productions. And as early as TOS , few writers seemed to follow those "official" warp scales. According to the semi canon sources, the speed of a TOS Warp factor equalled c, the speed of light mulitiplied by the warp facctor cubed. So warp factor 1 ws the speed of light, warp factor 2 was eight times the speed of light, and so on. Warp factor 6, the fastest speed that was safe to use for long periods of time was 216 times the speed of light.
And it should be obvious that the significantly higher warp speeds should have been chosen due to the vast distanced traveled during the five year mission. For example, in about a year Mudd traveled from Rigel to Deneb and then to Mudd's planet.
Many TOS episodes involved travel much faster than the warp scale. It is possible that the most extreme example was in "That Which Survives" where the Etnerprise has to travel 990.7 light years very fast. They start at Warp 8 and soon are travelling a little faster.
Warp 8.4 should be 592.704 times the speed of light, so it should take them about 1.671492 years to get there. But the estimated travel time is 11.337 hours, which would require a speed of 766,029.46 times the speed of light. So they are travelling 1,292.4317 times as fast as they should according to the warp scale.
There are many other examples of interstellar travel much faster than the TOS warp scale.
But there are some examples of interstellar travel in TOS happening at speeds similar to the TOS warp scale.
In "This Side of Paradise", at Omicron Ceti, Kirk says:
And obviously if the trip from Earth to Omicron Ceti took about 0.5 to 1.5 Earth years, the colonists' ship would travel at speeds consistent with the TOS warp scale.
In "By Any Other Name":
The Andromeda Galaxy is about 2,500,000 light years from EArth, so travel there in about 250 to 300 years would take speeds of about 8333.33 to 10,000 times the speed o flight, which is much slower than the speed in "That Which Survives". But Kirk seemed to imply that it would take at least 10,000 years, which would require speeds slower than 250 times the speed of light - close to warp 6 at 216 times the speed of light.
In TNG era productions a different warp scale is used, and ships are supposed to be faster than in TOS (see VoY "Flashback"):
But the entire plots of DS9 and VOY depend on TNG era ships, faster than TOS era ships, still taking many decades to travel 70,000 lgiht years, thus making their speeds average about 1,000 times the speed of light. Much slower than the fastest speeds in TOS and about twice the official TOS Warp scale, indicating that TOS ships shouldn't have been faster than the TOS warp scale..
And then there is Star Trek: The Motion Picture (1979), which had two science advistors, biochemist and science fiction writer Isaac Asimov, and NASA rocket expert Jesco von Puttkamer. In a thread: https://www.trekbbs.com/threads/distance-speeed-and-time-in-tmp.312160/#post-14252735 I calculated that the distances and times were consistent with V'Ger travelling at warp factor sevenof the TOS warp scale, with the Klingon's a had a base at Barnard's Star and if V'Ger came from the far side ofthe galaxy,and I think tht it is fairly proble that the science advisors also did the calculations.
And in that that thread I offered a possible explaination for the many contradictions in "galactography", the geography of outer space (a term coined by Asimov, I think) and problems with times, distances, and speeds of various voyages:
That is one theory to explain the many warp speed paradoxes in Star Trek.
Of course there are other theories which have been proposeed to explain warp speed paradoxes, and still other theories which are possible solutions which have not yet been proposed.
So I thought I would start a thread to list all of the known theories about solutions to the warp speed paradoxes.
Most of us have done math problems in school where we had to calculate how long a train will take to travel a specfied distance at a specifed speed, or if a train travels 150 miles in 2.5 hours what is its average speed, and so on.
And I suspect that most Star Trek writers, producers, and other creators hated doing those problems in school, because it seems like they never bothered with them ihen creating various productions, and the evidence about warp speeds is highly conradictory.
There have been separate "official' warp speed scales for TOS and for TNG era productions. And as early as TOS , few writers seemed to follow those "official" warp scales. According to the semi canon sources, the speed of a TOS Warp factor equalled c, the speed of light mulitiplied by the warp facctor cubed. So warp factor 1 ws the speed of light, warp factor 2 was eight times the speed of light, and so on. Warp factor 6, the fastest speed that was safe to use for long periods of time was 216 times the speed of light.
And it should be obvious that the significantly higher warp speeds should have been chosen due to the vast distanced traveled during the five year mission. For example, in about a year Mudd traveled from Rigel to Deneb and then to Mudd's planet.
Many TOS episodes involved travel much faster than the warp scale. It is possible that the most extreme example was in "That Which Survives" where the Etnerprise has to travel 990.7 light years very fast. They start at Warp 8 and soon are travelling a little faster.
.RAHDA: We're holding warp eight point four, sir. If we can maintain it, our estimated time of arrival is eleven and one half solar hours.
SPOCK: Eleven point three three seven hours, Lieutenant. I wish you would be more precise.
Warp 8.4 should be 592.704 times the speed of light, so it should take them about 1.671492 years to get there. But the estimated travel time is 11.337 hours, which would require a speed of 766,029.46 times the speed of light. So they are travelling 1,292.4317 times as fast as they should according to the warp scale.
There are many other examples of interstellar travel much faster than the TOS warp scale.
But there are some examples of interstellar travel in TOS happening at speeds similar to the TOS warp scale.
In "This Side of Paradise", at Omicron Ceti, Kirk says:
KIRK: Another dream that failed. There's nothing sadder. It took these people a year to make the trip from Earth. They came all that way and died.
And obviously if the trip from Earth to Omicron Ceti took about 0.5 to 1.5 Earth years, the colonists' ship would travel at speeds consistent with the TOS warp scale.
In "By Any Other Name":
KIRK: What's the point of capturing my ship? Even at maximum warp, the Enterprise couldn't get to Andromeda galaxy for thousands of years.
ROJAN: Captain, we will modify its engines, in order to produce velocities far beyond the reach of your science. The journey between galaxies will take less than three hundred of your years.
Spock Fascinating. Intergalactic travel requiring only three hundred years. That is a leap far beyond anything man has yet accomplished.
The Andromeda Galaxy is about 2,500,000 light years from EArth, so travel there in about 250 to 300 years would take speeds of about 8333.33 to 10,000 times the speed o flight, which is much slower than the speed in "That Which Survives". But Kirk seemed to imply that it would take at least 10,000 years, which would require speeds slower than 250 times the speed of light - close to warp 6 at 216 times the speed of light.
In TNG era productions a different warp scale is used, and ships are supposed to be faster than in TOS (see VoY "Flashback"):
JANEWAY: It was a very different time, Mister Kim. Captain Sulu, Captain Kirk, Dr. McCoy. They all belonged to a different breed of Starfleet officer. Imagine the era they lived in. The Alpha Quadrant still largely unexplored. Humanity on verge of war with Klingons. Romulans hiding behind every nebula. Even the technology we take for granted was still in its early stages. No plasma weapons, no multiphasic shields. Their ships were half as fast.
But the entire plots of DS9 and VOY depend on TNG era ships, faster than TOS era ships, still taking many decades to travel 70,000 lgiht years, thus making their speeds average about 1,000 times the speed of light. Much slower than the fastest speeds in TOS and about twice the official TOS Warp scale, indicating that TOS ships shouldn't have been faster than the TOS warp scale..
And then there is Star Trek: The Motion Picture (1979), which had two science advistors, biochemist and science fiction writer Isaac Asimov, and NASA rocket expert Jesco von Puttkamer. In a thread: https://www.trekbbs.com/threads/distance-speeed-and-time-in-tmp.312160/#post-14252735 I calculated that the distances and times were consistent with V'Ger travelling at warp factor sevenof the TOS warp scale, with the Klingon's a had a base at Barnard's Star and if V'Ger came from the far side ofthe galaxy,and I think tht it is fairly proble that the science advisors also did the calculations.
And in that that thread I offered a possible explaination for the many contradictions in "galactography", the geography of outer space (a term coined by Asimov, I think) and problems with times, distances, and speeds of various voyages:
One solution to the warp speed paradoxes is to imagine that there some type of wormholes or other space time tunnels connecting different star systems. A space ship can enter the mouth of such a tunnel and emerge from the mouth of the tunnel in another star system in much less time than it would take to travel the entire distance between the two systems, even at top warp speed.
So some starship voyages actually cross the spaces between stars using warp speed, while others bypass those vast distances by using those interstellar short cuts.
And so my theory is that on a space map the Federation would look like a collection of disconnected bubbles floating in space, consisting of stars systems connected by those shortcuts surrounded by spherical zones of space claimed by the Federation. And in some places two or more neighboring star systems would both be part of the Federation and the Federation would claim a larger zone of space around those systems.
And if other star traveling societies have discovered those space shortcuts their territories would also tend to look like disconnected soap bubbles in space maps.
Including the Klingon Empire. So my theory is that in the era of TMP the Klingon Empire rules a star system only a few light years from the Solar System, and claims a volume of space of space several light years around that system.
Thus when the Klingons detected V'Ger heading toward that system on a line toward Earth they would have sent three warships to that system to get ahead of V'Ger and then turn back and head toward V'Ger like they were coming from Earth, and attack V'Ger to make V'Ger think Earth was hostile to V'Ger.
The Klingon high command no doubt figured that if three warships could defeat V'Ger no harm would be done, since V'Ger wouldn't have been powerful enough to defeat Earth's defense system anyway. And they probably also figured if the three warships couldn't defeat V'Ger, it might be powerful enough to defeat Earth's defenses, so sacrificing a mere three warhships to increase the probability that V'Ger would attack and destroy Earth would be worthwhile.
That is one theory to explain the many warp speed paradoxes in Star Trek.
Of course there are other theories which have been proposeed to explain warp speed paradoxes, and still other theories which are possible solutions which have not yet been proposed.
So I thought I would start a thread to list all of the known theories about solutions to the warp speed paradoxes.