[clueless (OP)]

In order for anything to move at light speed, never mind "infinitely fast", it needs an infinite amount of energy. This cannot be obtained from a finite mass. So there's nothng to worry about - it simply can't happen.

All right then.

So, basically, what you are saying is that, well, Star Trek is lying to us?! Enterprise CANNOT travel faster than light?! Well then. That is not a nice thing to say to a Trekkie, is it now. Not to worry. I forgive you.

This discussion on Star Trek was split off from here - moderator 

[Janus]

In order for anything to move at light speed, never mind "infinitely fast", it needs an infinite amount of energy. This cannot be obtained from a finite mass. So there's nothng to worry about - it simply can't happen.

All right then.

So, basically, what you are saying is that, well, Star Trek is lying to us?! Enterprise CANNOT travel faster than light?! Well then. That is not a nice thing to say to a Trekkie, is it now. Not to worry. I forgive you.

As a fan of Star Trek myself,  I am quite capable of accepting the fact that FTL travel as depicted in the series is unlikely in the extreme if not entirely impossible, without it destroying my enjoyment of the show.  In the same way I can watch "Godzilla" without worrying about the fact that the cube-square law would make it impossible for a living creature that size to even support its own weight on land.   You merely invoke the " willing suspension of disbelief"  If it is necessary to assume FTL or that creatures can be that big to tell the story, then I'm fine with it. (Though sometimes this can be stretched to beyond the breaking point. Such as in the movie "Signs", where aliens for which water acts like acid decide to invade a world which is mostly covered in it, and of which the very atmosphere contains a good amount. The aliens in that movie wouldn't have been even able to walk around unprotected, as their bodies would have reacted with the moisture in the air.) 

Still, since the universe has holographic properties, which can explain many, many phenomenon, could there be an anomaly, like God, who "can" travel faster than light, and maybe even reach an infinite speed? Meh. Forget it.   

The main problem with your question is that it tries to treat "infinite" as actually having some assigned value.  "infinite" literally means "Not finite" or without limit.  In the case of defining what "infinite speed" is, this becomes more problematic.  Speed is expressed in distance per time.  Thus something that moves  10 meters in 2 sec moves 10m/2s = 5m/s.  This also the same as moving 2.5 meters in 0.5 sec.  So what does "infinite" speed mean.  You might say that it means moving an infinite distance in one sec.  But how far would would you move in 2 sec?  An infinite distance.   Or you could look at it in terms of how long it takes to travel a finite distance.   This would be zero time or Xm/0s, . But division of zero is undefined, not infinity.  So there isn't really anyway to rigidly define what "infinite" speed means.
Compounding things even further is the fact is that there are many levels of infinity, with some levels  larger than others.

[geordief]

The main problem with your question is that it tries to treat "infinite" as actually having some assigned value.  "infinite" literally means "Not finite" or without limit.  In the case of defining what "infinite speed" is, this becomes more problematic.  Speed is expressed in distance per time.  Thus something that moves  10 meters in 2 sec moves 10m/2s = 5m/s.  This also the same as moving 2.5 meters in 0.5 sec.  So what does "infinite" speed mean.  You might say that it means moving an infinite distance in one sec.  But how far would would you move in 2 sec?  An infinite distance.   Or you could look at it in terms of how long it takes to travel a finite distance.   This would be zero time or Xm/0s, . But division of zero is undefined, not infinity.  So there isn't really anyway to rigidly define what "infinite" speed means.
Compounding things even further is the fact is that there are many levels of infinity, with some levels  larger than others.

Can we say (with certainty?)  that "infinity" has no meaning outside a mathematical context and that even there it is understood/used  as a process rather  than an object?

[evan_au]

Star Trek is lying to us?! Enterprise CANNOT travel faster than light?!

No, Einstein's relativity (1915) says that you cannot accelerate something from stationary up to the speed of light while using a finite amount of energy.
- However, there are theoretical solutions in Relativity that might allow objects already travelling faster than light to keep travelling faster than light.

The script writers for Star Trek (1960s)  were well aware of this, and didn't want to annoy their (often pedantic) audience...
- Star Trek is fiction, and the writers were able to work around this objection with the wave of a pen
- The key is in the names: Impulse Drive and Warp Drive.
- You don't use the Impulse Drive to accelerate faster than light
- "Impulse drive" is for moving around a planet, below the speed of light.
- "Warp drive" is for travelling between stars, above the speed of light.
- Some theoretical physicists have suggested that you can bend (warp) space so that travelling a short distance through warped space results in travelling a large distance through normal space. The "Alcubierre drive" (1990s) is one such suggestion, but these suggestions often involve exotic things like negative energy or black holes. Certainly not something we know how to control at this time.
- This may be a case of science copying fiction?

See: https://en.wikipedia.org/wiki/Alcubierre_drive

I see that some proposed nuclear fusion reactions involve lithium, perhaps the rare "dilithium" of Star Trek was not so far off the mark...

[alancalverd]

Star Trek is founded on a number of axioms, including

aliens speak English

the more advanced a civilisation, the more rudimentary its hand weapons

even Shakespearian actors have to make a living (see also John Laurie alias Private Frazer "I starved as the greatest Macbeth of my generation, and now I'm making a fortune reading this sh1t.")

you can make a legend in a hangar with cardboard scenery if you really work on the script

hand grenades make great earphones, but don't pull out the pin

if you can't afford a model planetary lander, use a montage dissolve

a world class composer can knock out a memorable theme tune in a day - truly forgettable scores take ages

It was all great fun, and inspirational. I'm still working on Dr McCoy's wand that diagnoses hitherto unknown diseases, and my partners are designing the box that cures them.

[evan_au]

aliens speak English

We have got a bit off-topic here, but the premise in Star Trek is that someone has invented a "universal translator".
- Progress has been made over the past 5 years with alternate translation between two known languages, in something the size of a tablet computer
- Simultaneous translation (as done by skilled human translators) is still beyond our current commercial technology
- Translation into a totally unknown language would seem to be fundamentally impossible, unless both parties have a universal translator, and there is a third language that is known by both universal translators as an intermediate representation....

Assuming a universal translator certainly shaves years off each episode, while someone grasps the basic representation, vocabulary and grammar of a new language (let alone a different species!).
...just like assuming faster than light travel shaves millenia off each episode as they travel to the next star!

[clueless (OP)]

We have got a bit off-topic here, but the premise in Star Trek is that someone has invented a "universal translator".

I agree. First I mention infinity, and then: wham! Somebody mentions universal translator. I demand to know what infinity is! (Even though science is not my thing.) Somebody invent a time machine, travel back into the past and bring back, one and only, Stephen Hawking. Universal translator . . . How do you sleep at nights?!

[alancalverd]

- Simultaneous translation (as done by skilled human translators) is still beyond our current commercial technology

And humans too! I had a call on the headphones from an EU committee interpreter asking if I would ask the German chairman to speak more quickly. "He is using slow, formal German with the verb at the end of the sentence, so we can't translate it into any other language  because we don't know what he means until he has finished ."

[evan_au]

Star Trek is founded on a number of axioms, including

I would add: Artificial gravity is easy

...it certainly makes the filming much easier without everyone pretending to float around (like Gravity), and dealing with high G-Forces during evasive maneuvers.
You just need to tell everyone to sway to the left and sway to the right in unison...

It also means that you don't spend days or weeks travelling between planets at 1G acceleration

[syhprum]

I always find the communications the most difficult to believe when you can have a real time conversation with someone light years away.

[Janus]

I always find the communications the most difficult to believe when you can have a real time conversation with someone light years away.

In Star Trek they addressed that problem by assuming the existence of "Sub-space" radio.  While faster than a ship at even high warp, it wasn't instantaneous.   I don't think that they ever established how fast Sub-space radio worked, but was likely due to the fact that they wanted to flexible with it.   It allowed for communication over light years, without having to wait for years, but it still didn't allow Capt. Kirk to be constantly in contact with Star Fleet in real time.  This allowed for more autonomy on his part.  For example, in one episode, he sends message to Star Fleet telling them that he is going to take an action that they may not approve of.   They don't get the reply saying they trust his judgement, until everything is over at the end of the episode.  Later series of the franchise got a bit looser with its usage.

Though even when SF show/movies try to hold to the speed of light limit for communications, they can screw up.
Take for instance the Movie "Passengers".  In it they show a character sending a message to Earth, and the computer telling him that it will take 19 yrs for the message to be received and an additional 30 some years ( I don't remember exactly the figure for the answer to return.   It even showed a graphic showing the message going one way to Earth, and then back, with it having to travel more distance on the return since the ship would have increased its distance from the Earth.
This isn't how it would work.  Light speed is invariant.  Thus assuming the ship is maintaining a constant speed, it will always measure light as traveling at c relative to itself.  Thus, if the signal took 19 years to reach Earth, it means, according to the ship, 19 ly is how far apart the ship and Earth are when the message arrives  (they were closer when the message was sent)
The answer is sent from that distance from the ship and will arrive in another 19 years ( it doesn't matter how much the distance between Earth and ship increases after the signal leaves Earth.  Total round trip time: 38 yrs.

If on the other hand, it was assumed that the ship and Earth were 19 ly apart when the signal left the ship (which seems more in line with other facts revealed in the story),  Given the speed of the ship stated later (0.5c), the Earth would have receded to 38 ly from the ship by the time the message arrives, taking 38 yrs to get there, plus a 38 yr return leg for a 76 yr gap before you would get a reply, not the 50+ yr answer the computer gave him. (assuming all times and distances are as measured by the ship, which only makes sense, as our character would only be concerned with how long he would have to wait for an answer)
 What could mess up these figures is if the ship wasn't moving at a constant speed but under a constant acceleration, but this doesn't mesh with how long it is stated the trip length is and how far along the trip they are when the character is awakened early.

[Bored chemist]

It seems sci fi science is good enough for some...
http://blogs.discovermagazine.com/neuroskeptic/2017/07/22/predatory-journals-star-wars-sting/

[Bill S]

Can we say (with certainty?)  that "infinity" has no meaning outside a mathematical context….

Just when you thought it was safe to mention infinity…….!

That’s an intriguing question, Geordie.   Possibly, the Star Trek thread is not the place to do it justice.  You might consider starting a new thread with it.  An answer that was even remotely acceptable to the majority might save a lot of going round in circles later. 

[Bill S]

You might say that it means moving an infinite distance in one sec.

Distance is a measurement between points.  No two points can be infinitely far apart, so I guess this is a non-starter..

So there isn't really anyway to rigidly define what "infinite" speed means.

Agreed; but no less a figure than John Gribbin says: “So if a tachyon were created in some violent event in space, it would radiate energy away furiously…..and go faster and faster, until it had zero energy ……and was travelling at infinite speed”. 

[yor_on]

What we use to define a distance is not a ruler, it's 'time'.
The ruler as read on a map is 'static'
'Time' is observer dependent

[yor_on]

Then again, rulers ain't static.
But if you asked me the odds of rulers being what means something
Or 'time'

I would go for time, every time :)
Can't ignore it

[yor_on]

I never seem to get it clear, do I?
Locally measured your ruler is as true as your 'proper time'.

What a ruler needs though.
Is a 'sense' of time.

[Bill S]

What we use to define a distance is not a ruler, it's 'time'.
The ruler as read on a map is 'static'
'Time' is observer dependent

Isn't your ruler's length observer dependent, as well?

[evan_au]

I have been watching a SF TV series called "The Expanse", which imagines that travel within the Solar System is possible with a hydrogen fusion rocket. We don't know how to build such a rocket today, but the science may be quite possible in the next 100 years.
- When they accelerate hard, people are jammed into couches, and need chemicals to survive the stress - or they die from injuries
- During evasive maneuvers, any loose items cannon around inside the spaceship
- When the rocket stops, people float, or stomp around in magnetic boots.
- When the rocket is idling at 1g, actors walk around as normal
- They even imagine a rotating spaceship that can simulate gravity with centrifugal force

There are some video concessions to the reality of space:
- Like Star Trek, there is a noise when the camera zooms in on a spacecraft. In reality, sound doesn't carry through the vacuum of space. It's like they put a microphone on the spacecraft frame to give an impression of bulk and raw power.
- Like Star Trek, weapons leave a visible trail in space. In reality, energy beams or projectile weapons don't leave a visible trail in the vacuum of space, but that would make battle scenes rather visually dull (and hard to follow)!
- Many scenes are set in the asteroid belt, with gravity at less than 1g, but the actors walk around in 1g. (The occasional short 0g scene is difficult to simulate and film, but having much of the action at g/3 would be just too hard!).

In series 3 of The Expanse, they go beyond foreseeable technology to introduce interstellar travel using something like artificial wormholes.

[Bill S]

I have been watching a SF TV series called "The Expanse",

An enjoyable series.  find the character development more interesting than the technology.
Isn't your ruler's length still observer dependent, though?