Imagine many ships traveling close to the speed of light. If they diverge paths to explore distant galaxies, they could calculate their travel so that the same amount of time passes for all ships. Since traveling close to the speed of light will substantially slow down the passage of time for those on board the ship, this whole ensemble would allow many observers to simultaneously visit arbitrarily distant points in the universe in reasonable amount of time and without worrying about diverging time scale for those on different ships. I don't see any immediate holes in this idea but I wanted to see if anyone can spot some.
The one problem I can see with this scheme is it's very critical.
I mean: to have a significant time contraction effect you need to get very near to speed of light (effect is highly non-linear); this means a very small deviation in the projected path can result in severe desynchronization with little or no way to keep synch because of rapidly increasing distance between different "explorers" (they would recede from each other at speeds very near to 'c', with all implications on wavelenght red-shifting and such).
If you plan to have "round trips" and then meet again at start point (or somewhere else) you can easily miss your mates by centuries.
Of course this is (almost) the only way to "keep in contact" because any message sent (even if you are able to detect such red-shifted photons) would keep chasing after spaceship and arrive at a very slow rate (depending on actual speed); in practice you would get all them at an accelerated rate (and with no red shift) on the way back home (unless you postulate some kind of FTL messaging, of course, but that would defeat purpose of the whole construction).
I see two main issues. One is the observations. As you fly towards the target at a velocity close to speed of light, all the emitted light will be severely blueshifted. Per my calculation moving at 99.99% speed of light (299,762.4788km/h) should give you a time dilatation factor of about 70 (70ly journey feels like a 1year) which I think would be a bare minimum for this to be feasible. However, as you are moving at this speed, all the receiving light is severely blueshifted. Using this calculator https://keisan.casio.com/exec/system/1258042695 our nice and cozy 570nm is transformed into 4nm which is somewhere around x-ray radiation. You can't really do an observations at these speeds. You would need to slow down. (also worth pointing out, that you also need to shield the ship from all this high energy radiation)
Which brings us to the second problem. The time dilatation is funky subject. Nothing happens for the longest time and than it shoots off on the exponential. This means, that the crafts need to be perfectly synchronized. My example of 99.99%c will turn a 5 day pitstop into a 1 year delay behind everybody else. At 99.9999% one day puts you at 2 year delay. Any uncertainty will have serious effects. 0.0005% difference will influence the delay by almost a factor of 3. Technological precision necessary is mindboggling.
Connect these two and the level of planning necessary becomes troublesome. You need to synchronize at what time they need to slow down how long will they perform observations for, the rate of acceleration and finally they can begins slowing down only after all the ships have reconvened, lest some will be left behind. Other than that, yes. It is viable method (as far as I can see).
Yes, it is possible
One of critical points with that situation I did come by is - conservation of impulse.
It does not have immediate effect on them, but considering that they are in slow time, slower their common time is faster they move to the point when they observe that or can't sustain that anymore(if they are not careful). (They can move to a black hole as well, to keep that slow time, but it is a loss of mobility)
There are generally 2 ways - they can use reactive propulsion, or some kind of interstellar inter galactic metro massdriver type system, which may be more efficient than reactive propulsion, but may have the same problem if overstressed, and sure it uses energy all the time. Energy usage is not necessarly a big deal, as stars waste it constantly, but it is a thing to be avare of as well.
It easier to see the problem for ships case, as they accelerate their exhaust track is basically some sort of reactive mass which moves with significant speed, for fusion something up to 0.1c maybe, in direction of A point and B point.
- like a line of gas cloud between A and B points where some portion of mass of that cloud moves past point B , and nother "half" past point A
Considering that orbital velocities in galaxies aren't that high, stars move 10's of km/s, any meaningfull exchaust velocity exceeds galaxy escape velocity. So if you roam around you constantly loose energy and mass of that galaxy.
- fundamentally it is a result of following problem - it easier to push mass to greater distance, than pull mass from greater distance.
For pulling from great(anything above a billion plus km) distance you have more or less only one option - gravity.
Partially you can overcome the problem and prolong existance of such system, by modifying your galaxy, converting stars to some kind of statites, like some versions of dyson swarm, statites/stars around your galaxy black holes. Where your galactic metro network helps to keep the distances of those stars and all that, or maybe helps controllable compaction of the galaxy or something in that direction.
Then you have some treshold, how much mass can be mobile at any given time, the rest hast to wait, or more likly to live in orbits of blackholes, obiviously supermassive ones. How big is treshold for non-modyfied, natural galaxy - for our standarts it probably humongous, but it not necessarily so for galactic civilisation.
- not sure what is the best configuration of those metro routes, but probably looks like some plant roots type thing, with a center of mass of a galaxy and supermassive BH's to be at the core of that system. There probably are some things in beetween those roots as well for travel and technological purposes.
But for intergalactic routes, those routes will push galaxies away. And there is no forces, or better to say ways(there are some options but, applicability is limited by distance which is big but not infinite), to pull them together, and probably no ways to create statite version of galaxies, but there is a great attractor, and a place like that can be used for to be a core of such intergalactic system, maybe with a goal in mind to collect all those galaxies, as BH's have some value for survivial beyond the time, when all the stars go puff. Take look at Isaac Arthur youtube channel, there are good episodes on that BH's topic.
Sustainability is a problem, because if you slow time just a billion times, a year of subjective time means a billion in regular space. You go to school, and when you go to university our sun is puff, no more.
But travel to nearest galaxy still takes 8 hours(million ly), what a waste of time, eh.
So maybe not a critical problem, with a carefull approach, but it does not allow mindless mistakes, or there will be a point of no return very soon(in subjective time).
Central BH's and that metro thing represent some common timeframe, which let's say slowed down a billion times compared to regular space.
And sure enough if you plan to visit some planet, it will have some consequnces.
You have been there on a vacation last year and there was such a beautiful beach there, well, there is no more of it, you know a space faring civilisation evolved and collapsed, you know, only radioactivity and robots there. So due geological activities each visit as a new thing.
You do need to ascend from slow time to a regular one, and here I not ready to make statements, may be wrong, but your two weeks vacation in to wilderness will look like few miliseconds of absence, or could look like it, depends on how fast are the means to ascend and dive to and from normal time to regular space time.
Soo on two weeks vacation you probably can raise a civilisation from scratch, as it around of 40 million years in regular space.
Meaning moving in and out of frame will have consequences, as one can age and die faster than a human capable to notice thing, not talking when they actually notice someones absence. So it won't be exactly one time for everyone all the time.
So as being in the framework but a distance apart, let's say different sides of a galaxy, does not mean you can have a real time chat(emails may work, with complex routing prediction system). One can have an annual gathering at some date at hub place despite being few galaxies apart prior that, hangout for few days together and move back to your home galaxies.
So there are some nuances which need their own investigation.
pros and cons
To have all that, there should be some goal. A goal which is important for the civilisation. Convinience of work commutes from galaxy to galaxy, sounds fun and an interesting topic to investigate which differences it brings and all that, but it is wasted opportunity without a goal.
Let's say they made a ring in our galaxy, idk 50'000 ly diameter of that ring, a billion times slowdown of time - Hooperloop V5billion
Being in the loop, for subjective time your cycle time is aroud 2-3 hours. Let'say the ring goes trough a million stars, and each star hosts K2 super computer cluster. Each 2 or 3 (let's say it 2) hours you gather information and upload information to each cluster, which are in regular space and it means they, from your perspective, work a billion times faster than if they would be in your framework. So if you solve some problem, let say working on unification theory, technology development, etc then if things are done rigth you can have ample benefits from the situation.
But humanity also is somwhat a supercluster which could benefit from a billion times faster information processing, meaning being in regular time also has certain benefits, for a civilisation as it has more time to evolve before some points of no return for possible strategies.
If a civilisation waits for galaxies to arrive at great attractor place, or most likely they are on the move there as a civilisation, to be there and ripe the fruits of that place according their future oriented strategical plans of development for next few hundred billion years - break trough to a different universe, prepare for ripoff of space, outlive last free atom in universe etc
I mean goals should be grand, and other conviniences is just side product, so as it not always beneficial to be in slow space, if you did not set things in motion properly, etc.