Is it possible to somehow create a field where time dilation works in the opposite way and use it to create an interstellar highway?

Question

I want to make my world as realistic as possible, so no otherworldly FTL ideas like wormholes, teleportation or warp/alcubierre drives that will violate causality according to relativity. Let's begin.

Near a black hole, the gravitational time dilation can make spending a year there equal a million years in the outside universe. From your point of view, everything near you behaves normally, the clock ticks by at one second per second, light travels at 299,792,458 m/s etc. But you will see a clock in the outside universe tick a million times faster. Time of the outside universe runs a million times faster from your POV, and that subsequently includes light itself. Well, light still travels at 299,792,458 m/s, but since s is much shorter, it'll appear much faster. Light from the Andromeda Galaxy only took 2.5 years of YOUR time to reach you. Conversely, someone viewing you from the outside universe will also experience normal time and speed of light, but they'll see your clock tick one million times slower.

We've observed this effect back in 2015, where we PREDICTED a supernova down to the month. And it actually happened in December that year. Well, kinda. That very same supernova was seen in 2014. It came to earth in six different images due to the light being lensed by a massive galaxy cluster in front of it. Light passing near massive objects will appear slower to an external observer. That's why the one image that passed through the least gravitational disturbance, came to Earth first, in 1998. The next four images reached us in 2014 within 3 weeks of each other, then the last one in December 2015, just as predicted a few months earlier.

Now to the juicy part, is it possible to make a field with the opposite effect? One where observing from the outside universe makes everything inside the field appear a million times faster, and vice versa for an observer inside the field. One million years inside the bubble equals one year outside. Suppose now whatever you've made this field with, you somehow stretch it all the way to the Andromeda Galaxy. This is obviously gonna take many millions of years so assume someone has already done it for you millions of years ago. Bam! Now you have an interstellar superhighway, one billion kilometers in cross section, stretching all the way from our solar system to Andromeda. As you enter this tiny strip of distorted spacetime with your spaceship, you'll gradually see the outside universe redshift out of view and their clocks tick slower and slower.

You've finally reached your desired point. Here, your time is ticking a million times faster than outside. Now what? The Andromeda Galaxy is still 2.5 million light years away and it still takes 2.5 million years to reach it with lightspeed. "It's just gonna APPEAR much faster from the outside when I'll be long dead in my spaceship, such a stupid idea!" you might think, but what if I told you, you can use another trick in the book? Let me introduce: Special Relativity! You accelerate to 99.99999999995% of the speed of light, that's an impressive 0.15 mm/s slower than light itself! At that velocity, your Lorentz factor is one million, so your trip to Andromeda is a million times shorter. You decelerate at the end of your journey, 2.5 years later from your perspective. 2.5 million years would still have passed inside the bubble, which means only 2.5 years has passed in the outside universe. Now wait a second...

Did you just hack the universe? Would it even be possible to create such a contraption? Would it violate causality? Why or why not?

Answer 1

Short answer: no. It wont work. There is no field that can do that.

Long answer: kind of, a little bit. You almost reinvented the alcubiere drive, and all the requirements and paradoxes are the same. How can this work? The highway requires negative energy. All the matter we know today has positive energy, except probably the dark energy, but we dont know it anyway.

Closest thing we have is casimir effect, but it is extremely weak even at fraction of a micrometer, and time dilation from it is expected to be also extremely small. So already no big ships, more like data cable. On the scale of plank time saved per second. String diameter is micrometer.

Next step we can think of is make the gap even smaller, an example would be a carbon nanotube, with just a fraction of a nanometer gap hopefully making at least a bit stronger casimir effect. Still, even that will be barely noticeable in terms of time dilation, probably traders could value that. On the scale of parts per trillion of a second saved per second. String diameter is nanometer.

Next step would require to go below the size of an atom and forget the normal matter entirely. Material that could probably work is a neutronium - matter of a neutron star, arranged in a tube-like shape. But it is unstable in chunks below 200m, so it must be a really heavy tube. Such a tube across galaxies would exchaust all the matter in the observable universe, but hey, it could probably send your signal a bit faster. This could in theory achieve some meaningful time dilation, half a second saved per second. Time dilation from the heavy matter of the neutron star will be important as well, making the entrance and exit from the highway costly, both for energy and time spent doing so, only in the highway time dilation is beneficial, but in the entrance it is not, so entrance wastes some fraction of a second due to unfavorable time dilation nearby. Neutronoum explodes if it is picked apart into smaller chunks. String is unstable and will try to tangle. String diameter of picometer.

We've run out of matter at this point, but what if we go further? The only thing that is stronger than neutronium is the black hole itself. I dont know if black hole's horizon counts towards the stuff that creates casimir effect, but if it is, a set of tiny black holes, constantly radiating and being pumped back up through a laser, orbiting around a highway string. String diameter 1e-18 m evaporation time is 3k years. Time dilation is unlimited for this, but as you go more and more extreme evaporation time drops, and at some point a sneeze will set it all off, and these tiny black holes will start exploding. Also cost to maintain this road is so extreme, that you spend all of the observable universe's entropy that is still left every year or so.

Universe is too small and too poor in matter and entropy for your plans, sorry.

Answer 2

If you have any sort of FTL highway, no matter the details, you can get causality violations from it by a tachyonic-antitelephone construction. The construction works if:

• Your highway is localized, i.e., any effect of its existence on faraway objects goes to zero with increasing distance.
• The flip side of that: the highway is stable and not sensitive to arbitrarily small perturbations in the surrounding gravitational field.
• Lorentz symmetry (3+1-dimensional rotational symmetry).

Supposing those assumptions hold, you can paste translated and rotated copies of the highway into a flat background spacetime in such a way that there are closed timelike curves.

The living-near-a-black-hole approach to fast interstellar travel evades this argument because the region where the speed of light is faster isn't localized.

You could evade the argument by breaking Lorentz symmetry, but it seems difficult to do that in a way that's so weak that it evades the extremely sensitive experiments we've already done, but also so strong that it prevents construction of causality-violating highways.

It's been proposed that spacetimes with closed timelike curves are always prevented by some sort of feedback loop, which effectively breaks the locality/stability assumptions.