Physics has known for a long time how to build a time machine. The possibility in a real spacetime geometry was first noted by Van Stockum, but this possibility was only really first analyzed by Frank Tipler in the 70's. All you need is a massive rotating cylinder. And also it has to be infinitely long.
|This illustrates how frame dragging
can lead to time travel
This situation is worse than merely having a concept of physics that excludes time travel, or that merely says that time travel is impossible. For if time travel was excluded by theory, then we could always say the theory was incomplete. What we have instead is a system that fully allows time travel possibilities without prejudice, as long as we're able to break some other law of physics to get there. It's not just the stubborn "no" of a parental figure; it's like having your parents describe step-by-step exactly what you can do to eat chocolate cake for breakfast, and one of those steps is "eat infinite broccoli".
Physics also knows how to effect FTL travel. The speed of light puts a prohibitive barrier on
our ability to explore the stars, but a number of work-arounds have been proposed. Technically, relativity only prohibits local FTL movement, but says nothing of global FTL travel. So if you can distort space and time in just the right way, you can move however fast you want. One of the more frequently explored proposals is wormhole travel. Wormholes produce a kind of "short cut" in spacetime, and it is actually a Federal Law that when you want to discuss how wormholes work you must draw two dots on a sheet of paper, "A" and "B", draw the straight line connecting them, then fold your paper so "A" and "B" touch and jab a pencil through it. While going along the line you draw may take billions of years, going through the wormhole may take minutes.
|My lawyers also recommend I show you this diagram
Sadly, you can't make a wormhole. And even if you made a wormhole, the throat collapses when you try to travel inside of it, so you can't even use the wormhole for travel anyway.
Another proposal is the Alcubierre warpdrive. This contracts spacetime in the front and expands it in the back, producing what some call a "wave" of spacetime contraction that "tips over" the light cones inside the warp bubble. Locally, you're moving slower than light, but globally you may be moving, in theory anyway, as fast as you want.
But you can't make the Alcubierre warp drive either. If you took the mass of the universe and made it negative, the Alcubierre warp drive requires ten times that number in negative-mass matter to move a standard-sized spaceship. To clarify, we haven't even found one single particle of negative-mass matter.
Science knows how to make a Bag of Holding, and can even make a Bag of Holding that slows down time (see chapter 3 here). You can store a lifetime supply of hot pies and ice cream in the same box, and whenever you take them out the pie is still oven-fresh and the ice cream still ice cold, and so even twenty years later you can serve yourself delicious pie a la mode. But, like so many awesome things, it requires either negative mass or impossible mater distributions and can't be made.
I just made a post about how the Bag of Holding (aka, Van den Broeck Bubble) can be exploited to, potentially, travel to parallel worlds (if any even exist). This one is a lot more speculative, requiring ideas way beyond established science, but is at least partially based in what we already know about general relativity and curved-space geometry. It isn't really scientific, but if we wanted to know if there were other universes, this has potential to actually find them. But it also requires not only negative mass, but infinitely much of it. So we won't ever be able to try.
|Pictured: A guy wearing a green screen.
Not Pictured: An invisibility cloak
I recently calculated (as part of my research) how to make a slightly different kind of cloak, namely a shadow cloak. Also something you'd read about in fantasy books, the shadow cloak works on the same spacetime distortion principle as for a black hole, but now modified to work with optical materials (so not requiring it be made of actual black holes). A perfect realization would allow light to enter, but trap it there. If you were wearing it, you would appear to be not just covered in a black garment, but actually swathed in shadows. (Look at a black object, then look at an unlit hole; there's a big visual difference) You'd also probably heat up a lot (since all the energy is trapped), which would make this kind of material perfect for solar panels, increasing their efficiency probably to near 100%. But you can't make the shadow cloak, because it requires material parameters that are both infinite and negatively infinite. Like with the invisibility cloak, you can only realize this (if at all) for a single color of light at a time. Which vastly diminishes its coolness.
You can probably see where my knowledge tends to specialize, but physics knows a lot more cool things in the quantum domain, such as teleportation devices and solutions to the P=NP problem. All of which, we know how it would work, and only minor technicalities render it impossible. Things like wavefunction collapse, quantum decoherence, and the no-cloning theorem.
Any time there's something cool in physics, there's something else that renders it impossible.
Again, this isn't the situation of wanting to do something incredible and merely lacking a theoretical model to describe it. Our formulations of physics account for it exactly.
It's just that all the cool stuff is impossible.
More and more, it just seems like the Universe comes equipped with fail-safes against our ever doing the cool things of science fiction.