That's the interesting thing about dimensions and alternate universes. It might not be a matter of technology. Lets start with the universe one, its easier to explain. This is a fundamentally impossible thing to prove with direct evidence because of the following consideration. Everything that exists, from matter to energy to the physical laws that govern this universe are a part and contained within the universe. Literally everything you can or cannot imagine exist within this universe. The edge of the universe is where the edge of our reality is. Theoretically, if you left the bounds of the universe, the physical laws that govern the way you are literally held together (the basic electromagnetic force, strong/weak nuclear forces, and gravitational *although this one doesn't hold you together*) are not there. Without those laws, you would theoretically cease to exist. You wouldn't fall apart like a gelatinous blob because even that is made of something, simply the matter itself just goes away like poof. Law of conservation of matter is a law of our universe so outside our universe that is not necessarily applicable. We can't send a probe to another universe, or some kind of electromagnetic signal because those are all made of some kind of thing from this universe. Perhaps we could send a probe with a kind of warp bubble which has a contained amount of space around it outside the universe, that way the probe could exist but then you run into so many problems. Stability (if such a bubble could even be maintained), movement to the next universe (a warp bubble moves by expanding and stretching space around it to displace in space, but outside the universe there is no space to expand or compress, so it just might be separate. Not separated by space like earth is separate from the moon, but just a distinct entity from our universe. Not way to say it is so far away from our universe or anything because we can't talk about it as soon as it leaves our universe. Then there's the problem of time because time is also an integral part of our universe, so if something left our universe and were to say come back, there's no telling where in time it would come back. You see in physics, time is kind of like another spatial dimension in the way it determines what part of the universe it is in. You have the three axes of space then a location in time. Without the constant constraints of time moving forward for our universe (arguable point I just made, but this one is the most generally accepted) then this probe could appear in the future or the distant past with no way for us to control it theoretically.
Dimensions are possible to prove, but extremely difficult. You see, we cannot simply see or detect the higher spatial dimensions. We exist only in three dimensions (spatial). The fourth would be inconceivable to us and can only be modeled in computers (that is not to say it exists, for we can model in a computer N spatial dimensions where N is some whole number greater than 0 *depending on computing power*). To test it, we look in extremely high energy particle collisions. You see, in super symmetry, there is one part that talks about in the early moments of creation, in the extremely, crazily, dense and hot early universe, matter could theoretically have been excited to a higher spatial dimension than just the three that we exist in (one possible explanation of dark matter). So we try to recreate that in the CERN particle accelerator. What it would look like to us is the particles collide, and then destroy each other to create a bunch of different tiny little pieces (ranging from bosons to quarks to neutrinos) which will then curve and follow paths that are predictable. However, in extremely high energy cases we hope that some of the particles will literally disappear from the detectors. No decay, just gone. This would be where the particle was excited to a higher spatial dimension. So far we have been unsuccessful in proving the theory, but CERN is currently getting an upgrade, so big hopes for the future
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This could even be a wild goose chase. There might not be higher spatial dimensions, or if there are, this might be the wrong way to look for them. They have a few other ways to look for them, this is just the one I know more about.
So basically, its extremely difficult, hard, confusing, and strange to try and prove these two theories, but we are trying. I personally do not think we can "prove" alternate universes. However, it is an excellent theory that seems correct to me. However the technicalities are still hotly debated.
Hopefully that made sense
sometimes I start to ramble, lol.
