Are UFO's real?

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Linguistically a bit shaky but I think I understood that.

Some people believe at least some of the anecdotal evidence (ie. the right set of videos or the right case studies), so its tracing it - at least hypothetically - from being a 'given' and working backward.

Its not the only thing or group of things in the world that defies explanation and keeps resurfacing either. It ties into a lot of those as well.

To exploit your analogy its not 1+1 = 3, its 1+ x =3 where x is unknown to mainstream science as of yet and those who don't believe that there's enough evidence that there's such a thing as 3 or any such equation as 1 + 2 are actively telling the people who would suggest the possibility that x = 2 or that 3 exists that they need to stop smoking dope and listening to Pink Floyd.

We know that if 1+x=3, then x=2.

What is being argued by some is that the impossible becomes possible through greater technology. Thus, it is as if they were arguing that 1+1=3 with advanced technology that we don't have.

Ahh, but we do know how to bend space. All it takes is a gravitational mass. That's not going to help anyone exceed the speed of light, though.

There is one and only one known way for object in space to travel apart faster than the speed of light and that is for them to be so far away from each other that the space between them is expanding that fast. Note that in such a case that there is no acceleration of either object, it is purely due to the expansion of space. Also note that any two such objects will never be able to detect each other, much less meet, unless the universe were to collapse. I think that the distance they would have to be apart is thought to be on the order of twenty five billion light years.

Obviously, this is completely useless for going to visit other stars.

As far as the 1+x=3, we do know that x=2. What you are arguing is that with greater technological knowledge and advancements, that x could be something other than 2.

However, it does completely ignore my point.

The argument for at least some UFOs to be spacecraft from other star systems with aliens on board, you have to make massive rewrites of physics. That is like assuming that while to us 1+1=2, to a sufficiently advanced alien civilization, 1+1=3 (or some number other than 2). The argument is usually made by spouting off buzzwords of which the speaker has, at best, a very flawed understanding and often has no understanding of them at all.

Talking of bending space is hilarious. Even if it were actually possible to bend space, that bending of space would still propagate at the speed of light, not faster, and certainly not infinitely fast.

I don't claim at all that we know everything. What I claim is that what we know puts limits on what we do not know. For example, what we do not know is not going to be able to puth a spacecraft past the speed of light.

We're still breaking apart the components of space and baryonic matter to see what it even is. Finding Higgs/Boson was a big achievement but there's still so much we have yet to nail down or really figure out.

While its on an unrelated and unquantified tip, there are scientists, people quite close to this stuff, who suggest things like string theory or even suggest a holographic nature of reality (ie. space and time being illusory). The number of such scientists particularly at higher levels are increasing rather than deceasing which shouldn't happen if it isn't fitting the shape of their experiences in dealing with QM or if it were some type of hippy-dippy quackery.

That's not to say that increasing numbers of scientists wondering about something without a falsifiable experiment makes it true. I'm just trying to find a spot on the map of knowledge to where we are right now and identify our positioning between what we know and what we don't know. Sometimes I get the impression that people who would demand that we all assume that at any given 'now' moment that we're at the end of science have difficulties assessing what it is that's still unknown. I think part of that is when you research and bury yourself in one side of things its a bit like highway hypnosis, one thing becomes your whole world and reading the known all day causes one to sort of be hypnotized into feeling like the unknown is synonymous with the fictional. One has to remember that's not reality though - its more a structural cognitive problem of human memory, presence and adaptation to reality; ie. three pounds of grey matter doesn't seem like its enough for a person to hyper-focus professionally on something and not have it impact their perceptual balance.

I guess what I'm saying - if any of these UFO's are both a) not hoax and b) alien visitors, we have to throw the limits that we think we know out the window. That's a big 'if' but that's what we're looking at.

Research into quantum entanglement is the first step: Discovery of the mechanism that causes entanglement
i.e. instantaneous energy transmission.
Perception of the phenomena of quantum fields ( of which magnetism is one ) is a promising line of research as well.