I did disregard gravity since the density of the universe is pretty low on a large scale, so maybe there are some corrections to be made to take the (small) curvature of the universe due to gravity into account, but I think most of my explanation is still valid. If you can just imagine a universe without (much) gravity, I don't think there's anything wrong with the models I described. I will just give them again with a bit more detail:

The first reference system I proposed is an extremely simple one (but with complicated consequences) constructed along the lines of special relativity:

1. Pick some "stationary" point in our vicinity as the origin (of course not the earth or the sun, since they are revolving around the center of our galaxy, but some point in our local cluster of galaxies should do fine).
2. Using a set of standard "measuring rods" (just like Einstein used in his popular description of relativity), which are placed stationary to the origin of the reference frame, construct three perpendicular axes to assign space coordinates.
3. Place a clock at the origin which sends out a signal every second. Clocks are also placed at various other places in the universe and synchronised by listening to the origin clock and applying a correction of distance divided by light speed. A clock located one light second away, for example, would add one second to the received time to indicate current time in our reference frame. All these clocks are stationary in our reference frame, they are not moving with the expansion of the universe.

In this reference system, distant galaxies are flying away from us at high speed and are therefore subject to lorentz contraction and time dilation. They will appear shrunk in the direction of motion, and will age more slowly. They are also closer together because the space between them is lorentz-contracted as well. Obviously, an alien civilisation in those galaxies would consider themselves to be the center, and would say we are aging more slowly than them, but that's just the classic twin paradox and no contradiction. We are free to use our own reference system.

Anyway, using this reference frame, objects at large distances are younger because they have been aging more slowly ever since the big bang. At some distance away from us, objects are traveling at speeds close to c and they are so young that the big bang has only just happened for them. A little bit further, at c times the age of the universe, there's a singularity where the big bang is happening now.

Of course I realise that this is a strange way of looking at the universe, but it obeys the principles of special relativity (disregarding gravity) and therefore has the property that nothing exceeds the speed of light relative to the origin.

The cosmological model, which is a lot more practical to use, is constructed in a different way. Clocks at any point in the universe are set so they indicate the amount of time passed since the big bang as experienced by a local observer that is moving with the expansion of the universe, and distances are measured so that local light speed, relative to a local observer moving with the expansion (i.e. relative to "expanding space"), is c. Now the universe is the same age everywhere, looks the same everywhere (no more lorentz contraction from the expansion), but we gave up the property of nothing being able to go faster than light globally. Local light speed is c relative to local observers who are moving away from us, or in other words, relative to "expanding space". But those observers can fly away from us at speeds well in excess of c.

Am I making slightly more sense now?

Well, I'm not going to argue about the exact definition of c, but I certainly meant the fixed mathematical value. The silly example just tried to show how it is possible for things to go faster than c without causing any problems with relativity. If you choose a coordinate system that is not consistent with the definitions used in Special Relativity, then yes, you will find speeds greater than 3 x 10^8 m/s. This can be very useful, as is the case with the cosmological model (which, unlike my silly example, does preserve "local" speed of light but not global speed of light throughout the universe).

My silly example served no purpose other than to make the point that speeds are just something measured in some coordinate system and therefore the choice of coordinates can change the values. The notion of a galaxy moving away from us at some specific speed only has meaning if we also describe the reference system being used.

If we are using the cosmological model, it is perfectly normal for galaxies to be flying away from us at many times c. With a different set of coordinates, obeying the definitions of Special Relativity, we will only find speeds lower than c but the universe will look distorted because of lorentz contraction and time dilation. Which is why pretty much anyone uses the cosmological model and explains the resulting high speeds as "space itself expanding".

Well, with "arbitrary" I didn't mean to say there were no good reasons for using the cosmological model, quite the contrary. Obviously it's easier to use a reference frame in which the infinite universe is homogenous and the same age everywhere. I'm just saying that it's one of several possible choices of coordinate systems, and other choices would yield different times, distances and speeds. The whole idea of "space expanding faster than light" is in a way caused entirely by this particular choice of coordinates. The special-relativistic model (which pretty much nobody uses, for good reasons) does obey the speed limit but has the disadvantage of not being homogenous and treating our milky way as a special location at the center of a finite universe (like I described in my earlier, great-grandparent post).

I do prefer the cosmological model, but I think it's useful to point out exactly what it means, and where the contradiction with Special Relativity is coming from. Too many popular publications just say "space itself is expanding faster than light, and that explains it" while "space itself" doesn't really mean anything. They make it seem like space is some kind of expanding aether, which of course it isn't. Stuff in space happens to be flying apart, and we just chose a system of coordinates to make the description of the stuff easier. This happens to have the side-effect of creating the notion of an expanding "space" on top of which c has to be superimposed, but that's just a mathematical artefact caused by the choice of space-time coordinates.

Exactly, and I gave that example in my earlier great-grandparent post. In the cosmological model, the light from distant galaxies will never reach us because space is expanding too rapidly. In the special-relativistic model, that galaxy will never exist in our reference frame since its ancestral matter is moving away from us at a speed so close to c (and increasing towards it) that the passage of time is asymptotically grinding to a halt. Both views are consistent with the actual fact that we will never see that galaxy.

Well, if they are moving away from us at that speed due to the expansion of the universe, and everybody uses the cosmological model, then even the aliens in one of the galaxies will agree that the other galaxy is moving away from them at 1.8 c. Because that's due to "the expansion of space" (or in other words, the peculiarities of the cosmological model). If everybody uses models based on special relativity, the aliens will only measure the other galaxy at 0.99 c.

Just to make a tiny correction: relative to each other, as measured by one of them. If we measure them, using our reference frame, we will definitely see them moving away from each other at a relative speed of 1.2 c. Each second, the distance between them will have increased by 1.2 light seconds. But if you are on board of one of the objects, you will have a different clock and different distance scales. You will then measure 0.88 c.

Yes, light speed would be orders of magnitude greater than c with those silly definitions. Which is exactly the point: both light speed and the speed of local objects at different places in the universe can be different depending on which reference system you use, and this explains why things can go "faster than light" in some models, and light speed isn't always 'c'.

To make the comparison a bit more accurate: suppose I defined a non-cartesian reference system where the size of a metre depends on the distance to earth. Here on earth, it is the width of an atom but on Mars it's the length of our traditional metre. I can then go "faster" on earth than a ray of light on Mars since the ray on Mars is only doing 300000000 metres per second and I am doing more "metres" per second here. Of course that's still a silly example, but it's quite similar to what's happening in the cosmological model.

A reference frame that obeys special relativity will have the same light speed everywhere, and all objects will travel slower than c, but in the cosmological model light speed will have "the expansion of space" superimposed on it and objects travel away from us at speeds higher than c (but slower than local rays of light in the same direction). It's all just because of the coordinates used. Normally, objects moving away from us at high speed will be contracted in the direction of motion but the cosmological model uses contracted metres that make everything the same size again. And the scale keeps changing as the universe expands, artificially "moving" objects to ever greater distances. And clocks are artificially sped up. All of this throws Special Relativity out the window.

No matter which reference frame you use, you will never be able to outrace a beam of light at the same location as you. But you may be able to go "faster" than a beam of light that is many billions of light years away, since the "faster" just depends on arbitrary measurements without a direct objective relationship. In any case you can't actually physically pass a beam of light in the same direction as you.

Actually, they would have to compare some subset of the key over a classical channel, to detect eavesdropping and then use the remainder of the key for the actual secret communication.

Of course I disregarded gravity in my post. Black holes are a whole different ball game. But there too, you can use different coordinate systems to get different interpretations of the events, always yielding the same tangible results.

For example, you could easily argue that, at this moment, no black holes exist. Just before the black hole really becomes a black hole, local time will have slowed down so dramatically that it never actually becomes a black hole. It's forever stuck at the stage right before becoming a black hole. But change to a different reference system and there you go, they exist after all. Just change your definition of "now". In the second system, light inside the black hole may actually be retreating away from us even though it was aimed in our direction while in the first system, it is simply never emitted. I bet people have come up with reference frames that have time going backward inside black holes too. Or going imaginary (the complex number kind of imaginary). But no matter how you define your seconds and meters, you'll always get the same results if you apply General Relativity.

To explain this in a little more depth, what we call "space" is really just tied to an arbitrary choice of space-time coordinates. If we choose a different reference frame, distances and times will be different. Just to give a silly example, if I define a meter to be the width of an atom, or if I define a second to be the time required for the earth to go around the sun a thousand times, I can easily travel faster than c. So how does this apply to cosmology and general relativity?

Depending on the coordinate system you choose, the universe can really look radically different, even to the point of no longer being infinite. I will give two possible views, both equally valid even thought the first may appear strange. (So read the rest as well before labeling it as rubbish).

You can apply a classic "special(ly?) relativistic" coordinate system to the universe, with us at the center. The speed of light is the same everywhere, relative to us, just like Einstein said in the beginning. Things that are far away from us are moving away at high speed (but less than the speed of light) and are therefore aging more slowly. This means that some far away galaxy isn't just younger (defined as the amount of local evolution after the big bang) because we had to wait for its light to get to our telescope, it actually is younger "right now" even if we take the traveling time of light into account. Local clocks are really advancing more slowly. The effect increases with increasing distance, and at a distance of c times the age of the universe, the big bang is happening as we speak. Right now. This also means that the universe is finite (assuming nothing existed before the big bang, which is a big assumption). Not that it matters much, because we could never reach this "edge" anyway. It is retreating at the speed of light.

This model is quite interesting but a bit cumbersome for cosmology, so most people prefer to use the "cosmological model". They simply adjust the coordinates of time and space so that the whole universe is the same age and looks roughly the same everywhere, "right now". See, we just changed the definition of "now" and chose a coherently matching set of space coordinates so everything looks rougly the same size, that's all we did. In General Relativity, we are completely free to do so, you can pick pretty much any coordinate system you like. Things can move from the future into the past and back again as we change our variables, without impacting causality (which is all that matters).

Using the cosmological model, the universe is now truly infinite, the big bang is in the distant past everywhere and all the clocks are running at the same speed (as long as they are stationary relative to "space", i.e. moving away from us at the same speed as the average local galaxy). Now, however, the assumptions of special relativity no longer hold. In particular, the speed of light is no longer the same everywhere. Light speed is still the same everywhere locally, relative to "space" (the speed of the average galaxy in that area), but you have to take the properties of our peculiar coordinate system ("expanding space") into account. If at some distance, "space" and the objects in it are expanding away from us faster than the speed of light, the light from those galaxies will never reach us since it will actually be retreating as if it were running towards us on a conveyor belt moving the other way at a higher speed. The conveyor belt isn't "real", it's just an artifact of our choice of coordinates which does not comply with special relativity.

In the first model, those distant galaxies simply never come into existence since the local "space" is asymptotically stuck at a time shortly after the big bang. Things over there are moving away from us at increasing velocity approaching c, and time (rate of aging of that part of the universe) is grinding to a halt.

But do those places exist or not? Doesn't matter, that just depends on what you mean by "exist" or "now". All that matters is that we will never see them. In the first model because they will never exist. In the second model because their light will not be able to overcome the expansion of space.

Entanglement can be used to exchange keys for secret communication. It allows two parties to create a shared key without anyone being able to intercept it. In principle, this key can be as long as the message itself and perfectly random, so a simple 'xor' operation is all it takes to make the message completely undecryptable. In more detail:

Alice wants to send a secret message to Bob.
They (or anybody else, really) create a bunch of entangled photons, half going to Alice and the entangled counterparts going to Bob. This all happens at normal speeds (not faster than light), but can be prepared in advance.
If anyone tries to eavesdrop during transmission of the entangled photons, Alice and Bob are able to detect the fact that the photons are no longer in a superimposed state and start over with a new bunch.
Now Alice and Bob measure the photons. They have no control over the outcome of the measurements, which will be completely random, but they do know that they will both get the same result (or rather, exactly the opposite result). This becomes their cryptographic key.
Now Alice encrypts her message with this key and sends it to Bob using traditional communication channels, for example a carrier pidgeon.
Bob uses his identical key to decrypt the message.

The only faster-than-light part of the story is that the entangled photons "chose" their state at the time of the measurement. Before the measurement, they were in a superimposed state. This means the information for the key didn't even exist yet in any way and can therefore never be intercepted by anyone. It only came into existence at the time the photons were measured, simultaneously for Alice and Bob. (Take the word "simultaneously" with a grain of salt, because as the article shows, they can even be separated in time). And the encrypted message without the key is just a series of random bits.

What if a competitor with very large pockets publishes free versions of your software just to force you out of business?

So you can just wait until one day you're diagnosed with cancer, then go and get yourself insurance so the insurance company can pay for your treatment? I don't think insurance works that way.

Insurance is all about probabilities, they take money from a lot of people who have a low (normal) probability of getting sick and use that money to pay the few of them who do get sick. If clients are more likely to get sick, they'll have to pay a higher premium or the maths simply don't add up. And if you already know someone is sick and is going to need treatment, how can you give this person "insurance"? "O, you're going to need a couple of million dollars for your treatment? Sure, join up and pay a monthly fee of a few hundred dollars and we'll pay for your treatment." That just doesn't make sense.

Obviously I do know that insurance companies are making way too much money and could certainly do with a bit less, but you have to remain reasonable.

You mean that spot where they just started construction of a new McDonalds?

Being paid for finding a vulnerability and keeping it secret sure beats getting sued for disclosing it responsibly.

More likely, these supercapacitors will be outlawed in the US because they "contain drugs".