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I remember as a kid we’d settle arguments by whoever could say the highest number (or multiply by it; such as “I hate you more times 100, or I’m 50 times better than you). At some point we all learned of the existence of infinity, and that would settle it. Whenever someone said “infinity plus one”, the other would object by saying “but infinity plus one is still infinity!” implying that infinity was as big as you could get, and that all infinities were the same size. Turns out they’re not.

This may sound counter-intuitive to some of you. After all, infinity alludes to an endless size right? How can two things that are endless be bigger or smaller than the other?

Well the properties of infinite sets have been studied for quite some time. I’m not sure if he was the first, but Galileo Galilei identified a conceptual problem with infinite sets in his final scientific work Two New Sciences. I’m not interested in giving a history lesson so I’ll keep this post short and let you do you own research if you don’t believe me (and by now, you should have much more faith in me than that!).

His work identified a property of infinite sets that is now known as Galileo’s Paradox. The gist of it is this:

  1. Some numbers are squares (2^2 = 4; 3^2=9; etc.) whereas some numbers are not (prime numbers and other non-square integers, etc.). Therefore all numbers must consist of both squares and non-squares, and thus be more numerous than just the squares alone.
  2. However, every square has exactly one positive number that is its square root (basically just reversing the square operation). Therefore, there are as many squares as there are square roots.
  3. For every number, there is exactly one squared value (you can square any number by multiplying it by itself). Therefore, there are as many square roots as there are numbers (because every number can be squared so every number has a square root). Since there are as many squares as there are square roots, and there are as many square roots as there are numbers, then there must be as many squares as there are numbers.
  4. However, our premise was that there are more numbers than there are squares. Therefore it is a “paradox”, the solution to which is that some infinities are larger than others.

Galileo simplified this in his work with a very apt analogy that I think will help people visualise this concept better. Imagine two lines, one longer than the other. You can say that both lines are made up of an infinite amount of infinitesimally small points, however, you can also clearly see that one is longer than the other.

Later on, the mathematician Georg Cantor provided mathematical proof and definitions for sets and trans-infinite numbers, to which a great deal of resistance was put up by the other mathematicians of the time. The existence of larger infinities was and is of great philosophical importance. You can Google more of Georg Cantor if you wish; this post is merely for me to show you that not all infinities are the same.

Also, here’s an 8 minute video explaining this concept with some different examples by Numberphile. The guy presenting has a creepy smile and is way too excited about maths, but it’s still quite informative: http://www.youtube.com/watch?v=elvOZm0d4H0

And a much faster explanation by MinutePhysics (about 2 minutes): http://www.youtube.com/watch?v=A-QoutHCu4o

Teleportation is a thing of science fiction but is it impossible in our reality? Well, Chinese physicists managed to teleport photons over 97kms using quantum entanglement. The previous record, set in 2010, was only 16km so the physicists are hopeful that they will soon be able to make the technology feasible. Such technology would enable an ultra-secure communications system that is immune to eavesdropping.

The important thing to note here is that while perhaps a first step, this technology is far from teleporting any biological life anywhere. The physical object is not teleported, but rather, the information that describes it. If anybody read my article on Hawking’s Information Paradox, you would know a little about what I mean by information. The gist of it is that all matter has information (measured in bits) that describes every feature of that physical existence. Given such information, one could reconstruct an exact duplicate. An analogy that might help is if you had exact architectural plans, building materials, etc. for a building that just collapsed, you could reconstruct it the exact same way. This applies to all physical things, including humans and even subatomic particles.

Quantum entanglement is the mysterious link between certain particles in which they can share the same values (such as spin rate) even when separated over large (and theoretically infinite) distances. If two particles that have an entanglement link are far apart, say 97km, and one of those particles is takes on a certain property, the other particle will instantaneously do the same thing. The major difficulty of this is that the link itself is very fragile; it is very easy to break the entanglement. The Chinese scientists used a guide laser to make the entangled photons appear at two separate locations (97km apart) at the same time in a way that could be experimentally measured.

As mentioned above, this technology, at the moment, is mainly for communications. Nothing is faster than instant communication (imagine downloading anything literally instantly) and nothing can be safer because you’d have a hard time intercepting information that didn’t technically “travel” through any space.

So, recently scientists reported the discovery of a particle with observable effects likening it to the Higgs Boson. That’s a very complex way of saying “they think they found the Higgs Boson”. Some of you may not think this is a big deal. To those people, I say “I don’t believe you understand the gravity of this matter”. That’s the first of some of the Higgs jokes popping up.

Anyway, this is a huge scientific breakthrough and it pretty much shoots the whole neutrino affair out of the water. Why is that? Well, there was a lot more hype over the neutrino potentially surpassing light speed because geeks and opportunists started an avalanche of ill-informed statements. The most prominent of these was the whole “faster than light” travel fiasco. I wrote an article on the neutrino for a course at uni but I can’t be bothered finding it so I’ll sum up quickly why this is a stupid idea: the neutrino is also known as the “ghost particle” because it can travel through matter with minimal to no interaction. If something with that kind of amazing ability can’t surpass light speed (or was in doubt of surpassing light speed at the time that these faster than light dreams started multiplying) then what hope do humans have? Let’s put this in perspective. Suppose the neutrino did manage to break the light speed barrier. Well, you might say humans will use that technology to develop super-light speed travel. Errrrrrr. Wrong. What are you going to do, make a spaceship out of neutrinos? Let me remind you that neutrinos do not interact with matter. You’ll have a better chance at resolving the atheist-theist war than ever making even a seat out of neutrinos. There’s a lot more to the neutrino than that, and maybe I’ll put the information up here some time, but for now, rest easy knowing that we’ll always be stuck at sub-light speeds.

I sort of went off at a tangent here. The point was that the neutrino buzz was a fad; there was never really any substance to it. This Higgs boson ordeal, however, is mind boggling. I mean that literally. Even with my reasonable grasp of science, it’s a bit hard to wrap my head around. I asked my mom and stepfather (both PhD physicists who were top of their field in Australia before retirement) for a bit of clarification and arrived at the understanding I have now. I’m going to give a brief explanation of the Higgs Boson and Higgs field in the following paragraphs; if these do not interest you, you may skip, but that leaves you with a bigger question – what are you doing reading this if you’re not interested in science?

Ok, so let’s start with the Higgs field. Why? Because the Higgs Boson is a particle associated with the Higgs field in the same way a photon is associated with an electromagnetic field. The difference here is that the Higgs field permeates the universe. This is a bit hard to understand without an analogy. Let’s say that the universe is submerged within a tank of water – that is, all the planets and stars and galaxies are objects within this tank. The water would be the fabric of time and space – as well as the Higgs field. It is everywhere, in more ways than one. For example, you can bend the fabric of space time (with our analogy, that would be a ripple in the water). Whilst this may shorten the “distance” between two points, the ripple does not eliminate the space time in between – it merely distorts it.

So now that we’ve determined that the Higgs field pretty much encompasses the entirety of the universe (Einstein theorised a similar space time fabric, though I forget the exact name), what you need to know is that particles travelling through the Higgs field, and thus interacting with it, are affected by the Higgs  Boson. The Higgs Boson is a class of particle whose category is known as a Boson. It’s special because it transfers mass to certain elementary particles and thus explains why some particles have mass and others do not. Without mass, there would be no gravity and thus no universe – which is why you’ll hear that the Higgs Boson “holds the universe together”. You’ll also hear it called the “god particle” but Higgs dislikes that name – originally he wanted it called the “goddamn particle” but his editor thought it would be more attention grabbing if it was named the “god particle”.

Anyway, if we delve a little deeper (and further outside my comfort zone), we can attempt to explain how this mass is transferred. Most particles have a positive or negative, non-integer spin. This means that at each energy level of the particle, only one type of spin can exist for the orbiting electron. This is known as the Pauli exclusion principle. The difference with the Higgs Boson is that it can have zero spin or integer spins, thus allowing it to exist alongside another spinning electron at any given energy level. This essentially means that it can exist in multiple states (you may have heard of this quantum mechanics term before, especially since the popularisation of Schrodinger’s Cat). Because the Higgs Boson can exist where no other normal particle should, it has the potential to transfer mass (this is actually my own speculation, don’t quote me in any academic papers).

Anyway, that’s about as far into it as I’ll get. The crux of the matter is, the simple model has been completed. Scientists used this model for 50 years with no proof that the Higgs Boson existed, and now, finally, we have that proof. In short, we’ve discovered something that was fundamental to not only our creation, but everything we see around us in the universe.

The title of this post also mentions world powers, but I’ve rambled on a bit now. I’ll just leave with a quick paraphrasing of the well known Dr. Neil deGrasse Tyson. “On the day that we Americans like to tell ourselves that we’re the best (July 4), Europe reminds us how far behind we’ve fallen in science (Higgs Boson)”. Dr. Tyson has a deep concern that scientific power will shift away from the US, and wishes to reignite his country’s passion for science. I agree with his forecast; due to the nature of brilliant minds, the next generations of scientists will go to Europe instead of the US for their scientific goals, due to the infrastructure Europe can offer (Large Hadron Collider vs. the now closed Enrico Fermi reactor in the US). A large part of the US’s success is due to the infrastructure and opportunity available within the country, which attracted immigrants and geniuses together. As Dr. Tyson also points out, the greatest scientific achievements made by the US were made by immigrants (a German scientist started the US space program, for instance), and if their infrastructure falls behind, inevitably, their science will too. This will have a widespread effect that will eventually see the US removed as the world superpower (among other factors).

Well, those are my thoughts for the day. Forgive me for any errors in my scientific talk – as I said, the details of quantum physics elude me and I haven’t had the time to research the Higgs Boson as much as I did for the neutrino. Let’s just leave with a picture of the second (and perhaps more prominent) reason why Dr. Neil deGrasse Tyson is so famous now.

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