The scattering if electrons were the turning point in the way we looked at atoms. An experiment was devised that fired alpha particles at a sheet of gold foil, it was assumed that if the atoms that made up the foil were positive nucleons with negative electrons floating inside, on average the alpha particle travelling through would come out the other side in effectively a straight line.

When the experiment was performed something peculiar happened, the particles scattered in various direction, some even were reflected. Though a large amount were within a reasonable angle of the normal a large proportion went at large angles either way. This meant that the atoms cant have just been globules of positive and negative (neutron), as they were affecting the alpha electric fields.

It was later theorised and proven that atoms are actually mostly empty space. With a small nucleus that is positively charged and very small negatively charged electrons orbiting (sort of) around it. This explained the scattering as it was caused by positively charged alpha particles either repulsing the positive nucleus or hit it and bouncing off.

Now we discovered these neutral and positive nucleons in the atom, strange how they were very similar masses but different charges. This lead to the discovery that nucleons must be made of something, something smaller, possibly fundamental. And thus we started the discovery of the Standard Model, all the particles in the universe on one lovely table.

Everything in the known universe is on the standard model, bar some particles which we’re not sure about, such as gravitons and the Higgs boson. There are three main sections to the standard model Quarks, Leptons and Bosons. Each interacts with the universe differently, serving different purposes, some are mass behind what we touch, others the force carriers for the four fundamental forces.

What makes up a neutron or a proton? Quarks do. These are the charged, massive particles that make up most of what you see in the universe. There are three generations of quarks, all in pairs; up & down, charm & strange and top & bottom. Each pairs mass is larger then the previous, which is why seeing second and third generation particles is unusual as generally the universe prefers to use as little energy as possible. For each pair there is one positively charged and one negatively charged. The positively charged, in case of first generation, up particle is +2/3 and the negative, down, is -1/3 generally charges prefer to be integer values, so you wont see two downs or two ups floating around.

All matter has antimatter equivalents, this includes quarks, the only difference between quarks and anti quarks is that they have opposing charges, so the anti up is actually -2/3 rather then positive. Oh, and matter and antimatter of any type has a tendency to annihilate each other when they interact, sometimes at least, turning all their mass into energy which often decays to other particles, possibly even another anti and normal pair, which can then annihilate, and on and on.

Combinations of quarks, such as neutrons and protons are known as hadrons, there are two types of hadrons, baryons and mesons. Baryons are combinations of three quarks into an integer charged sub atomic particle, such as uud (proton) and ddu (neutron). The proton is a stable particle that’ll happily float around for quite a while not doing much, as is a binded neutron, as long as its in a nucleus it’ll last ages with decaying. A free neutron on the other hand will decay rather quickly.

Mesons are the other hadron, they are combinations of two quarks to form a neutral unstable particle. They do this by binding with the anti-matter of its, such as a up and an anti-up. Mesons only occur when annihilation doesn’t as if it did then there wouldn’t be any quarks to make into mesons.

Very small but still massive particles. All leptons have a special lepton number, this is a characteristic that only leptons have, and like mass and energy the lepton number must always be conserved. As with the quarks, there are three generations of leptons. They are split further into electrons and neutrinos, the three electrons are: Electrons, Muons and Tauons. The most common is the electron as it takes the least energy to form.

The other category,the neutrinos are paired with out electrons. There names are the electron neutrino, muon neutrino or tauon neutrino. They are always created together, you’ll never see a muon created with a tauon neutrino.

What allows things to interact with each other? Surely magnets can’t just magically be pushing each other away. There must be some interaction that we can’t see, and not so surprisingly there is. There are four known bosons: the photon, gluon, and . Each boson serves a specific purpose:

- Photon – The photon is the electromagnetic force carrier, it is used in the interactions in magnetic and electric fields. As the photon is massless it is able to travel at the speed of light (duh!) and also has an infinite range, it is also charge-less, though it has no mass it does have momentum… think about that.
- Gluon – The force carrier for the strong force, this is what holds nuclei together, the gluon is massless but has a very short range meaning the quarks it interacts with can only be interacted with when very close. It is also the strongest force in the universe, sensibly.
- The last two are the force carriers for the weak force, this is the force that controls decay interactions, depending on what decayed effects which boson is used in the interaction. The different charges of the bosons allow them to conserve charge in interactions. The weak force has a greater range then strong force which is why after a certain size nuclei become very unstable.

In March 2013 it was confirmed that the Higgs boson had been observed, though it will require more observations and research before we fully understand it in detail it is still an extremely important push forwards. The Higgs is what gives everything mass, it’s rather complicated how it works so I shan’t even attempt to understand it. Regardless, although it is not fully on the standard model of particle physics yet, it will be in the next few years as it is absolutely fundamental to all massive particles in the universe.

The elusive graviton, a particle we say must exist but doesn’t make any sense in our current view of the standard model. This would be the boson that carries the gravitational force, the infinitely ranged force that pulls all massive things together. There are theories that suggest it is in fact massive and makes up all dark matter but those are yet to be proven and are just theoretical physics. once we understand the graviton we will have a much better understanding of how gravity exists.

But what does make up dark matter if it isn’t these massive gravitons? Well it is a much discussed topic and I highly recommend the BBC horizon special which covers the main theories which are all very close to a possible conclusion. Personally my favourite is the massive gravitons for its further implications, but regardless physics isn’t a matter of liking or disliking it is a fact based look on everything around us, and in time we will find the truth, or at least what’s not true.

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]]>You must write a message in such a form that only you and your general can read the orders you are giving. To do this you have to encrypt it someway. In the past many techniques of encryption have been used to protect sensitive information, from simply shifting letters around the alphabet to complex, continually changing patterns such as the enigma code. We are at a point in time now, where the only flaw to most encryption techniques are human failure as the algorithms used are so complex that they are effectively impenetrable to today’s technology. To discover how we progressed so far we must start at the earliest common encryption technique.

Caesar’s Cipher also known as the Shift Cipher is one of the most famous cryptography techniques in history. Named after Julius Caesar who was known to use it for the correspondence of military intelligence, it has lasted this long in the history books for its simplistic genius. The Shift Cipher is an example of symmetric substitution encryption, meaning the encryption is a matter of substituting data by using a shared key and method of encryption/decryption that both ends must know.

Traditionally Caesar used an encryption key of 3, meaning A became D, which in turn became G. By sharing the key and using a Shift Disc the recipient of the message was able to decrypt the cipher (encrypted) text letter by letter until they were able to read the original message as intended.

An example of cipher text could be “Fusvg Pvcure” using a shared key of 13 the user receiving this data would be able to find that the cipher text becomes “Shift Cipher” when decrypted. 2000 years ago this was remarkable ingenuity, any messages intercepted were effectively impossible to read and therefore, any military movements were unpredictable.

Unfortunately, once it is discovered that a Shift Cipher is being used it becomes useless. Due to the fact that it is a very simple technique, even without a key it is very easy to decipher. All that is required is you take a word from the cipher text and try different shift amounts until you find a legible message, and then you’ve found the key. Ta Da!

For many years when cryptography was needed people stuck with the basics, sometimes changing the method slightly to insure protection from prying eyes. As more and more people learnt of the Shift Cipher it began to lose it’s effectiveness and over time use died out as it was no longer safe. It was replaced, in some cases, by the Transposition Cipher, by writing text into a grid with a certain (key) amount of columns and rewriting the text one column at a time, a much more complex encryption technique was born.

This once again is symmetrical encryption using a shared key between the sender and recipient to decode the message. Essentially the process is taking a message such as “ZechTechIsTheBest” and using a key of 4:

To convert into the cipher text we take each column and add it to the sentence, so it becomes “ZeTsechtchezhIBzTsez”. Looking at this without knowledge of the method would seem quite intimidating to say the least. As the technique is more complex it means that deciphering it without the key is much more complicated. As the key is not limited, like the Caesar Cipher (due to the length of the alphabet) it can effectively be impossible to guess for an infinitely long message. As the longer the message the longer the key could possibly be.

Once again though, it is only symmetrical encryption so if the key is leaked or stolen the cipher text is easily decipherable. There is clearly a flaw in both these techniques, and in fact all symmetrical key methods, if the key is stolen the encryption is pointless. This would not be a problem if the key did not have to be transported with the message, as this compromises the security greatly.

This is where public-private key encryption comes in awfully helpful. Imagine a method that used a pair of keys, one private that you keep secret and to yourself, and one public that you broadcast to anyone that needs it.

By generating a public and private key that are mathematically linked you can securely encrypt any information. To understand the magnificence that is PP Encryption consider these circumstances: Fernando wants to send a picture to his friend Juan, but wants to assure his girlfriend, who intercepts his messages, cant see it. Fernando requests Juan to generate a key pair and send the public key back. Fernando knows that if he encrypts the image with the public key, it can only be decrypted by the private key that only Juan has access to. So now Fernando can send anything he wants to Juan without worrying that anyone else can see it.

The interesting thing about Asymmetrical Encryption is that the key used to encrypt the data cannot be used to return the data back to it’s original form. This is the key (mind the pun) reason that this method is so effective and secure, because of it’s proven security AE is the standard for most the common security protocols, including Secure Socket Layer (the one you do your online shopping through).

Imagine the public key to be a set of instructions for a lock, exactly how to build the lock from scratch except, no matter how hard a person tries they cannot figure out what the key for the lock works or would look like. When a person wants to receive private data they can broadcast this set of instructions to everyone in the world so that they know how to generate the special lock. Another person decides to send a box of gold to the original person, they forge the lock from the freely available instructions and now the gold is secure. On the way to its destination several people try and use their own key on the box but alas they fail as no one but the original generator knows how to make a key for this lock. The gold arrives, and by using the key to the lock the person receives the gold.

This is currently the best form of encryption that we widely use, and for all intents and purposes it is all that is needed. Though, as time goes on and computers improve, become faster and more powerful they are becoming better at brute force attacks. Brute force is a manner of decryption by trying every possibility until one finally works. The reason this can often find the key if done locally and given enough time is because people often use weak passwords, there are list called password libraries, these large files contain common plain text passwords and often their hashed counterparts, we’ll talk about those in a minute. These have a very high rate of success as people are often not very imaginative with their choice of passwords.

When storing user passwords a company can use many different methods. It is unfortunately not uncommon to see lists of plain text passwords after server breaches, there is no real excuse for this apart from incompetence. A somewhat better method is encrypting passwords using symmetrical key encryption, this means that finding out the original plain text passwords is quite challenging but yet, as mentioned before, can still be done. This is where hashing comes in mighty useful. Hashing is the method of taking a piece of data, putting it through an algorithm and storing the output. The special thing about hash algorithms is that there is no way to turn the hashed password back into its origin. this is because hashing algorithms use a many to one standard, meaning that lots of different passwords go to the same hash. The ratio is just enough that trying to get a result back will either not work or get you a very large number of possibilities, but also there is a low chance that two randomly generated passwords will create the same hash. Thus, if a person breaches the server and finds a list of hashed passwords, there is very little they can do with them.

A rather wonderful thing about quantum physics is that it led to the discovery of quantum entanglement. It has been found that a pair of particles can be entangled in a quantum way, this means something rather awesome, if one of the particles changes state, as does the other, instantaneously no matter the distance. After you have recovered from the pure astonishment of this physical attribute you can begin to understand its importance. Data can be converted into quantum data, each particle being entangled with a duplicate partner, when a quantum particle is observed it has a state change, this causes both particles in the entanglement to change state. This means that when the data is sent, if it is observed en route the sender can see the disturbance and deal with the compromise in that stream of data being sent.

Unfortunately this method is still far from implementation, due to the technique still being worked on and the difficulty of sending quantum data through a complex network. If this method is developed and implemented though it will allow an almost impregnable method of security, something the world is in very much need of.

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]]>Vectors are an extremely useful topic to have a good understanding of and be able to apply. They allow you to store both a magnitude and direction for multidimensional motion, force or anything else that can have a backward or forwards. There are a lot of uses for vectors outside the classroom, in both further mathematics and physics (including game physics), for example they are often used to determine the movement of an airplane as they can consider both thrust and lift, as well as drag and the gravitational pull of the earth. This is just one of many uses for vectors, but before we go in to more detail we must understand how to interpret vector form.

There are two ways to write Vectors, one being magnitude-direction and the other component form (which can further be displayed in two different ways). Before we look at how to find vectors from two points we will look purely at how too read them. Starting with a component vector in column form, for example: component form in column is the simplest way to display a vector as you simple consider the top to be x, and the bottom to be y. Such that the coordinates of this point are . Simple! Next we look at how to display it in unit form, this is effectively putting the column into a traditional equation form, meaning this vector would be shown as .

is the unit vector in the direction and is the unit vector in the direction in this case there are so you got 2 times the magnitude of in the direction. Finally there is the magnitude-direction form, this can also be written as the magnitude-angle vector form. So far the distance and the direction the vector goes has been determined by two separate factors, one in and one in . In this form we have two parts, the magnitude and the angle from the x-axis, written as where r is the magnitude and theta the angle which can be in degrees or radians.In this form you can read it as the distance you travel, and the angle going clockwise from the positive x-axis. So, for example, if you were given the vector this would mean you travel 5 units, 45 degrees from the origin. Now we understand how to read vectors we can progress in learning how to use them.

The next logical step would be to learn how to convert between these two types of vectors. Converting from a magnitude-direction vector to a component vectors is relatively simple. Consider this would be a line that travels from the origin at the angle 45 degrees from the x axis. Now to convert this to component draw this as a triangle with the vector as the hypotenuse and then draw the and lines from the end of the vector back to there respective 0 points. This will leave you with a triangle, with the height being the component and the base being the component.

Using our trigonometry rules SohCahToa we can find that and thus if we write this in column which is this shows that the components are , one unit in the x-direction and one unit in the y-direction. As shown converting from magnitude-direction to component form is quite simple, component form to magnitude-direction is the same concept, just backwards. We’ll use the components we just found, so we know what we are aiming for. First, we need to find the magnitude of the vector, this is done by using Pythagoras’s theorem where the magnitude is the hypotenuse. Meaning r (magnitude) is this is exactly what we would expect.

The next step is determining the angle from the x-axis. Once again lets take SohCahToa into consideration, this time we know all the sides of our triangle, thus to find the angle we can use tan, and the two components meaning so we have now gotten back to . Lets summarize what we have looked at so far. There is now an understanding of how to read vectors in both magnitude-direction and component form aswell as converting between the two. If you’ve gotten this far, well done, vectors are not the funnest.

Point vectors are simply vectors, but are the components from the origin to a specific point, where as your everyday vector is just a distance and direction anywhere on a grid (or space for 3D but we’ll go into that later! Yay!). That was easy.

Now we can have some fun, if that’s what you’re into. Let’s say we have two point vectors on a grid: and well, we want to learn how to get from point a to point b. As point vectors we know how to get to them from the origin, so, the only route we know to get to b is to go and then as this will take us through the origin and then to adding and subtracting vectors is very simple. So we can write our new vector . So we have found the vector between point a and point b . A general rule for finding vectors between two points is taking the vector you start at from the vector you are trying to get to.

So we’ve worked out how to find the vector between two points, what if we want to find any point on the same line as these vectors. Well, we have a point vector and we have a vector parallel to the line we are looking for , well we know that any point on the line can be found by moving any distance in the right direction so simply put if we start at a point and scale the direction vector either way we can find any point. This can be written as using our previous numbers we can find the equation of the line that has and on it, lets use the former as our starting point, so . We have found our equation.

So next we want to be able to take a vector equation and convert it into its Cartesian counterpart. We will use the previously found equation because I’m lazy and it makes things simpler. Converting from a vector is quite simple if we consider we can make an equation for and now we have our and our which in both cases it shows they are proportional to thus if we make them equal to we can then combine them to find our Cartesian. So and . We can now equate these equations to bring us . This can then be neatened up to make the subject . Super, we have managed to go from a vector equation to a Cartesian in a few simple steps.

It is often useful to find the angle between to vectors, for example it is not uncommon to come across triangles in all parts of maths, physics and engineering which are just the vector lines, and finding the angle between them can be very handy. The process is not too complicated once you learn the dot product method, also known as the scalar product.

The dot product is a method of finding the scalar of two vectors, the formula for it is as shown: . This will find us the scalar product of the two vectors. We can then use the equation to find for angle. This only works when the two vectors are in the same direction, if one is in and the other out then it is simple enough to just move the vector up or down to find another a different angle, and you can use that to determine the angle you are looking for.

3D vectors are effectively the same as 2D, except they have an extra variable for the z-axis, or the k component, finding the magnitude is simple, and the angle can only be found between two vectors so is unnecessary here.

This being a brief introduction we are going to stop there, we now have a reasonable understanding of how to interpret and use vectors. For further information there are lots of online and book resources with much better and more detailed explanations at:

]]>Space-time singularities, theorized by Hawking and Penrose in 1973 were a major step forward into discovering

the history of the universe. As far as we know, there are four dimensions that we live in. The first three being spacial dimensions, descried as x,y and z. These are the dimensions we can actively move about in, in any direction we like. The fourth, more elusive dimension is time, not spacial, and can be considered quite abstract, this dimension is one we feel no real control over. We can not just turn around and walk in the opposite time, this is something only mass-less particles can do, and in fact, they don’t even move through time from their frame of reference.

A singularity is a point in space, a volume smaller than you could possibly imagine. All massive particles in the universe interact with each other, via what is known as Gravity. Although gravity is yet to be placed in a unified theory it is widely understood mathematically and physically. Any object in the universe will pull in to any other object, though this relationship is proportional to so for large distances the effect are very minute. Because of this, you get large amounts of mass all in close proximity, this causes them to get even closer, being pulled together harder and harder as they get closer and closer.

Over time you get a very large mass all in a smaller and smaller space. Gravity is described as a dip or well in space-time, this means, as the mass increases the well increases, and so to speak it pulls time in aswell, slowing it down. Penrose and Hawking suggested, that at some point the mass must pull in on itself to such an extent that there is no longer any further it can do so, it must reach a limit to how small a space anything can occupy in space-time. This is a singularity, in these points, time does not pass, light does not escape and there is no way to directly observe them.

The closest we get in the universe is black holes, these are huge masses, often much larger then suns. There is no direct way of observing a black hole. Though we can see them through their interactions with the universe, as described before, gravity can be seen as a well in space-time, it literally bends space. We notice this, when looking at a area in the sky and seeing two stars which are identical. This is because they are the same star, this star must be behind a black hole, and the light has bent around from different sides causing us to see twice of what there is. You can use this, as well as their effect on nearby objects to measure how big and how far away the black hole is.

Now, consider the universe as a whole lot of matter and light, just spread over a really big area, gravity affecting anything and everything in it, with mass. Over time this must pull in on itself, slowly accelerating in together, until all of this mass in the universe, all its energy are trapped in a very small area, getting smaller and smaller, until all the energy and mass in the universe are so tightly packed, there is no way it can occupy less space, it has reached a singularity. No time as the effects of gravity are too great, just a singular point with a crap load of energy.

The next step is the one that, right now, no one can prove, or understand. This singular point, with an immense amount of gravity, expands. At a rate faster then anything considered possible, the universe just expands, the mass spreading out within it. A really big bang. It has been suggested that its cyclical, a big bang takes place, then after an extremely long time, it peaks and then goes into a big crunch and thus the process repeats infinitely.

This explains how time can have a beginning and also how it can have an end, whether it is cyclical or not, our observed values for the age of the universe and the cosmological constant all work with this theory.

There is one, major and unavoidable problem with this theory for the universe. Einsteins theory of general relativity does not allow for singularities. Because of this, we have only been able to predict down to the first seconds, before this, it gets almost impossible to explain in a universe running on general relativity. There is though, another theory for how things work, quantum theory, the description of all the very small things in the universe. Although General Relativity and Quantum Theory are yet to be unified they are both, mostly, agreed upon, just they don’t agree with each other.

For most of the twentieth century General Relativity was the major theory to explain the beginning of the universe. A few attempts to explain it with other theories have come and gone in the last 40-50 years. That is until a new theory, published in February of this year suggested all previous perspectives were looking at it all wrong. In Physics Letter B Ahmed Farag Ali and Saurya Das authored “Cosmology from quantum potential”. In this publication they look at the universe from a quantum perspective. Considering equations originally derived using general relativity they correct these to allow for quantum effects. The two major points in the journal entry are replacing geodesics with Bohmian trajectories and allowing for very small massive gravitation.

Geodesics are described as as the shortest route on the surface of a sphere, from one point to another. Because of this, any two routes on the sphere may, unavoidably cross each other. This is analogous to singularities, by having trajectories that meet each other within these equations that describe the universe and its beginning we find that there must be singularities, whether general relativity likes it or not. This is where Bohmian trajectories come in useful, rather than following the surface of the sphere, they can effectively go through sphere, never having to cross paths. This means there is no requirement for singularities in this quantum corrected explanation for the universe.

Gravity is the most elusive force in the universe, with only guesses to how it works and no sure evidence, with this new explanation, it not only explains the particles used in gravitational interactions it also allows for dark matter the majority of the mass in the universe we just can’t see. In this theory, it describes gravitons as very small but still massive particles, making up dark matter and also allowing us to show how gravity fits into our current theories of the universe.

Both these points have some rather major implications, for example, if gravitons have mass it means that gravity cannot happen at the maximum speed of energy transfer, the speed of light, meaning that our equations for gravity, for very large distances may well be wrong. It actually has been noted that our predictions for probes we send into the solar system tend to be slightly off when being sling shotted around a planet, the direction they come out tends to be slightly off what was calculated.

The greatest implication though, is by using these non-crossing bohemian trajectories, there are no singularities. And by using this in our equations to find the amount of time the universe has existed, rather then previously getting around 14 billion years, we find a result of infinity. This meaning there is no age to the universe, it always has been and always will, time never started and will never end. Expansion of the universe is still unanswered with this theory, though there is no requirement for a big bang for this to take place so it does not disprove this theory either.

As impressive as this new theory is, and considering it falls within observed data so it does not require a rejigging of the standard model, it still is very young. Until further experiments take place and more evidence is found this theory will not be accepted. If it is proven though, this will change the way we look at everything.

For more information on this theory you can find the original article here.

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