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Spontaneous symmetry breaking

  • A good way to get an idea of what this is like is through water. Water has four different forms it could take depending on the conditions; frost, snow, ice and rime. Spontaneous symmetry breaking is sort of like this.
  • At the start of the big bang there was a single force which started off hot and as it expanded began to cool and in 1x10-46s (supposed to be scientific notation) gravity came into existence.
  • Now there is gravity and the force energy of the universe. This force energy then split into the strong nuclear force (SNF) at about 1x10-36s.
  • Then shorty after the massive inflation at 1x10-22s (where the universe expanded from about the size of a proton to that of a orange), the weak nuclear force and electromagnetic force (or electroweak force as we now know that they are the same) came into existence at the same time at 1x10-12s.
  • So from one force, in 1x10-12s all the different forces have fallen out.
  • In about 1x10-6 quark confinement would happen, from 3-20 minutes the nuclei would begin to form, there is still too much energy for the electrons to be bound to the nuclei. Atoms would not form for about 380,000 years.

Well this has been a brief and simple intro to spontaneous symmetry breaking, hope you guys liked it. 

roundlittledog:

nanodash:

physics-bitch:

Quantum Flavordynamics (Weak Nuclear Force)

  • This is basically the decay of a neutron into a proton by the emission of a W- boson.
  • The up and down part of quarks is known as their flavour, they can effectively change flavours, in this case it is a down quark into an up quark.
  • The W- has to be emitted for the flavour of the quark to change but it does not last long until it decays into an electron (e-) and an anti-electron neutrino (ν
    e )
    .
  • The W- boson (80GeV) is roughly 80x heavier than the neutron (1GeV) it decayed from meaning that it takes a lot of energy for this to happen so is seen happening inside stars which is basically just a big burning ball of protons.
  • The energy for this change can also be borrowed from the vacuum provided the energy is paid back, to do this we refer to Heisenberg’s uncertainty principle:

ΔE x Δt<h

(amount of energy borrowed from vacuum) x (amount of time borrowed for) < Plancks constant 

  • This shows that the energy debt has to be paid back in 1e-25 seconds in which time the W- boson can move the distance of part a proton before it decays.
  • This process is represented by the special unitary matrix two dimensional su(2) in mathematics. It is 2D because it is only changing ups and downs.

I have a deep and abiding love of high energy physics.

Weak physics is great! I have a few things to add/critique about the original post.

While p —> n + e + ν is characteristic of the weak interaction, it is but a raindrop in a downpour of others. There are entire classes of weak-mediated processes that I think deserve mention as well.

  • Charged Current Interactions: These are processes by which the lowest order decay is carried out by the charged and massive W+ or W− bosons. These processes typically involve an overall change of particle flavor. Flavor is a fancy word that describes the different types of particles. Thus these is an up quark flavor, a down quark flavor, an electron flavor, an electron neutrino flavor, etc. Flavor is a quantum number just like spin.
  • Neutral Current Interactions: These processes are mediated by a the neutral and massive Z boson. Unlike the charged current interactions, the Z boson cannot change flavor on its own. Thus (to lowest order) the standard model says there are no flavor changing neutral currents.

My point is that weak interactions come in a huge number of forms. They let the neutron decay into a proton (a semileptonic decay, because it involves quarks AND leptons), sure, but they also mediate the decay of a muon into an electron (a leptonic decay) and the decay of a kaon into pions (a hadronic decay). In fact, flavor may not change at all, like in Z-mediated electron-neutrino scattering!

Additionally, I think there’s some confusion in the original post between external particles and virtual particles. An external particle is one which goes into or out of the process in question, i.e. can be measured in principle. This is like the proton, neutron, electron, or antineutrino in the OP’s post. External particles are on-shell: that is, they have the mass you’d expect them to have and their energy content is consistent with Einstein’s energy-momentum relation: m^2 = E^2 - p^2. A virtual particle on the other hand, need not obey that relation. Virtual particles are those that appear between the initial and final particles in a Feynman diagram, like the W- boson in the OP’s post.

Virtual W-bosons need not have their mass "on-shell", so you don’t need the energy of a sun to produce them. In fact, any propagating particle is emitting and reabsorbing virtual W-bosons all the time. Hell, I can leave a sample of oxygen-14 sitting on a table (i.e. with hardly any energy at all) and it will readily decay. Kinetic energy is produced in rest-frame decays, not spent.  Carbon dating—for instance—is useful because carbon-14 decays spontaneously.

Furthermore, it’s always to be emphasized that conservation of energy is a statistical phenomenon. Even when an on-shell virtual W-boson is produced, energy conservation isn’t violated because energy conservation doesn’t apply there in the first place. That’s what the time-energy uncertainty relation is all about. Energy becomes a good conserved quantity only when enough time has elapsed to consider the system statistically stable.

Another important thing to remember is that in these processes we don’t measure the intermediate particles. In a lot of ways, virtual particles are more mathematical niceties than physical realities. The only thing we see in the lab is the overall p —> n + e + ν. Feynman diagrams like the one above (wherein we see specific intermediate processes) are really pictures describing terms in an infinite sum. We only obtain what’s going on when they’re all added together. No diagram is correct on its own.

Finally, a comment about the SU(2) group. The elements of SU(2) are 2 by 2 complex matrices which are “special” (determinant = 1) and unitary (look like rotations of a complex vector).  Because of those conditions, the 8 real parameters of a general 2 by 2 complex matrix are brought down to 3 real parameters. SU(2) is three-dimensional in the sense that we need 3 parameters to describe any element of the group. A representation of a group is a collection of matrices that behaves the same way as the group being represented. Thus, any element of a representation of SU(2) can be described by 3 parameters just like in SU(2). When a representation is utilized to describe the symmetry group of some particles, the number of rows/columns in the matrix representation determines how many particles the representation can simultaneously describe. That means I can describe the mixing of 2 nucleons, the mixing of 3 spin states of a massive vector boson, and even larger groups of particles using different representations of the same SU(2). There is an important difference between the dimension of a symmetry group and the dimension of a representation of the symmetry group.

rapt0rawsmsawce asked:

Hey dude, I love physics too! :D Just wanted to quickly ask if you could explain to me what the diagrams are, the diagrams like when you were talking about flavourdynamics. It seems like quantum mechanics, and I like quantum mechanics, but.... I don't know the diagram. :/ Thanks for the help!

Hey well the first diagram is a Feynman diagram showing the alpha decay of the neutron, it is just an easier way to visualise and understand the changing flavour of the quark as well as what is emitted (the W- boson) and what it breaks down to. The second is readings that were taken from a machine that I forget the name of showing the decay using strings.

Quantum Flavordynamics (Weak Nuclear Force)

  • This is basically the decay of a neutron into a proton by the emission of a W- boson.
  • The up and down part of quarks is known as their flavour, they can effectively change flavours, in this case it is a down quark into an up quark.
  • The W- has to be emitted for the flavour of the quark to change but it does not last long until it decays into an electron (e-) and an anti-electron neutrino (ν
    e )
    .
  • The W- boson (80GeV) is roughly 80x heavier than the neutron (1GeV) it decayed from meaning that it takes a lot of energy for this to happen so is seen happening inside stars which is basically just a big burning ball of protons.
  • The energy for this change can also be borrowed from the vacuum provided the energy is paid back, to do this we refer to Heisenberg’s uncertainty principle:

ΔE x Δt<h

(amount of energy borrowed from vacuum) x (amount of time borrowed for) < Plancks constant 

  • This shows that the energy debt has to be paid back in 1e-25 seconds in which time the W- boson can move the distance of part a proton before it decays.
  • This process is represented by the special unitary matrix two dimensional su(2) in mathematics. It is 2D because it is only changing ups and downs.

Quark confinement

  • for the purpose of understanding how this works we are going to imagine that something is trying pull an up quark from a proton which is made from 2 ups and 1 down quark.
  • As you try to pull the up quark from the proton a tube of energy is formed between the proton and the up quark.
  • eventually the tube of energy becomes enough for matter-anti-matter creation with an up and an anti-up quark.
  • the up quark goes back to the proton meaning that the proton has always stayed whole and the anti-up quark joins the up quark that was separated from the proton to create a meson.
  • this means that is is impossible to ever have a quark by itself.
  • the quarks themselves are make up 8MeV while quark confinement generates about 930MeV meaning that most of our mass actually comes from quark confinement.

Short version of the Higgs boson and Higgs field

The Higgs boson is the theoretical particle that gives rise to the mass of fundamental particles. It does this as a field that spans across the whole of the universe and you can think of it as someone trying to walk from one side of the room but they are up to their knees in water. The more drag the particle has in the field hence the slower it moves, the more mass it has. One thing to bear in mind is that this does not explain the mass created through quark confinement which is where most of our mass comes from.

The Higgs boson is predicted to have a mass of about 125GeV and would have a spin of 0 which is what makes it a boson.

Now, we know that mass and energy are interchangeable terms, photons have 0 mass and so one would expect then to have 0 energy, but E=had allows a photon to have energy but only when it is travelling at the speed of light.

Now this has been very brief and simple and not incredibly accurate, I hope this helps some of you understand the Higgs Boson.

The idea of dark matter first came about in 1933 when Fritz Zwicky made measurements of the galaxy.

From the visible matter in the universe, the outer stars would be moving too fast for them to be held in place in the galaxy. For them to be moving so slowly there must be around 400x more matter than we can see.

Then in 1975, Veru Rubin had the same measurements as Zwicky

However, there is proof of dark matter, we are fairly sure it exists as a result of gravitational lensing.

The dark matter is only found in and around galaxies but not in between them.

The common school of thought is that it is a particle. However, if it is a particle, it is a weakly interactive massive particle (WIMP particle) (doesn’t interact). It is thought that it takes up around 90% of the universe.

However, contrary to the school of thought that dark matter is a particle, in m-theory the 11 dimensions would allow for dark matter to be present in one of the dimensions as an energy, this could be a reason why we cannot detect it.

(The second photo shows high energy particles being emitted from a super black hole in the middle of a galaxy as black hole jets)

Light speed

  • Travelling at the speed of light would initially cause everything to appear further away.
  • You would almost be able to see behind you as you would be keeping up with the photons travelling with you. 
  • When travelling at the speed of light, to an observer you would appear to be almost frozen in time. 
  • Travelling at the speed of light from point A to point B assuming point B was 100 light years away, when you reached point B it would be 100 years ahead of you as you would experience time moving much slower meaning that you would not have aged those 100 years.

My simple black hole explanation

  • Mathematically anything could become a black hole if it is compressed enough (schwarzschiled radius). For the earth, this would be about the size of a peanut.
  • They seem to be caused by large suns that run out of fuel then collapse in on themselves.
  • As a black hole is caused by such a great mass being confined to such a small space, the gravitational effects are much greater therefore the gravitational lensing effects are much greater.
  • When around half of your vision is covered by the black hole, you have reached the photon sphere. At this point, theoretically if you stopped and looked to the side you would be able to see the back of your head as the photons reflecting off the back of your head would orbit right round the photon sphere to your face.
  • As the gravitational mass of a black hole is so much, it also bends time so to an observer watching an object move towards a black hole, it would get slower and slower as it approached until it reached the event horizon at which point light can no longer escape and the image of the object would become increasingly red-shifted until it disappeared.
  • As you get closer to the black hole, the gravitational effects on the closest part of your body are much greater than those further away so your body starts to stretch. This happens until your body would be nothing but a a string of molecules. When they reach the singularity (we are assuming that the black hole is a singularity) the molecules either disappear completely or appear elsewhere in the universe.

mucholderthen:

FLY-BY OF A SCHWARZSCHILD BLACK HOLE
What you’re seeing is a sequence of “Einstein Rings” 

Einstein Ring is a term from observational astronomy. It’s an artifact of the gravitational lensing of light (from a star or galaxy) by a massively massive astronomical object (like a black hole or another galaxy).

In order for an Einstein Ring to appear, all threethe light source, the massive lens, and the observermust all be aligned. In other words, it occurs when the object that you’re seeing as an Einstein ring is directly behind the object that is the gravitational lens.

Gravitational lensing is predicted by Albert Einstein’s theory of general relativity. Instead of light from a source traveling in a straight line (in three dimensions), it is bent by the presence of a massive body, which distorts spacetime.

The animation above is a simulation depicting a zoom-in on a Schwarzschild black hole in front of the Milky Way.
  • The first Einstein ring corresponds to the most distorted region of the picture and is clearly depicted by the galactic disc.
  • The zoom then reveals a series of 4 extra rings, increasingly thinner and closer to the black hole shadow. They are easily seen through the multiple images of the galactic disk.
The odd-numbered rings correspond to [images of objects] which are behind the black hole (from the observer’s point of view);  they correspond here to the bright yellow region of the galactic disc (close to the galactic center).
The even-numbered rings correspond to images of objects which are behind the observer.  These objects appear bluer since the corresponding part of the galactic disc is thinner and hence dimmer.  [WP]

SOURCE:  Einstein ring - Wikipedia).
The animation was created by Wikipedia contributor Urbane Legend.

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