Christos Leonidopoulos
Particle Physics: Electroweak Symmetry-Breaking mechanism, Exotica searches, hadron-collider triggers, future colliders.
Location University of Edinburgh
Activity
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Good to have you onboard, Lee.
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Oh that's a tricky one. It turns out that the first W boson in this chain (let's call it W*) is slightly heavier than the "normal" W. How's that possible, you may ask. It is, because particles do not have a fixed mass, but something like a distribution around a nominal mass (if you are curious, check out "Breit Wigner distribution"), so that W* as it turns out...
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@francisgan When I say "light is light", I meant that all photons travel at the same speed (c) in vacuum. Having said that, of course energy & intensity have a role to play in how harmful a light beam can be. But this does not change how fast the photons travel, if that makes sense?
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You do have radioactive decays inside the Earth, see e.g. https://physicsworld.com/a/radioactive-decay-accounts-for-half-of-earths-heat/ . The Thorium decay that the article mentions is effectively a beta decay that requires the exchange of a W boson.
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If by "single" you mean completely isolated/on their own, the answer is no. But they do appear either in pairs or in groups of 3 (sometimes more). The reason for that is QCD (Week-4) and colour-confinement.
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Christos Leonidopoulos replied to Daphne Jones
@DaphneJones Not at all, this is a legit blog post, written by physicists. SSB is the mathematical recipe which (sort of) explains how elementary particles acquire mass. But as I said earlier, it is really just a prescription through which we go from a (non-existing) zero-mass world (W1, W2, B) to the real world in which elementary particles have masses (W+,...
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Christos Leonidopoulos replied to Daphne Jones
We may be talking about different things. You may have several particles contributing to the production of a Higgs boson (e.g. W, Z, electrons, muons, etc) and you can depict all these with Feynman diagrams. In order to get the theory predictions to agree with the experimental data, it turns out that you need to take into account all these interactions (aka:...
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Christos Leonidopoulos replied to Daphne Jones
@DaphneJones I assume you mean the non-expert version? I went on youtube and typed "Feynman diagrams" and I found several good-quality outreach attempts. Want to have a look yourself?
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The presence-or-lack of vacuum is relevant only when it comes to massless particles (e.g. photons). Massless particles travel at the "speed of light in vacuum", well, when in vacuum. When inside a medium their speed is always smaller than that. Massive (ie. with non-zero mass) particles can never reach that upper-limit of speed (whether in vacuum or not). They...
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Christos Leonidopoulos replied to Daphne Jones
Hi @DaphneJones . All known interactions between particles (including decays) in Quantum Field Theory are described/represented with Feynman diagrams in which a "messenger" particle is being exchanged between the two interacting particles. We don't really know any other way of describing particle interactions.
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Electric discharge is the transmission of electric charges through a medium across an electric field. It is charged particles (think: electrons), not photons/light.
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You use the ring at the LHC where protons can go around again & again and pick up energy, and increase their speed.
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Light is light! what matters is the medium in which photons travel, not the wavelength/frequency.
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Not quite, but pretty close. Protons at the LHC travel at 99.9999991% the speed of light.
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@francisgan you can decrease the speed of photons by surrounding them with some material. You cannot increased it though, the speed of light at vacuum is the upper limit according to Special Relativity.
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All three happen from time to time! I just came back from CERN, teaching at Edinburgh on Monday morning!
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Christos Leonidopoulos replied to John Lateano
Compared to a massless particle (e.g. a photon), obviously the massive electron (one of the lightest known particles) has a mass that is gigantic & immense! :)
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@francisgan Classical Mechanics describes everyday physics, ie what we refer to as typically "large" & "slow" objects (e.g. think of a person or a car moving - yes even cars are slow in this prescription). Relativity enters the picture when we consider very fast objects (e.g. think of a spaceship travelling at 10% of the speed of light). Quantum Mechanics...
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Are you referring to the fact that we are using natural units here? (ie. some constants like ħ and c are missing) That's ok, this is just a convention to make equations a bit shorter/easier to parse.
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Not sure I understood the question. Are you asking if the mass at each vertex is conserved? Charge, energy, momentum have to be conserved at each vertex, but mass can be created & destroyed (assuming no rules are violated in the process). Matter & anti-matter enter in other conservation laws (e.g. charge is just one aspect of it), but not really in the mass,...
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Hi @CarstenDierks
Q1: can you be more specific about the Feynman diagram you are talking about? Since you are bringing up 3 particles, I am tempted to think that you may have forgotten a photon somewhere, can you please clarify?
Q2: This is true in general across energies (ie. as long the energy is high enough to create electron-positron pairs)
Q3: You can... -
It was noticed at some point that one could picture (for example) a negative-charge particle moving forward in time as a positive-charge particle moving backward in time. And that's about all there is to it. It is a mathematical manipulation that is used to try to make sense of something (negative energies) that looks very unintuitive. Of course, now we know...
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Christos Leonidopoulos made a comment
The negative-energy solutions in these QM equations appear when we try to switch from the classical description of the equations of motion to the relativistic one. It turns out that this is not good enough, and we need to switch to the full description of Quantum Field Theory with continuous fields that allows for particles to be created and annihilate. In...
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tell your friend that it's you who is right! :)
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@francisgan "The main facet of modern science is that we can repeat an experiment easily." Are you referring to reproducibility of the results here? For the specific case of the Higgs boson discovery we accomplish this by having two independent collaborations that report on their findings separately/independently and without advance notice of what the other...
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"most promising" means what we consider is most interesting from a physics point of view. For example, it could be because the fragments of the collisions look consistent with the decay of a Higgs boson. In this case, we record the collision so we can study it more carefully offline. Less interesting can be less rare or exotic physics processes that we...
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@francisgan "if everything goes well" means if we have done a good job of having the two beams aligned and we manage to achieve a good collision at the centre of the experimental apparatus so we can record it. If not, we are missing out.
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There are people with a very wild/wide range of backgrounds here. But we are trying to make sure we all learn while having fun.
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we all do!
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(a) Einstein, approaching this from a theoretical point of view, wanted to make Maxwell's electromagnetic equations uniform across all reference frames. For this to work, the speed of light would have to be constant.
(b) The Michelson-Morley result provided the experimental confirmation that the speed of light is, indeed, the same in different reference...
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Special Relativity is based on the observation (if you an experimentalist) or postulate (if you are a theorist) that the speed of light in vacuum is the same in all reference frames (in other words: all observers agree that the light travels at the same speed, no matter what the relative velocity among the various observers).
This does not make sense from...
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@francisgan yes, every Higgs boson decays practically instantaneously. What the plot is showing is the process of data-collection where we accumulate a large number of Higgs bosons over a long period of data-taking.
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Christos Leonidopoulos replied to John Lateano
@JohnLateano The photons are mass-less, we are fairly certain about this. What you describe as "massive photons" at the time of collision/interaction is in reality the effect of momentum. If a mosquito hits the windshield of a moving car, it is not its mass that creates the "thump", it is its momentum. Closely related, but not the same. Funny thing, the...
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@francisgan yes, we get about one Higgs per billion of collisions. The tricky part is that we do not get to store every single of these collisions but a very small fraction, the "most promising" ones. We do this with a highly selective filtering mechanism, called the Trigger. We will be discussing all this in Week-6.
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Christos Leonidopoulos replied to John Lateano
@JohnLateano The "mass x velocity" formula is indeed from the pre-Relativity era. The new/adjusted formula is modified to be "gamma x mass x velocity", where gamma is the relativistic Lorentz factor. For a slow massive particle, gamma ⁓ 1, and we recover the classic formula. For a photon with mass = 0, gamma is not defined (or you could say that gamma = ∞, if...
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Good to have you back, @SaraLeyshon !
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Good to have you onboard, @DanielJohnson
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I think the way to think about this is whether you need to "pay" to break free (e.g. think of a piece of metal in a magnetic field), or not (e.g think of a bullet moving in a zero-gravitational field: nothing can stop it). The +/- helps us picture whether we have an (energy) debt or a positive balance in our energy-bank account :)
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I am not sure I understand your question, but my guess is you are referring to the filtering mechanism of the experiments. We have about a billion collisions per sec, and we only select a few thousands of them (so: a few kHz). We accumulate data over a long period of time, and then we look for fragments/evidence of the Higgs in the recorded datasets. Does this...
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Good to see this attitude, @JosephineLord , and please remember: we are here to help.
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Christos Leonidopoulos replied to John Lateano
No, it is actually the force and the *change* in the direction of movement that have to be parallel to each other (or in the same direction). This can also be seen in more complex systems, e.g. 2D & 3D. Imagine an object moving on a circular trajectory, e.g. a planet moving around a heavier sun. To force the planet to be on a circular motion you need a...
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Hi @JohnLateano . The answer to your question is: both! We will discuss some of the technical details (not to mention, experimental challenges) in Week 6.
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Anyway, as it happens with these things, in 2012 Toichiro Kinoshita and collaborators calculated 12,672 such Feynman diagrams, which gave a theoretical prediction on alpha/2pi with a precision of 10 significant digits, or 0.25 parts per billion. This may sound crazy (it is) and unnecessary (it isn't). It turns out that experimentalists from Brookhaven about...
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This result was so important for physics that it got engraved on Schwinger's tombstone, see:
https://ibb.co/Wg34rkXThis theoretical development led to an arms race: experimentalists started getting more precise results, which forced theorists to include even more corrections in their calculations, and so on.
Mind you: These "corrections" are not...
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If you are a physicist, there is a very good chance you know that tomorrow a new result will be announced from the Muon g-2 experiment at Fermilab on the (so-called) anomalous muon magnetic moment. This is related to the spin of fundamental particles, and how fast they would wobble if they enter a magnetic field.
Paul Dirac (about a century ago or so)...
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It is that a collision is understood in today's terms as an interaction between two particles that exchange energy/momentum via a so-called mediator particle. So, every collision can be mathematically described via the exchange of a "messenger" between two interacting particles.
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Does this answer your question?
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@ThomasPruefling "collision" is another word for "interaction". QFT is teaching us that when two particles get "close enough" to each other (which is really determined by the range of the force/interaction) they interact. Sometimes they annihilate each other, create new particles, etc. Or you could have an inelastic collision, where the two particles push each...
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@ChamodSamarasinghe the size of the accelerator site has to do with the design energy the beam particles are accelerated to: the higher the energy, the larger the collider. If you think the (27-km long) LHC is large, you should read about the new 100-km long Future Circular Collider, which is currently one of the options for future colliders under...
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It is a subtle point, maybe easier to explain if I use the example given on pg. 11 of the lecture notes linked above. In that diagram we see a (so-called) off-shell Z (sometimes also called "virtual" Z or Z*) decaying into a "regular" Z and a Higgs boson (H). We could have replaced the Z/Z* by W/W*. The point is that Z & Z* (or W & W*) are different particles,...
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Hi @GuusLöhlefink . Yes, this indeed the case, but of course you can only check for a limited number of problems and biases with the much smaller dataset obtained with this method.
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@GarethWilliams x-axis: time elapsed in ps (or: travel time of B meson), y-axis: event-counts at given timestamp. Without the oscillations, one would expect an exponential decay: you start with a given number of B-mesons, you expect an ever-decreasing number following an exponential decay law. With the oscillations, you see this flickering pattern convoluted...
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Too early to claim new physics just yet.
The word is "cautiously optimistic":
https://theconversation.com/evidence-of-brand-new-physics-at-cern-why-were-cautiously-optimistic-about-our-new-findings-157464Here's another summary/commentary:
https://cosmicshambles.com/words/blogs/jonbutterworth/a-growing-anomaly -
Is that all?
No, there is something else. To understand this oscillation, we also need to add in the mix Einstein's Special Relativity that is telling us that very fast-moving particles tend to experience life quite differently than slow ones, and that the extra time they seem to gain (called time dilation) allows them to travel just far enough for us to be... -
But what I wanted to point out is something slightly different: In this plot you see two distributions, one created with particles (blue) and a second one created with anti-particles (red):
https://ibb.co/SQLfVH5Do you see that strange oscillating pattern? Do you know what is causing this?
This is the experimental observation of matter being converted... -
Christos Leonidopoulos made a comment
[Posting this a bit early in the Week discussing the experimental searches, as more closely related]
There is a good chance you may have already seen today's announcement from the LHCb collaboration at CERN about a reported difference between the way electrons and muons seem to interact with (so-called) B mesons.
Why do we care?
Oh, we care a lot.... -
Good to have you on the course, Jackie.
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So, we fixed the problem of negative energies by noticing that a particle traveling in one direction is equivalent to an anti-particle traveling in the opposite direction, very much like a negative particle traveling from left to right is equivalent to a positive particle traveling from right to left. You may have seen this trick before in condensed matter...
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Ok, let's take a step back and give a bit of context on the notion of the negative time (ie. particles traveling backwards in time). You are a theorist and are writing down equations (NB: this is happening at a time before anti-particles have been discovered or hypothesised). You are solving the QM equations and you find that one of the solutions to these...
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Christos Leonidopoulos replied to Richard Dennehy
@GuusLöhlefink Yes, lots of data already publicly open for people to explore and search for hints of their favourite theoretical model: http://opendata.cern.ch/
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"why does matter and antimatter, annihilate?"
I am not sure if I can answer this in a satisfactory way. Quantum Mechanics comes with a bunch of rules, as in: "process A can happen", "process B is forbidden", etc. So, matter & anti-matter annihilation is one of those things that are allowed (because it is not explicitly forbidden by a long series of QM...
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Hi @SeanBottrill.
I assume you are talking about the diagram on the right at the 6:25 timestamp. You can look at this in one of the following ways: You can either have a photon decaying into an electron and a positron (equivalently, an electron and a positron annihilating into a photon), OR, look at the whole thing as an electron traveling (from left to...
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Christos Leonidopoulos replied to Richard Dennehy
@GuusLöhlefink these are some good comments. We will be discussing these challenges in Week-6 (the experimental searches for the Higgs boson).
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Christos Leonidopoulos replied to DAVID KING
Good to have you onboard, @DAVIDKING
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Christos Leonidopoulos replied to Qingyang Zhang
Particles & anti-particles can indeed annihilate each other, but when this happens something new (e.g. photons or gluons) must be produced.
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Christos Leonidopoulos replied to Qingyang Zhang
Hi @QingyangZhang . No, anti-matter/anti-particles do not have negative energy, they have a mass term and a kinetic term, just like matter/particles do.
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Christos Leonidopoulos replied to Guus Löhlefink
Probably the most important physics theorem of the last century!
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All this goes back to the marriage of Quantum Mechanics with Special Relativity (SR). SR postulates that space and time are not separate entities, but rather a unified set of a (so-called) Minkowski space. In a similar way, energy and momentum form a 4-vector momentum (or 4-momentum for short). We also have newly defined 4-velocity and 4-acceleration. So...
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"could there be more than one conserved physical quantity?" --> I am thinking there may be two answers here. My first reaction is to say "no", but thinking a bit more about it, we may find ourselves in a situation with a slightly different view of how quantities could be grouped together. E.g. it turns out that energy & momentum are two components of the same...
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@GuangyiZhang It turns out that mass is just one form of energy, so saying that energy is conserved it implies that mass can be converted e.g. to kinetic energy or vice versa. "How do we know that it is the energy, rather than other quantities" --> we know this from the way the Lagrangian is constructed, we apply Noether's theorem and figure out what is "the...
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This game may sound ad-hoc, and to a large extend it is. These transformations of the Lagrangian most of the time do not lead to something meaningful. Every once in a while though, what is revealed to us are some new terms that look like new particles, or interactions between new particles. If we are unlucky, these new particles are nothing but a mathematical...
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Examples:
1. If you have a perfect pendulum that oscillates back and forth in a world without friction, the pendulum would continue to oscillate for ever. Doesn't matter if you observe it today, tomorrow, or a billion years from now. In Lagrangian-speak: your system is invariant under time shifts, which implies (math omitted) that the energy is conserved. So,... -
Hi @GuangyiZhang. The main idea is the following: You have a (mathematical construction, called) Lagrangian, which can describe our physical world. Theorists try to come up with transformations (ie. change one/some of the elements in this mathematical construction) that ultimately leave the Lagrangian unchanged.
This sounds a bit weird. Why would you go...
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@DawnRyder please see message posted above.
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So, please treat the equations as "added value". Besides the mathematical formalism (which, let's face it, is kind of necessary, otherwise it wouldn't be here), we can still discuss the underlying concepts with "plain" language (I know this is an oxymoron, but I am trying to make a point). So, please keep posting your questions, and we will do our best to...
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On the necessity of introducing the equations in this course, and the criticism questioning the value they bring in a MOOC that has been designed to address a very wide range of learners (like ours): We try to deliver lectures that can be appreciated by users with very different levels of mathematical skills. Another way to say this is that we wanted to give...
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Christos Leonidopoulos made a comment
Dear everybody who is struggling with the maths in this course. I will quote what we have put on the front page of the course: "Some of the video lectures are significantly more advanced and include University-level math material. However, people encountering difficulties with the most advanced material should still be able to answer the quizzes and complete...
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Imaginary numbers tend to be used as a representation for something orthogonal to real numbers. e.g. think of a 2D plane with the x-axis (real numbers) and the y-axis (imaginary numbers). We use these mathematical tricks for easy manipulations with phase/angle rotation, etc.
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For your second question, the tachyons are hypothetical particles that can indeed travel faster than the speed of light (in vacuum), but the catch is that they can never go any slower. So they are "trapped" somehow in the super-luminal world. Despite efforts, there has been no experimental evidence that tachyons are real.
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Hi @VeniaminRakhimov , these are good questions. The postulate that the speed of light in vacuum is the same in all reference frames has both experimental and theoretical foundations. Even though the Michelson–Morley experiment had already shown that the speed of light seems not to obey the classical laws of physics, Einstein has stated that his motivation for...
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Massive open online course.
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@BJohnson good to see you again!
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Hi @MickKrupa, we are here, and looking forward to your questions & comments!
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Hi @DavidBlack. We do not plan to extend support after the end of the course. We are paying out Mentors for the duration of the course (they are all PhD students in the School of Physics & Astronomy), and it is currently not foreseen to extend this past the regular runtime. We do plan to re-run the course next year. We only do it once per year though....
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Hi @HankovanBeinum . The expression E = mc^2 is true only for particles at rest. For particles moving (like photons do), the proper expression is E^2 = (mc^2)^2 + (pc)^2. So, even for photons which are massless, their energy is non-zero, as it is proportional to their momentum.
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As to why this is the case: it turns out that some of the tricks we have up our sleeves and been using for dealing with quantum field theory (e.g. the so-called renormalisation method which is a necessary ingredient for making predictions in QFT) do not work with quantum gravity. This is not to say that renormalisation is the right thing to do. But it is the...
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@DaphneJones I am afraid this question does not have a quick (and satisfactory) answer. Yes, gravity is one of the greatest puzzles, and we don't really have a good way of tackling it (ie. incorporating it with the rest of our Quantum Field theoretical framework). One of the main challenges is that it is extremely weak compared to all other forces and we don't...
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This has worked for several decades remarkably well. It has given us a practically complete version of a theoretical framework that explains the majority of the physical phenomena. What is interesting now, is that we are at a point where the SM is not giving us any further hints ("go discover particle X or interaction Y"), and the experimental searches have...
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Hi @DaphneJones , this is a good question. The executive summary is that the Standard Model and experimental searches have been walking hand-in-hand for several decades. In some instances, the SM makes a prediction, and the experimental discovery follows (e.g. W and Z boson discovery in 1983-84). In some other cases, an unexpected experimental finding (e.g....
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Hi @AgastyaIyer , yes, this is more or less correct. However, one needs to fold in our ability to capture these Higgs bosons in real time and store them for offline analysis. Typically, we aim to capture only a small fraction of them. To that end, we use a system called trigger, which is designed to run some sophisticated filtering algorithms in order to...
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Hi @NethmieSenadheera , we will try to do our best. Please ask, and you should get some answers from our mentors, at least until the end of the 7-week course.
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Yes, of course, this is definitely allowed (and as Feynman said, if something is not explicitly forbidden, it is mandatory [to happen]).
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In this particular case we are dealing with QED (ie. electromagnetic interactions) where the relevant detail is the electric charge of the initial or final products. Since the charge for both electrons/positrons and W bosons is the same, the interaction has the same strength in both cases (there are, of course, other factors that have to do with how massive...
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Hi @ElisavetFasoula . In principle, yes, the propagator does depend on which particles it connects to. For the particular example (W+ vs W-) the interaction has the same strength because W+ and W- have the same charge. Unless I misunderstood your question?
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Welcome aboard, @AdamNDIFOR
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@ElisavetFasoula : no. Noether's theorem is applicable to all physical systems, including classical ones. Lorentz invariance is a different kind of beast.
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Christos Leonidopoulos replied to Paul Twist
Good to have you back, @Marion63K
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Then comes experiment which confirms (as in: experimental evidence for) the existence of positrons, and more generally, anti-particles. So everything is now in order, and I finally understand the strange negative-energy solutions for my equation. Mind you, we do not have any experimental evidence for electrons (or anything for that matter) travelling backwards...
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Hi @DavidBrown , there isn't really anything beyond maths that requires the introduction of the notion of "reverse time". One should keep in mind that the terminology was introduced before anti-particles had been discovered (or thought to be necessary to explain experimental data). So, I think the way to think about all this is the following: I am a theorist...
