Feynman diagrams
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- Опубликовано: 25 авг 2024
- Fans of particle physics often encounter a series of doodles called Feynman diagrams. These mystifying scribbles were invented by Richard Feynman and they encode information on how particle physics collisions unfold. But they have an even deeper significance. In this video, Fermilab’s Dr. Don Lincoln gives you a peek into the deeper meaning of these important scientific pictograms.
Related video:
• Quantum electrodynamic...
This is one of the best explanations of Feynman diagrams I've seen on RUclips. Thank you for the clear explanation.👍
Yes, Feynman; however, who introduced and outlined the appropriate explication?...
Thank you Dr. Lincoln.
Ana M. Abreu.
At school, I was probably worst in math and physics, but at the same time very aware of their importance, and scientific discoveries in these fields will always have my special attention. I may have my own strengths, but I will always feel a bit of envy for those who are at ease with this kind of stuff and a bit sad for having absolutely no talent for it myself. I am thankful to people like Richard Feynman and Don Lincoln for explaining this in layman's language as best they can.
GiacomodellaSvezia
check out kahn academy
Use Khan Academy. You can start from the very beginning
Mr Lincoln is a pretty cool person.
Underrated
"Nature uses only the longest threads to weave her patterns, so each small piece of her fabric reveals the organization of the entire tapestry."
Richard P. Feynman
The intro gave me a 1998-2004 flashback. I yearn to return.
since it is a very lengthy calculation for 1 Feynman diagram, M.J.G.V. developed Schoonschip, this was one of the first computer algebra systems, developed in 1963 by Martinus J. G. Veltman, for use in particle physics.
"Schoonschip" refers to the Dutch expression "schoon schip maken": to make a clean sweep, to clean/clear things up (literally: to make the ship clean). The name was chosen "among others to annoy everybody, who could not speak Dutch". (from wikipedia)
during graduate studies I practised with Schoonschip .
Cool
I think they should have shown the other kinds of exchange forces (spring shape = gluons), that would have really drive home the point of how amazing these diagrams can be. But still a good video!
Fine man that Feynman!
+
No Fine Man diagrams here, only physics. Go see Leonardo Da Vinci for that Fine Man.
+rep
@@s0dfish110 ok boring boomer.
dont know never met the guy ....
Feynman himself would be proud of you doc Lincoln! Best explanation I've ever seen!
Ernst Stueckelberg came up with similar diagrams independently of and before Feynman. He also contributed to other areas of physics for which other physicists won Nobel prizes. Along with WIllard Gibbs, Ernst Stueckelberg is probably the greatest scientist you never heard of.
I love it when the equation becomes intense ;)
+zubmit I love hardcore math! :D
me too, but then we have integrals...
BlueHawkPictures Integrals are my favourite :P
Paramdeep Singh obheroi yeah integrals are cool but there are some especially in physics that are literally impossible to do with pen and paper man belive me I tried. Not even maple can evaluate them
+Paramdeep Singh obheroi Feynman diagrams actually represent path integrals. They are hairy equations to solve though.
8 years passed , still one of the best explanations
Dr. Lincoln! Love part 1! Could you give us a part 2?! Specifically, breaking down the electron variables I and O?
Dr Don - Your presentations work great for me - and a little humor is always good. This is heavy stuff.
Finally! Im up to these diagrams! What a great sunday im having so far! Thank you doctor and channel team
Wow! Thanks Dr. Don! great episode, informative and concise. I would like a little more of a hint to solve the equation but I have Feynman's QED book so I'll revisit that.
Thank you for answering a question that I wondered about for years!
This videos are really underrated. This channel should get even more views. That makes me angry.
It is important to make the point that the leading contribution is enough only in the absence of strong electromagnetic fields....
That's not an equation. It's just a term. What is it supposed to equate to investigate order to solve it?
It is a term in a perturbation expansion of the quantum mechanical probability amplitude to transit from the given initial state (two inbound electrons) to the final state (two scattered electrons). One needs to add all the terms to obtain the overall amplitude. Its absolute square corresponds to the probability of this process to occur. This probability is directly related to what is measured by detecting electrons at various scattering angles and counting them.
The perturbation series (if it converges) IS the solution of the problem. The diagrams with loops contain integrals (which diverge and are in need of treatment by renormalization). One needs to do those integrals.
Experimentally you typically observe collisions and count the particles that come out in various directions and energies (and possibly with various spin polarizations). You know the initial state from the way you set up the experiment, in terms of energies, numbers of particles, directions and spin polarizations. Combining this with the results of your counting, you infer the probability of certain reactions, expressed in well-defined quantities so that everyone knows exactly what they mean, like total and differential cross sections etc. (These are not literally cross sections of mechanical objects, but simply ways that express probabilities of processes.)
To compare experiment to theory, we need to compute the value of the cross sections based on some underlying theory: QED in this case. In Quantum Mechanics there is a complex probability amplitude associated with each way a physical process can happen. A Feynman diagram represents the quantum probability amplitude for the depicted way the process can happen. To get the probability of the process, we need to add the amplitudes for all possibilities and take the absolute square of the result. Then we needs to pay attention to the conventions of normalization etc. used by the experimentalists when they write down their cross sections etc., and take them into account. The result is a computed cross section that can be compared to the experimentally measured value.
The phrase 'solving the equation' is not really apt here. It is a computation. Note that the underlying theory (QED) is given here. That is not typically the case. For example, you might be curious how electron scattering is affected if you change the Standard Model a little, e.g. introducing SuperSymmetry in some way. Then you usually start by writing down your hypothesis for the modified theory in terms of a so-called 'Lagrangian'. The Lagrangian is directly related to the probablity amplitude through a concept of 'action', which is e raised to the power of (i/hbar) times the spacetime integral of the Lagrangian. This formalism guarantees that your theory will conform to both Quantum Mechanics and Relativity. Now you have to obtain the formulas for the Feynman diagrams of your theory, which after all is different from QED. In the early days of Quantum Field Theory (fifties) this was hard, almost as hard as Feynman doing it for the first time. But because the step from a Lagrangian to Feynman diagrams is so useful, people found ways to streamline the process, using a branch of mathematics called 'functional analysis'. This aspect of theoretical work comes a little closer to "solving the equation", although it still does not apply literally.
+materiasacra by diagrams with loops you refer when electron-positron pairs are created? Or also when an electrom i remited and absorved? I'm very intrigued by renormalization and the infinities that come with it.
The basic building block of Feynman diagrams in QED consists of a fermion (electron) line with a direction associated with it, and a photon line attached to it at a vertex point. You are free to orient the lines in any direction in spacetime, including spacelike directions and backward in time.
The simplest diagram would be the building block by itself. Depending how you orient the lines, this might represent an electron-positron pair annihilating into one photon, or one photon changing into an electron-positron pair, or an electron emitting one photon, or a positron emitting one photon, or an electron absorbing one photon or a positron absorbing one photon. However, all of that violates momentum conservation. To see this in the first case, consider the process in the center of mass coordinate frame. In that frame the total momentum of the initial electron-positron pair is zero. Momentum conservation requires it to be zero also in the final state. However, in the final state we have just one photon, which must have some momentum. There you have it: violation! So the single building block diagram does not occur by itself.
We need at least two vertices. One way to do this is by having two electron lines going from past to future, and have them interchange one photon. This is good old Compton scattering. But there are other possibilities. We could have one electron emitting a photon and reabsorbing a little later. This is the first example of a loop. It constitutes a 'radiative correction' to the electron mass. And... it is infinite. Another -somewhat weird- possibility is having no incoming lines at all (i.e. the initial state is the vacuum), and then have a vertex that produces an electron, a positron and a photon. All of this stuff disappears in a second vertex. This is a vacuum-to-vacuum transition, contains a loop, and.... is infinite. Experimentalists don't usually observe the vacuum directly (too Zen for them!), but the consideration is part of the theory. Then there is the possibility of one photon that turns into an electron-positron pair, and a little later turns back into a photon. Again a loop, and again... infinite. This exhausts the possibilities with two vertices. Then there are the diagrams with three vertices, and four vertices, etc. The number of possible diagrams increases very rapidly, which is an unattractive aspect of Feynman's theory.
Each time you can trace electron or positron or photon lines around we have a loop, and the contribution is infinite. We can classify these troublesome diagrams as pure vacuum properties (not directly observable), vertex corrections or propagator corrections.
Infinity is never the result of an experiment, so we need some theoretical development to get rid of the infinities: renormalization. The key notion of renormalization is that every experiment you can conceive of has a finite spatial and temporal resolution. There will always be details you cannot resolve. And that is precisely were the troublesome infinities occur. Properties like the charge and the mass of the electron do not really pertain to the 'naked' electron, but to an electron enveloped in a cloud of stuff that is allowed by the uncertainty relation of Heisenberg. Now the big question is: does the theory of a 'dressed' electron has the same mathematical form as that of a 'naked' electron, but with different values of the charge and mass? If it does, we can just assign the experimental values of charge and mass to the 'dressed' electron, and thus absorb all infinite contributions into these parameters. A theory that allows this is called 'renormalizable'. One of the great triumphs in the development of the Standard Model was the proof, by Gerard 't Hooft and Tiny Veltman, that the electroweak theory is in fact renormalizable.
Let's try to think about this a little more physically. A 'naked' electron (which we cannot observe, due to our limited resolution) emits a photon, this photon turns into an electron-positron pair, which annihilates back into photon, which is reabsorbed by the 'naked' electron. All of that is happening well within a volume that is generally much smaller than we can resolve. The charge of the 'naked' electron is taken to be infinite, as is the contribution of the Feynman diagram of this and related processes, so that the net result is finite. This is renormalization in action. What if we increase the energy of our probe, allowing us to resolve smaller details? Then we start to penetrate the cloud of 'virtual' particles surrounding the 'naked' electron. Here the word 'virtual' means that the particles live only so long as allowed by the Heisenberg uncertainty relations. What is the effect of this cloud? Part of it consists of virtual electron-positron pairs. During their ephemeral existence they feel the presence of the 'naked' electron, and are separated a little bit. The 'naked' electron draws in some virtual positrons toward it and repels some virtual electrons. This means that the vacuum around the 'naked' electron is electrically polarized. This vacuum polarization tends to screen the charge of the 'naked' electron. If we increase the energy of our probe, we penetrate some of this screening, and we experience a larger charge of the electron than we were used to at low energy. This is the notion of a 'running coupling constant': the electromagnetic interaction gets stronger with increasing energy. This effect is well-known and has been measured.
The strong interaction behaves differently. It is a so-called 'non-Abelian' gauge theory. This means that the particles that mediate it (gluons) themselves have 'charge'. This is not the electric charge, but the charge that is relevant for the strong force: color charge. The cloud of virtual gluons surrounding a quark tends to spread out the color charge. If we increase the energy of our probe and penetrate the cloud, we observe a smaller color charge than we were used to at lower energy. Hence with increasing energy the strong force gets weaker. There is hope that at extremely high energy the weakening strong force and the strengthening electroweak force meet and merge into some Grand Unified interaction. The energy scale were this should happen is many orders beyond current experimental capability.
Renormalization used to worry us a lot, back in the sixties and seventies, because it was perceived to be a failure of Quantum Field Theory, which was thought/hoped to be fundamental. Nowadays the consensus is that the Standard Model, and the framework of QFT, are 'effective' theories, i.e. emergent manifestations of a deeper and quite different theory that also describes quantum gravity. Renormalization is a good thing, because it allows the Standard Model to be meaningful. Almost nobody thinks that renormalizability of certain quantum field theories holds any deep clues about the underlying theory. This used to be quite different when I was a student.
Great overview video on Feynman Diagrams suitable for beginning physics students.
Outstanding video. Short, Sweet, Super Smart! Oh BTW the book on this is Diagrammar by Veltman and ‘t Hooft, the 1999 joint Dutch Nobel laureates for the renormalization of Yang-Mills Fields, and hence the unification of electromagnetism and the weak interaction, hence the term electro-weak interaction. Schoonschip!
I just watched a great documentary about Feynman!
What's it called?
4:58 What equation? I dont see an equals sign.
Nit picker. He is talking about the fact that the Feynman Diagram is equal to the expression he is showing. At 5:10 he shows you the equals sign.
zdcyclops1 lickley I don’t think it’s nitpicking. You say it’s an expression, but what does the expression stand for? Is it energy? Probability? What?
@@stoatzsanswich8744 Good question! It is called "Feynman amplitude", often denoted as M.
+Re Trend THANK you for asking that! Why does NOBODY ever FOLLOW THROUGH?
@@zdcyclops1lickley190 No. He is saying the FD represents an EQUATION. "FD = equation" is NOT the equation itself to which he is referring. Re Trend's question is absolutely valid.
This is a good talk. Thank you for making some things clear. Now, I promise* not to try to solve that equation (kids don't try this at home), but could you just talk about it a little bit, just so we will know what we missed by not going to grad school for physics? (I actually kind of wanted to, and I was good at visualization, but my algebra aptitude was not quite up to the job. Or maybe I was just lazy. Or more likely, some of each.)
-----------------
*Scout's honor
What this expression is equals to, there is no "=" sign, and when it apars at the end we have a nice drawing only.
Hey Sir Lincoln, kindly make a video about Satyendranath Bose's contibution.
Thank u so much Don! I finally understand Feynman diagrams because of you.
Perfect for a doodle game for physicist
In previous video u explain that colliding electrons is for precision AND that electrons dont contain other smaller particles (=elementary particle), but here You state that electrons emit and absorb photons when they collide - in the same way as when electrons change energylevel? How can a negative charged electron emit a photon, if it is not already "inside" the electron?
Exactly.... I think People Who are Watching this Videos have No Knowledge of Physics
"You won't learn it until your second year of grad school." I'll say. I'm at this point right now and it's kicking my butt. I'm so glad I'm experimental HEP not theoretical. QFT is tough.
I always encourage fascination with physics, yet I see so many strong opinions of Feynman diagrams here, by people who never tried to solve one.
It takes many intense years of building mathematical skills and physics knowledge to understand them as they really are, despite Dr. Lincoln's good presentation of aspects of these tools. Even the likes of Stephen Hawking hated the steep, persevering climb to understanding advanced physics, until he could build to an intuitive level. Yet the challenges become even greater in coming up with new ideas beyond the foundations of advanced skills.
"Who ever knew that doodling...". You cannot truly understand something until you visualize its context and relationships. I have no doubt Feynman started this path with the underlying question, "What the hell is going on?". He then worked to see it in his mind's eye then once he had a conceptual theory worked to align the equations and visualization.
In the business world you will note the importance of graphs and charts. A picture can indeed paint a thousand words but of much more importance is its ability to align the discussion and reduce argument. It does not need to be perfect at first but it is of benefit in its approach to shortening the iteration cycles to resolution. And that is how Feynman used the diagrams - to attempt drive to consensus that which could be, and to narrow the discourse on only the disagreements. The necessity of this is clear when you have strong minded, hyper intelligent individuals who have built a reputation upon one theory (agenda). It helps to move back from offense and defense motives to objectivity.
Another great video. Going through our archives now lol
Thank God for bringing you to this world. Much love from Vietnam!
Gods have nothing to do with this stuff.
Hadn't heard of these before. Good stuff.
So the diagram actually modularizes the equation? And you can first define the interactions using the diagram and then add the specific "equation modules" for the particular parts? Not only does this clarify things but it must be a great time saver. Am I correct in thinking that in the sample equation given (unless you label the l or O in the diagram) there's no way to tell the direction of the photon?
A video giving an overview of the electroweak force theory would be very appreciated.
I don't know who the heck are disliking these videos!! Why are they disliking these awesome videos? Or... are the disliking count mistakenly raised by RUclips itself! I don't think that anybody would dislike it... Whether they are humans or cotton headed ninny muggings Neanderthals or indeed orangutans, everybody will understand this video! LOL... This is dang awesome... Thank you very much Dr. Lincoln... I want more videos!!!!!!!!!!!!!!!!!!!!!!!!!!!
Some years ago I bought some bumper stickers proclaiming "Feynman Lives" with one of his basic diagrams on it. Not sure if you can still get them.
Why use Feynman diagrams? Why not express these subatomic reactions in a way similar to ordinary chemical reactions?
What does the Feynman notation give us that ordinary stoichiometric-style chemical reaction equation notation does not?
Furthermore, thank you for showing how you turn these Feynman diagrams into mathematical equations as I have heard often claimed, but PLEASE FOLLOW THROUGH. NOBODY ELSE DOES THAT!
The most interesting Feynman diagram I can remember is one that shows how an electron is ejected from a photon.
Naimul Haq Just one electron??
do we have any idea if the interactions we experience ‘in our world’ are made of any one of these specific interactions or possibly a whole bunch of different ones that are nonspecific outside themselves
The basic idea of QED, is that individual interactions are probabilistic. They may or may not happen, and there's no way of knowing whether they will (no hidden variables). What we can calculate, is the probability of a some particular outcome (outgoing particles) based on some set of incoming particles.
When we consider huge collections of particles though, as are present in our macroscopic world, these probabilities in fact manifest themselves as a percentage of the time some particular outcome occurs. So to us, macroscopically, the world appears deterministic: when we flip a light-switch, a known percentage of electrons in a copper wire, will undergo known changes in momentum, thereby moving through a lightbulb filament, a known percentage of whose atoms will emit (real) photons, producing a known perceived intensity of light.
So we know on average what will happen, but can never know for certain how some particular electron or photon will behave. That's a matter of chance (at least according to QED)
Very good explanations
Is that probability factor around 1/100 by any change the fine structure constant? It would fit in this numeric region.
yes
No
maybe
Perhaps
Thank you!
If it will make him feel better, I wasn't thinking about Dr. Don Lincoln when he mentioned 'the icon'. The truth is, I clicked pause to read his name for the first time, after having watched dozens of 'that guy from Fermilab's' videos before. I wasn't thinking of Feynmann either - I've always known him as a diagram. I don't care about who says what as much as I care about what whoever says.
Can anyone explain how this stuff is so intuitive to these guys? How does one come up with these amazing models?
+Jimmy Mcrustler _"Can anyone explain how this stuff is so intuitive to these guys?"_
Lots and lots of training.
Alcohol and time. Two things that help
AndDiracisHisProphet
Alcohol doesn't help at all, and time doesn't help unless you use it to study.
Michael Sommers
Au contraire
AndDiracisHisProphet
So tell us about all the great advances in science made by elderly drunks who never studied any science.
Cloud chamber video showed electron. making a Circular shape. Is that because of an interaction? Or if that there's the shape they leave in a cloud chamber.
Just what the doctor ordered. Thank you.:)
Excellent explanation!
crazy explanation
Really well explained for the interested layman.
Good explanation, but an expression is not an equation. 4:58 You shouldn't use the term "solve the equation", but rather "evaluate the term" to get the probability amplitude.
Dr. Don Lincoln thanks a lot!!!!!!
The main problem of solving complex math equations, is how you are dedicated and willful to spend your "time" understanding the principals, ways, and symbols of how math actually works.If philosophy is hard than math is hard.When i solve equations i concentrate to think like a philosopher,symbols don't really matter cause they could be anything you can imagine,i than look for previous knowledge of different math fields.I am actually not that good in math i am just stubborn and curious as a child to find out what could come up of the equation vs theory do they match or are they contradictory, basically math is language of nature,likewise every language have most of meaningful words i look at it if i have to bind them together to make meaningful sentence,and from that you could write a poem,or a book,or a library of books,and so on and on.There are two kinds of understanding math 1.visualization 2.abstraction,like Feynman i am visualization kind of person.p.s sorry for my bad English :-)
Does Moller Scattering really happen when one electron is going forward and another is coming at the same electron at an angle?
Can you give more examples?
All in a shell 🐚. Reducing e- & positron to a 2-D event needed a fine man.
Sir uncle explains it the best 😝🙏❤️
Respect 🙏
2:10 Why would any electron start to fire off a photon to begin with ??, what initiates this photon emission ? and which electron starts to fire ? wouldnt that cost energy ?
I love ur videos
Sweet mercy, I didn't expect (4:37)! Extraordinary
if there is a point in time when the electron emits the potion and another point in time when the second one receives the photon why do they change path at the same time?
could you please draw in the time axis? because it actually kind of matters a lot... seeing only the diagram without the animations could make you think that there ist an annihilition followed by a pair production going on there...
@5:00 Oh my, I took particle physics as an elective as a CS student in my 4th year and I did have to learn the math!
I haven't understood much of this explanation!
Doesn't the x-axis of the Feynman diagrams represent time?
Therefore is the visualization valid?
Most adorable professor right there
you could have mentioned that a fermion moving forwards in time on the diagram is equivalent to an antifermion moving backwards in time, that would of intrigued a lot of people.
Doesn't the example diagram at 2:08 mean an electron-positron pair annihilating to form a photon, which then becomes another electron-positron pair?
Light moves at cosmic speed limit for matter but not space itself. How does heisenberg uncertainty not apply to a photon being exchanged at a finite speed between 2 moving electrons?
It's like the electron knows to shoot where it's going to be not where it's at.. does this mean light takes a curved path even on such small scales as electrons being close enough to make the exchange?
The principle of uncertainty definitely applies to photons and other intermediate particles of the reaction. That's why you can have a Feynman diagram involving virtual particles with much greater mass than the original particles. (The intermediate reactions may not obey the law of conservation of energy, as long as the overall reaction does.) As for why the photon actually hits the other electron - it has to. Otherwise, the diagram wouldn't correspond to an overall reaction of elastic scattering of two electrons (two electrons deflecting each other without emitting or absorbing other particles), but to a different reaction - two electrons encountering each other and emitting a photon.
Dr. Lincoln i have a question for you if you have time to respond lmk please ty God bless
Is mu first because its based on scale and its smaller?
Is the exchanged photon real or virtual?
But what are the coordinates
are these photons considered virtual photons / particles?
It makes more sense to me to think of photons as waves instead of particles, because the light of stars travel such a large distance, the only way they could get to us is if light itself is contiguous and not discreet. But that is demonstrated by the squiggly line in a feynman diagram. )
annihilationHaven stop. Just stop
May I ask what software is used to create the animations doctor?
Isn't g sub mu nyu the metric tensor fr om general relativity?
superb
I know you didn't mention it in the video, but why is energy not conserved at the vertex of a time-ordered feynman diagram?
it is conserved.
Make a video on quantum Zeno effect's affect on dark energy
i cried when I try to calculate S matrix without feynman diagram.
I tried using the Dyson series directly, but botched it because I got a result that was not unitary! What was I thinking?!
Wow, that math made me feel dumb ... as did some parts of the explanations.
Perhaps a dumb question but why does the diagram not show two electrons colliding? Why does there have to be an obligatory photon projectile (positive charged particle being shot out of a negative charged particle)?
On the other hand, Feynman diagrams now make a completely different sense
@@cartervu8308 so more of a wave function than a particle?
Because that is how forces are treated in quantum field theory, they are due to the exchange of "force carrier" particles.
Should have explained the horizontal axis is time, and the vertical axis is space near 2:00, and that many folks draw their Feynmann diagrams with time as the vertical axis.
What he fails to mention is what the equation represents. Does it give the probability of that interaction or something else?
thanks great video ✨
A virtual particle might make the math work but it’s a fudge number to make the observations match the math, right?
I have a doubt regarding QED .If the emission of a photon by an electron is probabilistic then how can it be that it always scatters electrons when they are shooted towards each other.
Most likely outcome.
what is the diagram for the Higgs please
Don't worry... you both are amazing... !!!
Please make a video about "Quantum spin liquid" :D
So it mean when i touch something. There is tiny "light" transfer between the electron?
Yes, if QED is correct.
If one electron emits a photon and another recieves, then one should be at a higher energy state than the other just after the collision.. isn't it?
What does his shirt say?
+ScienceNinjaDude Thanks.
where can i get ur t shirt ??? its cool!!
Do you have to understand the equations to structure the diagrams? or do the diagrams help you solve the equations? How in practice to the diagrams answer questions and measurements in physics? Where do you find a set of rules to draw those diagrams?
This Video is absolutely a fantastic intro to this science, but leaves one extremely frustrated,
I'm not implying giving a total understanding of the Feynman diagrams, but this video is just dangling a delicious fruit out of reach, maybe if you gave us 30 minutes not just 5 the video would not fustrate.
ah that should be part of the video, it's sort of is but roundabout. all videos can10 minutes, but even i got a message from youtube that my other channel had been enabled to an hour.
don't think so, if you check subscribers on different channels, the ones with the most have longer videos, Lincoln is making miscalculation if he is presenting science and disseminating the channel.
+Nite Explorer I'm pretty sure Fermilab starting doing these videos to try and make abstract theoretical physics SOMEWHAT comprehendible to the "layman". To get more into what he's talking about, you really do need that much physics education. I'm relatively far into my undergraduate degree and I am pretty sure that I will never cover what these equations mean for a good 5-10 years.
Chuck Tewkay i going to stop watching these video's they leave you frustrated
+Chuck Tewkay - It's still up to Fermilab, and a good suggestion of Nite imo to make a longer video about this. Maybe dr. X (sorry, I don't know his/your name) would like to consider making one, taking into account the suggestions of +sidewaysfcs0718 and +s3cr3tpassword below ?
Thank you for sharing! =)
so I have to learn more about tensors to use qed?
Not really; just the minkowski metric, g^μν in this video, which is just a fancy way of writing c²t²-x²-y²-z². But you WILL have to learn all about Dirac Bispinors, the I's and O's in the video. They make my head hurt :(