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Think Like a Physicist
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Добавлен 17 авг 2018
Science tells us what reality is. We look at the tools scientists use to find out how the universe works and show how these tools can be applied to everyday life. We talk about how scientific models improve over time, do some probability and statistics, and discuss how to choose appropriate models for given situations. Basically, how to Think Like a Physicist.
Why News Reports of Scientific Results Need to Include the Error Bars
Here, we demonstrate the importance of reporting error bars on scientific results and how critical information can be lost if they're not included when described in the media. We look at a case of a hypothetical new experimental result that "disagrees" with the Standard Model prediction, and a hypothetical older measurement than agrees. We ask: do these two experiments necessarily disagree with each other?
Просмотров: 217
Видео
Putting Too Much Confidence Into Anecdotal Evidence
Просмотров 2295 месяцев назад
Humans tend to often act based on anecdotal evidence. Here, we look at one common practice (asking a friend how their experience with a given choice or decision worked out) from a data-analysis standpoint, and see just how little this practice actually tells us that we can use for making our decision. We look at this in the context of hypothesis testing, relating this practice to p-values and s...
Why is There So Much Stuff About Statistics on This Channel?
Просмотров 2347 месяцев назад
Concepts from statistics are important for the data analysis done by physics experiments designed to discover new laws of nature. Here, we briefly mention some of the most important statistics concepts that come up in experimental physics and explain why they pop up so frequently. These include: the Poisson distribution, the Gaussian distribution (otherwise known as the normal distribution), th...
Why Do Scientific Predictions Have Error Bars?
Просмотров 2638 месяцев назад
In science, we make hypotheses and test them. Often, this means comparing the predicted value of some quantity in nature to its measured value. You might be aware that measurements have error bars, but predictions, do too! We recently saw an example of where the error bar on a scientific prediction was especially important: the new (2023) result on muon g-2 from Fermilab. Here, we look at some ...
Did the DONuT Experiment Discover the Tau Neutrino? Part 2
Просмотров 29111 месяцев назад
This is Part 2 in a 2-part series on the discovery of the tau neutrino. In Part 1, we discussed how the DONuT experiment was the first to directly observe the tau neutrino. Here, we argue that other, indirect experiments had already established that it existed. References: Initial DONuT paper: K. Kodama et al., Phys.Lett.B 504 (2001) 218-224, hep-ex/0012035. arxiv.org/pdf/hep-ex/0012035.pdf Fin...
The New (2023) Result from the Muon g-2 Experiment
Просмотров 5 тыс.Год назад
The Muon g-2 Experiment at Fermilab just released an updated measurement of the anomalous magnetic moment of the muon. This is an update of their 2021 result which showed a deviation from the Standard Model prediction of 4.2 sigma. There are many types of new physics that could first show up as a deviation in the measured value of muon g-2 from its value predicted in the Standard Model. So, thi...
Did the DONuT Experiment Discover the Tau Neutrino? Part 1
Просмотров 538Год назад
Here, we take a look at the DONuT experiment at Fermilab, which was the first experiment to directly detect the tau neutrino. It took its data in 1997 and published results in 2001 and 2008. We describe the relevant interactions of tau neutrinos, give an overview of the experiment, and discuss their results. References: Initial DONuT paper: K. Kodama et al., Phys.Lett.B 504 (2001) 218-224, hep-...
The Discovery of the Top Quark
Просмотров 1,7 тыс.Год назад
Here, we talk about the discovery of the top quark, which was announced simultaneously by the CDF and D0 experiments at the Tevatron at Fermilab in 1995. We talk about how the top quark interacts under the electromagnetic, strong, and weak forces, and then discuss how it was produced at the Tevatron and how it subsequently decayed. We discuss how CDF and D0 looked for the top quark, and show th...
What is the Probability that Your Probability Calculation is (Very) Wrong?
Просмотров 215Год назад
Often, when probabilities are quoted in real-life situations, they are treated as exact. But, probabilities have uncertainties and limited ranges of validity. Here, we look at on class of situations where it's important to keep this in mind. If we have a method of calculating probabilities that usually returns large-ish values, it can be easy to ignore small effects that can occasionally make t...
Updated Results from LHCb
Просмотров 876Год назад
This is an update to a previous video, "New Physics in LHCb data?" ruclips.net/video/0TjAbcAOcAk/видео.html where we look at new measurements of R_K and R_K* recently released by LHCb. Previous measurements of these quantities appeared to mildly disagree with the Standard Model and hinted at the possibility of lepton flavor violation. Their new results are in agreement with the Standard Model p...
The Particle Physics Results You Didn't Hear About
Просмотров 563Год назад
Experimental results in particle physics tend to only get the attention of the press if they disagree with the predictions of the Standard Model of particle physics. This presents a skewed view of particle physics results it picks out those results that are genuine discoveries, but also those where experimentalists got really unlucky. Here, we try to give a more complete picture of the body of ...
A Not Very Useful Headline About Floods
Просмотров 130Год назад
A Not Very Useful Headline About Floods
Feedback Requested: Turning Think Like a Physicist Into a Course
Просмотров 2192 года назад
Feedback Requested: Turning Think Like a Physicist Into a Course
When We Think Events are Independent and They're Not
Просмотров 2912 года назад
When We Think Events are Independent and They're Not
Just How Important is the CDF W Boson Measurement?
Просмотров 1,5 тыс.2 года назад
Just How Important is the CDF W Boson Measurement?
That New Fermilab Result on the W Boson Mass
Просмотров 9 тыс.2 года назад
That New Fermilab Result on the W Boson Mass
The Standard Model is (Probably) a Spherical Cow
Просмотров 1,1 тыс.2 года назад
The Standard Model is (Probably) a Spherical Cow
(Human) Time Scales in Particle Physics
Просмотров 3652 года назад
(Human) Time Scales in Particle Physics
The Mathematics of the Learned Hand Formula
Просмотров 9342 года назад
The Mathematics of the Learned Hand Formula
New Physics Involving the Tau Lepton?
Просмотров 1,1 тыс.2 года назад
New Physics Involving the Tau Lepton?
Thank you-you do a great job of explaining this issue! I have a friend, who was a computer science/physics double major, and he said that his comp sci classes used Bayesian statistics, whereas his physics classes used frequentist statistics. Do you think his experience is common, and if so, would it relate to physicists dealing with repeated experiments more than computer scientists?
Saving me with this one, cheers :)
erm what the sigma
;-)
Superb exposition. Understanding how to parse the language (once the data is in and the results processed) is crucial and your content is the best there is at helping with that. Thank you.
Many thanks! Trying to be a science translator. ;-)
When you revealed the slide at 07'45" it was like a light switch had been flipped; I could see exactly where this was going even though I was oblivious up to that point. You have real pedagogical talent in this domain; if the channel wasn't notionally "physicsy" or if you repackaged the content into a channel for medical and/or financial types, you'd have a bazillion views I think.
Much appreciated! I'm glad it helped. Hmmm.....I'll give some thought to how I can link the material to applications. Thanks for the input.
The neutrino flavor is a descriptive explanation. We know very little about them. Neutrino's masses are equal or different ? What is the mechanism to oscillate between flavours etc etc... we need much better and sensible sensores.
Hi! Their masses are different. Let's call those masses m1, m2, and m3. Here's the tricky part: the neutrino with a mass of m1 is not, say, the electron neutrino. The neutrino that has a mass of m1 is a combination of the 3 flavors of neutrinos. Similarly, the neutrino with mass m2 is also a combination of the 3 flavors, as is the neutrino with mass m3. A flavor of neutrino is determined by how it interacts with a charged lepton and a W boson. So, for example, if a W- decays to an electron and an anti-neutrino, that anti-neutrino is an electron anti-neutrino. The analogous is true for W- decays containing muons and taus. But, as we said above, this doesn't correspond to a specific mass of the anti-neutrino. If you have a bunch of W- bosons decay to an electron and an anti-neutrino, and you measured the anti-neutrino's mass, sometimes you'd get m1, sometimes m2, and sometimes m3! If that sounds weird, it's because it is. The fact that the neutrinos with definite masses do not have definite flavor (and vice-versa) is at the heart of neutrino oscillations. Understanding it pretty much requires knowledge of quantum mechanics. If you've got a bit of background on that, let me know, and I'll try to explain. Thanks!
Excellent video. You have a talent for verbal emphasis and pacing and an intonation that really works for RUclips educational content, and your extensive preparation shows. Thanks! I now have a much better understanding of the discovery 'standard' and, especially, how the language is parsed. I have a fundamental question though (from around 06'51"), where does the 8.33 come from? The entire edifice rests on that number. Sigma is generated from the 8.33 value not the other way around, right? If there is, shall we say, a degree of "pliability" in the 8.33 value in your example, then the conclusions we draw at the margins could be fundamentally unsound, right?
Hi! If the errors are gaussian (and, for practical situations, that is actually a big if!) then the 8.33 and sigma are one and the same. In that case, the scientists doing the measurement are taking the sigma from the gaussian error distribution and quoting that as their error bar. One can ask, "How do they determine the value of sigma?" In particle physics, the answer to that is usually a lot of very hard work. Often, determining the error bar is more difficult than measuring the central value (here, the 649.2). Basically, physicists will try to figure out every important source of error in their measurement that they can think of, and try to get a good estimate of how large each of those sources of error will typically be. This means that they have to study their own scientific equipment, to see how precise it is. They have to do extremely complex simulations of both the physics processes they're trying to study and the apparatus they are using. They need to take into account statistical errors caused by the fact that their dataset is not infinitely large. Etc. Then they take all of these sources of error, and combine their effects to get the overall error bar. Is that error bar infinitely precise? Nope. It is always possible that some of the estimates that go into the uncertainty calculation turn out to not be good enough. Sometimes an important source of error is missed entirely. I can only think of one example I have here which demonstrates how good or bad these uncertainty estimates turned out to be. You might want to check out the video How the Measured Lifetime of the Tau Lepton Changed Over 30 Years: ruclips.net/video/xrLllaBiSWM/видео.html Here, we can look back on many measurements of the tau lifetime, with their quoted error bars, and see if those error bars were actually reasonable. Those results were produced by many different groups over many years, and they did a pretty darn good job of estimating their uncertainties. Let me know if that answers (or starts to answer) your question. Thanks!
Thank You!!
halflife? Measured? Of an intermediate particle? We measure photons and electrons and protons and other stable particles. No one has ever measure Z W q and so on because they are intermediate particles. They end before the detector... Half life? It is a model dependent fairy tale... You are talking snowhite my beautiful girlie :3 <3 Along with all the other lunatics.. :D
At no point does she make any reference to a specific particle - this is a lecture on statistics in physics, not physics itself, and she is speaking in general terms to illustrate important features about testing these models (and does a good job of it!). There is no illusion here that a model tells you everything about the world, and what she is teaching is exactly how we go through the process of challenging a model and its predictions experimentally. I add that she is a professional physicist, speaks knowledgeably on the subject, and you only discredit yourself by arguing in such a condescending and infantile way.
@@aidenpeleg2789 You do realize your argument is a heap of errors in logic, don't you? The last one being Argumentum Ad Hominem. Not even once did you touch the actual objection.
@@Kraflyn I did not “touch the actual objection” because my only point was your objection did not apply to this video and is thus not in question. The “ad hominem” would only be a fallacy if I were using it as a part of my “argument”, but it is just an addendum here. Nonetheless, I don’t want to drag out a comments war on such a nice video.
@@aidenpeleg2789 There is no excuse for errors in logic... Finding an excuse is another error in logic! :D
girlie.. we do not measure any of those things you say... Probabilities... Energies... We just measure the shinings at the detectors in the wall. The whisps... All these things you talk about that we "measure"... It is a model... A theoretical model... I love you! <3
i see you still believe in humans.. :3
:D :D :D <3
This is true science! Many add jokes, frills but that's implying biases so I prefer to stay away from them. You are serious and informative. Thank you for your truthfulness.
Much appreciated!
wooow !!! awssome explenation !!!! 👌
Thank you!
Thanks
Oh, wow! Sorry, I just noticed your comment and donation (and also on the other video)! Apologies, it's been a hectic few weeks! Much appreciated.
Thanks
Thank you
Ha...great video
Can I get your clarify with 1/3.5 x 10^6 in 10:30? Isn't it a process of: 10^7/3, that is 3.3 x 10^-6, round it, 3 x 10^-7.
Hi! Are you just asking about the numerical result? It's approximately 1/(3.5 x 10^6), which comes out to about 3 x 10^-7. I'm not sure I've answered your question, though.
Since H0 and Ha actually doesn't have to have a large gap between them in numbers, they technically just don't need to be the same. As suggested, suppose Ha is greater than H0, gathered a sample of size n, found its mean x bar is greater than the u in H0, and under a standard deviation sigma of population, the probability of getting x bar or larger values out of all the sample means of size n is calculated. Set an significant level, which if it's very large, for example, 40%, if the probability calculated above is less than it, than the H0 is rejected. Meaning that, the sample suggests the original hypothesis underestimates the u, at least for 10% (50%-40%) of the original supposed distribution. So the better interval estimates could be, in order to not rejecting the new hypothesis, using the same sample data, [u +(0.4-p), x bar + invNorm(0.4, u, n)]. Right?
Hi! I don't think I'm quite understanding your question, but let's see how far I get..... You're setting alpha = 0.4. Then, under the null hypothesis, in 10% of trials, you'll get a result that is above the expected value of the null hypothesis, but close enough that you do not rule the null hypothesis out. Am I reading that correctly? If so, what is the question you're asking toward the end? Can you explain this a little more?
I just found your channel and am really enjoying it!! Your explanations are so clear and insightful and the subjects are chosen very well. Really deserves to be seen by more people!
Many thanks!
I'm a bit confused at the prior choice of 1% in the coin flipping example. If it were up to me, I would pick the prior to be 50% because I don't know anything about that coin, and I want to learn everything I can from the data. In that case, 5 flips will tell me (using the same equation that was shown) that the probability that it's a fair coin is 1.5/(50+1.5) so 2.9%. What is wrong with my reasoning?
Hi! So, the reason that the Bayesian chose 1% is that they have been through the exercise hundreds of times, and they've never actually seen one of the novelty coins perform as advertised (ie, always coming up heads); it has always turned out to be a fair coin. So, basically, the Bayesian goes in with the belief that the probability that the coin always comes up heads is small. So small, in fact, that the probability that it's a fair coin that just happens to come up heads 5 times in a row is larger. (Note that we didn't consider other scenarios, like that the coin comes up heads 60% of the time, which does admittedly make our example rather artificial.) The Bayesian prior always has a subjective element to it, based on the beliefs one has before the experiment is performed. As an alternative example, the Bayesian might look at the coin and say, "Oh, wait. This novelty coin is made by a different company than all the ones that I've seen before. In that case, I will not assign a high prior probability to it being a fair coin. OK, let's call the prior probabilities 50-50." If they do this, the probability that the coin is fair after the 5 flips (all coming up heads) is (50%*1/32)/(50%*1/32+50%) = 1/33. While the Bayesian prior always has an element of subjectivity, treating all hypotheses as equally likely before the experiment is done also has its pitfalls. The xkcd comic referenced in the video description illustrates this very well. ;-)
@@ThinkLikeaPhysicist OK.. But if we don't know anything about the coin, there is no subjectivity in choosing the prior. It will have to be 50%. I think the Bayesian analysis adds the ability to introduce a prior knowledge on the model (for example probability the coin is fair or biased). I don't know if there's a way to do that in the frequentist approach. Is there? But even if we forget about the prior, and we take the likelihood function, normalize it and interpret it as a probability of a truth given a measurement (like the probability that the coin is biased given 5 heads,) that to me is a much simpler and transparent way to state the result than the frequentist way. So if you tell me that the probabilty of that coin being fair is 3% given five flips that are all head, I will believe it and ask for you for more flips :) In the case of the sun going supernova in the xkcd comic, I am perfectly fine with the interpretation that it's true at 97% IF we know nothing about how often the sun goes supernova. But that's not the case :)
@@phyzwiz Hi! As for adding prior knowledge into a model in a frequentist approach.....well, let's say your prior knowledge is another experiment you did. In the context here, it would be a set of coin flips you've done before. So, you've got the coin flips you did before, and the coin flips you're about to do. You can take both of those sets of information and combine them into one big set of information. You can then ask, under a certain hypothesis, how strange the combined result is. In that sense, you can add prior information in in the frequentist approach--you take all experimental data, and ask how likely or strange the whole set of data is under a specific hypothesis. But, if you're asking for the probability, given some result, that a hypothesis is true, you are, by definition, asking a Bayesian question. The only way I can tell you that the probability that the coin is fair is 3% after coming up heads 5 times is if I am going the Bayesian route. And that requires choosing a prior, which is up to the person making the choice. It simply is not the case that P(coming up heads 5 times | coin is fair) is the same thing as P (coin is fair | came up heads 5 times). We can't do that.
Excellent. Thank you.
id say you sound fun to sit next to on a plane :D
erm what the sigma
I just learned what this meant. ;-)
It's impressive that some folks can follow this and say, "A-Ha!!! So THAT'S how they did that!"
I started watching your videos from the begining. They're so good that I don't want to miss any lesson :) Thank you!
Much appreciated! My older videos are a bit less polished than my newer ones!
My first thought on this was that the distribution is not a Poisson disrribution, but more of a fat tail distribution, power law or Levy. The main assumption that the events happen at a constant rate is that they are independent in time is probably not true. So it is possible for instance that while there were 1000 foods in the last million years, so 1 flood per 1000 years, most floods cluster in groups of 10 a year every 10000 years.
Yup, and if floods have a tendency to cluster, the headline is even less meaningful! Good observation, and thanks for the donations! Much appreciated!
Thanks!
Thanks!
Very good explanation and video
Hi! Questions?
hi
Hi again!
@@ThinkLikeaPhysicist <3
flavors? does that mean i can eat them?
Could you provide us with the coding you used for the plots?
Hi! I'm afraid that my plots are usually made using obscure software that almost nobody uses, so I'm afraid it won't be useful to you. But, if you have any questions about what formulas or parameters were used for certain plots, let me know, and I can probably round that up for you.
Thank you for nice and clear explanation. It was helpfull.
You are most welcome!
If you're getting your information from the "News" you are not about real science 😂thank you for this channel ❤
You're welcome!
It's never disheartening now i know that and it helps thank you 😊❤
Could the Z boson just be what I would call a heavy photon or photon with a tiny bit of mass? Or could a heavy photon theoretically exist as a stand alone particle? Could a heavy photon interact with the Higgs field?
Hi! Yes and no. It depends on specifically what characteristics of the photon you give to this heavy photon. The Z, like the photon, is a spin-1 particle. In that way, they are similar. And, we could imagine other (hypothetical) spin-1 particles which we might call "heavy photons". The Z gets its mass from its interactions with the Higgs field. (I'm guessing, from your question, that you already know this.) The photon does not interact directly with the Higgs field, and does not acquire a mass. So, what's the difference between the Z and the photon such that the Z interacts with the Higgs field and gets a mass, and the photon doesn't? So, these spin-1 particles ("gauge bosons" as we call these particles like the photon and Z) interact with other particles. How they interact are determined by the quantum numbers of the particles. In the case of the photon, the relevant quantum number is electric charge; the photon interacts with particles that are electrically charged (like the electron), but does not directly interact with particles that are not electrically charged (like the neutrino). As the Higgs boson is not charged, it does not interact with the photon. We can relate this to why the photon does not get a mass. The Z's interactions are determined by a different combination of quantum numbers, which the Higgs boson does have. And thus the Z interacts with the Higgs; this is related to why the Z does get a mass from the Higgs field. We could imagine another heavy spin-1 particle whose interactions are such that it does interact with the Higgs boson, and it gets a mass in a way similar to the way the Z does. So, if by "heavy photon", you mean a heavy spin-1 particle, then, yup, you can look at the Z or this other hypothetical particle as a heavy photon. On the other hand, if you mean a spin-1 particle that interacts with particles through their electric charge (and only their electric charge), then no. Does that help?
Your channel is one of the most useful channels on RUclips. I also support the thinking aspect of science more than the knowledge aspect.❤
Thanks!
Hey your audio is great! Thank you
Thankyou Thinklikeaphysicist I'm here for all I can get :-)
Hi! Questions?
I once did a Master's in stats, now I'm uncertain about everything.
As a Bayesian Conspirator, there's nothing I hate more than hearing about the Filthy Frequentists and their ongoing heresies. But at least the presenter had a very pretty voice to ease the pain.
Ha! I got quite a good laugh out of this. ;-)
@@ThinkLikeaPhysicist I used this video to introduce a young person to this contentious issue. Since then they found a paper on the differing neurology between hearing and seeing which just happened to contain several instances of the term "Bayesian Heuristic" and they won't stop talking about it. It is a very well done video. :)
@@leo5961 That's great! Glad it was of use! Thank you.
Thanks for the video! I find that everyone says that "lambda (or r in this case) * delta_t is the probability", but I can't quite wrap my head around it. How are we interpreting that value as a probability when it's just the expected number of times an event will occur in a given time. @3:59, why is that the probability, conceptually?
Hi! Let's take a very long time T. The expected (average) number of times the event will occur in this time T is r*T. Let's divide this interval T into N sub-intervals. We're going to take N to be really big, so that each sub-interval is really, really short, and the probability of the event occurring more than once in any sub-interval is so small that we can neglect it. Then, if there are r*T occurrences of the event, r*T sub-intervals contain an event, and the rest will not. So, we choose a sub-interval at random; what is the probability that it contains an event? Well, that would be the number of sub-intervals that contain an event, divided by the total number of sub-intervals. That would be r*T/N, but T/N=delta_t, so it's r*delta_t. Alternatively, instead of trying to get p from r, we could try to get r from p. If we take p to be the probability that a given sub-interval has an event in it, then, if we have N sub-intervals, on average, p*N of them will contain an event. If those N sub-intervals, put together, make a time T, then the average number of events in time T will be p*N. But N is T/delta_t. So, the average number of events in a time T is p*T/delta_t. If we call r*T the average number of events expected in time T, then r*T = p*T/delta_t, which means r=p/delta_t. We can then turn this into r*delta_t = p. Let me know if either of those explanations helps! Thanks!
@@ThinkLikeaPhysicist Wow... wow... wow. I am truly speechless (literally screenshotted your response)! I have been struggling to understand that concept for a while now (as many just stated it as a given), but your explanation is beyond wonderful, I really thank you so much and applaud you for this clear and vivid explanation. I really can't thank you enough! Subscribed for sure, and even though I am no Physicist (I adore Physics though), I love your explanation. Thanks again
Hello, thanks for the video! Just want to confirm that, so the 3.1 sigma discrepancy just disappeared in the new updated result from LHCb?
Yup, afraid so. The result comes in line with the SM prediction after they treat their backgrounds a little more carefully.
Can you explain the forward-backward asymmetry? thanks
Hi! Which forward-backward asymmetry do you have in mind? Are you interested in a specific experimental result?
@@ThinkLikeaPhysicist A classic example is in electron-positron collisions resulting in the production of quarks. If more quarks are emitted in the direction of the incoming electron than in the opposite direction, this indicates a forward-backward asymmetry.
@@55846 Hi! I'm afraid I don't think I'll get a chance to make a video on it soon, but I'll keep it in mind in case I see a way to work it in. Thanks!
The +/- 11 GeV/C² came from nowhere. How would you know this is equal to sigma?
Great question! It's not easy. Here, I'm talking about a case where systematic errors can be estimated from detailed experimental studies. (To contrast, in statistics texts, one will often see the case where something is measured many times, and one can look at the spread in results. That's not what I'm talking about here. Here, I'm talking about a case where something is measured once, and an error bar is quoted.) OK, so, then where does sigma come from? It's strongly dependent on the case at hand, and requires detailed knowledge of the experiment. An experimentalist will basically try to come up with every important source of error that they can think of, and estimate how large those errors are likely to affect the final result. They may simulate making the measurement many times. For example, let's say you want to measure the mass of a particle that decays in a particle detector. You have to measure the energies/momenta of all of its decay products and then use them to calculate the mass of the particle you're interested in. But, your detector's measurements of those energies and momenta are not infinitely precise; hopefully you can figure out just how good those energy and momentum measurements are. (One way you can do this is by examining other particle physics processes occurring in your detector that are already well-understood--you can compare what you see in your detector with what is already known from previous experiments.) Once you know how well your detector measures those energies and momenta, you have to calculate how the errors on those quantities can filter through to your mass measurement. But something like this is just 1 source of error. In practice, there are several or many important sources of error that have to be studied. And the effects of those sources of error have to all be included to estimate sigma. I fear what I've written above is a bit too complicated and specific, so I'll try to summarize: the people doing the experiment need to understand their equipment and methods really well, and then they need to estimate how wrong their measurements are likely to be. This is often a very complicated process; calculating an error bar may be one of the hardest parts of producing an experimental result.