Hey all, just wanted to add a quick addendum to the video: When calculating for the plot and animation for the expected rates, I missed the symmetry factors corresponding to identical particles in final-states, essentially double- (or more) counting in the integrals over phase space. For most of the rates, the difference isn't too large -- a factor of 2 or 4 -- but for the phi phi -> 4 theta interaction in particular, the rate should be suppressed by another factor of 1/4! due to the four identical final-state particles. I've updated the document and the code to reflect this properly, so that *should* be correct, but unfortunately, the video was already done when I found this mistake.
Physicist here: nice work - I am always on the hunt for trusty RUclipsrs that I can sent folks to when cornered at a cocktail party. Wish there were more truly knowledgeable presenter on physics out there like you. regards, DKB
Thank you for this followup and for trying to get an animation! Very clear and concise throughout but i especially appreciated the 2D detector illustration of the difference between classical and quantum starting around 8:00
I always wanted to make a video about how to get particles out of field modes using animations. I’ve never been so glad to be beaten to the punch. This is fantastic work! Specifically making it clear that “particle nature” is dependent on having a detector to even “make sense” - and doing the classical analogy is a damn great idea!
I was recently thinking a lot about how to actually visualize the interaction dynamics of QFT and now the algorithm presented me your amazing video! Great approach and thanks for sharing your work :)
This is my first time seeing visually how non-interacting QFTs containing a single particle compare to the nonrelativistic wave equation behavior. I've been wanting to see that!! Thanks!
9:30 - it is smearing out over space, because you can't predict the direction. As you pointed out, though, a massless quantum must travel at the speed of light, so it can't really smear out radially. It would if there was mass.
Thanks a lot for the great animations provided ! In fact we need to keep in mind that the the differential equations the animations are based on not only are hard or impossible to solve, and hence supposedly all we see are approximations that are rather close when restricting the scope in a sensible way, but also the differential equations themselves don't claim to be "true" but are built to be a decent fit to the experimental measurements being done. (AFAIU this is generally how physics works). Maybe there are completely different ways to mathematically (algorithmically) model "Physics", avoiding differential equations, i.e. producing those (i.e. QFTs) as a prediction shortcut. But OTOH this supposedly needs a such high resolution that trying to create a simulation on a computer might be impossible. This said: I seem to have seen that in the animation with relativistic probability curves the probability always is smooth between + and - infinity in location. This would mean that there is a non zero probability for speed greater c. Is this intentional ? Is this due to calculation limitation, or does this need a sophisticated interpretation.
Nicely done as always. For a different way to think about QFT, however, perhaps have a look at my talk to the Oxford Philosophy of Physics Seminar on October 24th, "A Dataset & Signal Analysis Interpretation of Quantum Field Theory", which can be found on my RUclips channel (as I post this comment it's the most recent video; there's a link in the video description to a PDF of the slides). Some of the content is published, however it's nonetheless quite raw. It's one of sadly few interpretations that are focused on QFT and it includes a way to rethink renormalization that looks very different from the perturbation theory and lattice QFT approaches that you mention at about 18:00.
Awesome video! I'm finishing my master's and absolutely love QFT. I'm a very visual person, and sometimes I get lost in the math without something to visualize-this helps a lot! :) Just a quick question: I haven't had time to read the PDF yet, but what exactly is being plotted as "QFT" at 12:26? Does it differ much from a Gaussian packet propagating in a classical Klein-Gordon field?
I have another question We can’t know the momentum or energy level the particle would have (see 7:28). My intuition here is with real-world photons - we have complete uncertainty of what their classical wavelength would be (as that is tied to momentum), and this seems to suggest that indeed photons of different wavelengths should not be understood as different particles, but rather “manifestations” of the same particle (which is something that was not intuitive to me before this video). Does this intution make sense? I also understand that, regardless of whether we prepared the initial state with a one-omega particle or a two-omega particle (as the two-omega particle can’t convert into two one-omega particles without interactions - see 4:30), we would have an infinitely large spread in energy and momentum. But is there in this case a qualitative difference in the nature of the one-omega and two-omega particles? Even though different photon wavelengths should not be seen as different particles, does it make more sense to treat the two-omega photon as its own particle? (as I understand that the system with one two-omega photon is measurably distinct from either the system with one one-omega photon or the system with two one-omega photons)
26:07 I’m seeing a couple of extra low-momentum thetas in this still frame actually - is there an explanation for this, or could this be a much rarer theta-theta-theta-theta-phi-phi event?
Good eye! In fact, if you look closely at this frame, you'll actually see that this capture contains a phi phi -> 4 theta (3 in the "upper" detector and one in the "lower" detector) event as well as a phi phi -> 2 phi 2 theta event! So, you may be wondering how we know which particles correspond to which event. The answer in this exact case is the fact that I used some "cooldown" period for the events to fade in the code, so when going frame-by-frame to find the events I was looking for, I was able to compare the previous frame to this one, in which the phi phi -> 2 phi 2 theta event was only in the latter, but the phi phi -> 4 theta was in both. However, in an actual experiment, this is much more difficult: What one would typically do is add up the deposited energies/momenta of the detected particles and then compare to the known initial-state energy/momentum of the two colliding particles. What one should find is that only certain groupings of particles reproduce the correct initial state quantities, and therefore you would know that this is a "complete" final state. As for a phi phi -> 4 theta 2 phi event, this does in principle exist, but it isn't included in this simulation, mainly because I didn't include it in the list of interactions. As you said, this is due to the fact that this interaction will be *much* rarer than the four listed, both because it receives its leading contributions at a higher-order in perturbation theory, and also because it receives a large suppression due to the smaller phase space of producing 6 particles instead of 4. If my estimate is correct, this should lead to a ~5 order of magnitude suppression of the rate compared to the rarest event shown (10^-2 from the additional coupling squared and 1/(8*pi)^2~10^-3 from the two phase-space factors). To put this into perspective, with the same parameters used to make the animation in the video, one would need a simulation that lasts ~1 day or so to expect to see a single event. Needless to say that, for a 15 second animation, this is entirely negligible!
Awesome - thank you for the great explanation and for the excellent video! Makes sense that just like the four-theta events stand out from the “background” of the two-theta events, momentum sorting can help identify the origin of the detected particles even in more complex interactions like this one
Thank you! As for books, this is always a bit difficult of a question because it very much depends on your level, how you learn, and what you want to get out of it. I personally have the somewhat controversial opinion that Weinberg is a great book to learn the subject, and is typically my go-to resource. The thing I like about it is that he takes a unique approach of first constructing all of the possible Lorentz-invariant single-particle states, proves some very important principles corresponding to what one actually wants to calculate and only then shows how this is all accomplished by quantum fields. This is in contrast to pretty much every other text (that I have read, at least) which usually assumes a field theory, quantizes it, and then builds upon that. So I would personally say that if you want a strong conceptual understanding of the topic, this book is the way to go. The main drawback of Weinberg is that he tends to be a bit...verbose, and he doesn't really pull any punches. This means that I usually have to read a section several times before it actually sinks in what he is trying to get across, but you may have a different experience. Another thing you have to be a bit careful of is that Weinberg sometimes uses some outdated/non-standard conventions, so some of his results may look a bit different than what appears in other texts. That said, if you want something where you can more immediately get into calculating in QFTs, and don't really care as much about a comprehensive conceptual understanding, I would go with Peskin and Schroeder. This book doesn't really get into the weeds as much, but instead typically gets straight to the point of what you need in order to do practical computations. Many people also swear by Schwartz as a good middle ground between these two books, which I would agree with to some extent, though I don't always love his notation. However, I'm not as familiar with this book, so I can't comment too much on it. Hopefully that helps!
To briefly describe what you are doing in the first part of your video, are you computing something like to get the propagation from an initial position y to x (where x0 > y0), and for a general wave packet with uncertainty in position you take a superposition from multiple starting positions y, or ∫ d4y f(y) ? For reference I'm only in the 2nd chapter of Peskin's book.
Very cool! Thank you! L I’m looking forward to the future video(s) you mentioned :) Questions: My understanding is that in a QFT, even in the vacuum state, many observables wouldn’t have definite values - is that correct? (In case I’m using terminology in a nonstandard way: by “definite values”, I mean like, such that the state is an eigenstate of the observable operator, or, where the variance of the observable is zero in the state in question.) If that’s correct, are there reasonable ways to visualize, uh, the vacuum state? I mean, I get that the vacuum state is Lorentz invariant, so it should be uniform, and so I guess in some sense it would look like nothing (which is fitting for it being the vacuum), but what if visualizing something like… something about some observable? Oh, I guess maybe the thing would be the 2 point correlation function(?), but I guess you said that would be too hard to compute at least in the interacting case? Hm, what about the 2-point correlation function in the case of the free field, where you hold one of the two points constant at a particular time and place? Or would that pretty much be the same picture with the ring expanding outwards?
Good questions! It's always a bit tricky to talk about the vacuum in QFT since, but I will give it a shot. Perhaps the best way to think of the vacuum is not necessarily the state which has zero particles in it (since this turns out to be an observer-dependent quantity), but instead the state which has the least amount of energy possible. I talked about this a bit in my video on spontaneous symmetry breaking: the zero-particle state doesn't always align with the state of minimum energy, and depends on the notion of how one defines a particle in their theory. If these don't align, then one sees a minimum-energy state filled with particles. However, it is often most convenient to instead work in the case where the two states align. Of course, this is straightforward in the free theory because the particle spectrum and energy eigenstates can be found from those of the simple harmonic oscillator. Then, as you said, this vacuum state is not an eigenstate of many different operators (e.g. field operators), which leads to the interesting dynamics of the theory. The two-point correlator that you mentioned is exactly what is shown in the ring expanding outward (for the massless theory) as well as the animations featuring the comparison between the QFT and single-particle Schroedinger equation (for the massive theory). In interacting theories, this becomes more problematic because, in order to define the lowest-energy state, you must know the energy spectrum (i.e. energy eigenstates) of the theory, and in order to define the zero-particle state, you must have a notion of how to define particles in the theory. It isn't known how to do either of these in a generic interacting QFT, making the interpretation of the vacuum very difficult in such theories.
There is no PDF file with your more detailed explanations, nor any reference to a github site with code. I'd like to get a copy of both the pdf and the code that you've written, if that's possible. Thanks.
Bravo! Could it be that time is negligible at quantum levels and faster than light speed occurs but we find it hard to detect because we can’t factor in time (ie., the per/sec ‘time’ in c approaches zero…or infinity..)?
As far as we know, quantum systems still experience time in a "normal" way, in that the evolution of quantum systems can be described with the same time parameter as classical systems, i.e. quantum clocks still "tick" like classical ones. This is actually very important for building a relativistic theory of quantum mechanics because in special relativity, time isn't really treated differently than space, and in fact, what one observer calls time and space in their reference frame can mix together to form the time and space that another observer experiences. So if time were in any way "special" as compared to space in quantum mechanics, there would really be no way to construct a Lorentz-invariant theory of quantum mechanics! Hopefully I understood your question correctly, but if not feel free to ask any more questions!
This video makes me wanna break out my shark vacuum a couple magnets a bottle of white zinfandel on ice and go to town . Sorry i just couldn't hold back .
On how to visualise QFT calculations, Ive tried giving it a shot myself. From my working, I think it’s easier to show off the underlying concepts of fields coupling, which can be classically understood, then lifting that intuition into Feynman diagrams. ruclips.net/video/mFI7ZVUuZsY/видео.html Ive been out of touch with QFT since then, so am interested to hear your opinion on it, if you’ve seen this idea already, or just what you had in mind.
Hi, thanks for the suggestions and for sharing the video! I've had a watch and would be happy to have a bit of a discussion about the content. Overall, I definitely agree that a good first step is appealing to classical intuition -- in fact, this is exactly how I approached the discussion in the original video. I like the idea of doing this particularly to show how classical fields can couple to introduce non-trivial dynamics in a field theory. That said, I think that one must be very cautious when comparing the classical and quantum theories, since, although they can often look similar, the physics that they are describing tends to be *very* different. In particular, I personally find the extrapolation of classical field couplings to perturbation theory (subtle point: Feynman diagrams are a tool to efficiently perform perturbative calculations -- Feynman did not invent perturbation theory and one does not need Feynman diagrams to use perturbation theory) a bit misleading, and I think that similar explanations have led to some major misconceptions that I saw a bit in the comments of my last QFT video. It is always important to recall what one actually calculates in any physical theory; in the case of a QFT, one is calculating correlation functions of field insertions at particular spacetime points. Therefore, we can only ever definitively describe the probability distributions of making field measurements at these points, and we can never actually say what happens in between these measurements. So the "perturbative notion" that the particles are bouncing back and forth between different field types as it traverses between measurements doesn't really make a ton of physical sense since we can never actually assign a history between these points. Hopefully that all makes sense and like I said, I'm always open to more discussion!
We can compare qft to classical fields except for the "details", right? 😅 Like how we model and write particles with annihilation operator and a creation operation in another field and that instantly happens, cause symmetries, let's Gauge it and couple several fields using transients, cause we Heisenberg them too short 😅 Then we renormalise, infinity can't be really present in our lab experiments, stupid perturbation theory 😁 😳 😟 😔 So much for "classical" 🤣 Nice animations, good work, good approach to this topic 👍🖖
Hey all, just wanted to add a quick addendum to the video:
When calculating for the plot and animation for the expected rates, I missed the symmetry factors corresponding to identical particles in final-states, essentially double- (or more) counting in the integrals over phase space. For most of the rates, the difference isn't too large -- a factor of 2 or 4 -- but for the phi phi -> 4 theta interaction in particular, the rate should be suppressed by another factor of 1/4! due to the four identical final-state particles.
I've updated the document and the code to reflect this properly, so that *should* be correct, but unfortunately, the video was already done when I found this mistake.
Ha! I made the same errors during calculations for my masters thesis.
Ok thanks for the update.
Physicist here: nice work - I am always on the hunt for trusty RUclipsrs that I can sent folks to when cornered at a cocktail party. Wish there were more truly knowledgeable presenter on physics out there like you. regards, DKB
The amount of talent that vent into this video is through the roof
Thank you! That is very high praise coming from the great Higgsino Physics!
Thank you for this followup and for trying to get an animation! Very clear and concise throughout but i especially appreciated the 2D detector illustration of the difference between classical and quantum starting around 8:00
great video , nice time to publish it.
Yes, the video is good. Is this an especially good time to publish it? Did something happen?
I always wanted to make a video about how to get particles out of field modes using animations. I’ve never been so glad to be beaten to the punch. This is fantastic work!
Specifically making it clear that “particle nature” is dependent on having a detector to even “make sense” - and doing the classical analogy is a damn great idea!
I was recently thinking a lot about how to actually visualize the interaction dynamics of QFT and now the algorithm presented me your amazing video! Great approach and thanks for sharing your work :)
Wow, this is beautiful work! I've always been curious about how QFT works, as well as its implications for the Schroedinger equation
Oh, good - this material at 3-6 minutes in is valuable. This is something I'd always scratched my head over, and you clarified it for me. Thank you.
I’m wholeheartedly appreciative of all your beneficial contributions and presentations about Physics.
This is so perfectly timely for me since I'm just now getting to the interaction part of my QFT course. Thank you!
This is my first time seeing visually how non-interacting QFTs containing a single particle compare to the nonrelativistic wave equation behavior. I've been wanting to see that!! Thanks!
This is a very unique and helpful presentation of the topic! Well done!
We love your contents. Thanks for sharing this amazing knowledge with us. Amazing efforts .. Thanks!
9:30 - it is smearing out over space, because you can't predict the direction. As you pointed out, though, a massless quantum must travel at the speed of light, so it can't really smear out radially. It would if there was mass.
Thanks a lot for the great animations provided !
In fact we need to keep in mind that the the differential equations the animations are based on not only are hard or impossible to solve, and hence supposedly all we see are approximations that are rather close when restricting the scope in a sensible way, but also the differential equations themselves don't claim to be "true" but are built to be a decent fit to the experimental measurements being done. (AFAIU this is generally how physics works). Maybe there are completely different ways to mathematically (algorithmically) model "Physics", avoiding differential equations, i.e. producing those (i.e. QFTs) as a prediction shortcut. But OTOH this supposedly needs a such high resolution that trying to create a simulation on a computer might be impossible.
This said: I seem to have seen that in the animation with relativistic probability curves the probability always is smooth between + and - infinity in location. This would mean that there is a non zero probability for speed greater c. Is this intentional ? Is this due to calculation limitation, or does this need a sophisticated interpretation.
Nicely done as always. For a different way to think about QFT, however, perhaps have a look at my talk to the Oxford Philosophy of Physics Seminar on October 24th, "A Dataset & Signal Analysis Interpretation of Quantum Field Theory", which can be found on my RUclips channel (as I post this comment it's the most recent video; there's a link in the video description to a PDF of the slides). Some of the content is published, however it's nonetheless quite raw. It's one of sadly few interpretations that are focused on QFT and it includes a way to rethink renormalization that looks very different from the perturbation theory and lattice QFT approaches that you mention at about 18:00.
Very good video.
Awesome video! I'm finishing my master's and absolutely love QFT. I'm a very visual person, and sometimes I get lost in the math without something to visualize-this helps a lot! :) Just a quick question: I haven't had time to read the PDF yet, but what exactly is being plotted as "QFT" at 12:26? Does it differ much from a Gaussian packet propagating in a classical Klein-Gordon field?
The king has returned 🫡
Thanks this was really cool!
This is great, thanks!
I have another question
We can’t know the momentum or energy level the particle would have (see 7:28). My intuition here is with real-world photons - we have complete uncertainty of what their classical wavelength would be (as that is tied to momentum), and this seems to suggest that indeed photons of different wavelengths should not be understood as different particles, but rather “manifestations” of the same particle (which is something that was not intuitive to me before this video). Does this intution make sense?
I also understand that, regardless of whether we prepared the initial state with a one-omega particle or a two-omega particle (as the two-omega particle can’t convert into two one-omega particles without interactions - see 4:30), we would have an infinitely large spread in energy and momentum. But is there in this case a qualitative difference in the nature of the one-omega and two-omega particles? Even though different photon wavelengths should not be seen as different particles, does it make more sense to treat the two-omega photon as its own particle? (as I understand that the system with one two-omega photon is measurably distinct from either the system with one one-omega photon or the system with two one-omega photons)
@13:00 aren't you talking about a quantized version of the Freud number?
erm i just collapsed my wave function on this video
26:07 I’m seeing a couple of extra low-momentum thetas in this still frame actually - is there an explanation for this, or could this be a much rarer theta-theta-theta-theta-phi-phi event?
Good eye! In fact, if you look closely at this frame, you'll actually see that this capture contains a phi phi -> 4 theta (3 in the "upper" detector and one in the "lower" detector) event as well as a phi phi -> 2 phi 2 theta event! So, you may be wondering how we know which particles correspond to which event. The answer in this exact case is the fact that I used some "cooldown" period for the events to fade in the code, so when going frame-by-frame to find the events I was looking for, I was able to compare the previous frame to this one, in which the phi phi -> 2 phi 2 theta event was only in the latter, but the phi phi -> 4 theta was in both.
However, in an actual experiment, this is much more difficult: What one would typically do is add up the deposited energies/momenta of the detected particles and then compare to the known initial-state energy/momentum of the two colliding particles. What one should find is that only certain groupings of particles reproduce the correct initial state quantities, and therefore you would know that this is a "complete" final state.
As for a phi phi -> 4 theta 2 phi event, this does in principle exist, but it isn't included in this simulation, mainly because I didn't include it in the list of interactions. As you said, this is due to the fact that this interaction will be *much* rarer than the four listed, both because it receives its leading contributions at a higher-order in perturbation theory, and also because it receives a large suppression due to the smaller phase space of producing 6 particles instead of 4. If my estimate is correct, this should lead to a ~5 order of magnitude suppression of the rate compared to the rarest event shown (10^-2 from the additional coupling squared and 1/(8*pi)^2~10^-3 from the two phase-space factors). To put this into perspective, with the same parameters used to make the animation in the video, one would need a simulation that lasts ~1 day or so to expect to see a single event. Needless to say that, for a 15 second animation, this is entirely negligible!
Awesome - thank you for the great explanation and for the excellent video! Makes sense that just like the four-theta events stand out from the “background” of the two-theta events, momentum sorting can help identify the origin of the detected particles even in more complex interactions like this one
Cool vid! Are there any books you recommend for learning QFT?
Thank you!
As for books, this is always a bit difficult of a question because it very much depends on your level, how you learn, and what you want to get out of it. I personally have the somewhat controversial opinion that Weinberg is a great book to learn the subject, and is typically my go-to resource. The thing I like about it is that he takes a unique approach of first constructing all of the possible Lorentz-invariant single-particle states, proves some very important principles corresponding to what one actually wants to calculate and only then shows how this is all accomplished by quantum fields. This is in contrast to pretty much every other text (that I have read, at least) which usually assumes a field theory, quantizes it, and then builds upon that. So I would personally say that if you want a strong conceptual understanding of the topic, this book is the way to go.
The main drawback of Weinberg is that he tends to be a bit...verbose, and he doesn't really pull any punches. This means that I usually have to read a section several times before it actually sinks in what he is trying to get across, but you may have a different experience. Another thing you have to be a bit careful of is that Weinberg sometimes uses some outdated/non-standard conventions, so some of his results may look a bit different than what appears in other texts.
That said, if you want something where you can more immediately get into calculating in QFTs, and don't really care as much about a comprehensive conceptual understanding, I would go with Peskin and Schroeder. This book doesn't really get into the weeds as much, but instead typically gets straight to the point of what you need in order to do practical computations.
Many people also swear by Schwartz as a good middle ground between these two books, which I would agree with to some extent, though I don't always love his notation. However, I'm not as familiar with this book, so I can't comment too much on it.
Hopefully that helps!
Please do a vid about electromagnetism
This guy understands physics. He uses imagination just like Einstein. Cool stuff
Great video!
To briefly describe what you are doing in the first part of your video, are you computing something like to get the propagation from an initial position y to x (where x0 > y0), and for a general wave packet with uncertainty in position you take a superposition from multiple starting positions y, or ∫ d4y f(y) ? For reference I'm only in the 2nd chapter of Peskin's book.
Very cool! Thank you! L
I’m looking forward to the future video(s) you mentioned :)
Questions: My understanding is that in a QFT, even in the vacuum state, many observables wouldn’t have definite values - is that correct? (In case I’m using terminology in a nonstandard way: by “definite values”, I mean like, such that the state is an eigenstate of the observable operator, or, where the variance of the observable is zero in the state in question.)
If that’s correct, are there reasonable ways to visualize, uh, the vacuum state?
I mean, I get that the vacuum state is Lorentz invariant, so it should be uniform, and so I guess in some sense it would look like nothing (which is fitting for it being the vacuum),
but what if visualizing something like…
something about some observable?
Oh, I guess maybe the thing would be the 2 point correlation function(?), but I guess you said that would be too hard to compute at least in the interacting case?
Hm, what about the 2-point correlation function in the case of the free field, where you hold one of the two points constant at a particular time and place?
Or would that pretty much be the same picture with the ring expanding outwards?
Good questions! It's always a bit tricky to talk about the vacuum in QFT since, but I will give it a shot.
Perhaps the best way to think of the vacuum is not necessarily the state which has zero particles in it (since this turns out to be an observer-dependent quantity), but instead the state which has the least amount of energy possible. I talked about this a bit in my video on spontaneous symmetry breaking: the zero-particle state doesn't always align with the state of minimum energy, and depends on the notion of how one defines a particle in their theory. If these don't align, then one sees a minimum-energy state filled with particles. However, it is often most convenient to instead work in the case where the two states align.
Of course, this is straightforward in the free theory because the particle spectrum and energy eigenstates can be found from those of the simple harmonic oscillator. Then, as you said, this vacuum state is not an eigenstate of many different operators (e.g. field operators), which leads to the interesting dynamics of the theory. The two-point correlator that you mentioned is exactly what is shown in the ring expanding outward (for the massless theory) as well as the animations featuring the comparison between the QFT and single-particle Schroedinger equation (for the massive theory).
In interacting theories, this becomes more problematic because, in order to define the lowest-energy state, you must know the energy spectrum (i.e. energy eigenstates) of the theory, and in order to define the zero-particle state, you must have a notion of how to define particles in the theory. It isn't known how to do either of these in a generic interacting QFT, making the interpretation of the vacuum very difficult in such theories.
@ Thank you!
There is no PDF file with your more detailed explanations, nor any reference to a github site with code. I'd like to get a copy of both the pdf and the code that you've written, if that's possible. Thanks.
Ah! Never mind. I found the github link.
Bravo!
Could it be that time is negligible at quantum levels and faster than light speed occurs but we find it hard to detect because we can’t factor in time (ie., the per/sec ‘time’ in c approaches zero…or infinity..)?
As far as we know, quantum systems still experience time in a "normal" way, in that the evolution of quantum systems can be described with the same time parameter as classical systems, i.e. quantum clocks still "tick" like classical ones. This is actually very important for building a relativistic theory of quantum mechanics because in special relativity, time isn't really treated differently than space, and in fact, what one observer calls time and space in their reference frame can mix together to form the time and space that another observer experiences. So if time were in any way "special" as compared to space in quantum mechanics, there would really be no way to construct a Lorentz-invariant theory of quantum mechanics!
Hopefully I understood your question correctly, but if not feel free to ask any more questions!
This video makes me wanna break out my shark vacuum a couple magnets a bottle of white zinfandel on ice and go to town . Sorry i just couldn't hold back .
On how to visualise QFT calculations, Ive tried giving it a shot myself.
From my working, I think it’s easier to show off the underlying concepts of fields coupling, which can be classically understood, then lifting that intuition into Feynman diagrams.
ruclips.net/video/mFI7ZVUuZsY/видео.html
Ive been out of touch with QFT since then, so am interested to hear your opinion on it, if you’ve seen this idea already, or just what you had in mind.
Hi, thanks for the suggestions and for sharing the video! I've had a watch and would be happy to have a bit of a discussion about the content.
Overall, I definitely agree that a good first step is appealing to classical intuition -- in fact, this is exactly how I approached the discussion in the original video. I like the idea of doing this particularly to show how classical fields can couple to introduce non-trivial dynamics in a field theory. That said, I think that one must be very cautious when comparing the classical and quantum theories, since, although they can often look similar, the physics that they are describing tends to be *very* different.
In particular, I personally find the extrapolation of classical field couplings to perturbation theory (subtle point: Feynman diagrams are a tool to efficiently perform perturbative calculations -- Feynman did not invent perturbation theory and one does not need Feynman diagrams to use perturbation theory) a bit misleading, and I think that similar explanations have led to some major misconceptions that I saw a bit in the comments of my last QFT video. It is always important to recall what one actually calculates in any physical theory; in the case of a QFT, one is calculating correlation functions of field insertions at particular spacetime points. Therefore, we can only ever definitively describe the probability distributions of making field measurements at these points, and we can never actually say what happens in between these measurements. So the "perturbative notion" that the particles are bouncing back and forth between different field types as it traverses between measurements doesn't really make a ton of physical sense since we can never actually assign a history between these points.
Hopefully that all makes sense and like I said, I'm always open to more discussion!
Happy 2025! I only made it 20 pages in Weinberg’s “quantum theory of fields” before I couldn’t follow how one equation implied the next ha ha
We can compare qft to classical fields except for the "details", right? 😅
Like how we model and write particles with annihilation operator and a creation operation in another field and that instantly happens, cause symmetries, let's Gauge it and couple several fields using transients, cause we Heisenberg them too short 😅
Then we renormalise, infinity can't be really present in our lab experiments, stupid perturbation theory 😁
😳 😟 😔 So much for "classical" 🤣
Nice animations, good work, good approach to this topic 👍🖖
The sound is very low.
You misspelled Æther dynamics
Quantum is a click bait paycheck word for fools 😂.