Horizon Radiation
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- Äas pĆidĂĄn 16. 01. 2018
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Learn about Horizon radiation and why it's essential for us to understand as we continue our journey towards the Unruh Effect and Hawking Radiation.
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Both theories of relativity, special and general, tell us that many things are observer dependent. Different observers might disagree about the speeds, lengths, or times, but the laws of physics should be the same for everyone. And for two observers with very different, but constant speeds - inertial observers - the vacuum itself should appear the same.
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"As simple as we can, but no simpler."
What a brilliant summary of what makes this show as distinguished and as amazing as it is.
Long time listener, first time caller. WOWOAH YOU JUST BLEW MY MIND. Such a succinct and clear analogy! Here I was my whole life thinking Hawking radiation is just have a virtual particle falling off the wrong side of the fence and some how you've made me see the connections between QFT, event horizons, vacuum energy, Fourier transforms all in the same episode. You guys are honestly one of the best things on the internet, and it's a damn shame we don't live in a world where y'all are more famous than Beyonce. :) THANKS GUYS!
when I think I'm doing well and I think I've been quite clever, I come here a sit with my mouth open and say to myself "i need to re-watch this over and over and over and I bet I'm still stupid after that". Sometimes I understand things and get excited and then I'm lost within moments again.
knowlage isn't equaly inteligenz.
See, I'm in the habit of running through CZcams videos in the background while doing other things, like folding my laundry or writing. Then I get halfway through a PBS Space Time video, realize I have no idea what's going on, and I have to restart it and actually watch.
The clergy in Europe in the Medieval age spoke in Latin so nobody but elites could understand them.
Pepper Spray Almost right: They spoke in Latin so they could all understand one another. They refused to stop in the Renaissance so no one could understand them.
Haha lol
I don't know what he's saying, but I like it! PBS Spacetime helps maintain humility.
I like Turtles
It is really easy. It is like analyzing electrical signals that we do in university instead they analyze the oscillations in the space.
This video is like the horizon. I can move toward it and keep coming back forever, but I'll never get it :-(
i'm an undergraduate senior studying physics at an esteemed university and I still don't understand a lot of it. (except fourier transforms which are lovely)
I think watching all the preceding videos in this particular series back to back will help. :)
Acceleration can create an event horizon just like gravity can via Einstein's equivalence principle.
Im hoping that one day after watching enough of these (and over and over again) i will suddenly have a moment of clarity.
Xperim well actually acceleration can give rise to an effect similar to Hawking radiation, the Unruh effect:)
I understood the part where you hit a drum and it makes a noise. Can somebody explain the rest to me?
You can hit a space-drum to make noise, this noise is 'Nothing here'. If you then poke a hole in the drum the drum is different, it's changed. You can't hit it the same way to make the 'nothing here' sound, no matter how you hit it you'll only make a 'something here' sound that's a little bit different from the original drum.
The rest is the same, only Fourier-transformed and quantized :)
NOPE
Last time I was this early the universe was still opaque
I'm afraid this comment travels back and forth in time and shows up in a lot of spacetime's videos.
Ferdinand Kraft I'm sorry but your comment make me feel a bit violated.
That's too bad. Premature ejactulation is no fun. Try taking a couple shots of gin first.
I love how the video starts off pretty chill and then later turns into an intuitive explanation of the field operator. I mean thatâs something most QFT books and courses struggle with. :D
One of the best, purest videos you've made. It's not as exciting as Strange Stars, but its able to be followed, and it is a culmination of so many lessons.
Epic. Stoked for next set of videos. Solid mind blow. You've gotta be one of the best in your field to be able to write this stuff. Well explained, succinct, and always pleasurable experience. Thanks for giving me a second college degree.
Exciting stuff! I gobble up these episodes with joy! Thank you very much for keeping the knowledge flowing!
Superb content as per usual, glad to see a channel actually thought-provoking physics content, keep up the good work.
So cool! Can't wait to finally understand Hawking radiation!
I'll hold my clever and probing comment for when you explain some more of this.
You stopped just when things got interesting, you TEASE!
MrRolnicek same
Hes a showmam. Always leave them wanting more ;)
Science-Tyrion really left a cliffhanger right over there
None of this is in the Bible. Fake News!!!
Jesus voted for Trump and was packing heat when he did it.
Finally, I was waiting for this! Congratulations for the videos!
i am perpetually blown away by how accessible the information presented is made by the guy. really well done. can't stop watching
I m gonna watch it 3 times so, I can understand for today.
ooooh look at genuis over here only watching it 3 times lol
Make it infinite times for me, I am afraid.
"for today" đ
Amrut Prasad Sethy the for today bit is just too true
Exactly.))
As an undergraduate studying Astronomy & Astrophysics, watching this show constantly assures me that I've made the right path in life. Thanks for doing what you do.
The best show ever!!!!!!! You are explaining one of the most difficult and counter-intuitive ideas in physics in a brilliant way!!! I hope this show never ends!
I'm amazed with how much SpaceTime is developing us so we can understand QFT and Hawking Radiation, most of my professors don't put so much effort in to teaching. I am loving it, thank you so much for all of this
If the Neutron Stars have iron surfaces, do they sound like heavy metal? \m/
Empire Empire - Neutron stars are what heavy metal would be like if you subjected a few billion billion billion tons of it to a few billion billion billion atmospheres of pressure, obliterating its atoms by forcing all its electrons into nuclear reactions, squeezing a million tons of it into every cubic millimetre, heating it to a trillion degrees, giving it a magnetic field billions of times higher than anything possible with iron and maybe leaving the whole thing spinning several hundred times a second. Itâs way more metal than metal
rad858 Pretty accurate.
It'll be to hard for any of our ears xD
+rad858
But the crust of a neutron star is indeed predicted to be made of elemental iron. It would still be at extremely high temperature and pressure, but it would not be the "nuclear pasta" we predict in the interior.
Perhaps they sound like Metallica's Orion :)
Nice. I wait every week for your episodes!
Amazing episode, I really discover a new concept here. Looking forward for next ones !
A spectacular instalment. I'm taking a lot away from this, Spacetime team; Jouissance! I'll be sure to watch it once more come Sunday.
The Quantum Field Operator: Learn to Play the Phi-hat. Budumtsss
Can you guys start colour coordinating the components in your equations to make them easier to break down and understand?
that would be nice.
I would hate that!
Jim Fupanda Why?
I do that in my presentations sometimes, but I feel like an alien because nobody else does it.
_Start_ color coordinating components in the equations? I'm curious why they stopped in this one. Go back over some past episodes, and you'll see that's actually been done before on this channel. Iirc, the components of Einstein's field equation were color-coded to give a better idea of what, exactly, Î is supposed to mean.
Blowing my mind, every time. Your videos are the perfect mix between ELI5 and actual science.
Great video and bizarrely good timing. My department were just discussing Hawking radiation in our last journal club.
So looking forward to the Hawking-radiation vid ;)
It will fly over most peoples heads. This one was just the beginning.
14:20 I had a very similar impression of Penrose's theory, as he exposits in The Emperor's New Mind. Clearly Roger Penrose is quite smart and a brilliant physicist, but the support he draws on for his quantum microtubules theory from outside his field is basically mistaken.
Where he tries to use computer science, he is simply wrong and we programmers know it as an everyday thing. For instance, he feels an unbridgeable gulf between the human brain and a computer because the former processes information in parallel. Except the concept he actually needs for his argument, multithreading, has been done on computers for decades, and even hardware multiprocessing is now quite common.
Crucial to his argument is the idea that humans can understand Goedel's undecidability and that proves that the human mind transcends classical computation and so we must have quantum brains, which leads him to posit microtubules. But it's hardly clear that (a) us understanding Goedelian undecidability implies our minds transcending it, (b) an understanding of Goedelian undecidability is unavailable to computers; in fact it's representable in any number of software proof systems, (c) that quantum computation can do any better, or (d) that microtubules could offer any assistance here even if they were in some sort of superposition, rather than immediately decohering as quantum superpositions do outside laboratory controlled conditions.
Let me close by repeating that Roger Penrose is a brilliant man, just well outside his area of expertise here.
"(c) that quantum computation can do any better"
It's actually worse than that. He doesn't claim that it's a quantum effect; he claims that it's a "post-quantum" effect. He suggests rejecting quantum mechanics and replacing it with his theory, that has a "nondeterministic" ingredient in the wavefunction collapse. This "nondeterministic" ingredient would be the secret sauce that allows humans to understand incompleteness.
There are many problems with his argument, such as the ones you pointed out. But it fails for a very simple reason: Gödel's theorem applies to formal systems that are complex enough to represent arithmetic. We are good at many things, but we are not, in fact, capable of representing arithmetic, because we have finite memory. We can represent a subset of arithmetic at best. Even if we were well described by a formal system (which we aren't), we wouldn't really be Turing machines, but actually closer to a finite state automaton. Gödel's incompleteness theorem doesn't apply.
But, as you say, there's no reason to suspect his nondeterministic secret sauce would help things even if incompleteness did apply to humans. I don't think he even defines what is meant by "nondeterministic" and how a "nondeterministic" result differs from a garden variety random number.
Thanks! I read The Emperor's New Mind some years ago and some details have blurred over time.
Penrose's current version of the theory is Orch-OR (en.wikipedia.org/wiki/Orchestrated_objective_reduction) in collaboration with a biologist, Stuart Hameroff. Good luck finding the original research papers it's supposedly based on (hint: the tubule researcher is Anirban Bandyopadhyay). Hameroff now claims it means a QM life-after-death is possible. Deepak Chopra now appears to be associated with their work, which should tell you all you need to know...
The paper in question is entitled "Atomic water channel controlling remarkable properties of a single brain microtubule: Correlating single protein to its supramolecular assembly", though it came after Orch-OR which to my knowledge wasn't really based in anything but some misconceptions collectively held by Penrose and Hameroff.
The problem with this paper, as far as I can tell, is not for what it says (I'm not an expert in that particular field so I can't review it properly) but for how it's been (mis)represented. For example, the word "quantum" _never_ appears in it! The claim some make is that this paper found "energy levels" which are supposedly evidence of quantum mechanics. Well, hydrogen atoms have energy levels, but so does a kazoo. Energy levels are a general phenomenon that happens in either classical or quantum mechanics, which is why spectroscopy experts know they shouldn't interpret discrete spectra as evidence of quantum mechanics.
The second feature supposedly quantum mechanical are the conductivity properties of the microtubule. This, however, ignores that this paper (allegedly) explains those in terms of water trapped in the interior of the microtubule, that is, it's water that's conducting, not the microtubule itself.
All in all, there's always someone trying to steal your wallet.
Thank you so much for setting a new standard in physics education. Too often the informal, conversational style presented here is tied with entry-level information. Thatâs great and extremely important (especially for demystifying astrophysics to the general public). However, taking a deep dive into QFT and Hawking Radiation with concise, well-crafted videos like this keeps me engaged with new topics more than a 2-hour lecture does. Thatâs important too - but Iâm not formally studying any of this and I donât have much time. But I have a solid foundation in basic physics, and I now get to experience all of the benefits of this style of production, but with new, challenging topics.
This really elevated my understanding! I've never thought about horizons in this way!
This might be slightly off topic here, but since in QFT, we think of particles as waves in their respective fields, does the Doppler effect apply to them? If so can that also change the properties of the particles according to observers?
Yes, Doppler effect applies. You change your frame of reference to a moving one, waves change their frequencies for you, this is interpreted as change in their momentum. Because in QFT momentum ~ spatial frequency.
Yep. Makes calculating redshifts of far away things a bit more difficult since you have to pick apart Doppler redshift from the cosmological redshift caused by the universe expanding. Luckily its not that much more difficult and using the Doppler variety allows them to determine things like a system is orbiting since the cosmological redshift will be approximately constant (for a given object over our typical periods of observation..) while the Doppler will change from red to blue and back based on where the object is in its orbit relative to our viewpoint.
There's apparently also a gravitational redshift coming from general relativity that I don't know much about but I imagine it has to be taken into account whenever you're looking at anything that might have passed through or near a strong enough gravitational lens/well.
Well, the Doppler effect _sort of_ applies. I'm not sure how it works in other quantum fields, but technically it's not the same for light as it is for sound. Whereas sound waves are actually compressed in front of a moving body and stretched behind it, photons experience the "relativistic Doppler effect," in which the light wave itself doesn't change, but the portion of space time in which it oscillates a given number of times is perceived to have different volume and period from different reference frames. (Or the volume _actually changes_ in the case of redshift due to universal expansion.) Given that other quantum fields interact with the universe in a similar way (ie: they are waves in and of themselves, rather than waves in a medium), I imagine that they also exhibit a relativistic Doppler effect rather than a classical one, but I could be wrong.
altrag All of those redshifts are basically the same thing: Photons oscillate x times in a given volume of space time, but the volume of space or time changes based on reference frame, giving it an apparently longer period. Doppler redshift comes from a change in reference frame (relative speed of the emitter and receiver moving away from each other); cosmological redshift comes from the space the light travels through getting bigger while the frequency _relative to the original size of space_ remains the same; and gravitational redshift comes from the slowing of time within a gravity well making the frequency appear slower to an observer outside the gravity well. One of the really fun things about physics is how all sorts of apparently different things are just the same effect seen in what we perceive in our day-to-day lives to be a different situation.
2:25 vacua
4:12 vacuums
hmmmmmmmmmmmmmmmmmm
octopi
octopuses
octopodes
hmmmmmmmmmmmmm
octopae)
Vacua would be more consistent with the old form, vacuums sounds better imo.
Testicles, Testes
Penises, Peni
octopussy
Great Fan here. Big Thanks to you Sir for uploading such precise explanations about the "SPACE TIME"
what an amazingly impressive video to convey an amazingly complex topic! thank you!
gonna have to watch this one twice matt
Very informative information on this subject, I've done some research on Supersymmetry but I can never quite get a handle on it. I would love to hear an episode about it, I believe since you do such an amazing job spelling things out to us intermediate and advanced nerds that we would find it very eye opening. Love the videos and keep it up! đ
Can't wait to see the next Hawking Radiation video.. This is getting cooler and cooler than ever before. Great effort!
Great Episode! I can appreciate formulas like these a lot better now that I've taken a class in quantum mechanics. Keep 'em coming!
Can u give more explaining equations on your videos?
Make a vid on explaining those equations in detail? (Just the equation)
Thumbs up, you rock Matt. Thanks for sharing this incredible knowledge
YOOU BROKE MY MIND WITH YOUR DESCRIPTION OF THE VACUUM AS INFINITE CANCELLING MOMENTUM CARRYING PARTICLES, THANK YOU
Holy shit, this is the first episode I've had to re-watch to understand. This is getting so intense but SO INTERESTING
Nohb'dy 11 I'm on my 3rd watch haha... It is interesting but Dam I felt dumb watching this
You must watch anlot of rick and morty
Random thought, what if the discrepancy in theory and observation with QFT vacuum energy are due to the horizon of the observable universe?
Meaning that the calculations are for an infinite one? Or maybe even one which has a boundary, that defines its vacuum energy.
The boundary of our observable universe, the CMB, is from the end of the opaque period, so we cant actually see the event horizon beyond. Secondly whatever messing up of the drum skin it is doing at the event horizon, it can't influence the field or anything we can observe ever, as we are inside a receding the event horizon unlike the one around a BH. I was also curious when reading up on black holes and QFT if anyone had dared to apply the maths to the whole universe. Apparently no one has, so please go ahead and become famous..
Tore Lund 1. The boundary of our observable universe isn't the CMB and 2. He isn't mentioning the observable universe. Of course the observable universe is finite. The Whole universe though.... This video is mentioning the QFT so that it could explain the field equation and general relativity. They make predictions base on precise measurements that were made by doing small experiments that we can do. We can't measure an infinite pressure and energy that was made by and photon shooting drumstick. It's all just a theory. A well proven theory in fact. You can't just make a mathmatical model of the universe. Ther are regions wher we can never go and come back like inside a blackhole. Theories are well proven but they aren't exact every time. Like Hawking's 100$ bet on the higgs not existing and the aether of light predicted by many scientists in the late 20th century.
That is not what I'm saying, The event horizon is just behind the CMB, beyondthe maximum cosmological redshift! And I'm not commenting the video, but the thought experiment suggested by "deadly bean" in this thread. Cheers
Tore Lund I don't think the opaque period has any bearing on whether or not we "observe" the horizon of the observable universe in a quantum sense. I also think you're wrong to assert that the horizon cannot affect us because we're inside it and accelerating away. It should just result in a different kind of change than the one caused by a black hole horizon. He mentioned in the video that accelerating already causes a horizon effect so perhaps this would be easy to account for, or perhaps it would be really difficult/impossible since the expansion is governed by general relatively.
Deadly Bean As for your question, it's a good thought but I'm sure that they either have accounted for it already or there is some reason why they cannot. It's not like it's some obscure problem that no one cares about, it's arguably the most important problem in modern physics. I'm quite sure every straightforward or simple possible solution has already been tried.
I have been waiting so long for them to make an episode on Hawking radiation. Online sources have been pretty vague, as far as I have encountered. Good work guys!
Excellent topic and presentation!! Thx
DĂ©jĂ vu, I've been in this place before, higher on the beat I know it's my time to be mooooooooooorrrrrrrrrrrrrrrrre
Please make one on weyl Fermion. !
Cartoon -Ish yes?
Dear PBS Space Time, Thanks again for another high quality, accurate and entertaining physics video! With Love, David
The graphics with these explanations has gotten better. Makes it more possible to understand this.
jesus i only have a Bsc in physics spare me
bowie brewster and this is an easy episode. Try wachting the einstein field equetion episodes
Must have barely scratched that out then..
You are not alone, brother!
give me the secrets of your OST. what are the music you use in your videos?
concise, to the point and without "woo", excellent presentation.
I love you guys - I cannot wait to get further into my physics studies. You all inspire me so much every time you put out a video. Wish I wasn't so poor, or else I'd throw excess funds at you all!
For the first time pbs uploads a video when I am awake. (It's 10:04pm over here)
Jenny Anydots
Calm down dude. What are you so mad at? It's just a CZcams comment. If you didn't like it, dislike and move on! Life is too short for hatred. #peace
Jenny Anydots
OK
Jenny Anydots
So, how was your experience with the dog?
Jenny Anydots
Umm... No you aren't! LOL!!
9:45 if they all cancel out and leave a vacuum, where is the energy of the vacuum, the intrinsic energy of the quantum fields?
Or the vacuum just means no oscillations of the field and therefore no particles, but the field itself still has its energy?
Also, great video, as always. Can't wait to Unruh and Hawking radiation.
It just means that the average or expectation value of the number of particles is zero. The thing is that the vacuum state for one of observers seems as thermal spectrum of particles for the other.
Oh thanks, I think I get it; but the quantum fields still have their intrinsic energy, don't they?
Also at 11:15 as inside that horizon (a black hole's one for example) there is also a horizon, shouldn't particles also create inside? Shouldn't there be uncancelled modes inside the horizon too?
Yes, even when the expectation value of the particle number operator is zero you still get a zero point energy.
Regarding the horizon part. Yes, but the regions are causally disconnected, they are inaccessible to each other.
You can see something similar in the Unruh effect with an accelerating observer. You also get a thermal spectrum of particles in a very similar way to the Hawking radiation:)
Useful overture to the upcoming video on Hawking radiation and the Unruh effect especially for those who are familiar with the basics of quantum field theory (but didn't go through as thorough as a prospective theorist) and representations of operators in location and momentum space. Kudos for actually writing down the field operator. Nicely done, I learned something.
btw, it's not pronounced 'Un'-ruh, but more like ' _Oon_ ruh'. I knew the guy years ago, and 'Un-ruh' didn't bother him. But just for the record.
Well Explained with animations. Thank you for the awesome videos
There actually is a sci-fi book about concious stars, Whipping Star by Frank Herbert
Great book
and a wrinkle in time has stars metamorphing to save planets from Darkness
Same idea, only off in terms of scale in Solaris with its sentient ocean.
Well, why couldnât every thing have a, itâs own, consciousness, including each universe. And how could we, caught in the dystrophic middle (relatively at the bottom), ever grasp that.
Shirley Mason It takes one to know one :)
Anton Lifshits LMAO!!!!
Yeah, that got me too.
What a great episode I didn't get everything but the bits I understood helped me understand the universe more.
Matt and the team at pbs. thank you so much.
Huh?
When you said making math infinte is easy to solve I just screamed "What!!???"
I like these episodes that are a little harder to understand. Makes me watch them a few times to understand what the heck you just said
I barely understand any of this. BUT just listening to this kinda calms me down. Your voice is just soothing the feelings of being calm and relaxed.
Although sometimes i do learn a little bit
I would still like you to fully defend your case against Penrose :)
Well Pen doesn't make a very strong case to defend against. He assumes that quantum something is responsible for consciousness and builds from there. But from everything we've seen from neurons they run on simple regular computation at the cellular scale and aside from that we have no evidence that computation of any kind must cause consciousness. (When you are unconscious your brain isn't flipping off an entire mode of computation, it's simply performing the same computations it always does but for a different global result.) It's very nearly claiming that a 'soul' is needed for consciousness for all the evidence we have for it and the intangible link is proposes.
5:00 I'm sorry but the way your camera, lenses, and green screen are positioned it looks a bit too much like you're flying in Dragon Ball Z style. How many episodes before you go Super Saiyan? Edit: Upon further observation, you do resemble Princess Trunks with that hair, and how your hands are resting resemble Masenko attack (just not aimed out), and you do talk about space and time a lot....
Lol. actually he went super saiyan already. sometime late last year. He's just chillen right now.
"All Hail Princess Trunks!"
I was just sorta bothered because his feet looked funny, but I'm going to imagine this is what's happening now.
WORSHIP ME EARTHLINGS, THE GALACTIC FRIEZA ARMY WILL SOON DESTROY THE EARTH
"Doggie want a biscuit ?"
Aaaaaah, Iâm sooo excited. This is one of the very topics Iâve wanted to know about for a long time! Unruh Effect ftw!
This video answered a long standing question I had! I always wondered if from the perspective of a photon it exists to itself, seeing as no time passes between emission and absorption to the photon, but not to the much slower person
This is inspired by Mathologer's recent debunking of the Numberphile video: In the video, we discovered the various ways to add different infinite series. Is there a similar method to add infinite waves and make sense of the result? I can't even wrap my head around how an infinite number of momentum waves can add up to a finite value. Infinity is a mind-breaker :(
It's strange, but just like sound, when you hear a synth play a saw wave, you don't hear the saw wave, but instead the infinite harmonic sine waves that it would have taken to add together to approximate that saw wave. Seriously. Otherwise harmonics would not be a thing at all in music. The only way harmonics arise is from this additive property of waves.
So in a way, every time you listen to a song with synth (or anything that's not strictly a sine wave, for that matter), you are hearing infinite things add up to one thing tone (ideally- obviously the real world is more complex than that, but in an ideal world....)
_"Is there a similar method to add infinite waves and make sense of the result?"_
It's called integration, and it's symbolized by an elongated S: â«. You learn about it in your first semester of calculus.
It's called a Fourier transform, you can use one to break any signal up into a superposition of an infinite number of sine waved at different frequencies. It's even fairly straightforward to calculate the coefficients for each component.
You sound like you're struggling with the concept of convergent series though, so maybe do some more reading up on that.
"This is inspired by Mathologer's recent debunking of the Numberphile video"
I would caution against taking the debunking too seriously, as it itself contains mistakes that invalidate the main argument. The problem is that it enforces a definition of "equality" that is not enforced by the mathematics, but rather a choice. What I mean by this is that when we say that 1 + 1/2 + 1/4 + ... = 2 we mean something rather different than what we mean when we say 2 + 2 = 4. The latter is a "true equality" in the sense that the binary operator +, when applied to 2 and 2, does give identically 4. The former is very much not that. What we mean by 1 + 1/2 + 1/4 + 1/8 + ... = 2 is that, for a given arbitrary epsilon greater than 0, there exists an integer N_0 such that for all N > N_0 the sum of the first N terms of (1 + 1/2 + 1/4 + 1/8 + ...) is within epsilon of 2. It's a useful definition, but it's not mandated by the structure of infinite series. It's a choice. You could choose something else. For example, you could choose to use the (analytically continued) Riemann zeta function to give meaning to the equal sign for a case where the definition based on partial sums fails. *There's nothing to say that this choice is wrong.*
Rigorously speaking, the arguments presented in the numberphile video did have mistakes. However, these are very mild mistakes in that someone with very little mathematical training could easily fill in the gaps and produce a corrected argument. The essence of the idea is there, and it is correct. I wish they had explained analytical continuation in their video, as it is what gives strength to this sequence of seemingly crazy manipulations, but their core argument is simplified in the right way: most of the formal baggage is removed but the essence remains.
I haven't made it all the way through Mathloger's video yet, but the mathematical details and commentary are accurate and valuable. Just don't be misled by the one bit of unjustifiedly strong opinion in the video, that the sum "is" the limit of partial sums. That really is a choice, and it's up to you and your colleagues to agree or disagree on which one to use.
"There's nothing to say that this choice is wrong."
Everything in mathematics is a choice, but we need to stick to those choices consistently or else nothing in mathematics would mean anything. The fact that 2 + 2 = 4 is a choice. We could just as well have 2 + 2 = 5, but doing so makes mathematics incomprehensible. Only by sticking to standardized rules can anyone figure out what any mathematics is supposed to mean.
YEAHHHHHHHH still not even close to first!
Ray Martin Your avatar picture is perfect for your comment lol.
I'm currently working on a PhD in nonlinear dynamic and i must say that your channel is awesome and really well explained.
I'm really like to see that QFT is an extension a nonlinear dynamic in multiples dimensions of space-time.
It's kind of beautifull in its own way !
Really reminds me of topology: Holes, aka "Horizons" defining things :)
I'm really looking forward to the following vids.
2,043rd
475 th!
theRealRindberg seventh lol
I am excited for where you guys are headed!
Amazing video... going deeper to abstract and difficult concepts... I will try my best to understand but i can't promise i will
Thats cool... but do you knoe da wae?
Stop
Hammer time!
Excellent video on the topic. But need to watch it again.
Definitely one of the best science youtube channels
You are awesome bro thank u so much for breaking down difficult knowledge.
YES! this is the subject that I wanted to study for awhile! There's something about it that makes me very curious...
I love your videos !!
I would absolutely LOVE it Matt if you made a video breaking down these quantum field equations like you did with Einstein's field equations
Wow that's really amazing idea!
I love this channel so much, PBS Space Time, i am like Johnny 5 from the movie Short Circuit, input, innnpuuuutttt, with that being said, feed my brain baby !
I generally have a general understanding of the Space Time videos and this one was the first that I was mostly lost.
I watched all the QFT episodes again in one go and finally understood this episode. Though the key point to understanding it is the Heisenberg uncertainty principle, the Fourrier transform, Fourrier pairs and how momentum-position behaves like time-frequency
Now it's time to grok en.wikipedia.org/wiki/Second_quantization to get to real QFT from those more or less classical field descriptions.
Love your explanation.
Wow, this video sums up many vids on Quantum Field Theory. Thanks.
Finally a correct laymans explanation of the basics of Hawking Radiation. Thx.
Ha ! Nice video - wish it would have been around re. my last funding effort, a simple proposal to greatly speed up Bayesian imaging processing (which in the standard âspaceâ of the image is computationally nasty due to correlations between points) by doing it in Fourier space (because as in the QFT case the modes can be treated, in out case optimized, independently). We eventually were able to convince the reviewers that that was something interesting to work on but maybe we could have used Mattâs clarity of presentation to speed things up !
I feel like a number of these videos will be super helpful during my GR class this semester :p
It has always fascinated me , how most of people only live on this 2D surface, never looking up, wondering how big is this universe we live in, how complex it can be. And only by looking up, you start to look down, and by down i mean in to the universe of the small, quantum level. Only then you start really deeply looking in to nature of the nature itself. Creating your own Arcams razor, only then you learn that you dont even know how much there is to know. This makes you a skeptics machine, eating non energy invested opinions of a common 2 dimensioneer like beast. Thank you pbsst, for creating a really highly intellectual videos, whit huge amount of think about value, on a truly rational level, that very small group of youtube channels can deliver. Im following you for years it fells, and i will continue to do so. Physics is my passion for since i was 7years old, i am now 26 and an general manager at a european costal cinema firm, i never finished colidge, and i love physics more than anyone i know personaly.
Thank you again for delivering as always. Excuse my english, after all i am from europe.
And please ,it feels like there is a new person on the team. Please reduce the intensity of music , it really takes my focus away from deep thinking.
Best regards
A awesome video
Continue this way
Great video!
Horray for a video just beyond my current knowledge of physics! Looking forward to the next event as I continue to expand my horizon.