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What's a Hilbert space? A visual introduction
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- Опубликовано: 19 авг 2024
- *Updated sound quality video here:*
• What's a Hilbert space...
A visual introduction to the ideas behind Hilbert spaces in ordinary quantum mechanics.
Music: / peacefully-es-jammy-jams
Manim: www.manim.comm...
My left ear enjoyed this. Great video anyways.
If this will happen anytime again, turn ON the MONO AUDIO in phone settings, by doing this your both ear will enjoy the video : )... Bcs mono audio combines the left and right audio channel...
@@WillHunting1100 oh thanks.
Lmaoo!! It only worked for me when my phone was vertical.
@@qxxnocasino7927 Turn ON Mono Audio in phone settings.
Watch it backwards in a mirror and your right ear will
Hello, I appreciate the explanation a lot. However, it would be better if you lower the background music a bit, because sometimes can't hear what you say, to the point that I have to use subtitles :). Keep up the good work!
I second that! Also, a better microphone and articulating words better would help a lot. I stopped watching the video because I got frustrated with the voiceover
Nice presentation but the background music was way too loud and made it difficult to understand what you're saying
Audio is left ear only, Otherwise great video.
If this will happen anytime again, turn on the MONO AUDIO in phone settings, by doing this your both ear will enjoy the video : )... Bcs mono audio combines the left and right audio channel...
Fabulous video! This exactly what I was searching for thank you.
Redo this and drop the background music by a factor of 4. Your musak is louder than your voice.
Thanks for the feedback, something went wrong with the audio indeed, I will fix it this weekend :)
@@physicsduck6711 subscribed for very cool video and for taking constructive criticism like a champ 👍
Yeah, your voice is also panned to the left, which is a bit irritating. I guess that was a mistake. XD Apart from that, it's a great video. :)
Ugh, I care about the math and not the physics.
Rip
I thought it was just a space which is complete according to the norm induced by its dot product, and being complete means that every Cauchy sequence converges in the space
this was my understanding of it also, the key being that "every Cauchy sequence converges in the space". This video is better ruclips.net/video/_kJUUxjJ_FY/видео.html&ab_channel=QuantumSense
You are correct. I think this video is very much not meant for people who want a mathematical understanding of a Hilbert space.
Keep going man ❤ you doing good
The Mathematician Answer:
hilbert space - a finite or an infinite dimensioanl complete inner product space i.e an inner product space that's complete w.r.t to the metric induced by the inner product
fock space - the direct sum of a bunch of tensor products of a bunch of hilbert spaces (whose completion is a tensor algebra)
The Physicist Answer:
oh it's basically where vectors (which are quantum states) live in and it also has a dot product in it. and a fock space is just a combination of a bunch of hilbert spaces you can use to describe the quantum states of a system of a bunch of different particles lol that's literally it
So physicists explain it in a simplified version.
@@cybersecurityguyalso ignores a lot of details
I checked my earphones twice 😁😁
I used to quip that "when you're sitting in the HILBERT ROOM you have to look sharp and keep your bearings, or some strange things will soon be happening"🎆.😵💫 ("room" and "geometric /numerical space" are rendered by the same word in Swedish, my native language: "rum") 😀
Cool! How do you make these animations?
With Manim community! I linked their website in the description. It's a Python library originally created by the creator of 3Blue1Brown in case you are familiar.
@@physicsduck6711 Thanks! Yes I am familiar with 3Blue1Brown
Great work man . Loved fhe content . As everyone already said edit the sound or upload a new one keeping this one intact
This is a good video, but I think it overlooks *why* this is a hilbert space. would be helpful if you used the quantum mechanical examples to explain the properties of the representation that make this space is a Hilbert space and not some other type of space/representation.
I still don't see where's the difference between hilbert and eucildean space
Good job RIPPING OFF, 3BLUE 1 BROWN
I wouldn't listen to the others; the background and animation music make the video delightful. :)
Isn't a Hilbert space just a complete vector space whose norm is derived in the conventional way from its inner product? It doesn't need to be a set of functions.
Little known fact, the originator of the "born rule" is the grandfather of the singer Olivia Newton-John
thank you man for you explication but you could higher the music I can't hear it
Background music is so irritating
Hi you have a mono audio on i cant watch it on headpones
So a Hilbert space is just a vector space with a 3rd binary operation which is the dot product? Is that it?
The background music makes this video far too difficult for me to hear. Please reconsider the need for continuous music.
one earbud has only music, the other has mostly narration, thought i'd somehow skipped to a new video with only music
THe content is great but the background music is too loud and unnecessary. Can you please reload the video without background music. Thank you
In the example of a Hilbert space you use the example of x1, x2, x3 as the axis - and vectors represent the probabily of finding the particle in positon x1, x2, x3.
But is the idea in a bonified hilbert space to generalize this so that we have infinite dimensions where every direction represents a position in space? - and we do this so we can have nice properties like the length of all vectors is 1 - that we can use for doing math and figuring things out.
Does this tie into space filling curves like the Hilbert curve? As thats a way to map real numbers to positions which we might use to label our infinite dimensions -- or is that completely unrelated other than the mathematician who made them 😅
It is great but the side music annoyed me. It was an obstacle to concentrate to definitions and speech.
Plz reduce background music, although content is good where hard to listen to it
Same. This is a great video. I'd really love to hear it without music. Was difficult to hear you talk.
why the music?!
great explanation of this difficult topic
Assuming the necessary assumptions, let *H* be a Hilbert space.
-Andrew Dotson
Dude. Audio.
This is great but just FYI your voice is coming through only the left side-- not in stereo. It's fine for speakers but is distracting on earphones.
Consistency of a theory is manifested in a hilbert cube, whose interior is empty.
I'm still confused, what's the difference between a Hilbert space and your run-of-the-mill metric space or inner product space?
A Hilbert space is a inner product space for which the corresponding metric space is complete. So the key point is that it is complete.
@@FiniteSimpleFox
And what does "complete" mean precisely? I don't remember him mentioning that in the video.
That’s because this video isn’t a mathematical description of a Hilbert space, it’s an intuitive description of a particular class of Hilbert spaces that physicists commonly simply call “Hilbert space.”
A complete metric space means that every Cauchy sequence in that space converges to a point in that space. It’s pretty analogous to being closed in topology.
A good intuitive description of what “complete” means isn’t really possible in a RUclips comment. Maybe a wiki article helps.
en.wikipedia.org/wiki/Complete_metric_space
It always makes me sad when there is good content but it has one extreme red flag making it completely unwatchable like the audio mixing in this video. How can you not notice this?
Great, thanks!
nice
Background music is too loud to listen
Thank you 🙏
IT'S VERY CONFUSING
Why only 3 vids?
What is this a math explanation or a f**kin' hotel wine-bar!!!???
whats the song??
I can barely hear your voice over the music.
Pure torture with that music
MUSIC IS SO ANNOYING
If you turned off the piano we could actually try to decipher your mumbling...
why must the sum of all the probabilities of finding the particle in a vector space must be equal to 1 ? that might be true in classical mechanics but in a system with superpositions where the particle might be superimposed on or in several locations all at the same time surely the probability of finding it somewhere must be some number greater than 1
A physicist's introduction to finite dimensional inner product spaces... 😅... But a physicist doesnt need to study functional analysis if he can do calculations... As long as reisz representation theorem holds you can do all the hand wavy things with dirac notation... Nice video though...
Bed music is too loud and makes it hard to follow, much less concentrate, on what is being said.
Were hilbert space????? Vectorial space with intern produt + all Cauchy sequences are convergent. You speak noting of hilbert space but only space of states (a la Cohen) . please more caution a respect of mathematics
Sorry but the background music is louder than your voice 😢
Bro is Nederlands
Neither of my ears enjoyed this.
what a waste of time