This was so hot (no pun intended) and reproducible that the prize was awarded one year after discovery. Quite rare in those days already.
Notation used in quantum mechanics.
Ket is just a vector. Though generally in the context of quantum mechanics, this is an infinite dimensional vector in a Hilbert space like .
Bra is just the dual vector corresponding to a ket, or in other words projection linear operator, i.e. a linear function which can act on a given vector and returns a single complex number. Also known as... dot product.
For example:is basically a fancy way of saying:that is: we are taking the projection of along the direction. Note that in the ordinary dot product notation however, we don't differentiate as clearly what is a vector and what is an operator, while the bra-ket notation makes it clear.
The projection operator is completely specified by the vector that we are projecting it on. This is why the bracket notation makes sense.
It also has the merit of clearly differentiating vectors from operators. E.g. it is not very clear in that is an operator and is a vector, except due to the relative position to the dot. This is especially bad when we start manipulating operators by themselves without vectors.
This notation is widely used in quantum mechanics because calculating the probability of getting a certain outcome for an experiment is calculated by taking the projection of a state on one an eigenvalue basis vector as explained at: Section "Mathematical formulation of quantum mechanics".
Making the projection operator "look like a thing" (the bra) is nice because we can add and multiply them much like we can for vectors (they also form a vector space), e.g.:just means taking the projection along the direction.
Ciro Santilli thinks that this notation is a bit over-engineered. Notably the bra's are just vectors, which we should just write as usual with ... the bra thing makes it look scarier than it needs to be. And then we should just find a different notation for the projection part.
Maybe Dirac chose it because of the appeal of the women's piece of clothing: bra, in an irresistible call from British humour.
But in any case, alas, we are now stuck with it.
"De novo" means "starting from scratch", that is: you type the desired sequence into a computer, and the synthesize it.
The "de novo" part is important, because it distinguishes this from the already well solved problem of duplicating DNA from an existing DNA template, which is what all our cells do daily, and which can already be done very efficiently in vitro with polymerase chain reaction.
Notably, the dream of most of those companies is to have a machine that sits on a lab bench, which synthesises whatever you want.
The initial main applications are likely going to be:but the real pipe dream is building and bootstraping entire artificial chromosomes
- polymerase chain reaction primers (determine which region will be amplified
- creating a custom sequence to be inserted in a plasmid, i.e. artificial gene synthesis
News coverage:
- 2023-03 twitter.com/sethbannon/status/1633848116154880001
- 2020-10-05 www.nature.com/articles/s41587-020-0695-9 "Enzymatic DNA synthesis enters new phase"
Nuclera eDNA enzymatic de novo DNA synthesis explanatory animation (2021)
Source. The video shows nicely how Nuclera's enzymatic DNA synthesis works:- they provide blocked nucleotides of a single type
- add them with the enzyme. They use a werid DNA polymerase called terminal deoxynucleotidyl transferase that adds a base at a time to a single stranded DNA strand rather than copying from a template
- wash everything
- do deblocking reaction
- and then repeat until done
And analogously for matter, appears in the de Broglie relations relating momentum and frequency. Also appears in the Schrödinger equation, basically as a consequence/cause of the de Broglie relations most likely.
Intuitively, the Planck constant determines at what length scale do quantum effects start to show up for a given energy scale. It is because the Plank constant is very small that we don't perceive quantum effects on everyday energy/length/time scales. On the , quantum mechanics disappears entirely.
A very direct way of thinking about it is to think about what would happen in a double-slit experiment. TODO think more clearly what happens there.
Defined exactly in the 2019 redefinition of the SI base units to:
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