Flip Tanedo
@fliptanedo.bsky.social
Particle physicist. Flip spends his time thinking about dark matter while covered in chalk dust. https://particle.ucr.edu
This thread is lightly edited from a post at the place formerly-known-as-twitter, FlipTanedo/status/1706301780290936939
I'm reposting after students in my Physics 17 course asked about the birdtrack diagram on the cover of the course notes.
sites.google.com/ucr.edu/phys...
I'm reposting after students in my Physics 17 course asked about the birdtrack diagram on the cover of the course notes.
sites.google.com/ucr.edu/phys...
Physics 017 - Agenda
Please note that all future weeks are subject to change based on student and instructor feedback.
2025 Course Notes, periodically refined. Last update: 1 Apr (correcting eq. 3.5.18; thanks Casey O.)
S...
sites.google.com
April 5, 2025 at 9:56 PM
This thread is lightly edited from a post at the place formerly-known-as-twitter, FlipTanedo/status/1706301780290936939
I'm reposting after students in my Physics 17 course asked about the birdtrack diagram on the cover of the course notes.
sites.google.com/ucr.edu/phys...
I'm reposting after students in my Physics 17 course asked about the birdtrack diagram on the cover of the course notes.
sites.google.com/ucr.edu/phys...
The indices in the corresponding expressions are understood to be written with respect to abstract index notation. In this sense, they are coordinate free. Thus I do not think a more manifestly coordinate-free notation would be significantly clearer.
April 5, 2025 at 9:56 PM
The indices in the corresponding expressions are understood to be written with respect to abstract index notation. In this sense, they are coordinate free. Thus I do not think a more manifestly coordinate-free notation would be significantly clearer.
For example, we applied the torsion free assumption with the following diagrammatic rule: two circles around something with no lines is zero if the lines on each circle are antisymmetrized with each other.
April 5, 2025 at 9:56 PM
For example, we applied the torsion free assumption with the following diagrammatic rule: two circles around something with no lines is zero if the lines on each circle are antisymmetrized with each other.
Τhis was my first example where birdtrack notation were significantly more clear than the analogous index expressions, even though they are in one-to-one correspondence.
April 5, 2025 at 9:56 PM
Τhis was my first example where birdtrack notation were significantly more clear than the analogous index expressions, even though they are in one-to-one correspondence.
The remaining term is proportional to the curvature tensor with its three lower indices antisymmetrized (blue). The entire quantity is zero (first step) and for any scalar (dot) or vector (circle), thus the blue highlighted piece must vanish. This proves the assertion.
April 5, 2025 at 9:56 PM
The remaining term is proportional to the curvature tensor with its three lower indices antisymmetrized (blue). The entire quantity is zero (first step) and for any scalar (dot) or vector (circle), thus the blue highlighted piece must vanish. This proves the assertion.
All but the last term vanish: the first one from torsion freedom, and the second from a combined symmetrization and anti-symmetrization of the same pair of indices.
April 5, 2025 at 9:56 PM
All but the last term vanish: the first one from torsion freedom, and the second from a combined symmetrization and anti-symmetrization of the same pair of indices.
Apply the chain rule for the inner (highlighted in blue) covariant derivative. This means the dashed blue circle is applied to each node inside it.
April 5, 2025 at 9:56 PM
Apply the chain rule for the inner (highlighted in blue) covariant derivative. This means the dashed blue circle is applied to each node inside it.
The first step, following a hint from Penrose's book, is to evaluate the following quantity for some arbitrary vector field (ξ) and scalar field (φ).
By the torsion free condition (highlighted in yellow) this quantity is zero. Next we expand the left-hand side.
By the torsion free condition (highlighted in yellow) this quantity is zero. Next we expand the left-hand side.
April 5, 2025 at 9:56 PM
The first step, following a hint from Penrose's book, is to evaluate the following quantity for some arbitrary vector field (ξ) and scalar field (φ).
By the torsion free condition (highlighted in yellow) this quantity is zero. Next we expand the left-hand side.
By the torsion free condition (highlighted in yellow) this quantity is zero. Next we expand the left-hand side.
The (Riemann) curvature is analogously defined from an antisymmetric covariant derivative.
April 5, 2025 at 9:56 PM
The (Riemann) curvature is analogously defined from an antisymmetric covariant derivative.
The torsion free condition is that the antisymmetric second derivative of a scalar vanishes.
April 5, 2025 at 9:56 PM
The torsion free condition is that the antisymmetric second derivative of a scalar vanishes.
Wigglies (bars) indicate (anti-)symmetrization of indices.
April 5, 2025 at 9:56 PM
Wigglies (bars) indicate (anti-)symmetrization of indices.
Covariant derivatives are dashed circles.
April 5, 2025 at 9:56 PM
Covariant derivatives are dashed circles.
Some notational background: Tensors are nodes and indices are lines. Lines that connect nodes are contracted.
April 5, 2025 at 9:56 PM
Some notational background: Tensors are nodes and indices are lines. Lines that connect nodes are contracted.
Eligible PhD students should feel empowered to bring up these awards with their advisors.
March 21, 2025 at 5:41 PM
Eligible PhD students should feel empowered to bring up these awards with their advisors.
High-energy theorists should also consider nominating their soon-to-be PhDs for the APS DPF Sakurai Dissertation Prize. Nominations will be due in September.
www.aps.org/funding-reco...
www.aps.org/funding-reco...
J. J. and Noriko Sakurai Dissertation Award in Theoretical Particle Physics
The American Physical Society is a nonprofit membership organization working to advance physics by fostering a vibrant, inclusive, and global community dedicated to science and society.
www.aps.org
March 21, 2025 at 5:41 PM
High-energy theorists should also consider nominating their soon-to-be PhDs for the APS DPF Sakurai Dissertation Prize. Nominations will be due in September.
www.aps.org/funding-reco...
www.aps.org/funding-reco...
She writes about "magic pill-ism," the hope for scientists to come up with a pill to cure cancer, and her exasperation comes through when she argues that this magic pill-ism blinds us to the human choices that we continue to make are the ultimate origin of many of our modern maladies.
March 17, 2025 at 7:09 PM
She writes about "magic pill-ism," the hope for scientists to come up with a pill to cure cancer, and her exasperation comes through when she argues that this magic pill-ism blinds us to the human choices that we continue to make are the ultimate origin of many of our modern maladies.
She then pieces together how a combination of American institutions were critical in forging a path forward: accountability of politicians, research institutions like universities, and local newspapers.
The timeliness with contemporary challenges is hard to miss.
The timeliness with contemporary challenges is hard to miss.
March 17, 2025 at 7:09 PM
She then pieces together how a combination of American institutions were critical in forging a path forward: accountability of politicians, research institutions like universities, and local newspapers.
The timeliness with contemporary challenges is hard to miss.
The timeliness with contemporary challenges is hard to miss.
I'm impressed by how prescient many of the book still is.
Carson points out that the USDA had supported chemical insecticides even when they were shown to be dangerous, wasteful, and often counterproductive. It contextualizes the loss of faith in "big government" by affected populations.
Carson points out that the USDA had supported chemical insecticides even when they were shown to be dangerous, wasteful, and often counterproductive. It contextualizes the loss of faith in "big government" by affected populations.
March 17, 2025 at 7:09 PM
I'm impressed by how prescient many of the book still is.
Carson points out that the USDA had supported chemical insecticides even when they were shown to be dangerous, wasteful, and often counterproductive. It contextualizes the loss of faith in "big government" by affected populations.
Carson points out that the USDA had supported chemical insecticides even when they were shown to be dangerous, wasteful, and often counterproductive. It contextualizes the loss of faith in "big government" by affected populations.
In Ch.12, Rachel Carson points out that until the 1950s, pediatric cancer was incredibly rare. From the 50s onward, more American children died of cancer than any other disease. Carson raised the alarm that many of these cancers are present before birth and are intrinsically environmental in origin.
March 17, 2025 at 7:09 PM
In Ch.12, Rachel Carson points out that until the 1950s, pediatric cancer was incredibly rare. From the 50s onward, more American children died of cancer than any other disease. Carson raised the alarm that many of these cancers are present before birth and are intrinsically environmental in origin.
Those in Riverside: participation in the book club comes with purchasing the book from our host, Cellar Door Books:
Silent Spring: www.cellardoorbookstore.com/book/9780618...
Silent Spring Revolution: www.cellardoorbookstore.com/book/9780063...
Silent Spring: www.cellardoorbookstore.com/book/9780618...
Silent Spring Revolution: www.cellardoorbookstore.com/book/9780063...
www.cellardoorbookstore.com
March 17, 2025 at 7:09 PM
Those in Riverside: participation in the book club comes with purchasing the book from our host, Cellar Door Books:
Silent Spring: www.cellardoorbookstore.com/book/9780618...
Silent Spring Revolution: www.cellardoorbookstore.com/book/9780063...
Silent Spring: www.cellardoorbookstore.com/book/9780618...
Silent Spring Revolution: www.cellardoorbookstore.com/book/9780063...