We already know that some particles interact extremely weakly with others. Neutrinos were postulated as a "dark" particle in order to preserve conservation of energy and momentum, but it took more than a decade before they were observed directly. There's no reason there couldn't be another particle with an even weaker interaction.
In a similar vein I highly recommend Behind the Curve, which is a documentary about the flat Earth movement. It was a pretty fair film and tried to get to know the people involved in the movement and what it was that motivated them.
It was interesting to see that one of the main figures featured in the documentary started out pretty generically wanting to get into conspiracy theories and started reading up on one after another until he found a particular one that clicked.
I think the long term impact of this will be to strengthen the importance of social ties in academic publishing. As it is there are so many papers published in many fields that people tend to filter for papers published by big names and major institutions. But the inevitable torrent of AI slop will overwhelm anyone who is looking for any gems coming from outsiders. I suspect the net effect will be to make it even more important that you join a big name institution in order to be taken seriously.
Given the mountains, the sun would appear to set when it descends below some altitude angle. Given the equation in the wikipedia article you'd then just solve for the hour angle. (You'd then have to use your latitude to convert the local solar time to Mountain Standard Time.)
Thank you for the kind words! Yes, I think you're right about the missing factor of rho. And rho^2 is being drawn from a chi-squared distribution, not a chi distribution. (But the mode I stated is correct for a chi-squared distribution --- I must have omitted the squares when typing this up.)
I've found that there can be a lot of randomness for what makes the front page. Not too many people read the "New" page and articles drop off it pretty quickly, so it can be hard for a niche article to attract the handful of votes it needs to appear on the front page. (Though there is a "second chance" feature which helps to ameliorate this issue.) So there's a lot of randomness to what makes it onto the front page.
For instance I submitted an article three times (spaced a year apart). The first two times the article got no upvotes. The third time it got 600+ and hit the top of the front page. It's just a matter of who happens to be looking at the New page at the time.
Mark-to-market can create liquidity crises when coupled with capitalization requirements, though. This can happen in, e.g., bond markets.
Say a bank is sitting on a pile of very safe bonds. If the interest rate suddenly increases, the mark-to-market value of the bonds goes way down. The bank would still expect to get the full value of all the bonds at maturity. But if the bank has to mark-to-market, the current value may be low enough that capitalization requirements force the bank to sell all the bonds in a fire sale. So even though the bank in theory could have held onto the assets and gotten exactly what it had expected from the start, it instead ends up taking a big loss.
This article probably omitted it for simplicity, but you would discount the income stream over time. Projected income at the 20 year mark is valued much less than income next year. That helps to account for the uncertainty.
How would this help? If the existing operators refuse to lower rents and leave their spaces vacant then under this scheme no one else can build new spaces which rent at lower rates. You would just be stuck with vacant properties at above-market rates.
You don't need a full fledged theory of quantum gravity to describe Hawking radiation. Quantization of the gravitational field isn't relevant for that phenomenon. Similarly you don't need quantum gravity to describe large elements. Special relativity is already integrated into quantum field theory.
In some ways saying that we don't have a theory of quantum gravity is overblown. It is perfectly possible to quantize gravity in QFT the same way we quantize the electromagnetic field. This approach is applicable in almost all circumstances. But unlike in the case of QED, the equations blow up at high energies which implies that the theory breaks down in that regime. But the only places we know of where the energies are high enough that the quantization of the gravitational field would be relevant would be near the singularity of a black hole or right at the beginning of the Big Bang.
Intuitively you would think that the tide is being formed because the Moon is "lifting up" the water at the point closest to the Moon. But this contribution is actually very miniscule to the tidal effect. Instead the bulk of the tides are produced about 45 degrees away where the tidal force is parallel to the Earth's surface. This has the effect of dragging the water closer to the tidal bulge.
It's kind of interesting to compare this to Ptolemy's eras. In the Tetrabiblios, Ptolemy argued that man went through seven ages in his life, each associated with a different celestial object.
1. Infancy --- The Moon. Since the Moon waxes and wanes more rapidly than any other celestial object, this period is characterized by the fastest development.
2. Childhood --- Mercury. As Mercury is the fastest of the planets, at this age children have the short attention spans and flit from one thing to the next.
3. Youth --- Venus. Starting around puberty, a man's mind starts to become focused on love.
4. Young Adulthood --- The Sun. A man comes of age, he starts to think about his work and people begin to take him seriously.
5. Middle Adulthood --- Mars. In his mid 30s a man's demeanor becomes more severe. He realizes he has certain goals he would like to accomplish and there is not much time left to achieve them.
6. Maturity --- Jupiter. By his mid 50s, having achieved what he can in his life, he has arrived at a position of authority in the community. He has gravitas and respect.
7. Old Age --- Saturn. By his late 60s, he starts to decline physically and mentally.
Later on it looks like he classifies him as a "vanity angel" rather than a "strategic angel." It sounds like it can be useful to have someone with name recognition as an investor when you're talking to people who aren't very familiar with the space.
It's true that it leaves open the possibility of a conserved quantity that is not associated with a symmetry. But the kinds of conservation laws we are thinking about, like conservation of energy, do originate from a symmetry. So if the symmetry is broken it is very reasonable to assume that the conservation law would be broken as well.
Noether's theorem tells us when we would expect conservation laws to hold and when we would expect them to fail. In the case of global energy conservation, there would have to be a global time invariance associated with the spacetime. But this is manifestly not the case in an expanding universe. It is generally not even possible to have a well defined notion of global energy in a dynamic spacetime.
Taylor & Wheeler's Spacetime Physics is similar. They emphasize the importance of frame invariant representations. (I highly recommend the first edition over the second edition, the second edition was a massive downgrade.)
Kip Thorne was also heavily influenced by this geometric approach. Modern Classical Physics by Thorne & Blandford uses a frame invariant, geometric approach throughout, which (imo) makes for much simpler and more intuitive representations. It allows you to separate out the internal physics from the effect of choosing a particular coordinate system.
It's hard to prove rigorously which is why people usually refer to it as the "manifold hypothesis." But it is reasonable to suppose that (most) data does live on a manifold in the strict sense of the term. If you imagine the pixels associated with a handwritten "6", you can smoothly deform the 6 into a variety of appearances where all the intermediate stages are recognizable as a 6.
However the embedding space of a typical neural network that is representing the data is not a manifold. If you use ReLU activations the kinks that the ReLU function creates break the smoothness. (Though if you exclusively used a smooth activation function like the swish function you could maintain a manifold structure.)
