Lorentz Jr

Right, but that's not what I meant by "geometry". I was referring to gravity as curvature of space, which I don't think is present in GTG. Yes, of course. But there's a difference between shallow phenomenological models and deeper, more robust models. The deeper ones always involve a model of what things are made of and what principles govern the behavior of the constituent parts, even though those principles aren't always obvious from the behavior of the systems in normal circumstances. Models of what goes on "under the hood", as we like to say here in the States. So, again, a topological map of a geographical region isn't going to help you during an earthquake. And a doctor or a mechanic needs to have a deep model of the cells and tissues and organs in the human body or the mechanisms inside the machine, not just a schedule for when the person wakes up and goes to work every morning or the external size and shape of the machine. "Deep models" is all I mean by "ontology". Maybe it's not the best word. Genady seems to think my usage of it is nonstandard. But it could be very useful to have a deeper model. We're not going to develop any warp drive or hyperdrive based on relativity, and there could also be uses for a deeper model of gravity. For instance, in unifying it with quantum theory. I take what I can get, Markus. If there were an equivalent theory without Minkowski space, I would be interested in that. Not really. What I mean is that the principle of relativity bothers me more than modeling gravity as the curvature of (any) space. Ilja Schmelzer's General Lorentz Ether Theory is an example of "GR without SR", so to speak. Yep. And I'm interested in that.

Do them one at a time. Single variable substitutions. (That is, introduce one new variable at a time, but it can depend on both x and y.) If you don't like the complicated expression inside the fractional power, start with that one.

I'm not trying to participate in the substance of the discussion, Phi. I was just trying to clarify @MigL's distinction between inner thoughts and outward behavior.

Acts of omission.

How do you explain Brownian motion? You need to have some idea of what water is made of. How do you predict the life cycles of stars? You need to have some idea of what's inside them. How do you develop ways to travel faster than the speed of light? You need to have some idea of what matter and the vacuum are made of. Ontology is necessary for fundamental research. Existing theory is fine for developing applications, but developing new fundamental theories requires some kind of intuition about what those theories will describe. How can you unify gravity and quantum theory without having some idea of what they describe? Without some intuition about the nature of the underlying reality, all you can do is flail around wildly with ten-dimensional fantasies that don't describe anything. EDIT: Another good example is troubleshooting. If you want to fix a clock or an engine, or figure out what's making a person sick, you have to have some idea of what's inside the clock or the engine or the person. You can't use phenomenological models of how the things normally behave when their behavior is abnormal. BTW, I don't get that Feynman reference.

No, I think it's part of physics. It's part of what defines physics as a science, as opposed to a branch of pure mathematics. As I was saying recently, ontology is useful in predicting what's likely to happen in situations that haven't been studied yet. During earthquakes, for instance, in the discussion about maps and territories.

No, GTG is defined in flat Minkowski space. It models gravity in the way that Einstein first tried, as a gauge-invariant "index of refraction". Hestenes suggests that Einstein only resorted to using geometry because that's the only math that was available to him at the time. I don't necessarily prefer GTG, I just use it as a counterexample to show that the geometric interpretation hasn't been proven to be "real". As I said before, I don't object to theories because my thinking is conventional and they seem "radical" to me. I object to theories that seem unscientific to me. Neither QM nor GR bothers me nearly as much as SR, i.e. the principle of relativity itself, and QM only bothers me because it assumes that quantization must be a static property of matter (rather than a dynamic property of interactions), and that seems to be forced on it by SR. I'll try not to give that impression in the future. I'm certainly not a mathematician, but the amount of math in theories has nothing to do with how I evaluate them. I'm not in favor of pseudoscientific fantasies, I'm not in favor of "theories" that don't make predictions (or make 10500 predictions), and I'm not in favor of the current fashion (as I see it) of treating math as a substitute for physics. Many Worlds says energy eigenfunctions of the universe are "real", interpretations like quantum information and Von Neumann–Wigner seem to deny the reality of the universe itself, and the current consensus seems to be that thinking about ontology is nothing more than a navel-gazing exercise for philosophers. It's like the physics profession has been hijacked by mathematicians. Page 36.

Because the photons interact with the detectors. The "presence" of one slit doesn't really count after the photon interacts with the detector behind the other one, and if there's any space between the slits and the detectors, that should result in at least some (very) minimal amount of diffraction between them.

Yes, occasions when there's only one slit present. I meant in the presence of a second slit. I didn't mean there's no such thing as single-slit interference, any more than I meant earlier that a single electron carries a large amount of electric charge.

Not in a practical sense, no. The amplitude of a photon's wave function will be very low on the other side of the star from the photon's source.

Yes, I think that's theoretically possible, although the likelihood falls with increasing numbers of photons (dueling posts): With all due respect to @exchemist and @Genady, not only photons, but also electrons and other forms of matter, have been shown to act like waves (for instance in double-slit experiments), so there's no clear evidence that quanta of any kind pass through only one slit, take only one path, or have only one direction. In fact, multiple paths are explicit in Richard Feynman's path-integral formulation of quantum mechanics. Although, to "compensate" for that, I guess you could say, all photons take all directions, or at least their wave functions do. So the probability of one reaching your eye or telescope is still about the same as it would be for classical particles, as long as there are enough of them.

Continuing the calculations by Mordred and swansont: The sun's spectrum peaks in the visible range, so let's guess that its visible output is on the order of 1025J/sec. The energy of a visible photon is roughly hf = 10-33Jsec * 1017/sec = 10-16J. So the output of visible photons is 1025J/sec / 10-16J = 1049 per second. One light-year = 3*108m/sec * 3600 * 24 * 365 sec = 1016m. The diameter of our galaxy is D = 100,000 light-years = 1021m. The area of the spherical shell the photons pass through is roughly 10 D2 = 1043m2. The area of a 6-inch telescope is about 0.01 m2. So the area ratio is 10-2 / 1043 = 10-45. And finally, the rate at which visible photons reach the telescope from a star on the other side of the Milky Way is: 10-45 * 1049/sec = somewhere in the vicinity of 10,000 visible photons per second. Of course, this is only a rough guess, and different stars have different parameters, so let's say it's probably at least about 1000 per second, and maybe as many as 100,000, for an amateur telescope and an average star somewhere in the middle of the galaxy.

Schrödinger himself presented the scenario as a criticism of non-realist interpretations. His whole point was that it doesn't make sense.

We're talking past each other, Markus. I was referring to fundamental scientific principles and alternatives to modern mainstream theory, not high-school physics. This is ad hominem, Markus. I take comments by forum posters the same way. Well, I don't know enough about the subject to judge the theory myself, but it's published, so I'm going to give it the benefit of the doubt. There's also gauge theory gravity (with another article and a Wikipedia article), which, if I'm not mistaken, is virtually identical to GR at all experimentally observed field strengths, and has what seem to me to be the advantages of disallowing exotic sci-fi phenomena like wormholes and time loops. Considering theories "radical" has nothing to do with my objections, Markus. My suspicion of current quantum theory is based on thinking it may not be radical enough (being formulated in terms of particles, which are derived from classical intuition), and my suspicion of relativity is based on thinking it may be unscientific (I'm not convinced by the "geometry" argument of time dilation in the twin paradox). But of course no one has found a preferred frame, so I try not to be ideological about the subject. I won't mind any theories that are developed in the future, as long as they don't do unscientific things like making 10500 different predictions. 🙄

Another thing I forgot about. Maybe someone can discuss what affected survival rates.

Hah! So I was right in the first place. I guess that makes sense, given how closely they resemble modern mammals. Thanks.

Except for sabre-toothed tigers, mastodons, and/or probably other species. 🙄 Maybe it would be more accurate to say that some mammal species were small and at least some of the small ones survived. Also, the asteroid supposedly hit in Mexico, and our ancestors came from Africa, which is on the other side of the planet. So maybe there weren't quite as many extinctions on that continent.

No, there was an extinction event. I think most mammals were relatively small back then. Lots of them, so I guess a few must have survived.

Placentalia existed at the same time as dinosaurs. They're mammals. Apparently the fossil evidence is a bit thin, but if you start with primates (or humans) and work your way back, placentalia are our closest ancestors that were alive 100 million years ago. Apparently the connection between mammals and dinosaurs dates back to amniotes, about 300 million years ago.

Maybe. They haven't been quite disproven though. There's a theory of geometric gravity without relativity, and it seems very strange to me that physicists wax philosophical about abandoning cherished misconceptions, while at the same time clinging to the classical ontology of matter as being made of solid entities of one kind or another, in the face of wave-based quantum theories. Like throwing out the baby and keeping the dirty bathwater because we've gotten so used to it. It's said that truth is stranger than fiction, and modern physics is one of the classic examples of that phenomenon. But I wonder if maybe 20th-century physics is the fiction and the truth is even stranger....

No more OP.... df = -2y dy, so f-1/2 df would be -2 f-1/2 y dy. But the integral in the problem is f-1/2 dy, which would be - f-1/2 df / 2y. So still not f-1/2 df.

You know, I've gotten into a lot of arguments about this lately (my thread), because I find the things I've been reading about modern physics so horrifying (19th-century principles of science being displaced by quantum and relativistic ideas that IMO seem more like mysticism). If you take quantum wave equations seriously as indications of what matter really is, your computer exists as a very complicated wave but not as a collection of particles. According to objective-collapse theories, quantized amounts of the wave keep collapsing repeatedly, creating the illusion of solid matter. The various theories differ in how and why the collapses occur. So an electron flying through the vacuum is literally a wave packet that spreads out in space, while an electron in a bubble chamber is a wave that keeps getting re-localized by interactions with the fluid in the chamber, and an electron in an atom is an ordinary(-ish) standing wave. These models seem radical because they reject the classical notion of matter as being made of "particles", which are just very small "objects". But classical ontology isn't a fundamental principle. It's just very familiar. It's an aspect of a specific class of models that are based on intuition developed from macroscopic observations.

DBB is a strange beast. The wave affects the particle, but not vice versa. So you have these unused ghost branches of the pilot wave floating around forever. Personally, I don't believe particles exist at all in any meaningful ontological sense, so I like objective-collapse interpretations (see my signature, for instance). No data supporting them yet, but I'm glad someone is investigating them.

Just to be on the safe side. The dinosaurs didn't know about asteroids, and look what happened to them.

You're integrating f-1/2 dy, not f-1/2 df.