KJW

Ok. There's no harm in admitting a lack of knowledge. Perhaps I was being harsh in expecting skills you genuinely do not have, especially given the festive spirit of the thread. I apologise. However, the questions I asked are legitimate: 1: Whenever you supply numbers to a formula, those numbers have units which should also be shown. Otherwise, how are we to know that the speed is in metres per second and not (say) miles per hour. Same applies to units of mass and energy. 2: It seems odd to specify a number as "5972200000000000000000000" instead of 5.9722 x 10^24 when you've already specified a number as 5.367545678×10^41. Also, the speed of light is 2.99792458 x 10^8 m/s when expressed in scientific notation. 3: This is about the accuracy of the numbers in the calculation. The accuracy of the final result is no greater than the least accurate number in the calculation. In your calculation, the least accurate number is the mass 5.9722 x 10^24 with only five significant figures. Therefore, the accuracy of the result (energy) is no greater than five significant figures. That is, 5.3675 x 10^41. The extra digits you supplied are just meaningless noise. It's obvious that you had just taken the number straight from a calculator.

For those interested, here is the metric I derived of a simple model of a ball of matter of mass [math]M[/math], radius [math]R[/math], and of uniform density: [math](ds)^2 = f(r^2) (c\ dt)^2 - \dfrac{(dr)^2}{f(r^2)} - r^2 ((d\theta)^{2} + \sin^2(\theta)\ (d\phi)^2)[/math] [math]\text{where:}[/math] [math]f(r^2) = 1 - \dfrac{2GM}{c^2} \bigg(\dfrac{1}{2 \sqrt{R^2}} \Big(3 - \dfrac{r^2}{R^2}\Big)\ H(R^2 - r^2) + \dfrac{1}{\sqrt{r^2}}\ (1 - H(R^2 - r^2))\bigg)[/math] [math]\text{and}\ \ H(x)\ \ \text{is the Heaviside step function:}[/math] [math]H(x) = {\begin{cases}1, & x \geqslant 0\\0, & x \lt 0\end{cases}}[/math]

For those interested, here is the metric I derived of a simple model of a ball of matter of uniform density: [math](ds)^2 = f(r^2) (c\ dt)^2 - \dfrac{(dr)^2}{f(r^2)} - r^2 ((d\theta)^{2} + (\sin(\theta)\ d\phi)^2)[/math] [math]\text{where:}[/math] [math]f(r^2) = 1 - \dfrac{2GM}{c^2} \bigg(\dfrac{1}{2 \sqrt{R^2}} \Big(3 - \dfrac{r^2}{R^2}\Big)\ H(R^2 - r^2) + \dfrac{1}{\sqrt{r^2}}\ (1 - H(R^2 - r^2))\bigg)[/math] [math]\text{and}\ \ H(x)\ \ \text{is the Heaviside step function:}[/math] [math]H(x) = {\begin{cases}1, & x \geqslant 0\\0, & x \lt 0\end{cases}}[/math]

1: Where are the units? 2: Why are there all those zeroes for the mass but the energy is given in scientific notation? 3: Why is the energy given to ten significant figures when the mass is only given to five?

I probably brought it up to illustrate how far-reaching the 2nd law of thermodynamics is. When it came to choosing between a violation of the 2nd law of thermodynamics, and a principle that I was unaware of but seemed necessary to prevent the violation of the 2nd law, I chose the principle that prevented the violation of the 2nd law.

Until recently, I believed that the event horizon didn't form until the entire mass was inside its Schwarzschild radius. The rationale behind this belief was that when the mass was almost but not quite inside its Schwarzschild radius, there was no smaller radius for which the mass inside this radius was inside its Schwarzschild radius (though I wasn't considering the increasing density closer to the centre, assuming this would be insufficient). However, I derived a metric of a very simple model of a ball of matter of uniform density. To my surprise, when the entire ball of matter is inside the photon sphere (1.5 Schwarzschild radius), the event horizon forms at the centre and expands as the ball contracts (until the event horizon meets the radius of the ball at the Schwarzschild radius). The reason the event horizon forms before the ball of matter has collapsed inside its Schwarzschild radius is because the event horizon depends on the gravitational potential which continues to become more negative inside the ball all the way to the centre, unlike the gravitational acceleration which is maximum at the surface in accordance with Birkhoff's theorem (shell theorem in Newtonian gravity). That is, my original belief was based on an erroneous view of what causes the event horizon (gravitational potential vs gravitational acceleration), though the metric makes it very clear. For a spherically symmetric collapse there is no change in the gravitation outside of the original radius of the matter (assuming matter isn't ejected). This is also a consequence of Birkhoff's theorem. Thus, there cannot exist spherical gravitational waves.

This rings a bell. I think you may have mentioned it before. Maybe it was in the context of @Prajna ’s machine with magnets, the one he tried to make before AI drove him bonkers. I have mentioned it before, but I don't remember if I've mentioned it on this forum. You might have seen me mention this on the old forum. What I find remarkable about this principle is that it's not really about anything "thermodynamic", but rather it's about the geometry of mirrors and lenses. At the time I first considered this, I realised that to capture the entire output from a source, only a prolate spheroid with the source at one focus would focus the image of the source onto the other focus, in which case the image is the same size as the source.

Yes, I enjoy analysing "perpetual motion" machines. I actually came across one which I could not debunk without invoking a principle that I was not previously aware of. The principle I invoked was that a focused image of an object cannot be brighter than the object itself.

Sure there is also statistics there, but stimulated - especially in superradiance, also in laser ... or wave behind marine propeller pushing or pulling energy from resonator is quite deterministic. For example white hole would emit, causing excitation in sensor of telescope. Applying T/CPT symmetry to this scenario, shouldn't black hole cause deexcitation of telescope sensor if prepared as excited? Just like absorption, stimulated emission is not deterministic. In the case of absorption, a photon has a choice between two options: 1, excite the molecule by being absorbed; or 2, do nothing. Each option has a probability. In the case of stimulated emission, a photon also has a choice between two options: 1, de-excite the molecule by stimulating the emission of a photon; or 2, do nothing. Each of these options also has a probability. In fact, the probabilities for stimulated emission are identical to the probabilities for absorption. Thus, when the number of excited molecules equals the number of unexcited molecules, there is no longer any net absorption or net stimulated emission. If [math]\text{X}[/math] and [math]\text{Y}[/math] from my previous post describe unexcited and excited states of a molecule, then the rate equation in my previous post describes the rate equation for absorption and stimulated emission, in which case the rate constant also depends on the illumination. It may come as a surprise that it is stimulated emission rather than spontaneous emission that is the reverse of absorption. However, the dependence of the rate constant on the illumination for both stimulated emission and absorption manifests the symmetry of the equations describing these two processes. Thus, both stimulated emission and absorption depend on the notion of causality and are therefore time asymmetric.

A clock, like anything else, has lower mass when lower in a gravitational potential well than when above. The work done lifting the clock (or whatever) increases the mass of the clock. An atom in an excited state will have a greater mass than the same atom in the ground state. This difference in mass will have the same proportion to the mass of the atom regardless of where the atom is in the gravitational potential. Therefore, the energy of the photon emitted will be lower for the atom that is lower in the gravitational potential well and thus will be gravitationally redshifted. But it is gravitational redshift as the primary phenomenon that determines that mass is lower when lower in a gravitational potential well. However, it is important to note that these differences in mass are measured from the same location. Measurements performed locally will not indicate any differences, as required by the principle of relativity.

There was also an episode of QI that dealt with this: One other thing that Sandi Toksvig could have done was flip the card upside down to reinforce that it was indeed she and not the mirror that flipped the writing.

Sure, e.g. throwing a rock to a lake symmetric in equations, there appear asymmetries of solutions ... for physics we know many such asymmetries , like entropy gradient, emission asymmetry (e.g. circulating electron losing energy), tendency for black hole formation from direction of Big Bang. But solving physics by the least action(GR)/Feynman ensemble(QFT) using e.g. boundary conditions in Big Bang and Big Crunch, they seem very similar just hot soups - symmetric ways of solving from symmetric boundary conditions, shouldn't the solution be also symmetric? If the equations are time symmetric, this does not imply that the solutions are also time symmetric, though it does imply that a time reversal transformation of a solution is also a solution. But it should be noted that there is no special reason for such a solution to lack time symmetry. To attribute the lack of time symmetry of a solution of a time symmetric equation to something like the second laws of thermodynamics is wrong and a misunderstanding of the nature of symmetry in mathematics and the physics based on such mathematics. For example, consider the second-order ordinary differential equation: [math]\dfrac{d^2 x}{d t^2} - k^2 x = 0[/math] This is invariant under time reversal [math]t \Rightarrow -t[/math]. The general solution is: [math]x = C_1\,e^{kt} + C_2\,e^{-kt}[/math] where [math]C_1[/math] and [math]C_2[/math] are arbitrary constants of integration. For [math]C_1 = C_2[/math], the solution is symmetric about [math]t = 0[/math]. For [math]C_1 C_2 \gt 0[/math], but [math]C_1 \neq C_2[/math], the solution will be symmetric about some [math]t \neq 0[/math]. However, for [math]C_1 C_2 \lt 0[/math], the solution is unsymmetric about any [math]t[/math]. In this case: [math]x = C_2\,e^{kt} + C_1\,e^{-kt}[/math] is the time reversed solution about [math]t = 0[/math]. So, although this symmetric differential equation does have symmetric solutions, it also admits unsymmetric solutions. As the equations are purely mathematical, the reason for the existence of unsymmetric solutions is also purely mathematical. Now consider the reversible reaction mentioned in an earlier post: [math]\text{X} \rightleftharpoons \text{Y}[/math] The rate equation for this reaction is the pair of first-order ordinary differential equations: [math]\dfrac{d\text{[X]}_t}{dt} = -k\,(\text{[X]}_t - \text{[Y]}_t)\\\dfrac{d\text{[Y]}_t}{dt} = -k\,(\text{[Y]}_t - \text{[X]}_t)[/math] where [math]\text{[X]}_t[/math] and [math]\text{[Y]}_t[/math] are the concentration (or number) of [math]\text{X}[/math] and [math]\text{Y}[/math] at time [math]t[/math], and [math]k[/math] is the rate constant. Under the time reversal [math]t \Rightarrow -t[/math], [math]\dfrac{d\text{[X]}_t}{dt} \Rightarrow -\dfrac{d\text{[X]}_t}{dt}[/math], [math]\dfrac{d\text{[Y]}_t}{dt} \Rightarrow -\dfrac{d\text{[Y]}_t}{dt}[/math], and therefore [math]k \Rightarrow -k[/math]. Thus, the rate equation is covariant rather than invariant. It is covariance that is required of the laws of physics, a weaker notion than invariance. However, the equation itself does remain unchanged under time reversal. Also, the equations are symmetric with respect to the interchange of [math]\text{X}[/math] and [math]\text{Y}[/math]. This rather than time reversibility is what the notion of reversibility is referring to. The solution of the equation: [math]\dfrac{d}{dt}(\text{[X]}_t + \text{[Y]}_t) = 0\\\text{[X]}_t + \text{[Y]}_t = \text{[X]}_0 + \text{[Y]}_0[/math] [math]\dfrac{d}{dt}(\text{[X]}_t - \text{[Y]}_t) = -2k\,(\text{[X]}_t - \text{[Y]}_t)\\\text{[X]}_t - \text{[Y]}_t = (\text{[X]}_0 - \text{[Y]}_0)\,e^{-2kt}[/math] [math]\text{[X]}_t = \text{[X]}_0\,\left(\dfrac{1}{2} + \dfrac{1}{2}\,e^{-2kt}\right) + \text{[Y]}_0\,\left(\dfrac{1}{2} - \dfrac{1}{2}\,e^{-2kt}\right)\\\text{[Y]}_t = \text{[X]}_0\,\left(\dfrac{1}{2} - \dfrac{1}{2}\,e^{-2kt}\right) + \text{[Y]}_0\,\left(\dfrac{1}{2} + \dfrac{1}{2}\,e^{-2kt}\right)[/math] For [math]k \gt 0[/math], the usually forward time direction value, both [math]\text{[X]}_t[/math] and [math]\text{[Y]}_t[/math] approach [math]\dfrac{1}{2} (\text{[X]}_0 + \text{[Y]}_0)[/math] as [math]t \to \infty[/math]. By contrast, for [math]k \lt 0[/math], the reverse time direction value, provided [math]\text{[X]}_0 \neq \text{[Y]}_0[/math], both [math]\text{[X]}_{t'}[/math] and [math]\text{[Y]}_{t'}[/math] move away from [math]\dfrac{1}{2} (\text{[X]}_0 + \text{[Y]}_0)[/math] as [math]t' \to \infty[/math] (NB, [math]t'[/math] is reverse time and therefore [math]t' \gt 0[/math] even though [math]t \lt 0[/math]). The difference between the first equation and the second set of equations is that the first equation is a second-order equation without any first-order derivatives, whereas the second set of equations are first-order equations. Unlike the second-order derivative, the first-order derivatives change sign under time reversal. Considering the rate equation from a physical perspective, the rate constant is a transition probability per time (with dimension [math]\text{T}^{-1}[/math]}. Thus, it is naturally a positive number. Its change in sign under time reversal represents a time asymmetry in the laws of physics. Specifically, the notion of causality is time asymmetric with the effect in the future of the cause. This would appear to statistically eliminate time reversed solutions although microscopic reversibility still applies.

If the equations are time symmetric, this does not imply that the solutions are also time symmetric, though it does imply that a time reversal transformation of a solution is also a solution. But it should be noted that there is no special reason for such a solution to lack time symmetry. To attribute the lack of time symmetry of a solution of a time symmetric equation to something like the second laws of thermodynamics is wrong and a misunderstanding of the nature of symmetry in mathematics and the physics based on such mathematics. For example, consider the second-order ordinary differential equation: [math]\dfrac{d^2 x}{d t^2} - k^2 x = 0[/math] This is invariant under time reversal [math]t \Rightarrow -t[/math]. The general solution is: [math]x = C_1\,e^{kt} + C_2\,e^{-kt}[/math] where [math]C_1[/math] and [math]C_2[/math] are arbitrary constants of integration. For [math]C_1 = C_2[/math], the solution is symmetric about [math]t = 0[/math]. For [math]C_1 C_2 \gt 0[/math], but [math]C_1 \neq C_2[/math], the solution will be symmetric about some [math]t \neq 0[/math]. However, for [math]C_1 C_2 \lt 0[/math], the solution is unsymmetric about any [math]t[/math]. In this case: [math]x = C_2\,e^{kt} + C_1\,e^{-kt}[/math] is the time reversed solution about [math]t = 0[/math]. So, although this symmetric differential equation does have symmetric solutions, it also admits unsymmetric solutions. As the equations are purely mathematical, the reason for the existence of unsymmetric solutions is also purely mathematical. Now consider the reversible reaction mentioned in an earlier post: [math]\text{X} \leftrightharpoons \text{Y}[/math] The rate equation for this reaction is the pair of first-order ordinary differential equations: [math]\dfrac{d\text{[X]}_t}{dt} = -k\,(\text{[X]}_t - \text{[Y]}_t)\\\dfrac{d\text{[Y]}_t}{dt} = -k\,(\text{[Y]}_t - \text{[X]}_t)[/math] Where [math]\text{[X]}_t[/math] and [math]\text{[Y]}_t[/math] are the concentration (or number) of [math]\text{X}[/math] and [math]\text{Y}[/math] at time [math]t[/math], and [math]k[/math] is the rate constant. Under the time reversal [math]t \Rightarrow -t[/math], [math]\dfrac{d\text{[X]}_t}{dt} \Rightarrow -\dfrac{d\text{[X]}_t}{dt}[/math], [math]\dfrac{d\text{[Y]}_t}{dt} \Rightarrow -\dfrac{d\text{[Y]}_t}{dt}[/math], and therefore [math]k \Rightarrow -k[/math]. Thus, the rate equation is covariant rather than invariant. It is covariance that is required of the laws of physics, a weaker notion than invariance. However, the equation itself does remain unchanged under time reversal. Also, the equations are symmetric with respect to the interchange of [math]\text{X}[/math] and [math]\text{Y}[/math]. This rather than time reversibility is what the notion of reversibility is referring to. The solution of the equation: [math]\dfrac{d}{dt}(\text{[X]}_t + \text{[Y]}_t) = 0\\\text{[X]}_t + \text{[Y]}_t = \text{[X]}_0 + \text{[Y]}_0[/math] [math]\dfrac{d}{dt}(\text{[X]}_t - \text{[Y]}_t) = -2k\,(\text{[X]}_t - \text{[Y]}_t)\\\text{[X]}_t - \text{[Y]}_t = (\text{[X]}_0 - \text{[Y]}_0)\,e^{-2kt}[/math] [math]\text{[X]}_t = \text{[X]}_0\,\left(\dfrac{1}{2} + \dfrac{1}{2}\,e^{-2kt}\right) + \text{[Y]}_0\,\left(\dfrac{1}{2} - \dfrac{1}{2}\,e^{-2kt}\right)\\\text{[Y]}_t = \text{[X]}_0\,\left(\dfrac{1}{2} - \dfrac{1}{2}\,e^{-2kt}\right) + \text{[Y]}_0\,\left(\dfrac{1}{2} + \dfrac{1}{2}\,e^{-2kt}\right)[/math] For [math]k \gt 0[/math], the usually forward time direction value, both [math]\text{[X]}_t[/math] and [math]\text{[Y]}_t[/math] approach [math]\dfrac{1}{2} (\text{[X]}_0 + \text{[Y]}_0)[/math] as [math]t \to \infty[/math]. By contrast, for [math]k \lt 0[/math], the reverse time direction value, provided [math]\text{[X]}_0 \neq \text{[Y]}_0[/math], both [math]\text{[X]}_{t'}[/math] and [math]\text{[Y]}_{t'}[/math] move away from [math]\dfrac{1}{2} (\text{[X]}_0 + \text{[Y]}_0)[/math] as [math]t' \to \infty[/math] (NB, [math]t'[/math] is reverse time and therefore [math]t' \gt 0[/math] even though [math]t \lt 0[/math]). The difference between the first equation and the second set of equations is that the first equation was a second-order equation without any first-order derivatives, whereas the second set of equations are first-order equations. Unlike the second-order derivative, the first-order derivatives change sign under time reversal. Considering the rate equation from a physical perspective, the rate constant is a transition probability per time (with dimension [math]\text{T}^{-1}[/math]}. Thus, it is naturally a positive number. Its change in sign under time reversal represents a time asymmetry in the laws of physics. Specifically, the notion of causality is time asymmetric with the effect in the future of the cause. This would appear to statistically eliminate time reversed solutions although microscopic reversibility still applies.

It should be noted that for the retarded solution, there is a concomitant decrease in the orbit when gravitational radiation is emitted. For the advanced solution, there is a concomitant increase in the orbit when gravitational radiation is absorbed. The difference between these two is that gravitational energy is naturally lost from the orbit, which is radiated away as gravitational radiation, whereas in the reverse, gravitational energy has to be supplied to the orbit by an input of gravitational radiation, which although possible, is unlikely to occur naturally.

Stimulated emission prevents one from inverting a population by simple absorption. It is very much a thermodynamics thing. For example, one of the reasons for using stronger magnets in NMR spectroscopy, and thus increasing the energy separation between the nuclear spin levels, is to reduce the population of the higher energy level relative to the lower energy level, thereby improving signal strength against saturation resulting from stimulated emission.

I've tried a few things and I couldn't get RationalWiki to ask my permission to download, nor any evidence of a surreptitious download. What is the file type of the download?

Well, I just managed to solve a problem on my computer where the Bandcamp website didn't work properly. It turned out the problem was that I had NordVPN running in the background (I wasn't actually using the VPN, just the app was running in the background). It's not the first time I had a problem with NordVPN running in the background. I mention this to point out that problems can have unexpected causes.

Thanks. I'm on a Windows 10 desktop PC. I opened the RationalWiki website and nothing untoward happened, including anything downloaded to my "Downloads" folder.

How did you know this happened, and to where did the file download?

True, but I don't think the different altitudes are necessarily equivalent in terms of the satellite function. But it's the number of satellites being planned for the future that is the scary part. From the article: Back at the start of 2019, there were right around 2000 active satellites in orbit around planet Earth. Here in 2025, there were 3000 now-active Starlink satellites — satellites that are part of just one company’s megaconstellation — that were launched just this year, alone. Many other companies are launching their own satellites as well, some of which are very high-impact, large, reflective, and heavily light-polluting. As of December 7, 2025, there are more than 17,000 satellites in orbit around Earth, with announced plans to increase that number into the many hundreds of thousands over the next few years. While everything is in working order, even such a high number of satellites would probably be able keep themselves far enough apart. But it's when things go wrong that there may just be too many things in orbit for everything to remain stable. Bear in mind that it's not a perfect vacuum up there, so satellites require thrusters to maintain orbit. Thrusters can also prevent collisions, so the ability to control a satellite is quite important with regards to avoiding the Kessler syndrome. I think I'll defer to someone with greater expertise on this. However, two points that I did note was that the lab origin cause has no actual evidence, whereas the evidence for the natural zoonotic spillover scenario is found in the genome of the COVID-19 virus itself.

I thought that but accept that it is a bit of hyperbole. I'll admit that I was open to the lab origin conspiracy theory. Although the article of this thread has further details, the following is a link to an article titled "Ask Ethan: Couldn’t COVID-19 have originated in a Chinese lab?" (April 11, 2025): https://bigthink.com/starts-with-a-bang/covid-19-origin-chinese-lab/ According to the article, the limitation on the number of satellites in orbit around earth is based on the idea that if there is a solar event that disables a number of satellites' ability to be controlled, then those satellites will eventually collide with other satellites, producing debris that collides with yet other satellites, leading to a cascade that produces so much debris that we are no longer able to send anything into space.

This is not correct. As neutral molecules approach each other, there is attraction until the atoms try to get within each other's atomic radii, then there is a sharp repulsion. Also, gravity is too weak to be significant in intermolecular interactions. Intermolecular interactions are electromagnetic in character. Even for uncharged molecules without permanent dipoles, transient induced dipoles called "London forces" result in attraction between molecules.

[math]{\partial^2 x \over \partial t^2}[/math] [math]\displaystyle {\partial^2 x \over \partial t^2}[/math] [math] \dfrac{\partial^2 x}{t^2}[/math] [math] \frac{\partial^2 x}{t^2}[/math] [math]\displaystyle \frac{\partial^2 x}{t^2}[/math]

From: https://bigthink.com/starts-with-a-bang/10-scientific-truths-unpopular-2025/ (December 9, 2025) Scientific truths remain true regardless of belief. These 10, despite contrary claims, remain vitally important as 2025 draws to a close. 1.) 2024, the latest full year on record, saw the highest CO2 levels and the highest average temperatures since we first began tracking them. 2.) Interstellar interlopers are real, and while we found a new one (only the third ever) in 2025, they are still not aliens. 3.) We broke the record for most distant galaxy ever found but still haven’t spotted the first generation of stars. 4.) Earth’s orbit has a finite “carrying capacity,” and if we exceed that, such as with megaconstellations of satellites, it will inevitably lead to Kessler syndrome. 5.) The germ theory of disease is real, and vaccination is the safest, most effective strategy to combat these deadly pathogens. 6.) SARS-CoV-2 led to COVID-19 in humans as the result of a natural, zoonotic spillover event, not as the result of a leaked pathogen from a Wuhan Lab in China. 7.) The Universe’s expansion is still accelerating, the Hubble tension remains an important puzzle, and the much-publicized evidence we have is insufficient to conclude that dark energy is evolving. 8.) “Passing peer review” doesn’t make a scientific study true; it just means the study is robust enough that it’s passed the “start line” for consideration by the community. 9.) We’ve found evidence for organics on Mars (again), but still have no good evidence for life on any planet other than Earth. 10.) You still need to know science in order to do it; “vibe science” is nothing more than AI slop. See https://bigthink.com/starts-with-a-bang/10-scientific-truths-unpopular-2025/ for details on each of the 10 scientific truths that somehow became unpopular in 2025.

What difficulties are you having with this?