Lorentz Jr

You said "the short answer, less gravity" and "This answer assumes that the density is the same throughout the planet depth." So it looked like you were saying "less gravity assumes that the density is the same throughout the planet depth." The boundary between increasing gravity and decreasing gravity (i.e acceleration as a function of r) is constant gravity: [math]\displaystyle{a(r) = \frac{Gm(r)}{r^2} = g}[/math] [math]Gm = g r^2[/math] [math]G dm = 2 g r dr[/math] [math]\displaystyle{\rho(r) = \frac{dm}{dV} = \frac{dm}{ 4 \pi r^2 dr}}[/math] [math]\displaystyle{\rho(r) = \frac{dm/dr }{ 4\pi r^2 } = \frac{2gr}{4\pi r^2 G}}[/math] So [math]\displaystyle{\rho(r) = \frac{k}{r}}[/math], where [math]\displaystyle{k = \frac{g }{ 2 \pi G}}[/math]. In other words, the acceleration will be g all the way down as long as the density is inversely proportional to the distance from the center. It will decrease with r (ie. increase with depth) if the density depends on r more sensitively than 1/r, and will increase with r (decrease with depth) if it depends less.

No, you had it right the first time. The derivation of the shell theorem that exchemist just mentioned applies to each (spherically symmetric) shell individually, regardless of its density. For constant density, the gravitational field is linear in the radius: [math]\displaystyle{a(r) = \frac{G m(r)}{r^2}}[/math] [math]\displaystyle{a(r) = \frac{G \rho (\frac{4}{3} \pi r^3)}{r^2}}[/math] [math]a(r) = G \rho (\frac{4}{3} \pi r)[/math] [math]a(r) = G \rho (\frac{4}{3} \pi R) \displaystyle{ \left(\frac{r}{R}\right)}[/math] [math]\displaystyle{a(r) = \frac{GM}{R^2}\left(\frac{r}{R}\right)}[/math] [math]\displaystyle{a(r) = g\left(\frac{r}{R}\right)}[/math]

Well, I don't want to get into another flame war with another senior poster by pointing out that "Now you’re just making stuff up" is a perfect example of "not a single word of supporting logic or evidence", or the fact that a phrase means something doesn't imply that someone isn't using it for empty rhetorical purposes, so ... thanks for chatting, guys. Have a nice day.

Ah, "moving the goalposts". I've seen that expression on this forum before. Never with any explanation of what the goalposts are or how they've been moved, only as little one-line "zingers", as though quoting that catch phrase somehow proves anything. 🙄

What's the reason? At the point in time when I set a clock to zero, t=0 corresponds to "now". Please enlighten me, swanson. So far, your comments have been just as vague as iNow's.

That's true, but the technicalities of signal propagation still don't prove that the word "now" has no meaning, regardless of whether they're organic or inorganic. Even in relativity, any given observer can construct a model of their surroundings at t=0. For example, if we determine that some nearby star was at a point in its life cycle where it was about to go nova when it emitted the light that we just received recently, we may conclude that the nova has occurred by now and we can expect to detect it fairly soon. And this is the Speculations area, so we're not even limited to the relativistic model. Your point remains ambiguous, because you haven't backed it up with a single word of supporting logic or evidence.

There's no such thing as "measuring now", any more than measuring "yesterday" or measuring "tomorrow". You can measure anything that can be measured, and you can measure it anywhere in the universe you can get to. If you measure it "now", you'll perceive it "300-700ms" later, and whatever you're perceiving "now" happened "300-700ms" ago. If you measure something that was caused by some other event that occurred more than one light-day ago, you may even be measuring evidence of something that happened a day earlier, but you're still measuring properties that physical systems have at the time you measure them, not "measuring now" or "measuring yesterday". The biology of human perception has no direct connection with the physics of time.

You said "the present doesn’t even exist" based on the idea that it takes "300-700ms" for "a wet meat computer" to "sense" it. The misunderstanding seems to have been yours since your comment isn't relevant to the topic.* * (or, more precisely, the premise of the comment isn't relevant to the conclusion.)

You're confusing physics with biology. Regardless of how long it takes us to perceive things, and regardless of how inaccurate those perceptions may be, we can still reasonably infer that something existed some time ago to cause those perceptions, and from our memory of past perceptions, we can reasonably infer that the past state(s) of the world around us probably led to a current state that exists now and will probably lead to more perceptions for us at some time(s) in the future.

No, it doesn't. In relativity, time is a full-fledged dimension, the universe is a four-dimensional block, and the flow of time is considered to be an illusion. The only special thing about time (in SR, anyway) is that the sign of its coefficient in the space-time metric is the opposite of the spatial dimensions (and it's multiplied by c). And it's often presented that way when nonphysicists ask about it. If you persist in your questioning, though, they'll eventually admit that relativity is just a model and nobody really knows what time is.

The thing about gravity is that inertial mass is the same as gravitational mass. That's too much of a coincidence to ignore, so geometric models make sense. Geometric theories have fewer arbitrary parameters, and physicists like that, because theories with fewer parameters are less likely to be mistakes out of the theorist's imagination. So objects don't really "fall", they just travel along the straightest possible path in a curved world. Those paths are called "geodesics". No push, no pull (except for other forces besides gravity), just motion. That's not the standard convention anymore. Objects get harder to accelerate, but mass is considered to be constant and the increase in apparent inertia is written explicitly as the gamma factor ([math]\gamma[/math]). The effects of relativity are well known and experimentally verified. GPS without relativity is less accurate. Special relativity is built into general relativity. From a theoretical standpoint, GR replaces SR. SR is only used in situations where gravity isn't important because it's much simpler than GR. Yeah, I'm with you on that one. That's what Lorentzian theory is about. As I said, though, it's not mainstream theory, so this forum only allows discussion of it in the Speculations area. Yep. I'm with you on that one too. We just don't know enough to say for sure.

Yeah, that is a bit counterintuitive. It's mainstream theory though, and most physicists seem to believe in it fervently. People like the Cambridge group behind gauge theory gravity have proposed alternative theories based on an optical analogy, but they're a tiny minority.* A scientist should be open to anything that's consistent with the principles of science. The problem right now is that the experimental data available to us since the turn of the 20th century are so confounding: The speed of light seems to be the same for all observers, subatomic phenomena seem to be nondeterministic, and no one has been able to detect anything to indicate that the universe has a special reference frame of its own. It all seems to violate the traditional scientific principles developed in the 19th century, so the 20th-century physics community abandoned them to a a large degree and formulated new ones. And string theorists have even been challenging the one most important, defining principle of science: it should make predictions that are in agreement with experimental data. Maybe the world is weary of science. Maybe we have too many high-tech weapons and we're on the verge of blowing ourselves to smithereens, so people want to get back to nature and restore some balance in life. At least until Elon Musk can colonize Mars. 😊 * I originally mentioned Ilja Schmelze's GLET, but that uses the same geometric model of gravity as GR.

Why do you play "Gotcha" with people, making critical comments without providing any more information to explain your criticism? The context was Genady's comment "A accelerates to a faster relative speed and catches up with B". I didn't start it.

The formulae in question are the Lorentz transformations. The Lorentz transformations are nonlinear in the relative velocity.

Because the principles that govern their behavior are independent of their histories (according to SR). Don't be silly. [math]\gamma[/math] is nonlinear in the velocity.

That depends on what you mean by "determines". "Breaking the symmetry" means making it possible to mathematically determine who ages more, but my counterexamples show that the acceleration itself can't directly cause a slowdown of aging. Yes, that's right. Because the Lorentz transformations are nonlinear.

The acceleration breaks the mathematical symmetry of the paradox, but it doesn't provide a physical mechanism that can cause the aging difference. This can be disproven with two counterexamples: If one performs the experiment around the Sun instead of, say, Alpha Centauri, with exactly the same accelerations (which would have to be very high in this case, given the relatively short distance to the sun), the difference in elapsed times is a matter of minutes rather than years. There's a three-observer variant of the experiment (which I like to call the "triplets paradox" ) that involves no acceleration at all but has the same result. One spaceship flies by Earth and travels to Alpha Centauri, and the other one gets up to speed near AC, heads toward Earth, crosses paths with the first one, and flies by Earth.

Yes, it's powerful and beautiful and symmetric, but it doesn't make sense. There's no reason the apparent laws of physics shouldn't be affected by the observer's state of motion at all. It only seems reasonable based on our primitive intuition of space as a substanceless geometric void, because how can nothingness have a reference frame? On the other hand, how can a substanceless void support fields? And if the vacuum has some kind of substantive existence (which GR says it does), why wouldn't it have its own reference frame? If "explaining" SR is simply a matter of describing the math behind it, then SR is inconsistent with any deterministic mechanism whatsoever to explain why time dilation occurs in the twins paradox. According to SR, nothing happens in the spaceship any differently from the way things happen on Earth, and yet somehow less time passes on the spaceship. That's fundamentally unscientific. As I was saying earlier, the relativistic "explanation" relies on the same kind of frame-changing errors that perpetual-motion machines are based on (and that Einstein, as a competent patent clerk, must have been intimately familiar with). It's a kindergarten-level problem in control theory: There has to be some mechanism that causes the difference in elapsed time, and there has to be some difference between Earth and the spaceship that the mechanism can detect so it acts on them differently. To make a simple analogy, you can't drive your car around town unless it has an engine in it, and you can't start the engine unless you do something (like turning the key in the ignition) that it can detect. And you can't make the car go faster or slower unless you interact with the engine though the gas pedal. There has to be a mechanism, and there has to be something that controls it.

Who knows? In principle, it's the frame of the vacuum, not matter, so for all we know, all the matter in the visible universe could be moving relative to it. I wouldn't want to guess about that.

But it's often presented as a "why" explanation. Sean Carroll and Lee Smolin have both said relativity can be "explained" by a "change of intuition", and I've encountered similar comments on internet forums. I always have to argue with people for at least a page of comments before they admit what you just said. And the Lorentzian picture is consistent with a relatively simple "why" explanation. If the vacuum (a) has its own reference frame, (b) implements both center-of mass motion and internal time evolution of matter, and (c) has a fixed capacity to do so, then time dilation is a simple matter of "time sharing": the "processing power" required to implement CoM motion leaves less power remaining for internal motion, so that motion proceeds more slowly. Because I'm trying answer the "why" question, and mathematics doesn't do that. At least classical geometry feels like an answer. Anyway, I'm tired of arguing about this subject. One of the key tricks that people use in "explaining" perpetual-motion machines is changing reference frames. Once all of the machine's behavior is analyzed in the same reference frame, it becomes clear that there's no perpetual motion. Relativity does the same thing. The only way you can "explain" anything in relativity is by changing reference frames. That's all I have to say, and I'll understand if you don't agree.

I'm not convinced. The length of a world line is just the behavior of a local, comoving clock, and I don't trust a clock in a gravity well to measure anything except its own behavior, any more than I would trust a person who has been drugged with tranquilizers to count out seconds for me. If the laws of physics are the same everywhere, then there's no such thing as "local physics"; there's only physics. Actually, I wasn't entirely comfortable with the word "singularity". I'm not sure what would be the best word for that. My position is that the event horizon is physically meaningful because any "observer" inside it will be totally time dilated, i.e. in a sort of "suspended animation". It's the same argument as in the twin paradox: You can talk all you want about "local time" or "local physics" or "local reality", but the astronaut will have a rude awakening when he lands back on Earth and discovers that he's missed out on several years of history during his journey to Alpha Centauri and back. The only difference is that we don't know how to get things back out of black holes.

In other words, how deep is the Tower of Turtles? 😄 Certainly not fields. The most obvious explanation is that they're properties of the vacuum. I could have sworn I saw a youtube video where John Spence called them "liquids", but I can't find the quote. Maybe it was someone else. Maybe Sean Carroll, in a different video. 🤔 There are only two distance-preserving forms of velocity addition: Newtonian (3-translation) and Einsteinian (4-rotation). What's the reasoning behind that? I learned the rule a long time ago, but I've forgotten where it comes from, and I haven't been able to find any references to it. 😣 Anyway, my point is that relativity hasn't been absolutely proven. Lorentzian theory with Newtonian geometry (absolute space) is still scientifically viable. The apparent laws of acoustics depend on the observer's motion relative to the surrounding air, and there's nothing unnatural about that. And researchers at the Pierre Auger Observatory are looking for violations of Lorentz invariance in ultra-high-energy cosmic protons. (They haven't found anything yet, but there's no proof that they can't.) Have you ever tried running your computer at those speeds? Maybe there would be problems. I don't buy the geometric argument for time dilation in the twin paradox ("The astronaut is younger because he took a shorter path through spacetime"). It seems like meaningless wordplay. Minkowski space is a very nice mathematical abstraction, very useful and convenient, but I don't see how it qualifies as "geometry" in the same physically intuitive way that 3D space (or any space with all positive terms in the metric tensor) does. As I said about GR, curvature is okay, because I can extrapolate from the shape of a balloon. But to my mind, adding negative terms to the metric invalidates the space as an intuitive explanation for physical phenomena, including time dilation (which is "real", i.e. frame-invariant, in the twin paradox).

Thank you, Mordred. You're absolutely right about that. 🙂 I don't think so. This is the thing about relativity that reminds me of New Age mysticism. "Every individual's perspective is equally valid." I think GR breaks down at the event horizon and that's the end of it. It's not a non-physical singularity, it's a physical singularity. No more time evolution for anything inside. I'm sure the math from the infalling observer's frame is very interesting and fun to work out, and it makes for entertaining fiction, with all those newly created universes and whatnot, but I don't think it really matters. The observer is completely time dilated in the coordinate frame, and I think that frame most closely approximates "ontological reality". This is the Lorentzian view of space and time. This is also something that distinguishes black holes from neutron stars and ordinary matter. The effect that prevents neutrons and electrons from collapsing in a weaker gravitational potential is their own internal degeneracy pressure, but black holes are a whole 'nother story. What prevents them from collapsing any more than they do is the disabling of the vacuum itself. Like it turns to molasses because of the gravitational stress, and then keeps getting thicker and thicker*, until the infalling observer is in a state of ... "suspended animation", I guess you could call it. It's hard to say for sure, of course, because we can't look inside the BH. But I think this picture is more "valid" than the relativistic one, because it's naturally consistent with Bekenstein-Hawking radiation. * (meaning more and more "viscous", so to speak)

I don't see any reason not to take the math seriously. I also don't understand why Georges Lemaître called the event horizon a nonphysical coordinate singularity. The θ=0 or π axis is a nonphysical singularity because the coordinate system is defined in terms of it, but the event horizon of a black hole is a calculated result. Personally, I suspect that Lemaître's singularity at r = 0 is nonphysical and the BH is full of matter suspended in the inactive vacuum all the way out to the event horizon. Black holes as frozen stars It looks like the Russian thing may be a myth.

Has it ever occurred to anyone that the "frozen star" model of black holes provides a simple and obvious explanation for the fact that the entropy of a black hole is proportional to the BH's surface area? (the Bekenstein-Hawking formula) If the BH is frozen on the inside, then only a layer on the surface has any unrestrained degrees of freedom. There's no need for complicated hologram theories. (a) General relativity breaks down at the event horizon; (b) the vacuum inside the BH is incapacitated by some kind of stress associated with the gravitational potential, so nothing inside the event horizon can move*; and (c) the only source of entropy is the outer layer of matter at the event horizon. * (In other words, the vacuum's state might be something vaguely analogous to whatever high-pressure/high-temperature solid allotrope of iron Earth's inner core is made of.)