elfmotat

When he's talking about information, he's speaking of entropy which is a measure of the system's hidden information (information which has been "course-grained" away). Total information, if you can keep track of it, is always conserved. Entropy is not conserved. The amount of "stuff" present doesn't need to change for the entropy of the "stuff" to increase. For example, take the picture below: At the top, two types of gas molecules are present in a box but are separated by a barrier. At the bottom, the barrier has been removed and the gasses have been allowed to spread out and mix together. The bottom box's entropy is greater than the top box's, just from allowing the gasses to mix. In geometric units (c=G=1), the area of the event horizon (of a non-rotating BH) is [math]A=16 \pi M^2[/math], and its entropy is [math]S = A/4 = 4 \pi M^2[/math]. If we were to assume a perfect collision between two black holes of mass [math]m_1[/math] and [math]m_2[/math], where no energy is lost, the new combined BH would have a mass [math]M=m_1 + m_2[/math]. Its entropy would therefore be [math] S = 4 \pi (m_1^2 + m_2^2 + 2 m_1 m_2)[/math], whereas the entropy of each BH before collision would be [math]S_1 = 4 \pi m_1^2[/math] and [math]S_2 = 4 \pi m_2^2[/math]. We therefore see that [math]S > S_1+S_2[/math]. The entropy generated from their combination is [math]S_{gen} = 8 \pi m_1 m_2[/math].

Hi! Unfortunately I've been pretty busy working, working on my degree, and playing music to get much physics self-study done for a while. I'm looking to get back into it, so hopefully I'm not too rusty.

Your intuitions are good. Newtonian gravity can be derived from GR with the assumptions that: 1) gravity is weak, and 2) matter is non-relativistic. In particular you assume that the metric is nearly flat, different only by a small amount [math]|h|\ll 1[/math]: [math]g_{\mu \nu} = \eta_{\mu \nu} + h_{\mu \nu}[/math] You plug this into the Einstein Field Equations (making use of the fact that matter is non-relativistic so all but the 00-component of the Stress-Energy Tensor will be zero), and you're left with the differential equation: [math]\nabla^2 h_{00} = -8 \pi G \frac{\rho_E}{c^2} = -8 \pi G \rho_M[/math] where [math]\rho_E[/math] is energy density, which we can replace with mass density [math]\rho_M[/math] because matter is non-relativistic. Note the similarity to the Poisson Equation for Newtonian gravity: [math]\nabla^2 \Phi = 4 \pi G \rho_M[/math] for gravitational potential [math]\Phi[/math]. Indeed we can simply identify [math]h_{00} = -2 \Phi[/math] and they are equivalent. So using only the assumptions that gravity is weak and matter does not move fast, we obtain the fundamental equation of Newtonian gravity from GR. (The inverse-square law can be derived from Poisson's equation.) AFAIK your suggestion to replace the denominator of the inverse-square law with the interval (proper distance perhaps?) does not really have any meaningful interpretation.

Oh, so you're arguing for a particular interpretation of QM? This sounds a lot like the De Broglie-Bohm interpretation. Unfortunately that's probably not going to be very useful. There is no test you can do to distinguish which interpretation is 'correct.' They're called interpretations for a reason!

I agree. My point was that "time 'actually' being effected" is a vague and ill-defined concept.

Also, what exactly is the difference between "two observers observing time differently," and "time 'actually' being effected"? What test should we contuct to determine if time has actually been effected if measuring differences with clocks is not sufficient? All 'clocks' are effected in the same way, including biological processes. If it were otherwise, we'd be able to measure time differences between different types of nearby comoving clocks, which is not what we observe. (Also, this would provide a way to measure 'absolute' velocity, violating the Principle of Relativity!) In what way does this not constitute time being effected? I'm not sure how to convince your father that time and space are interwoven other than to point him to the math. The math interweaves them, and the math agrees with observation and experiment.

You should point out that: 1) Human brains evolved to intuitively understand slow moving (compared to c), macroscopic, gravitationally weak phenomena. It should not be surprising that we fail to intuitively understand fast moving, cosmic scale (or micro scale), gravitationally strong phenomena. Common sense is not useful in these regimes, and will lead you down the wrong path more often than not. 2) That time dilation's existence is not under debate. Relativity is one of the best tested fields in science. As an everyday example, GPS systems must account for time dilation due to both motion and gravitation. They would drift off-mark significantly without relativity.

Most people take a linear algebra course after taking multi-variable calculus. Regardless, much of Special Relativity can be learned with basic algebra and the Pythagorean Theorem. There are many good explanations of the 'light-clock' thought experiment floating around, which is a good starting point.

Yes. There are a number of definitions of 'mass,' each with different properties, some of which are very rarely used, and some which aren't very useful. Just to name a few, in SR there's rest mass, relativistic mass, transverse and longitudinal mass. In GR things get even more complicated when trying to come up with definitions of non-local mass. As a result there are the Komar, ADM, and Bondi definitions, among others. https://en.wikipedia.org/wiki/Mass_in_special_relativity https://en.wikipedia.org/wiki/Mass_in_general_relativity Usually when people talk about 'mass,' what they are referring to is rest mass, and usually the context will make clear to what one is referring. Note that multiple definitions of a quantity is not particularly unusual. For example, in SR there's the coordinate acceleration, which is defined as [math]a^i := \frac{d^2 x^i}{dt^2}[/math]. This vector is not invariant under Lorentz boosts (which is not surprising because it is explicitly coordinate-dependent). There's also the four-acceleration: [math]a^\mu := \frac{d^2 x^\mu}{d \tau^2}[/math]. This vector is Lorentz-invariant, in that its magnitude does not change under boosts and corresponds to proper acceleration (i.e. the acceleration it actually 'feels', or that an accelerometer would actually read). In GR the four-acceleration is redefined as: [math]a^\mu := \frac{d x^\nu}{d \tau} \nabla_\nu \frac{d x^\mu}{d \tau} = \frac{d^2 x^\mu}{d \tau^2} + \Gamma^\mu_{\lambda \sigma} \frac{d x^\lambda}{d \tau} \frac{d x^\sigma}{d \tau}[/math]. This vector is invariant under all diffeomorphisms in that its magnitude corresponds to proper acceleration. Thanks!

I'm not sure what you're asking. Mass remains constant under a change in reference frame, if that's what you mean.

Special or General Relativity? If you're already familiar with SR and want to move onto GR then I agree with ajb's recommendation. If you're new to it I recommend reading Spacetime Physics by Taylor and Wheeler. Carroll's full GR textbook is excellent as well.

He's positing that mass is some functional of the stress (tension/compression) of the aether field... which seems immediately false, unless there's some way to get discrete mass values for elementary particles in this manner.

You seem to be describing some sort of field whose properties determine mass. If you could formalize this it would help narrow down exactly what you're talking about, and whether or not the idea is self-consistent and consistent with observation. I'm not sure how this is a problem. Any ToE is going to have broken symmetries, resulting in interacting components. For example electroweak symmetry -- at low energies the symmetry is broken resulting in EM and the weak force. Is the universe more 'boring' because we know they unify at some level?

Okay: There is no wave-only explanation of the photoelectric effect (unless you count QED as being 'wave-only'). That's why it's a well-known effect! It forced physics to adopt a particle approach. What does this mean? Mass isn't a measure of compression in any model I'm aware of. Why do you think this should be the case? And compression of what? The 'medium' you keep referring to? Again, you haven't defined this well enough for us to comment. The first two assumptions seem reasonable for any 'medium' that's supposed to fill space, but I don't see why you're assuming it should be compressible. How does it get compressed? How does it evolve? What are the dynamics of this medium? What is "absolute consistency" and how does a finite speed of light imply it? Not always! Not even most of the time! These are parameters that cannot be explained by any current theory. How does your model seek to explain them? That's interesting. Could you expand on this? I think you're trying to come up with a physical 'theory' without really understanding what a physical theory is, and without having all the facts. How very generous.

Why? The term "empty space" implies that there's space (i.e. not zero distance between all objects) and that it's empty. You can define distances in space without needing any matter, or any type of "medium" as you call it. Your proposed "medium" is not well-defined, and it has no explanatory power, theoretical basis, or evidence for its existence. Physics is incomplete, for sure, but that doesn't mean making up nonsense is a good way to fill in the gaps. As of yet many of them cannot be. There are many tunable parameters in the Standard Model that cannot at present be explained by any deeper theory. (Because we don't have a deeper theory yet!) I'm curious how you're able to do any physics without math. It's not entirely clear what you're trying to do because you haven't expressed or defined any of the concepts you're discussing to any satisfying degree. You also appear to hold a number of misconceptions. We're not clear on how to help, because frankly none of us know what you're talking about!

Given two unit quaternions, [math]p[/math] and [math]q[/math], you can always find another unit quaternion [math]r[/math] such that [math]rq=p[/math] which represents the amount you need to move [math]q[/math] to match [math]p[/math]. Solving for [math]r[/math] gives: [math]r = pq^{-1} = p~ \textup{Conj}(q)[/math] The angle between [math]p[/math] and [math]q[/math] is the angle of [math]r[/math], which is given by: [math]\alpha =2 \textup{cos}^{-1}(\textup{Re}(r )) =2 \textup{cos}^{-1}(\textup{Re}(p~ \textup{Conj}(q)))[/math]

I was under the impression that you saw the gap as a problem to be fixed. "Right" or "wrong" choices being those that do/don't close the gap. It implies they're too weak to think and decide for themselves. Maybe you're right, societal influences play a particularly massive factor. I just don't think we're that easily programmable, especially when it comes to important life decisions. Do you have any evidence of systemic attempts to dissuade women from entering STEM? That's a bad analogy. Getting bad feelings from being harassed is not the same as letting societal pressures control your life decisions. The former can't be helped, as it is not their choice to be harassed. The latter can be helped -- it is entirely within their control. Swayed? Sure. So magnificently manipulated by the international community that huge cross-cultural gender gaps emerge and stabilize? Seems unlikely. Okay. I'm still not convinced by this though. How would you even test the "subtle societal pressures plays large role in career choice" hypothesis? It is a fact that males and females are biologically predisposed to have at least somewhat different interests (see post #2). It is my opinion that this accounts for different career choices. It is my opinion that this probably plays a larger role in the STEM gender gap than culture, given that it is a stable cross-cultural phenomenon. My arguments are tailored to reflect those opinions. What careers, in the developed world, are still restricted to men? What field could I get a job in as a man but not as a woman? We've had equal opportunity laws for decades. I see absolutely zero evidence for systematic discrimination of this kind. No. For example, Alaskan crab fishermen should be paid more than a common carp fisherman. Hazard pay. That men are more likely to take these types of dangerous jobs is irrelevant to whether they should pay more.

Do hiring managers also choose your college major for you? The same gap is reflected there. You disingenuously removed the next part, where I asked Phi to explain what is wrong with my reasoning. It's now considered a strawman to ask what is erroneous about an argument?

Women decide for themselves (at least in modern western countries) what careers they go into. Obviously you must think they choose wrong en masse, resulting in the STEM gap. What, exactly, is incorrect about the above? Do you agree that women decide on their careers for themselves (usually, at least)? Do you disagree with those choices at a systemic level? Do you think you know better? Do you agree that that sounds a bit disrespectful? Do you have any studies (or anything else) which demonstrate a clear link between advertisements and career choice? This reminds me of the "video games will make you violent" argument that lasted for a decade or so before the assertion was conclusively put to rest. I don't think you're giving humans enough credit. I never said it was an all or nothing problem, nor did I ever imply it. I was careful to phrase my reply as a question -- as in "do/don't you agree with this(?)". If you go back and read my posts I was careful to say biology plays at least some role. I never said it was all biology, and I never said culture plays no role. I'll ask that you don't attempt to psychoanalyze what I 'need.' It puts me in the uncomfortable position of having to defend my own feelings, which you have now portrayed as possibly deranged. If the gap is the result of human beings making life decisions, what is there to help? Do you want to somehow socially engineer all careers so that the demographics are 50-50? Why? Wouldn't that just shift lots of men and women into fields they don't really want to be in? That's the opposite of helping. In free societies where people are free to choose their own careers, gender gaps inevitably form. This is a demonstrable fact, and I don't find it to be a "bad" or "wrong" phenomenon. Just like I realize men will continue to die at ~20x the rate of women at work, commit suicide at ~5x the rate of women, and the prison population will probably always be ~90% male. Equal opportunity does not always result in equal outcome. That's pretty perpendicular to the point I was making (my aside was still driving the same point), but I would agree that people who take risks for their job should be compensated. Well, I'd personally never refer to any group of people as "the X crowd." Not because it's disrespectful, but because that combination of words is not really in my vocabulary. I'd also personally not find it particularly offensive if thread's title was, for example, "why is the male crowd not attracted to nursing(?)".

You didn't link to those sections. You linked to the "biological explanations" section, for which there is only a short paragraph about spatial intelligence. What am I supposed to assume when you link to a specific section of a wiki page? I completely understand what you're saying. I'm definitely not trying to misrepresent anyone's position. If you can locate any instances where I have done so and not corrected myself, please point them out.

The problem is everybody else? Good luck convincing everybody else.

I suppose I could do without the colorful language, but I don't understand your objection. You think the gender gap in STEM is mostly cultural in origin. You assume (or at least implied) that cultural influence is driving women away from the careers they really​ want to be doing. I just find the lack of respect for womens' agency a bit irritating. These are adult women making adult decisions about the fields they want to go into. It almost sounds like you're saying they've been brainwashed by society into not majoring in engineering. The notion that culture is creating the gap is hard to see. Shouldn't this mean that in gender-egalitarian societies the STEM demographics should float somewhere around 50-50? Because that would be demonstrably false. See, e.g., Norway, Sweden, and Denmark. As an aside, it's also a bit funny that nobody ever mentions the workplace-death gender gap, which is about 20:1 male to female workplace deaths. Do you think this is culturally motivated? Do you think males are biologically predisposed to be willing to do more dangerous work? The latter is certainly demonstrable, with testosterone being positively correlated with risky behavior. Not really. No more than "male crowd" would be, at least. How would you rephrase the title to make it seem less divisive? I wasn't referring to your stance (which I thought was pretty plain from the wording and context -- but I guess not), I was referring to the general sentiment of the thread. The original source of disagreement was between myself and iNow, because he expressed incredulity at the notion that biology had much if anything to do with it. Obviously my wording was hyperbolic, so if that annoyed you I apologize.

This is why you get negative rep points. Because your posts reek of arrogance and condescension.

Your position is that males have on average better spatial intelligence? Okay. That seems corollary to my point. Your previous posts (save the one where you originally posted the wiki link) seemed to express incredulity at the notion of biological explanations.

I have been using the qualifier "in part" throughout. I used "could be" once, in reference to your thinking it is bizarre that biology "could be" a factor. That doesn't mean I'm saying it isn't a factor. It's a statement about your position, not mine.