Carrock

I was referring to 'we can survive permanently down to just above half the present oxygen concentration at sea-level.' As only trees are destroyed, presumably on a continuing basis, I'd expect everything but trees to increase to replace the trees.

As the falling oxygen will be replaced by increasing carbon dioxide the question is whether global warming or carbonic acid poisoning will get us first!

From http://www.snopes.com/science/well.asp NASA has wisely given up disproving Apollo hoax theories. It's easier but just as pointless as proving each and every biological structure has not been intelligently designed.

If the book exists, its claim is false so I won't be reading it.

When the commander gets killed by friendly fire, all his troop will demonstrate team spirit by agreeing his death was an accident.

In the real world, how long does it take to write/generate the unbounded finite sequence 1,2,3,4,5,[...]? ([...] represents the numbers I didn't have time to write) It's impractical to continue up to even the number of electrons in the observable universe (or some finite number you choose) and you will never reach infinity as each successive number is finite. Much of mathematics is shorthand for something impractical or impossible to work out with basic arithmetic using pencil and paper.. If you think the above math is ok, what is the problem with being unable to write every term in an infinite sequence? [crossposted with Strange]

Some ordinary diodes like the glass protected OA79 produce detectable current if you shine a bright light on them. They don't require light to permit external current to pass through the internal diode and nor do solar cells. If you accept this diagram as accurate you will note note that your diagram is essentially equivalent to two of those in series. If one cell gets no light and its equivalent current generator drops to zero, the current that the other cells would produce can pass through the still forward biased internal diode. The purpose of the added zener diodes in your circuit is to permit current to pass if a solar cell goes partially or completely open circuit and probably to limit the array's maximum off load voltage. If, say, a rooftop solar panel in a location with mains power is reliable enough that spending £3 on diodes would on average increase lifetime enough to produce an extra £1 of electricity, I wouldn't condemn a designer for failing to include those zener diodes.

A few errors in the above: The main reason for a series diode is to prevent the cells being damaged in darkness by reverse voltage. If current is being taken from a partly lit battery, a cell in darkness is still forward biased but the diode (in the model) only passes external input current with no additional photocurrent; it absorbs rather than produces energy. It's possible to bypass a faulty or unlit cell but more than a simple diode is needed.

From https://en.wikipedia.org/wiki/Theory_of_solar_cells This shows clearly that a series dark cell is a forward biased diode if the other cells are producing current. It's common to include a low forward voltage (eg Schottky) diode in series to prevent cells at night eg discharging batteries charged in daytime. If illumination is uneven, or to guard against a cell going inefficient, a Schottky diode could be placed in parallel, conducting only if the cell is dropping rather than raising voltage. The last thing you want in a solar cell is a low forward voltage drop.

Without analyzing this equation I agree with your conclusion. I hope we agree that the gravitational potential distant from the BH is higher than it is near the BH. From the above ref: 'curvature=energy' is an oversimplification. More precisely, curvature is caused by energy and a lesser amount of energy is associated with the curvature. The negative gravitational P.E. near the BH ensures that there is lower energy density in that curved space than in distant 'flat' space. Agreed. However due to the negative gravitational P.E. near a BH the curved space has a lower energy/density than distant space. If gravitational P.E. is ignored it would have higher energy/density due to curvature. Ignoring gravitational P.E. the energy density increases as you approach a BH. I don't recall disputing this. Including (negative) gravitational P.E. the energy density decreases as you approach a BH. I don't think I'm missing anything. Sorry; I misunderstood. Do we agree about negative gravitational P.E.?

quote #1 quote #2 Robittybob1: I regret saying I was done with this thread. I've found it difficult to work out the conventions used above, especially as my understanding of GR and especially black holes is limited. You seem to have a similar problem. I'll go back to my Apollo example and use a pseudoclassical qualitative (ie mostly accurate) approach using what I think are Mordred's conventions. I'm sure he'll quickly correct me as necessary. In the Apollo capsule special relatvityish reference frame: As the capsule falls towards earth tidal forces (from the nearer part being increasingly attracted to earth more than the more distant part) increase; the increasing stress gives the capsule more energy - analogous to quote #1. If the tidal tidal forces were sufficiently large, the capsule would be torn apart and form an accretion disc. Setting the capsule's gravitational potential energy at all times to 0 (quotes #1 and #2), the earth/moon's gravitational potential energy increases enormously as the capsule falls. [Mordred may be using an event horizon or similar as a reference, with similar effect.] With this approach, the capsule's kinetic energy, transformed to heat in the atmosphere, has been created from nothing as has the increase in gravitational potential energy of everything but the capsule. All this for a special relativityish approach when general relativity would be more helpful - specifically using a distant place as an unchanging reference for gravitational potential energy. A rehash of a conventional energy conservation approach using distant gravitational potential as a zero reference: As the capsule falls its gravitational potential energy reduces [becomes more negative] and is transformed to kinetic energy, a little gravitational radiation, heat etc. The increased (tidal) energy in space around the capsule is far less than the reduction due to lower gravitational potential energy. Dealing with two orbiting BHs is much more complex but a similar approach can be used. We might have to look at that in another thread. It doesn't seem right for there would have to be some mechanism to replenish the energy on the outside if that was the case. Using an energy conservation approach: The energy for gravity waves does not originate from the spacetime geometry outside the event horizon. Nor from within. Set gravitational P.E. at zero at great distance from the BH. As a mass (or another BH) approaches the BH its gravitational P.E. becomes increasingly negative due to the BH's gravity and this P.E. is transformed to kinetic energy, heat, gravitational waves etc. As above, with limited exceptions due to extreme conditions, the locally higher 'tidal' energy aka 'spacetime geometry' is less than the negative P.E. Spacetime geometry does not originate energy for gravity waves. All of the energy produced is from the incoming mass interacting with the BH's gravity and other incoming masses. Black holes and their environs do not create energy.

Surely it has at least zero point momentum.

You don't need the reference to claim that black holes create positive gravitational energy i.e. 'a region of higher gravitational potential' in violation of those conservation laws. As you will not clearly state whether you consider gravitational energy to be positive, at least where black holes are concerned, in violation of conservation laws, I'm done here.

We're entirely agreed; the latter sentence is not contentious. From the reference equation 43 is a mathematical formulation of energy and mass conservation laws; there is no suggestion black holes create energy or a nearby 'positive energy/density region' which would violate conservation laws. As I've mentioned before, there is a convention on this site that it should be possible to follow posts without going offsite. I'm certainly not going to read section 3 to try and guess its relevance.

To save me reading through your entire reference, please quote the claim that accretion discs must exist whether or not matter is falling towards the black hole. You seem to be claiming that black holes create positive gravitational energy and some of this creates gravity waves during mergers. You're ignoring my post #15, particularly the last line. AFAIK no one is missing that fact.

I don't think using the Schwartzchild radius of a BH as a reference for gravitational potential is helpful here. You may not intend this, but you seem to be suggesting that masses cause nearby spacetime ( and matter ) to have greater energy than distant spacetime ( and matter ) while the usual idea is that on average the mass-energy of matter etc is exactly or nearly equal to its negative gravitational mass-energy. An analogy for the local high energy of an accretion disk would be an Apollo capsule flying through the atmosphere at 25000 knots after falling from the moon. Locally, a vast amount of kinetic energy seems to have been created from nothing; the simplest way to avoid this is to say that the capsule's increased kinetic energy is balanced by its decreased gravitational energy. If a BH created a nearby positive energy/density region that energy would be absorbed by the BH causing exponential mass-energy creation.

I just went outdoors to check the temperature (14 Centigrade). Is it a warm day?

Tech savvy criminals will presumably now abandon this iPhone and use a secure method of encryption. A law against secure storage of data in America and elsewhere would generate a lot of new jobs. Perhaps it's time to build on the successes of the war against drugs and the war against terror with a new war against security.

This is an instance when our perceptions mislead us because accuracy in normal situations is unhelpful, even dangerous. If you see a running lion or a fast car in the distance, not heading towards you, it seems slow and not much of a threat. If it's getting any bigger, it's worth some extra attention. You give most of your attention to more important things. Anyone who's tried to approach a nervous wild animal will be particularly aware of this attitude. Think of walking along a quiet road near a busy road and giving equal attention to each of the dozens of cars on that road and the one car on the quiet road which happens to be heading straight towards you.

One of Richard Feynman's tall tales was about a discussion with philosophers about whether an electron was a thing. To clarify their definition of a thing, he asked if a brick was a thing. They never did get back to the electron.....

Creating a spacecraft with a 100 microFarad capacitance at 100kV is a few orders of magnitude beyond current technology.....

Solar panels are basically diodes optimised to produce current from incident photons. So a dark panel in series with lit panels is basically a forward biased diode. It will pass current with a small voltage drop ( eg about 0.6v for silicon).

I only intended the reference once, but used cut and paste without checking. As you expect me to read your references without specifying which part, I thought you would be happy to do the same or at least google "dimensional analysis". I looked at a few references and didn't find any suitable examples. I only use it as an informal quick check of equations and I thought you would want a formal description. I was taught it in an off the syllabus end of term maths class at school and don't know or care if I'm using it correctly as long as it gets results. This is problematic when I refer to it here. Informal worked examples of dimensional analysis using all my knowledge:-) .. There may be errors. [latex]dU=-pdf[/latex] Since dy/dt in this context is equivalent to y/t, multiply both sides by t; set sign positive (also ok). then L.H.S. = energy R.H.S.= pressure x force In S.I. units L.H.S. = kg*m2*s-2 R.H.S. = (kg*m-1*s-2) * (kg*m*s−2) = kg2*s-4 The dimensional inequality is sufficient to show the equation is not valid. Also useful: exponents must be dimensionless. Worked example: [latex]V=V_0 e^{-\frac{t}{RC}}[/latex] [latex]\frac{t}{RC}[/latex] ie [latex]\frac {time}{resistance*capacitance}[/latex] must be dimensionless. In S.I. units [latex]\frac {time}{resistance*capacitance} = \frac{s}{(kg*m^{2}*s^{-3}*A^{-2})*(kg^{-1}*m^{-2}*s^4*A^2)} =1[/latex] Exponent is dimensionless. It's often possible to find dimensional errors by inspection if the equation is simplified e.g. [latex]\dot{r}=-3\rho \frac{\dot{r}}{r}[/latex] solving for [latex]\rho [/latex]: [latex]\rho = -\frac{r}{3}[/latex] which 'looks' as well as is wrong. Perhaps you meant [latex]\dot{\rho}=-3\rho \frac{\dot{r}}{r}[/latex]

This post was quoted on another thread by Mordred Beyond a demonstration that the 'right' answer need not depend on correct equations I don't see its relevance there so I'm responding to it here before looking at the rest of his post. It's quite simple to spot many of the errors but I haven't made much attempt to spot the more subtle ones. dv=-pdF fails dimensional analysis. Implicitly requiring the volume to be cubic or irregular is problematic initially and would require your next correct equation to be changed. Perhaps you meant [latex]V={\frac{4}{3}}\pi r^3[/latex]? Why bother defining it when you don't bother defining most of your other terms? [latex]\rho=-3(\rho+p)\frac{\dot{r}}{r}[/latex] fails dimensional analysis. [latex]\rho=\frac{M}{4/3\pi r^3}[/latex] I expect it's OK but I've never been that strong on explicit and implicit operator precedence. Why not put [latex]\rho=\frac{3M}{4\pi r^3} [/latex] or at least avoid using different styles in the same equation [latex]\rho=\frac{M}{\frac{4}{3}\pi r^3} [/latex]? [latex]\rho=\frac{dp}{dr}[/latex] looks wrong but with no context it's not obvious. [latex]\dot{r}=3\rho \frac{\dot{r}}{r}[/latex] fails dimensional analysis. [latex]c=f\lambda=\frac{2L}{N}[/latex] fails dimensional analysis. With so many errors and so few definitions and intermediate steps it's very hard to follow this post. To quote the expert I only used dimensional analysis and only for the obvious errors so there may well be other errors. (Having dimensional homogeneity is a necessary but not sufficient requirement for an equation's validity.) The thought of having to fully check every relevant equation in the rest of Mordred's post on the other thread is rather daunting and I am wondering if there's any point. Halfway through this post I lost the will to post but I eventually decided to finish it so I wouldn't have wasted my time completely. If the errors here are not fixed and much more detail provided I would recommend reading these cosmology lectures which cover extremely similar ground in a much clearer and more accurate way. Somewhere along the way I forgot that my objection was the inappropriate use of classical physics to derive cooling of the CMBR. Using pv=nRt is perfectly valid. So in terms of admitted mistakes Mordred is winning with fewer than me.

I wasn't criticising Mordred's results, simply his use of part of a classical theory to prove results inconsistent with that theory. I suspect we ascribe different meanings to the phrase 'Mordred's analysis works.' Some gas laws are used in cosmology. I didn't see pV=nRt being used in your offsite references as a well known explanation of the cooling of the universe. Quote please. 'Energy is conserved' : can you demonstrate that your definition of energy conservation is the same as that used in pV=nRt? See eg. http://www.preposterousuniverse.com/blog/2010/02/22/energy-is-not-conserved/ Irritating isn't it when someone posts bare links because they're too lazy to quote or can't/won't present a possibly refutable argument? 'pressure in the FLRW metric is the direct result of particle to particle interactions. Reference and quote please, not just another set of offsite links. If you believe the above, presumably you think there was a sudden drop in pressure when the CMBR decoupled from matter, or the CMBR is still in equilibrium ie its photons are still interacting. Which is it? 'This is termed an adiabatic gas in thermodynamic terms.' CMBR cooling probably is adiabatic. From your reference https://en.m.wikipedia.org/wiki/Equation_of_state_(cosmology): As both equations agree 'that particles with higher kinetic energy exert greater pressure' and they are closely related I presume you are saying that [latex]w = \frac{p}{\rho}[/latex] and pV=nRt can be used interchangably in cosmology. I'm familiar with more than one scale factor so I don't know which you're referring to. Your scale factor is not referred to in your reference; perhaps you're confusing the symbol t(time) with T(temperature). Reading and trying to understand your references might help you avoid such errors. I'm guessing your scale factor is the first referred to here. I expect you can easily prove/refute the above using pV=nRt but here I demonstrate my close mindedness by saying your analysis will be incorrect.