decraig

What if your angular displacement is 2[math]\pi[/math] ? The linear displacement is zero. The equation should be about infinitesimals: [math] \Delta \theta r = \Delta L[/math] where [math]\Delta L[/math] is small.

Enthalpy, are you saying that a particle doesn't have mass until it's measured?

Where? I only find mock-ups, CAD drawings and cartoons.

What is the direction of recoil before the system decoheres? Name a direction. The point is that the system is in a symmetric state.

The state of recoil is indeterminate with the same radial symmetry until it is measured or decohered.

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I'm sure the OP was referring to energy and momentum conservation of a closed system. Otherwise we should be speaking of an energy continuity equation where we would include both the energy of the system as well as the energy flux in or out of the system. The same thing goes for momentum. At the Newtonian level these can be shown to be a result of Noether's theorem and the properties of Euclidian space and absolute time. The same can be said of charge conservation vs. charge continuity. Stepping outside the Newtonian scope, energy to date, is not well defined on the curved manifold of general relativity. Noether's theorem does not apply. Without a proper definition of the energy of a system, nobody really knows. It is interesting to note that charge continuity, however, is well defined on a curved manifold. It is most elegantly stated as simply dJ=0 in the language of differential forms, and is a direct result of applying an electromagnetic potential field to spacetime. The same elegance is not to be found for either energy or momentum. The apparent reason for this is that neither is a fundamental quantity. So why do the conservation and continuity equations forr energy and momentum fail while those for charge do not? Total charge is to total energy as electric current is to momentum. Why do we know of a continuity equation for one pair and not the other? The short, rough answer is that charge-current obtains from a 3 dimensional object and energy-momentum from a 4 dimensional object. The details involves some modern math beyond the scope of this forum.

Given is a sufficiently flat spacetime. Define the vector [math]\mu= (E/c^2, p/c) [/math], invariant under the Poisson group. mu is the norm of the mass. [math] < \mu, \mu> =m^2[/math] Or [math] |m|=\mu [/math] From this we can get [math]c^4m^2=E^2-p^2c^2[/math]. In the common understanding, [math]E=pc[/math] so that the mass of light is zero. However, for radiation emitted from an atom, or particle annihilation, in the center of momentum frame, the emission is radially symmetric. This implies that the total momenta of an electromagnetic quanta is zero, giving nonzero mass; [math]m=h\omega/c^2[/math].

I don't have much disagreement with you. Of course time doesn't exist. How hard is that to understand. But, in the consensus, it seems to be a major conceptual problem. However, I take issue with your time measurement problem. What does a volt meter measure? It indirectly measures voltage. Perceptually I measure the position of the needle over a card, or the opacity of some liquid crystals in an LCD display. Time is what is measured with a clock be it Cesium or a mechanical escapement. That's what they are made for. The outputs of these two devices are bijective: one-to-one and onto.

Something is wrong with the problem statement, or your rendition. It could be either (15 cm)^2, or 15 cm^2. In practical design a ~3.9 cm x 3.9 cm core crosssection would have magnetic pathlength of about 36 cm, in my estimation for an E-I core. You might have better luck in the Engineering folder of this forum.

"...but another thing entirely to say that the universe has temporal dimension," you say. You are putting words in my mouth. Argue this with someone who claims it. "A clock provides a standardised unit for comparing systems which are spatically extended," you say. And yard sticks, and thermometers too, but so what? ------------------------------------------------------------------------------ What is this straw horse, swansont is talking about? Is your argument: Time does not exist, therefore physics or reality is a social construct, and we can get back to animism, post-realism or the lastest -ism currently fashionable to the postmodernist left?

solved

Going back to the original post: You propose a cause and effect problem. Since there is no order of events in how these quantities relate, I don't really think it is a so easily answered as posed. However... The volume of an object contracts just as the length. [math]\gamma = \frac{1} { \sqrt{1-v^2/c^2} }[/math] [math]L=L_0/\gamma[/math] [math]V=V_0/\gamma[/math] Density of a uniform extended object: [math]\rho_0 = m/V_0[/math] r0 is the density, m is the invariant mass and V0 is the volume in the rest frame of the object. In the inertial frame where the object is in motion with velocity v. [math]\rho =m/V = \gamma \rho_0[/math] Gamma is greater than or equal to 1, so the density of the invariant mass increases with velocity.

Yes, of course true for a test particle with an idealized black hole having time-like Killing fields. Not true under less idealized circumstances, where we would include a radiating black hole with shrinking [math]r_s[/math]. I addressed this in post#1, item 4. We could modify the Schwarzschild solution to have [math]r_s[/math] a function time, though I didn't think at the time that such detail was a necessary addition to the logical argument. It would be an exponential decay rate. The model would make the point better evident. However, I'm somewhat mystified by the statement. I used the in falling test particle to set up the machinery for point #2 of my last post, #29.

1) Can even a single particle of light classically cross the event horizon? Under what seem the most ideal circumstances we might use the Schwarzschild metric where the particle is moving radially inward. The reduced Schwarzschild metric is [math]c^2d\tau^2=(1-r_s/r)c^2dt^2 - dr^2/(1-r_s/r)[/math]. The particle follows a null geodesic; [math]d\tau^2=0[/math]. [math]0=(1-r_s/r)c^2dt^2 - dr^2/(1-r_s/r)[/math] Therefore the coordinate velocity is [math]v=dr/dt=c(1-r_s/r)[/math]. Sanity check: at large r, [math]dr/dt \rightarrow c[/math] as expected. How long does it take the particle to reach rs from some finite R, where [math]R>r_s [/math]? [math]dt= (1/v)dr[/math] Integrating both sides, [math]T = \int_{R}^{r_s} \frac{1}{c(1-r/r_s)} dr[/math]. At [math]r=r_s[/math] the integral diverges to infinity. For an observer outside the event horizon, with coordinate time t¢, [math]dt'/dt[/math] remains in finite ratio.* Therefore [math]\int dt'[/math] also diverges to infinity. The particle never crosses the event horizon in the coordinates of an outside observer. ----------------------------------- 2) Now we want to make a Schwarzschild black hole. Consider that all of the energy is within the Schwarzschild radius but for one particle of light. We can define this radius would the particle be in the interior. Again, the amount of time required for the particle to reach [math]r_s[/math] diverges. It appears that, classically, we cannot make a Schwarzschild black hole. * There is at least one condition to be met for this to be true. The observer in the primed coordinate system cannot be in a state of accelerated motion such that an event horizon develops. Normally we can say that an event that transpires in one coordinate system also transpires in another. But introducing coordinate singularities make exception.

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'Time' is a word. Define it any which way you want. Einstein defined time as that measured with a clock. This is my preferred definition. Notice that this definition does not define things such as when time is zero. Intervals of time are defined. Absolute time in this sense was not addressed by this man. Physicists would say the that the laws of physics are classically "gauge invariant" with respect to time. (PAM Dirac proposed otherwise.)

Ok. I'm not very good at thermo, at all, but this has to do with the partitioning of energy. Different gasses have different degrees of energy 'freedom'. By freedom, the thermo guys mean the count of the different states of motion and internal motion of molecules in a gas. Oxygen, which is the predominate gas in the atmosphere in this geological age, can do a few things. The two atoms comprising oxygen can oscillate away and then to each other, and they can also spin about their center-of-mass. The equation would be different with an atmosphere of, say, C02 that does not have the axial symmetry of oxygen.

OK. This is interesting. It is my belief that Newtonian physics, Einstein gravity and all the rest are human inventions: Physics is not discovered but invented, in my way of thinking. I still ask, where or when are these magical LAWS OF NATURE sequestered? Where are they? If they are no where in space and time, Gabrelov, then these hypothetical laws would not be physical but metaphysical. Would you proposing that physics is metaphysical? I think they are only a phantom (but secretly wish to discover what they are). I remain in extreme contradiction; preaching one thing and passionately hoping for the alternate. ============================================ So with all this, where no one has a clue, where us humans, who pretend to intellectuallity, and can hardly pull it off--------------- Yet at the same time, we remain smug. We know better; the Universe created itself from nowhere and nothing, there is no God, and we can fathom anything. B.S.

So, what? First, your quoted article has nothing to say about a central singularity. And so what if it did? You seem to be drifting off topic. This article was about string theory, of all things. Generate a sufficiently complex theory among the many string theories and you can explain anything you want. If the information paradox is in your interest Strange, which is what this article is about, you might look into research on how information might remain encoded in the surface structure of black holes, instead. ------------------------------------------------------------------------------------------------ For others: It is not correct to dismiss the event horizon because it is only a coordinate singularity. The event horizon is central to the issues I have presented in the opening post, rather than any hypothetical central singularity, be it physical or not. ------------------------------------------------------------------------------------------------ For all of you following this thread: Please forgive me for the outburst. Despite my combative nature, I will endevor to act in a gentlemanly manner. Polite and encouraging and supportive. (All good things!) Not for fear of moderators, but because I am ashamed of what I see when I later read my own ranting posts.

G00d grief!!!!!!!!!!!!!!!!!!!!! I should never have started this frikin thread. Those who have an piss ant's education in relativity beyond the special theory, raise your hands. Those who don't, but are in love with black holes, can count themselves among the faithful, unthinking followers of authority. Do you really want to understand the mathematical underpinnings of general relatvity? No one will care. Is this the naked singularity requiring infinite energy density, or have you got something meaninful? This is a very good point Airbrush. I've wondered also. If you could instruct me how black holes could produce jets, and not incipients produce jets, I would appreciate it A

i4 Of course. Given an acceleraed coordinant system there is no sigularity. It could be over the event horizon in the accelerated frame. This is one of the reasons (thought relatively minor), it is so difficult so make true statements about black holes (within the context of general relativity, of course).

OK. fair enough. Let's start from the beginning. I'm not publishing, im just perpetually irritated by what I consider to be outlandish unsubstanciable claims. To get the jist of the whole problem, you must understand that there is coordoninate sigularyity at the surface identified as the event horizon'. This mean that the Jacobian metricc is all jacked up, and thing go to infinity in one direction and the ratio of coordinate displacements tend toward zero in the other. This is a very bothersome boundry. ....................................But what if nature precludeds it. In other words, what if all the fancy equations that have all the easy science geeks jacked up about are pretty and shiny but are not physically realizable? What is various processes are theoretially permissible but require infinite time. How woud your mathetical foralsisms stack up not (to be fair, I've read your profile. I will not publish my own---sorry)

Its more than a little difficult to comment on these attacks for me, at this time. (And I won't bother with the spell checker.) There seems to be some human demand for the fantasmagorical that drives various demands for recognitiion of some ideas, no matter how ill founded or ill conceived. I will respond to various frture attacks as I can, and find interesting. I suggest you know the subject matter better than a couple 4 years of relativity or you may not fair w I would suggest not listening to the mongers without a speculative ear.