Iggy

That's right. A circular Schwarzschild orbit is, [math] \frac{r}{r_s} \left( \frac{v}{c} \right)^2 = \frac{1}{2} [/math] if r_s/r is 0.5 then v would be 0.5c or about 150,000 km/s. No, there wouldn't be any need, and you wouldn't expect, the two people to agree about the length of a meter or velocity. Schwarzschild coordinates, that we've been using, are not what the person orbiting the black hole would properly measure with his ruler especially if he were orbiting it. I think velocity would be reciprocal between two observers who are the same radial distance from the black hole, one orbiting it and the other static. But, not with two observers who have different radial distances. There is a useful wikipedia page here, http://en.wikipedia.org/wiki/Gullstrand%E2%80%93Painlev%C3%A9_coordinates I think it should matter to some degree. The closer you get to event horizon, the more Newtonian approximations break down. For example, you found a velocity of 150144 km/s for an orbit at r=2rs. We figured time would be dilated by a factor of 2. If we decompose time dilation into velocity and gravitational potential we'd probably get something close to two, but not exactly because it is so near to the event horizon. Let's see, Velocity time dilation would be, [math]\frac{t_0}{\sqrt{1 - v^2/c^2}} = \frac{1}{\sqrt{1 - .5^2/1^2}} = 1.15[/math] Gravity, [math]\frac{t_0}{\sqrt{1 - 2 \cdot M / r}}[/math] where M = G x m(sun) / c^2 [math]\frac{1}{\sqrt{1 - 2 \cdot 1480 / 5900}} = 1.42[/math] Combining gravity and velocity (1.15 * 1.42) gives 1.63, so not exactly 2. The closer you get to the event horizon the more Newtonian approximations break down.

Right, I think that was Slinkey's question as well. You have [math]t_0 = t_f \cdot 0.5[/math] so if [math]t_0 = 1[/math] then [math]t_f = 2[/math] because [math]1 = 2 \cdot 0.5[/math]. While 1 second ticks on the orbiting clock 2 tick on the distant clock. The distant clock ticks faster.

Prov. 6:16-19 might be of interest -- a list of sins that God hates. I guess, implicitly, they would be sins that he hates more than others. I do understand where you're coming from though (e.g. James 2:10) and I agree with Mr. Skeptic's interpretation--the pregnancy metaphor. I could see a different argument to that. In his "I send you forth as sheep amidst wolves" speech, Jesus told his apostles, "for it will not be you speaking, but the Spirit of your Father speaking through you." (Matt. 10:20). Also, Lemur was quoting Paul from I Corinthians and in the same epistle he tells the Corinthians, "If any man think himself to be a prophet, or spiritual, let him acknowledge that the things that I write unto you are the commandments of the Lord." (1 Cor. 14:37) effectively attributing the epistle to Jesus--at least in a theological sense. If I recall correctly, Peter also invoked that kind of authority in one of his epistles, but I can't find where right now. In any case, I think a good argument could be made for not regarding any scripture as privileged. Your interpretation seems--enlightened--for lack of a better word. It feels better, or at least more fair, to condemn all promiscuity equally. But, I'm sure I couldn't interpret the bible that way. In the new testament homosexuality is called unnatural, shameful, and perverted, and death considered its due penalty. Because of this, God gave them over to shameful lusts. Even their women exchanged natural relations for unnatural ones. In the same way the men also abandoned natural relations with women and were inflamed with lust for one another. Men committed indecent acts with other men, and received in themselves the due penalty for their perversion. (Rom 1:26-27) Since the only reference to homosexuality in the bible is to strongly condemn it, I don't think it can be interpreted as commensurate with heterosexuality -- even in the sense that both are immoral if they are lustful. I don't, personally, consider homosexuality immoral and I can't logically reconcile that with the bible so I’m forced to reject the bible as a source of morality. As for homophobia coming from secular culture -- homosexual acts were widely considered acceptable in the Greco-Roman world. That changed when the culture became Christian and homosexual marriages, followed by homosexual acts, became illegal and punishable by death. I believe it was a direct Christian adaptation to the culture. That sounds sensible to me. Buddha, they say, just about starved himself to death searching for enlightenment. After eating and regaining his strength and his mental faculties he realized that he was more likely to find truth if he wasn't so deprived of human necessities. (Buddha’s Fasting) "Better is the sight of the eyes than the wandering of the desire" -Ecc. 6:9

Sorry it took a while for me to respond. This thread didn't show up where I check the "my content" section. I guess that proves one can't observe a black hole thread unless you're inside it I'm not aware of any tests between purely inertial clocks with different gravitational potential. That sounds right, but I'm not sure if you were still thinking of GPS. They aren't geosynchronous. This is the part I was referring to, The link you gave mentions it as well, Slinkey's paradox is, in other words, sometimes formulated in a different but very similar way. That is, if the definition of a black hole invokes future infinity then it is paradoxical for the black hole to exist for a finite amount of time as with a closed universe or with Hawking radiation. Hawking himself mentions what I think Slinkey is saying in his 2005 paper: So, when Slinkey says, He is agreeing with Hawking and others. I think it is an open question that probably won't be solved until we get a good and confirmed quantum theory of gravity.

If each clock is free falling then each is in a locally inertial frame, but if they have different gravitational potential then they run at different rates from gravitational time dilation. Further from a mass a clock runs faster and closer to the mass it runs slower. A good and verified example is that the atomic clocks on GPS satellites run faster than identical clocks on the ground. http://users.datarealm.com/herrmann/time.htm

It does indeed collapse to a smaller size, but this takes essentially an infinite amount of time for that to happen from our perspective due to time dilation. While it is slowly collapsing, getting closer and closer to forming an event horizon, it is also very slowly (from our perspective again) evaporating by emitting pre-Hawking radiation which lowers its mass. The argument would be that it loses mass quicker than it is able to form an event horizon, so that you never really have a true black hole. It would be almost indistinguishable from a true black hole from our perspective.

Here is their paper, Observation of Incipient Black Holes and the Information Loss Problem I read it. It's very interesting. The authors tied up some loose ends the following year, Quantum Radiation from Quantum Gravitational Collapse And here is a rebuttal, Pre-Hawking Radiation from a Collapsing Shell where they report that quantum effects make the collapse time finite to an observer at infinity so that a horizon is formed and pre-Hawking radiation is not a solution to the information loss paradox. Edited to add: Slinkey, this looks like a good background on the time it takes to fall into a black hole as viewed from far away in general relativity: Falling Into and Hovering Near A Black Hole. It mentions a similar question to yours but having to do with a closed universe which only exists for a finite time (rather than the finite time of an evaporating black hole)

The rubber does not expand uniformly at any scale. The universe does expand uniformly. It's a falsified model. If you knew what a model was, you might know that. If you knew what you were doing, or were willing to learn then I would invest further in a discussion. It's clear you are not.

The active fuel from the core is currently being held in the spent fuel pool. http://www.voanews.com/english/news/Confusion-anxiety-abound-near-Fukushima-118285529.html http://www.dailygalaxy.com/my_weblog/2011/03/japan-crisis-update-spent-fuel-rods-could-go-critical.html

Yes. I would assume so. This does not, however, mean that expansion is the cause of increased entropy. With adiabatic expansion entropy is constant. In the current model of cosmology, where

Good point. I had considered evaporation but figured it would be a second order effect of a first order approximation especially if the room containing the pool was sturdy-enough and airtight-enough to act as a vapor pressure cap on the pool at least until the room exploded. Right. I should have explained better. I was reading an article saying there was some disagreement between the NRC and TEPCO about whether there was water in reactor 4's pool. I thought "even if there was water at the time of the explosion at reactor 4, it would surely be well on its way to boiling off by now" which led me to wonder "is it possible to estimate how long the pool could contain water given only the info that has been published?" Now that I’ve searched for it I have better info, So the temp rose roughly 60 C in 3 days making the pool dry at roughly 13 days after the quake assuming no other complications such as damage to the pool or a return to criticality of the fuel. That said, I don’t believe there is any steam rising from reactor 4 which is consistent with the NRC’s claim that the pool is dry. Since the core’s current un-spent fuel is in the pool, this seems like a rather large problem to me.

Having no complications at a plant that is having problems is not only a bad idea, it is impossible by definition. The pool is uphill from the ocean.

But, you have to account for temperature lowering with the increase in volume. If the universe is an isolated system, meaning it doesn't transfer heat or mass to any kind of surroundings, then simple expansion would be adiabatic. Change of entropy in adiabatic expansion is zero. You might like section 2.3 of Thermodynamic Asymmetry in Time.

I agree. I certainly don't mean to argue that everything will be fine with the pools for some time to come. The New York Times reported that imaging from a Global Hawk drone indicated that there was a major rupture and I'm sure there are other scenarios (like maybe a return to criticality from a conglomerate of melted fuel) that would result in a dry pool at this point. I'm just wondering if we can find an estimate for when the pool would be dry given what we know about the rate that the pool heated up and assuming no other complications.

If the heat of vaporization of water is 40,650 J/mol and the specific heat of liquid water is 75.3 J/K/mol and it takes roughly 5 days to heat the spent fuel pool from roughly 25 C to 100 C then would the pool be expected to completely boil off in roughly 36 days--36 days after it started boiling that is? This assumes, of course, that the pool isn't ruptured by the melted fuel. Thanks in advance.

"In the present state of the world, it is difficult not to write satire" -Juvenal As a citizen of the united states, I’d like to know if this God is omnipresent. I mention this only because if he plans on staying in the country then he should apply for a visitor’s visa. This may sound harsh, but we’ve had a terrible problem with immigration. I’d like to know what God intends on doing while he is here. If he were to heal all the sick, for example, then he would be stealing the jobs of millions of hard working Americans in the medical and pharmaceutical industries. If he healed all wounds then gun companies would lose millions and I’d personally feel like my second amendment right to threaten a person with a gun somehow got violated by a confusing loophole. It’s just that we don’t need non-citizens coming here and stealing our jobs and voiding our rights no matter how smart and powerful they say they are. And, terrorism! We should have to do a background check on this fella. Of course he says that all of the documentation on him (eg bible, quran, torah) is wrong, but isn’t that a little convenient? All along we know him as this one God and suddenly he shows up as someone else. This is clear and convincing evidence that he has changed his identity in order to perpetrate some nefarious scheme. This is exactly why non-citizens especially need to be subject to secret and aggressive surveillance at all times.

From a position inside the skin of a balloon you will see things stretch in tangential directions and things compress in the radial direction. We see galaxies moving away in all directions. If you don't know what relativity is or what it does then you can't know if you are rejecting it. Also, you don't know what it is or what it does. I'm not sure if it is germane, but I also would like an answer to this question. Owl, you imagine the world a certain way. We have shown with logic that your vision of the world is internally inconsistent and physically impossible, so what do you hope to accomplish? Do you think you are debating us?

Answered in post #218.

9 I was sure you were being sarcastic. I animated frames for relativistic velocity addition for you a few days ago in your Minkowski / twin paradox thread. It is post #61. Which animation do you mean? The blue guy's reference frame measures the wrong value for the speed of light. If you can't solve that problem or understand why it is a problem then you have no hope of discussing any matter of relativity.

If you reject length and time dilation as means of solving the paradox then you must introduce some other means of solving it. You have not done and cannot do that. According to the diagram, the blue guy will measure different values of speed depending on his speed compared to the special orange guy. According to the diagram and the thought experiment we set up, only the orange guy will measure c for the speed of the ray of light. This means that the speed is not constant. We humans have been to many different frames of reference and we have noticed that the speed of light is always c. This means that your view is inconsistent with reality and inconsistent with a constant speed of light. You have to understand this inconsistency before you even begin to understand what relativity does. You also need to understand basic mechanics and I'm not convinced you do. The distance does not contract in earth's frame. Using the correct relativistic physics (relativistic thermodynamics--eg Tolman 1934) the person in the non-earth frame would not suspect earth's temperature to be anything other than what it is.

I've lost faith in genealogy. My family tree says that I'm descended from a Dutch guy who lived 350 years ago. But, I live in the U.S.--I'm not Dutch. If Dutch people still exist and I'm supposed to come from Dutch people then how come I'm not Dutch? For example, my ancestor supposedly lived in "New Amsterdam", but I've looked on a map and there is no such place. Genealogists tried to explain how my ancestors were Dutch, but I'm not Dutch so they invented a 'new' place that is kind of Dutch, but not really--so they just called it "New Amsterdam". Plus, my Dutch/Not-Dutch ancestor was supposedly named "Jan" one day then suddenly had the name "John" the next day. A person is either a "Jan" or a "John", and they don't change from one to the other overnight. My Dutch ancestors are supposedly on my father's side of the family, but an ancestor at the same time on my mother's side of the family was also named "John" and they lived in England. Is this supposed to be coincidence? Why did "Jan" suddenly get the name "John" if he was not related to my English side of the family and didn't know them at all? Genealogists can't explain that. Also, no one knows where "Jan" came from. Genealogists can't explain who his mother and father were. Louis Pasteur disproved spontaneous generation so there is no way that I could be descended from this person. I'm supposed to believe that he just popped up out of the ground and here I am a dozen generations later? Genealogists are wrong. Aliens designed my DNA and impregnated my mother. This explains why British people are still British and Dutch people are still Dutch, but I am neither. It's because I'm not descended from them. I have no ancestors on this planet. http://en.wikipedia.org/wiki/Argument_from_ignorance

Thank you, Spyman. It may also help you, Owl, to see the thought experiment from both perspectives. This is the world according to the center observer: This is the world according to the left observer: The speed of light is c according to orange (the first image) and 1.8c according to blue (the second image). The red arrow, in other words, moves faster in the second image. This shows that absolute distance and time mean a variable speed of light. Some people have to see this to get it. Real world measurements show that the red arrow should move c in both frames of reference (ie in both images). In other words, two people who are drifting away from each other can each consider themselves at rest and find that light moves 1c away from themselves or toward themselves. That is not the case in this thought experiment. Your response has been to ignore the world according to blue, to call it "confused", and talk only about the world according to the orange guy. I believe that all people--orange and blue alike--are created equal. I know that all inertial observers--orange and blue alike--find that light recedes 670 million miles in one hour. That is not the case in this thought experiment. This thought experiment demonstrates the very first thing that a person has to understand before they begin to learn relativity. The first postulate of relativity is that the speed of light is the same in all inertial reference frames (ie for all inertial observers). The description of reality that this thought experiment is based on is inconsistent with that postulate and it is inconsistent with the real world. That is why everyone objected when you said that the speed of light is constant and that distance and time do not depend on reference frame. People objected that the two statements contradict each other like I did in post 146 and Sisyphus did in post 140. In post 160 you asked "how exactly do my statements contradict each other". It has taken dozens of posts to answer that question in a way that you might understand, and I sincerely hope that you do now understand.

I never said that the central observer shoots the laser. They can all three shoot a separate laser and the results will be the same. They all start the thought experiment in the same location. Under your system of absolute distance and time the person on the left must conclude that light travels 1210 million miles in one hour. He also, under your system, must believe that light travels 670 million miles per hour. This is a contradiction. Do you understand what a contradiction is? Your beliefs contradict themselves. This thought experiment demonstrates that fact. In other words, you are unable to solve this paradox in the confines of your beliefs. Absolute distance and time feel right to you and you accept that the speed of light is constant. But, you've never done any mechanics based on those assumptions so you don't really know what they entail. I'm telling you that a constant speed of light means that every inertial observer must figure the distance between light and himself changes at 670 million miles per hour. This thought experiment which uses your ideas of distance and time has an observer figuring that the distance between himself and light changes at 1210 million miles per hour. The speed of light is not constant in your description of reality. The speed of light is constant in reality. Your description of reality is therefore wrong.

The laser was fired by the guy on the left from his position. Those two statements contradict each other and you are incapable of understanding why. If someone shoots a laser and one hour later the light is 1210 million miles away then the speed of the laser is 1210 million mph. If you don't understand that then you don't understand what "speed" is which I think is probably the case. He didn't journey left away from himself. All inertial observers must figure that light travels at c--not just one person. You think the center observer is special? You think everyone in the universe should figure the speed of light compared to this one special guy? How do we find this guy? In this thought experiment the speed of light is not constant. In the real world the speed of light is constant (for inertial observers). The only reason you can't recognize this is because you can't understand it. I'm not sure if you want to understand, but I can guarantee that if you try to debate people who try to explain it to you then you never will.

An airplane also doesn't "push" sound faster the faster it goes. That isn't the point of relativity. It's completely beside the point. The speed of light is constant which means that all inertial observers measure light at 670 million mph. In your thought experiment a person floats weightless in deep space. He shoots a laser and one hour later finds the beam 1210 million miles away. If you cannot understand the contradiction between those two things then everything else is moot. Your only response has been to call the inertial observer "confused" and to point out that there is another inertial observer somewhere else doing something else and that guy measures the beam at c. I'm sure you feel like no one is understanding you or listening to you. You don't realize how very simple and simply flawed your assertions are.