Strange

The star that formed the black hole would have been moving through (orbiting) the galaxy, in the same way as any other star. It will continue to do that after it becomes a black hole. There may well be binary systems where one of the stars has become a black hole; they will continue orbiting one another in the same way. Exactly the same as any other object with that mass.

So for pure maths, you are arbitrarily allowed to treat 0 as either 0 or 1 for the purposes of multiplication? And you think that will have no wider implications? The canonical form of a polynomial equation is: [math]a_n x^n + a_{n-1}x^{n-1} + ... a_1x + a_0 = 0[/math] But, according to you, that is the same as: [math]a_n x^n + a_{n-1}x^{n-1} + ... a_1x + a_0 = 1[/math] I don't think so.

That almost sounds as if he were proud of it. I think I would be deeply embarrassed to have come up with something like that.

I was in Italy once with an Italian friend from another part of the country. The locals asked him what country he was from. The idea of a national language is quite a modern one. It probably followed the invention of printing.

How do you decide which to use?

It is neither absolute nor limited. Why are you polluting your thread with irrelevant (and patently false) statements?

Ah, good point. I was thinking of the temperature of the interstellar medium (which is much warmer).

If it were empty, then it couldn't have a temperature. What is "massless energy"? What is the connection between "massless energy" and magnetism?

Exactly. You have just proved that potential is not "inversely proportional to speed", as you claimed. This appears to have nothing to do with the subject of this thread. I suggest you start a separate thread on the nature of truth and its possible relationship to science, if you want to discuss that. (This is also a shoddy caricature of science, so I don't expect that thread to be very productive.) So you agree that your statement "truth can be found anywhere" is incorrect?

I don't see why not. That is what makes it relative, not absolute. But, as noted, velocity is not inversely proportional to velocity, even if you ignore relativistic effects. What does "truth" have to do with it? I thought this was a discussion of science. But you are contradicting yourself: if "truth can be found anywhere" then that must include peer reviewed journals so it can't be true to say it's not there.

Let's just look at (a) again: a) 2 is represented by the combination of two things: the "defined" value 2 combined with "x,x" (two spaces/boxes) My interpretation of this was something like (2, [][]) - where [] represents your spaces/boxes But then you say: And "(1v,1v,X,X)" doesn't look like option (a); it looks like option (b): b) 2 is represented by the combination of two things: the "defined" value 1 placed in two spaces/boxes. My interpretation of this was something like ([1][1]) But I am still very confused. (I am also busy and tired - I will try and come back to this later; see if I can make sense of it...) Just as an aside, why add all this complexity about "defined values" and "spaces"? Why not just say, "when there is a division by zero, I am going to treat it as division by 1". It seems a lot simpler and achieves the same result. One place I can see this might cause problems is in calculus: many functions which are currently differentiable and therefore continuous, might not be continuous and therefore not differentiable.

There are multiple dialects - some mutually incomprehensible - in both these countries. In the United Kingdom, there are at least 4 distinct languages. In the past there were more. You need to define what this word "race" means. There are multiple ethnic groups in both these countries. For example, the majority of people in China are Han Chinese, but there are also Zhuang, Uyghur, Hui, Manchu, Miao, Yi, Tujia, Tibetan, Mongol, Dong, Buyei, Yao, Bai, Korean, Hani, Li, Kazakh, Dai and others. Many of these do not speak Chinese as their main language. (And note that Chinese is a family of languages, not a language.) In Israel there are significant numbers of Christians and Muslims (which causes some tension). In Iran there are Moslems, Zoroastrians, Christians, Jews, etc. Cuba has political dissidents. (N Korea has dead people. I'm not sure you can call this sort of brutal repression "homogeneity".) So, you have provided a few examples which you claim meet ONE of your requirements, but looking closer we see that they don't really meet any.

It is not that it is smaller than previously thought, but using a different way of measuring it gives a different (and unexpected) value. Previous measurements were done using electrons, the measurements in this article used muons. As the article says, there are several possible explanations. The most likely (?) is that QED, despite its success, is "wrong". But as we have very few clues as to what a better model would be ... I can't see why. "One way to measure the mass, say, of a proton, is to put it in a mass spectrometer. Accelerating it in a known electric field gives it an amount of kinetic energy proportional to its charge. Causing the proton to move in a circular path in a uniform, well-calibrated magnetic field allows the momentum to be measured quite precisely." https://van.physics.illinois.edu/qa/listing.php?id=1209

Does it?

That is correct; it can't. Off the top of my head, that looks wrong, even in a Newtonian world. Potential (gravitational) varies linearly with height, whereas free fall speed varies (I think) with the square root of height. Or, to look at it another way, when in free fall the object swaps potential energy for kinetic energy. Kinetic energy is related to velocity squared. And that isn't taking into account that in GR velocity addition and acceleration are not linear. Correct. We can allow that for the purposes of this discussion. No. See below. No. It will accelerate continuously. Although not physically plausible, it could fall from infinity to an infinite mass and it would accelerate continuously and get closer and closer to (but never reach) the speed of light. To go back to your black hole example, an object in free fall towards a black hole from infinity will reach the speed of light as it crosses the event horizon (for any sized black hole). At which point, I don't think there is a meaningful definition of speed (compared to the outside world). You could measure their velocities from a third frame (in which case the velocity between them is limited to be less than 2c) and get different values from either of them. Ditto a fourth, fifth, ...

Not sure what the "event horizon at the edge of time" is. But the (gravitational) potential of a black hole depends on its mass. So there isn't any upper limit here. Unless, in practical terms, the entire mass of the universe is in a single black hole... So not absolute at all. No. And it doesn't matter how large the potential difference is. The very fact that it is an asymptotic limit implies that there isn't (or doesn't have to be) an upper limit to potential difference. However large you make the potential (tending towards infinity) the final velocity can increase (tending towards c).

And that is why the idea of "relativistic mass" is discouraged by many people. It leads to erroneous arguments like that. But what do you mean by "an absolute value"? The velocity is still relative and is observer dependent. It is not absolute, even though there is an upper limit. Actually, I'm not sure it is clear that there is an upper limit. The value of c in this context is rather like infinity: you can get as close as you want; whatever speed you are doing less than c, it is possible to go faster.

Almost (should be any value less than c). But this is relative velocity. Not absolute. (Unless you are using the word "absolute" in a non-standard way?) This doesn't follow. However large the applied force (or potential) the speed is still limited to be less than c. But it seems you are using "absolute" to mean "maximum" or "limited". Is that what you mean? If so, one of my answers would be different.

Please show some evidence that gravity does not follow a square law. If you want to use the speeds of stars in galaxies as evidence for this, please show this mathematically. This is not magic; this is the normal process for physics. This is how all particles were discovered. Dirac proposed the positron on purely theoretical grounds; later it was detected. The neutrino was hypothesized because its effects were seen; later it was detected. Higgs described the Higgs boson decades before it was detected. And so so and on. There is no magic here. So you are just changing the cause of the extra curvature of space-time from dark matter to something else you have invented (which has identical effects)? So the orbits of moons, planets and satellites are not caused by gravity? And one of those "effects" is the speed of orbiting bodies. Again: please either show (in mathematical detail) where those calculations are wrong. Please also show your calculations of the stars velocity. How can the mass of the stars not add to the total mass of the galaxy? It would be helpful if you showed the calculations that support your claims.

False False False (Note that using a larger font doesn't make it true.)

Does exercise produce vitamin D?

If it is your idea, then we can safely ignore it. Forget the velocity but look at the speed? What are you talking about? Anyway, please present a mathematical proof that extra mass can not produce the observed speeds. Otherwise we can dismiss this as another empty claim. Please provide some objective evidence that this "simple impression in the fabric of the universe" exists. Please tell us what the cause of it is. And please provide a mathematical proof that this can produce the observed speeds. The whole point is that dark matter explains the velocities of all the stars (and dust) through the galaxy. If you disagree, please stop shouting and provide a mathematical proof that dark matter cannot reproduce the observed velocities. You claim certain well-established quantum effects don't exist. Please provide some support for this claim. Calling it "magic" does not count as scientific evidence. Of course. No particles that are known to exist currently meet those requirements (otherwise we would know what dark matter was). (Neutrinos satisfy the second requirement but have too little mass for the former.) A number of hypothetical particles meet the requirements. Which is why there are a number of research projects to look for direct evidence of those particles. Please provide some objective evidence that this "imprint in the fabric of the universe" exists. Please tell us what the cause of it is. And please provide a mathematical proof that this can produce the observed speeds. Your unsupported claims are getting really old.

People are very clear about the (kind of) evidence for dark matter. This is, of course, nothing particularly novel. We have been on the same situation many times in the past: aware of "something" causing an effect but not knowing what that thing is. Neptune and neutrinos are probably the canonical examples. Not surprisingly, the time taken to do the direct detection is increasing over time - we have already found the "low hanging fruit": if dark matter was easy to detect we would already know what it was. And the easiest explanation for that is the existence of extra mass that we cannot see. Nicely, the distribution of that extra mass required matches what is expected of matter that only interacts gravitationally. And the amount of that extra mass is consistent with the various other indirect measurements. Can you show us the maths for your model and how it produces the observed rotation velocities? And your evidence for that claim is? https://en.wikipedia.org/wiki/Argument_from_ignorance#Argument_from_incredulity.2FLack_of_imagination Show us where the maths is wrong, please. Huh? Of course not. It is the unexpected relationship between radius and velocity that is one of the many lines of evidence for dark matter. Can you show us the maths for your model and how it produces the observed rotation velocities? Where does it say it they are two dimensional?

I don't think that lack of vitamin D is a cause of osteoporosis. (On the other hand, people being treated for osteoporosis do need to ensure they get enough vitamin D.)

I apologise for not being clear. What I meant was that I was not making a logical argument. I was not saying, for example, that B exists and therefore it was created by B. I was simply suggesting an alternative possibility, that B was spontaneously created (by nothing). But you claim to have proved that their cannot be a creator. Therefore, if as Hawking asserts, the universe was created by the laws of nature then you dismiss this as impossible. If Poplawski has a mathematical proof that black holes could create new universes, you say he must be wrong (without even looking at the maths). If Penrose suggests that the universe was created by the collapse of another universe you wave this away with your "proof". It must be nice to be able to easily dismiss the ideas of some of the greatest minds of our time. If only that glib dismissal were true. http://rationalwiki.org/wiki/Absence_of_evidence I don't disagree with that. I have often made the same point myself. But it would be the height of idiocy to extrapolate from that to say that we are unable to design computers because we don't understand quantum theory. Or that evolution cannot be explained by natural selection because we don't understand how to merge GR and QM. Or that computational drug discovery is impossible because we don't have a theory of abiogenesis. You are adding strawman to your arguments. You will soon have the complete set. Definitions change (in time and context).