MWresearch

No, it's not. I guess I wasn't clear about the experiment. Something that's bigger than a critical sphere with less mass than critical mass is accelerated to around 3% the speed of light where it appears to take on the mass of 52kg and contract to an a=8.5, b=8.5, c=8.5 ellipsoid, also called a sphere. I'm also not really sure what you mean by "mass is weighted" because weight is different than mass. Rest mass is rest mass, I agree, but as I said, it has the illusion of changing under the equation m'=mo/sqrt(1-v^2/c^2).

I'm really not sure what you're saying. I'm not weighing anything, there's not that much gravity in space anyway. It kind of seems like you're saying things moving at the same velocity do not measure each other as being contacted or dilated, which I agree with. As I also said before, I don't think the number of atoms is actually increasing, but that doesn't change the equation m'=mo/sqrt(1-v^2/c^2). The theoretical experiment is taking place in space where a chunk of U235 has been accelerated to what becomes a constant speed at around 3% the speed of light relative to Earth, neglecting Earth's orbital motion, rotation, atmosphere and gravitational field as effects on measurements.

I think I specifically stated that the number of molecules doesn't change as a result of relative velocity and even went so far as to call it an illusion. But as I stated before, I do want an equation that considers the number of atoms if it's necessary. But, relying on that point wouldn't resolve the situation from the point of view of the person asking such a question because they you haven't actually proven that number of moles stays the same. If the mass increases then mathematically you could extrapolate the number of moles to increase even though in reality the number stays the same.

Sometimes when I have complicated equations involving trig functions I ask wolfram for a solution and it spits out a bunch of imaginary exponents. My guess is it has something to do with the taylor series for e^(i*pi*x) equals cos(x)-isin(x) and e^(-pi*i)=-1, and even in third semester calculus I still haven't seen anything where I solve equations using that identity. But, sometimes I don't want to solve for a number, but rather a formula, and I don't always have wolfram around. So how do I solve complicated trig equations by using Euler's identity? Like let's say I have sqrt(sin(2x)^2+cos(5x)^3)=4. How do I solve that with imaginary/complex exponents?

No model is perfect. The multiverse assumes that all universes have some similar components of physics but at inherently different values, it doesn't assume that any random thing is possible. There are constraints on multiverse theory as with any theory, it doesn't say there is a universe where 2=5 or x =/= x.

Right, and I'm just trying to do the mathematics to prove that the same events hold true for other frames of reference. And the college I'm at already said they'd be interested in doing a summary/story/article on the paper once its finished, so might as well finish it. I already have the shape stuff figured out if I assume that 20.21g/cm^3 is remotely accurate. Using that number I set up a system of equations and solved for the velocity necessary to create length contraction and mass increase that creates a density increase from 18.075g/cm^2 to the critical 20.21g/cm^3. Now all I need is an equation that can be used in both the rest frame and relativistic frames to show that even though the density has the illusion of being 20.21g/cm^3, the probability of a chain reaction is still close to 0. For that, I need to find an equation for the probability of a chain reaction that is a function of whatever time based stuff causes a chain reaction on its own, assuming that mechanism is correct which Swansont never cleared up, and then anything that might be affected by length contraction which will effect the cross section and probability of slow neutrons striking a nucleus, like the average radius of nuclei and neutrons. I guess I will just have to let the paper not be completely accurate and state that I made assumptions for the sake of seeing the problem through.

Once again this website is really glitch for some reason. It never lets me use the quote feature and my entire paragraph just got erased. Anyway, the density isn't affected by time dilation, but more by length contraction and mass increase. The mass increase is kind of weird, more of an illusion since you're not actually increasing the number of atoms, and its similar with length contraction since you're not actually compressing an object, but the physical circumstance in this scenario could easily happen in something like a rock flung to near the speed of light by a black hole nonetheless. Anything that travels distance over time or happens over a period of time would be affected by time dilation. The half life, the specific activity, the fission rate, and I'm hoping it's not much more complicated than that. Though calculating the relativistic values for a Lorentz boost is pretty easy, you just multiply or divide by gamma, it still makes my head hurt when I see 20 variables that I've never heard of before and I can't sort everything through.

Ok, then we are on the same page I just misinterpreted your diagrams.

I have no issue with clearing my name. But this level of talk actually is part of standard physics, its actually all introductory lecture notes on nuclear engineering which I was thinking about going into if not mechanical engineering or physics, from googling stuff I see things like "introduction to nuclear engineering. By the end of this course students are expected to calculate fission rates, give critical mass...etc." which I tried studying on my own, but without any guidance I became lost and could not even figure out what I'm looking for. If you must know prematurely, I'm doing a theoretical research on the conservation of probability in different frames of reference. When I was talking about relativity with a physics professor, we stumbled upon the issue about what would happen if a nuclear bomb was going near the speed light which might have been on this very website. Since its density would appear to increase it might detonate in one frame but not in the other. I know from relativity that causality must be upheld. If the bomb doesn't explode in one frame especially the rest frame, it cannot explode in the other, and I'm trying to prove it mathematically since we obviously can't do that type of experiment in real life. With reference to Swansont, I did actually find the six and four factor formulas, but I guess in my ignorance I still do not see how to use that formula. From what I see, that formula only calculates the neutron multiplication factor. Is that what I need? I don't know, it seems like there's more to probability than a neutron multiplication factor.

Actually I am thinking it's possible that you were on the right, but that you didn't label your time axis in the diagrams. In a spherical universe, if you were to freeze time, two rays shot in opposite directions or parallel directions would not converge. Do you agree?

Perhaps this is just a matter of the interpretation of curvature. From my interpretation, if the mass density and pressure are high, this will not necessarily cause two light beams in opposite directions to converge specially whils holding the time evolution of the universe fixed and drawing a straight line, but only through the time-like closure of the universe wherein it eventually completely contracts after a certain amount of time. If it is put into terms of pressure, a photon should experience equal "pressure" from all sides which leave no net directional change.

However, there are problems with using both relativity and higgs fields. If you explain gravity through bosonic interactions, then there is no need for curvature. Yet, the equations in special and general relativity remain extremely accurate when treating time and space as dimensions with changing metrics. The combination of relativity and quantized bosonic models of gravity have not been completed. You also stated the topography of the universe as a function of energy density. While it may make sense at first when you consider that matter and energy appear to distort space, those distortions are only local. They are not the inherent curvature of dimensions and their measurement depends on the frame of reference. A spherical universe would imply non-local effect on the non-orthoganlity of dimensions, independent of position and time. This difference is important because in a universe distorted by a large amount of mass, emitted light beams in opposite directions will not necessarily converge.

If space was just a vacuum there would be nothing to permeate the physical dimensions by which matter and energy exist. There would be no length, no width, no height, no time.

What space is physically made out of is a mathematically abstract medium that can only be quantified in terms of dimensions: the 3 special dimensions and time, sometimes more dimensions depending on the model. In recent science, new models of space are quantized. It is projected that there exists the smallest units of space and time travelable, the Planck length and Planck Time. Though it is not proven that these quantities possess the significance they are claimed to have, quantizing space, especially using Planck units solves many problems of infinitely small objects, limits the least and most amount of energy particles can have, allows particles to cross into the event horizons of black holes and gets rid of infinitely divisible space. In that sense, space exists more like pixels on a computer.

Here's what I need: An equation which gives me the probability of a chain reaction as a function of mass, the size of individual atoms, the probability of neutrons being absorbed into a nuclei to further a chain reaction, and something to do with the resting specific activity which on its own would cause a chain reaction, assuming that mechanism is correct. But to be frank, I can't really pinpoint the point of what you are saying. If I have two piece of Uranium 235 that has a mass of 52kg in a sphere 17cm in diameter, will that alone detonate itself? Because otherwise I cannot think of why they would need to separate subcritical mass pieces in that gun bomb model. As for the special relativity aspects, I'll just assume that since it's a simpler or ideal situation that is being assumed that the time dilation and length contraction happen normally according to the square root equations with v^2/c^2. But, as I said, I don't really even know what to research. Even if I assume values of critical conditions, I still don't know the grand equation that determines the probability of a critical or supercritical mass creating a chain reaction in itself.

Well, if you look at modern cosmological models, space itself in a vacuum can also move and twist.

If you don't mind me suggesting, couldn't something traveling at a constant velocity be moving yet not be acceleratable? For instance, photons always travel at the constant speed of light in a vacuum and their speed cannot be changed.

Ok, but what about all the other stuff I said? Or could you elaborate more on how that link answers all of my questions?

Ok, I see. But, is neutron bombardment from some special event the only mechanism by which the chain reaction initiates? Because if I could simply the problem if 100% pure U235 on its own causes itself to undergo a chain reaction once critical conditions are met without any sort of neutron bombardment gun, it would make the situation less unnecessarily complicated. Although, since neutron velocity and mass and energy aren't really the focus of the theoretical experiment, perhaps I can just assume a situation after detonation. That equation mentioned in another link about prompt critical, it says the number of fissions per unit of time is modeled with an exponential equation which is what I mentioned before. In that equation, if I know the number of moles of U235 and thus the number of U235 atoms, I can calculate how many fission events are necessary to use up all of the fissile material. In relativistic frames of reference, can I easily substitute the temporal or time-aspect of the equations with simply modified lengths of time that are affected by time dilation, using the equation t'=to/sqrt(1-v^2/c^2)? And, I guess it also matters that the nuclei aren't moving near the speed of light, because then there might be even more time dilation I would need to account for. Would the speed that the nuclei and neutrons move at be negligible for calculating addition special relativistic speeds?

"You can add neutrons if you have an alpha emitter and something that releases neutrons when bombarded, such as Polonium and Beryllium. That will help trigger the reaction and give you extra neutrons at the outset." I'm not really sure what you mean. But, what about the mechanism for which the process triggers? Another thing I'm confused about is the mechanism by which the reaction triggers at critical mass. If enough mass is collected, the mass goes critical on it's own, and neutron guns are just for moderation reactions in nuclear reactors? And what about the equation that uses the factors? Specifically, I need something I can use in different frames of reference in a space environment, and space is really big, I can assume a four factor formula in an infinite environment where neutron reflection and the temperature of the medium is negligible. But, is that something that will even show the probability of a chain reaction in different frames? I'm not sure, I don't know what the actual equations are for determining fission probability based on like, nuclear density, material volume, temperature, some cross section thing, criticality, specific activity or ect.

Another thing I'm confused about is the mechanism, because I see different examples like in a nuclear reactor and theoretical or in a bomb and it seems like they have different mechanisms for triggering fission. It seems like for the sake of a theoretical situation where ideal conditions are assumed, I don't need to calculate more math about a neutron gun right? If I have critical mass at critical volume, that's it, the decay from the high specific activity optizes the probability of the reaction triggers on its own right? Or no?

I wouldn't really care about critical mass if I knew the equations I am suppose to use and how to use them. When I was doing research an article said the number of uranium atoms that break into materials followed an equation of something like e^(k(t-1))... or something along those lines, and "k" is some criticality number, and if the mass is exactly critical it made k=1 which made the equation simpler and I also don't really know how I'd calculate a given *super*critical mass or density, let alone just regular critical mass.

You're right, I completely missed that. That makes a lot more sense now. That's why we need peer review Although, even at that density, it still doesn't specify the specific compound, whether it's pure or not, what atmosphere it's at or what temperature, I'm still at a loss. Perhaps it can be confirmed by some complicated equation involving all of those variables which is still unknown to me.

Right, I already stated multiple factors affect critical mass, but I'm assuming a spherical shape. Perhaps it would help if you referenced a formula relating critical mass and spherical dimensions.

I just had a ridiculously huge glitch when trying to insert a link and I had to erase everything I said be refreshing the page because the website wouldn't let me click on anything else. Thanks for clearing up the discrepancy then, that makes more sense. I understand that if you just have enough mass then the reaction goes critical, but whenever you add mass without compressing the material, you must also be increasing the volume as well, and multiple articles bring up the issue with density, compression, temperature and surface tension. So, density must have some role, at least in terms of the number of atoms in a volume or a cross section and there must be a way to put the final equation into terms of a relationship into mass and volume, whatever that final equation may be. The Wikipedia article that scienceforums.net wouldn't let me link to references a physicist who worked on the Manhattan project and states "An ideal mass will become subcritical if allowed to expand or conversely the same mass will become supercritical if compressed."