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No, it doesn’t. What it does say is that you can decompose a Euclidean 3-volume into a finite number of subsets, each of which is itself a non-measurable collection of infinitely many points, and then reassemble these subsets in a new way. The crucial point here is that you cannot uniquely and self-consistently define the notion of ‘spatial volume’ for a non-measurable infinite collection of individual points, so this decomposition does not preserve the original volume, contrary to naive intuition. It’s a subtle ‘trick’ of sorts to do with Lebesgue and Banach measures. IOW, the Banach-Tarski paradox breaks down and reassembles a 3-volume in a way that does not itself preserve the original volume. Thus it is hardly surprising that you can turn a ball into two balls in this manner - in fact you could turn a ball into anything at all in this manner, no matter how big or small. It isn’t a true paradox, and most certainly not an inconsistency in mathematics. Also, don’t forget that unfortunately we do not really live in an infinitely sub-divisible 3-dimensional Euclidean world where such a procedure could in fact be implemented - it would be a neat little trick with lots of interesting applications!

I don't know how long is a long time for you, but do you remember old fashioned steam railway engines or steam powered traction engines, steam rollers or other steam propelled equipment, or have you seen pictures of them ? They had one thing in common, they were big and very heavy. All that machinery to provide steam propulsion is very bulky and heavy. And yet their makers knew about thermondynamics and mechanics and made them about as efficient as it is possible to be. With various grades of liquid or liquified gas fuels it became possible to use different and far lighter mechanics for the propulsion drive. Now that is where the internal combustion propulsion is at today. A far ligher drive mechanics meaning a far lighter chassis meaning far more efficient use of the fuel. Furthermore it doesn't require to carry either a large and weighty tank of water or additional weighty mechanics to recover the water from the steam and recycle it. And don't forget that some heat is extracted in cold countries to heat the passenger cabin. So yes, it is possible but just not practicable, there are better ways to use the fuels. Note also the even more and smaller engines such as racing car engines wear out far more quickly than engines designed for road vehicles. It is somebodie's law that says the more efficient and highly tuned a car engine is the more servicing it needs and the shorter its service life.

There are additional replies better than I can give here: https://astronomy.stackexchange.com/questions/32445/head-on-collision-of-two-black-holes If energy is lost from a system (in its CoM frame), the system loses mass. The binary system is losing mass equivalent to the gravitational wave energy radiated away, before the collision. If an individual component of the system doesn't radiate energy itself, that component don't lose rest mass. Radiating gravitational waves can reduce angular momentum, so the remnant BH should be decreasing its angular momentum during merger and ringdown. After they're merged, the system only has the one object in it. Your question is basically asking about the components of the system before the merger, and the system as a whole after, that's the main difference. Also, I think the energy radiated while merging is vastly greater than that radiated during the inspiral phase.

OK I'll accept that it is not homework. I do not see any essential difference between looking up on Google and asking a real person so Granite has a Moh's hardness of 5.5 - 6.5 and decays by chenmical weathering to clay, which was (and still is) used to make bricks and tiles and of course Hammurabi's famous clay tablets for writing cuneiform on.

Non-locality means that the outcome of an experiment/measurement performed at a specific point (be that in spacetime, or in some abstract state space) depend explicitly on what happens at another point; so the outcome is not uniquely determined by physical conditions in a small local neighbourhood alone. Consider again the example of the entangled wave function I gave earlier. The respective observable here is the probability of finding one of the particles in a specific state. For example, the local probability of finding particle A in the state ‘1’ is exactly ½; simultaneously, the local probability of finding particle B in state ‘1’ is also exactly ½. The global probability of finding state ‘10’ is 1/2, and the global probability for ‘01’ is 1/2. Neither of these probabilities is a function of coordinates - distant or otherwise -, or indeed a function of the state of the other particle. At the same time, the probability of the overall composite state to be ‘00’ or ‘11’ is exactly zero - again, without this being a function of any coordinates. At no point is any of these probabilities a function of coordinates or distant states at all, so it is meaningless to speak of this situation as being non-local. It is, however, quite meaningful and natural to speak of the overall composite wave-function as being non-separable, which is purely a stochastic statement and has nothing to do with locality. It is also an example of the absence of local realism, which is a more general concept than locality. No, that is not at all what entanglement means. Please refer back to my previous post - entanglement means that the overall wave-function of the composite system has a reduced set of possible composite states as compared to the same system sans entanglement relationships. At no point does this make any reference whatsoever to the spatial separation between these particles. Again, entanglement is purely a stochastic phenomenon to do with the form of the overall wave function, it is entirely separate from any embedding of this situation into a particular spacetime. Note also that you can entangle more than just two particles at a time, again irrespective of how far the constituents of such an ensemble are from each other. Also no. Decoherence is a purely local phenomenon - it means that local degrees of freedom of a wave function become coupled with local degrees of freedom of its immediate environment, e.g. as a result of performing a measurement. Note that the global situation - i.e. the original system plus the environment it came into contact with - remains completely coherent, and thus global unitarity remains conserved in this process, as of course it must be. For example, if you perform a spin measurement on particle ‘A’ of our entangled pair, then its spin direction becomes coupled to the mechanism of the measurement apparatus. You now have a new statistical correlation - between particle A and the measurement apparatus which it comes into contact with it, as opposed to particle A with particle B. The exchange of information involved here is thus purely local, even if the entanglement between possibly distant particles is broken in the process. Two particles being entangled fundamentally precludes the possibility of them interacting in any way after the point when the correlation has first been established, irrespective of the nature of such an interaction (FTL or not). Interacting particles cannot be entangled, since the composite wave function of such a system cannot have the form quoted earlier while still maintaining local probabilities of ½ during the measurement of the entangled property.

If one thinks of the most widespread mineral material used by early man for building and for early artifacts, the rest can be confirmed fairly easily, using Moh hardness as a check.

I missed the “before” The emitted energy is small before the collision. For rotational KE, the mass would be proportional to this, as E/c^2

Looks like puzzle of some kind. Search net for the Mohs scale, lookup mineral with 6, lookup 2, and deduce what kind of mineral it is.

Hello, Roman, and welcome. I don't know if this is homework or not ? - but it really belongs in Earth Science anyway. We don't do people's homwork here, just help them find the answer for themselves. So a suggestion, I wasn't aware that there was any civilisation in what is now the Ukraine before the Babylonians, but I think the answer you are looking for can be found by looking up Hammurabi and how his laws were written. See what you make of this hint and tell us about the homework or source of the question please.

Your punch velocity needs to be: 3725.95mph https://www.boredpanda.com/physics-major-calculates-how-hard-to-slap-chicken-to-cook-it/ Now, should you ever wish to cook a steak by dropping it from a great height (instead cooking a chicken by punching or slapping it), the required height depends on the level of doneness you prefer (rare, medium, well done). https://what-if.xkcd.com/28/

Put some Gallium to a Piece of Aluminium and watch after one week.

I suspect you are talking about androgenetic alopecia. Fundamentally, the condition is related to sensitivity to androgens and especially DHT, and not exclusively to androgen levels itself (though higher levels can increase the effects in sensitive folks). For example, age-paired groups of folks with and without hair loss have no significant difference in androgen levels. Rather, there is something in the signaling cascades (for example number of receptors and there is some evidence of second involvement of certain second messenger pathways) that affects follicle growth. Also, there is a difference how hair on top of the head reacts to DHT and hair on the rest of the body (one aspect being is the number of androgen receptors, for example).

Even vaccines work that way. They provide a blueprint ( or a map, if you like the GPS guided bomb analogy ), so that you body's own defenses can target the specific intrusive virus, with antibodies.

Perhaps antibody therapy for relevant cancers https://pubmed.ncbi.nlm.nih.gov/22437872/ and https://www.criver.com/eureka/magic-bullets-the-next-evolution-in-targeted-cancer-therapy and the term has meaning in the history of micrpbiology https://www.smithsonianmag.com/smart-news/syphilis-cure-magic-bullet-180964644/

While I would hesitate to call a nuclear weapon a precision instrument, there are treatments in medicine that you can describe as precise. Proton therapy, for example. You send a beam of protons at a tumor, and tune the energy so that the protons will deposit the bulk of their energy in the tumor rather than the healthy tissue, so you disrupt the tumor. (They have a proton therapy center at TRIUMF, where I did a postdoc)

Generally not, I would have thought. The technologies involved are so different. But I seem to recall reading there are therapies that can "mark" a tissue for destruction, by an agent that is introduced subsequently and which acts selectively on the tissue that has been marked. This could be considered, superficially at least, a bit like the illumination of a military target by a laser. Maybe someone with medical knowledge can comment on whether my recollection has any basis in fact.

How much are you willing to pay?

What's really scary, is how easy it is to be made scared of a label 'fundie christian', 'musies', 'buddhist' et al; and the Armageddon we're persuaded to unleash on "THEM" to protect ourselves. Which leads to another interesting question, why does a prepper, prepare? They're wealthy enough to store food, build extra shelter and spend so much time "training", that it seems illogical that they wouldn't actively seek the disaster they seek to avoid...