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7h
comment Quantum entanglement definition
Dear @user115519, quantum computers use pretty much the most general entangled states of $N$ qubits (i.e. states on a Hilbert space with $2^N$ basis vectors) that you can get. Perhaps, the states with the complex amplitudes $0$ and $i^k/2^{m/2}$ are more likely to appear in useful quantum calculations than others. But in general, you can't make any assumption about the state of a quantum computer at all and quantum computation indeed dramatically exploits this great freedom. If you restricted the "character of allowed entanglement" in some strong way, q. computers would lose their advantage.
16h
comment How could we travel to the nearest supermassive Black hole?
"Exotic matter" (in this sense, e.g. of having some negative energy density) is a hypothesis that is considered ruled out by physical arguments - and almost all practising physicists would agree that some matter that "clearly violates the null energy condition" is impossible. Its being ruled out or implausible doesn't mean that we must stop calling it a "hypothesis".
17h
comment Quantum entanglement definition
As I tried to communicate in the answer, as long as one uses the ket vectors (formalism of quantum mechanics) all the time, the physical meaning of "entanglement" is nothing else than a "correlation" between two objects. The reason why we don't use a "correlation" is just that people are used to automatically assume classical physics when someone says "correlation". For this reason, "entanglement" is sometimes meant to denote only "correlations of the kind that couldn't be predicted by a classical theory". But that doesn't mean that they're not in principle the same "kind" of a correlation.
17h
comment Quantum entanglement definition
@ToddWilcox - the entanglement is absolutely omnipresent and it's routinely observed all the time. Some physicists have become famous for nothing else than this "recreational quantum physics", like Anton Zeilinger. By today, all the experiments with the quantum information such as Bell's theorem, GHZM, Hardy's, and others have been verified by real-world experiments. But entanglement is seen in lots of experiments that are not motivated by either "quantum foundations" or "quantum information/computation". Lots of forces and stability of molecules etc. is due to entanglement. The QE is generic
17h
comment Quantum entanglement definition
@user115519 - I think it's right. One must just be careful that the "discarding" is done correctly in the quantum mechanical formalism, i.e. by projection operators that "cut" some terms in the wave function, parts of the wave function that are natural in the appropriate basis. When we say that options are simply discarded etc., it doesn't mean that the options or their discarding may be described by classical physics. One must always use the appropriate logic and formalism of quantum mechanics - and the usage of no word means that the rules of classical physics may be used.
17h
comment Quantum entanglement definition
@innisfree - I completely agree. The entanglement is a logical connection between the systems, not a causal one (at the present). Well, the logical connection usually has an explanation in terms of some causation, but that causation occurred in the past and usually involved another system influencing both subsystems.
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answered Quantum entanglement definition
1d
comment How could we travel to the nearest supermassive Black hole?
The total energy of the later states of the Universe would still be zero because the energy is conserved - but there would be both positive and negative contributions. It would be analogous to the pencil.When it's already falling, the potential energy is lower (negative relatively to the initial state) than zero, while the kinetic energy of the pencil is positive. In the Universe, the analogy of the falling pencil would be a cosmic cataclysm (cosmos filled with huge amounts of hot radiation etc.) that would begin immediately.
1d
comment How could we travel to the nearest supermassive Black hole?
The vacuum has to stay the vacuum, so it must be the state of the Universe with the lowest energy - often labeled by the number zero. If there existed states of negative energy (energy lower than the vacuum's), the set of configurations in which the Universe may be would resemble a pencil standing on its tip. Even if the forces were balanced, any tiny deviation would lead to the pencil's exponentially growing deviation from the unstable position, and the pencil would fall. Similarly, the Universe would get filled with lots of tachyon waves moving everywhere.
2d
comment What ds>dQ/T mean?
There is no objective identification which part of the system is the system and which part is the environment. It's the total entropy that grows more than the bound. This extra growth may take place both in the system and in the environment.If the environment has blue and red ink which gets mixed to a purple ink, the entropy of the environment goes up. If the same inks appear within the system, the entropy of the system goes up, even without any heat transfer.
2d
comment What experiment would disprove string theory?
Dear Philip, my answer makes it quite detailed that this isn't the only way to disprove the theory. However, if you could prove (or back by strong evidence) your statement, it would be a great news for the validity of string theory because that situation would mean that you have proven the theory, in any sensible sense of the word "proof". To think that it would be bad news means to misunderstand the basic rules of logic. The dream of physical theories is to survive (or survive for as long as possible), not to be killed.
Apr
30
comment How do I calculate the differential cross section with respect to the transversal momentum?
Apologies, Shawn, you could force me (or someone else) to solve the full problem, but I think that if that happens, it could only be used to cheat. I am not really helping you anymore. You really shouldn't try to solve similar complex problems such as the parameterizations of differential cross section before you are sure enough about the relativistic dispersion relations, among other more basic things. In all these 2-to-2 problems, there are four momenta obeying $p^2=m^2$ with the obvious $m$, and 4-momentum conservation holds. One has to be sure about these matters before more complex stuff
Apr
30
comment What is the difference between the Big Bang Model and the Λ-CDM Model?
These explanations appear in many reviews, textbooks, introductions. I was intrigued to mention the book "A Most Incomprehensible Thing: Notes Towards a Very Gentle Introduction to the Mathematics of Relativity" (buy at amazon.com or elsewhere) which has pages 315-320 about the FRW stuff etc. What I like about this book is that there is already a section in the updated book about the 2015 LIGO detection. ;-)
Apr
30
comment What is the difference between the Big Bang Model and the Λ-CDM Model?
You may look at the Wikipedia entries for the radiation-dominated era en.wikipedia.org/wiki/Radiation-dominated_era and similar pages. The timing and average temperature and energy density and speed of expansion etc. are all calculable (obeying various power laws). Cosmologists first simplify Einstein's equations to the Friedmann-Lemaitre-Robertson-Walker equations for a uniform universe with uniform matter, and solve this much simpler ordinary differential equation that only depends on time. The different eras differ by different ratio pressure/energy_density.
Apr
30
comment What is the difference between the Big Bang Model and the Λ-CDM Model?
Dear @SyedAli, we don't measure the value "50,000 years" directly in any way. I already answered this question in the previous comment. Nevertheless, we feel sure that the theory is right already from the first three minutes because it produces e.g. the right percentages of the light nuclei as we observe, and those were created in the first 3 minutes. This agreement (plus CMB curves etc.) is a source of a big confidence that the theory is correct, and that's why we also believe the equations of the big bang that the radiation era took 50,000 years, and many other things.
Apr
29
comment What is the difference between the Big Bang Model and the Λ-CDM Model?
Dear Syed, cosmologists aren't directly observing the radiation-dominated era. The matter dominated era ended relatively recently (now it's the cosmological-constant-dominated one, forever), and the transition was never sharp in any way. The standard evidence for TBBT is listed here: schoolsobservatory.org.uk/astro/cosmos/bb_evid
Apr
29
comment How do I calculate the differential cross section with respect to the transversal momentum?
The last equality follows tautologically because if you define the longitudinal parts of the 3-vectors as vectors at all, they are 1-dimensional vectors, so the inner product of the vectors is the same as the product of the "only components". No, the derivative of $t$ with respect to $p^T$ surely isn't zero.
Apr
29
answered How do I calculate the differential cross section with respect to the transversal momentum?