KJW

The difficulty with explaining entanglement is that there are two aspects to it: the correlation and the quantum superposition. Both are necessary for there to be entanglement. The correlation can be explained in purely classical terms. But the quantum superposition cannot. Therefore, simply explaining the correlation in classical terms is not enough. The tricky part is that multiple particles, even distantly separated particles can form multi-particle states in quantum superposition such that a measurement of any of the particles can be a measurement of them all. However, being in quantum superposition implies that the multi-particle states satisfy Bell's theorem which highlights the inadequacy of explaining the correlation in purely classical terms.

Measuring one entangled particle doesn't affect the other entangled particle. The correlation between the entangled particles already exists within the two-particle state even in the absence of measurement so that measurement of one particle is a measurement of both.

No. According to the no-communication theorem: "In physics, the no-communication theorem or no-signaling principle is a no-go theorem from quantum information theory which states that, during measurement of an entangled quantum state, it is not possible for one observer, by making a measurement of a subsystem of the total state, to communicate information to another observer. The theorem is important because, in quantum mechanics, quantum entanglement is an effect by which certain widely separated events can be correlated in ways that, at first glance, suggest the possibility of communication faster-than-light. The no-communication theorem gives conditions under which such transfer of information between two observers is impossible. These results can be applied to understand the so-called paradoxes in quantum mechanics, such as the EPR paradox, or violations of local realism obtained in tests of Bell's theorem. In these experiments, the no-communication theorem shows that failure of local realism does not lead to what could be referred to as "spooky communication at a distance" (in analogy with Einstein's labeling of quantum entanglement as requiring "spooky action at a distance" on the assumption of QM's completeness)."

You mentioned "entanglement". Unfortunately for your idea, you have a popular but mistaken view of what entanglement is. Entanglement is not a communication channel between remote entities. Entanglement cannot be used to communicate information. Entanglement is a correlation between entities that had at some time a causal connection. The entanglement persists while the entities are isolated from the environment but is generally broken by any interaction with the environment (e.g., a measurement of any of the entities).

Yes, it is worth keeping in mind that even as we sit in front of our screens, there are frames of reference relative to which we are moving at arbitrarily high speeds even if those frames of reference do not correspond to any observer or object.

No, but I had to dispel the view that if Falcon 2 is more massive from the perspective of Earth then Earth is less massive from the perspective of Falcon 2.

Also: [math]\text{For }v \approx 0: \\ \dfrac{1}{\sqrt{1 - \dfrac{v^2}{c^2}}} \approx 1 + \dfrac{1}{2} \dfrac{v^2}{c^2}[/math] [math]\text{Therefore:} \\ m_{\text{relativistic}}\ c^2 - m_{\text{rest}}\ c^2 = m_{\text{rest}}\ c^2 \left(\dfrac{1}{\sqrt{1 - \dfrac{v^2}{c^2}}} - 1\right) \\ \approx \dfrac{1}{2} m_{\text{rest}}\ v^2[/math]

In special relativity, the energy-momentum vector is a four-component vector in spacetime. The time component corresponds to the energy, the three spatial components correspond to the momentum, and the magnitude of the vector corresponds to the invariant rest mass. (Note however that for dimensional consistency of units, E=pc=mc2). Because it's being described in the earth's frame of reference, and in that frame of reference, the energy component of the four-component energy-momentum vector is increasing, though the invariant magnitude of this vector is not changing. The formula that describes the invariant rest mass in terms of energy and momentum is: [math](mc^2)^2 = E^2 - (pc)^2[/math] ........................................ [math](m_{\text{rest}}\ c^2)^2 = E^2 - (pc)^2 \\ E = m_{\text{relativistic}}\ c^2 \\ p = m_{\text{relativistic}}\ v \\ (m_{\text{rest}}\ c^2)^2 = (m_{\text{relativistic}}\ c^2)^2 - (m_{\text{relativistic}}\ \dfrac{v}{c}\ c^2)^2 \\ m_{\text{rest}}^2 = m_{\text{relativistic}}^2\ \left(1 - \dfrac{v^2}{c^2}\right) \\ m_{\text{rest}} = m_{\text{relativistic}}\ \sqrt{1 - \dfrac{v^2}{c^2}} \\ m_{\text{relativistic}} = \dfrac{m_{\text{rest}}}{\sqrt{1 - \dfrac{v^2}{c^2}}} [/math]

The assumption is that the Falcon 2 is getting its power to accelerate from an external source, and that the rest mass of the Falcon 2 is not changing.

No. If an object is at rest relative to the Falcon 2, then its mass in the frame of reference of the Falcon 2 will be the rest mass of the object. Note also that in the frame of reference of the Falcon 2, the mass of the Falcon 2 will be the rest mass of the Falcon 2. Also, in the frame of reference of the Falcon 2, the mass of the earth, which is moving at 99.99%c relative to the Falcon 2, will be approaching infinite.

It's worth noting that if the shift in frequency is directly proportional to the frequency (if the ratio of frequencies is independent of the frequency), then the redshift is a time dilation. If the shift in frequency is directly proportional to the frequency, then any amplitude modulation of the signal will also have its frequency shifted in direct proportion to its frequency, and therefore the rate of any mechanical clock will appear to be similarly altered. By contrast, if the redshift is due to an energy loss without time dilation (e.g., Compton scattering), then the shift in frequency will not be directly proportional to the frequency.

It's worth noting that it is possible in principle to measure the value of c by performing the Fizeau experiment and applying the relativistic velocity-addition formula.

Actually, such numbers don't have to be prime, it is sufficient that they are not divisible by either 2 or 3. Also, 1 or 5 (mod 6) implies 1 or 2 (mod 3).

There is no Nobel Prize in Mathematics.

This is a big question. I don't think there are any general answers, with the answer depending on the particular situation. For example, let the two systems be two different points in some abstract space. Then does the measure of difference between the two points depend on the path between them? In thermodynamics, functions of state such as entropy are defined explicitly such that the differences are independent of the path between the initial and final states in state space. By contrast, distances between points in ordinary space or spacetime do depend on the path between them.

As an Australian living in Australia, I watch an Australian TV program called "Planet America", which provides a somewhat humorous view of US politics, though it isn't a comedy. In that show recently, I saw an advertisement from the Democrats appealing to women with Republican husbands to secretly vote for Kamala Harris.

And I will add that it is irrational to be concerned about trace amounts of methanol from the normal consumption of aspartame.

When I was in Year 2 at a regular public school, we were taught matrices, including matrix multiplication. They didn't seem at all useful to a seven-year-old. I didn't encounter them again until senior high school, when their use was revealed. I do not remember when I learnt about negative numbers.

It's been my experience that most people are good. But there are certainly a***holes out there that spoil it for everyone else. It's probably not fair to judge humanity as a whole based on the relatively few a***holes who cause problems. On the other hand, it's wise not to forget that not everyone is a good person and that one needs to keep their wits about them.

You could measure the proper length of a moving object using a ruler that is moving alongside the object, bearing in mind that the object is still moving relative to you, the person doing the measurement.

What has nuclear weapons got to do with travelling to the moon? I would have thought the more appropriate question would be: Was being able to travel to the moon worth the exoneration of Nazi scientists?

Related to this is the problem of determining the molecular formula of a compound from the molecular mass obtained using a high-resolution mass spectrometer.

He probably is if one assumes that what he says is NOT true.

I don't know to what extent it applies to American politics, but in Australia, minor parties and independents can have an exaggerated level of power in the case where the winning party failed to win the majority of seats and must negotiate with the minor parties and independents who won their seats. (Firstly, it must negotiate with the minor parties and independents to actually be the winning party because if no party wins the majority of seats, it is NOT the party that won the most seats that wins government, but the party that gains the majority of seats with support from the minor parties and independents who won their seats. Then once the winning party is in government, it has to negotiate with minor parties and independents on policy.)

Didn't Trump build a wall, or at least part of a wall? He said he was going to build a wall, and make Mexico pay for it.