KJW

The stars in galaxies are not glued to the expanding space. They are quite free to move independently of any expansion of space. Thus, if a star exhibits some tendency to move away from the central core of its galaxy due to the expansion of space, then the gravity from the central core will pull the star back into the fold. If a star orbits its galaxy at some particular distance from the centre of the galaxy, then even after the space has expanded, the laws of physics will maintain the distance at which the star orbits, noting that the laws of physics are based on local scale, not cosmological scale.

No, it's not what i think. You say that, but then you say things like: The notion of a variable c might seem reasonable from a superficial perspective, but when one considers it more deeply, it becomes clear that it is really quite meaningless, in the "how long is a piece of string" territory. No, that's not what I meant. Suppose that in the past, before the standard of length was defined in terms of the speed of light in a vacuum, one performs a measurement of the speed of light in a vacuum. One can do this by measuring the time it takes for light to travel in a vacuum the distance of the standard of length and return. From the measured time and the known distance, the speed of light in a vacuum is determined. Now consider that currently, with the standard of length defined in terms of the speed of light in a vacuum, one performs a measurement of a given length. One can do this by measuring the time it takes for light to travel in a vacuum the distance of the given length and return. From the measured time and the known speed of light in a vacuum, the given length is determined. But note that the same experiment is performed in both cases. That is, in both cases, one is measuring the time it takes light to travel some distance in a vacuum... a measurement of the speed of light in a vacuum. To make this more explicit, consider in the second case that one can define the given length as a temporary standard of length with the unit of "tmpstd". Then one is measuring the speed of light in a vacuum in units of tmpstds per second. Dividing the defined speed of light in a vacuum in units of metres per second by the measured speed of light in a vacuum in units of tmpstds per second gives a value in units of metres per tmpstd corresponding to the length in metres for the given length. I agree that the speed of light in a vacuum is conceptually distinct from c. The speed of light in a vacuum is a property of light or electromagnetism in general, whereas c is a value that relates units of length and units of time with regards to the equivalence of length and time in spacetime. Whereas one can use the same ruler to measure lengths in the east-west, north-south, and up-down directions by simply rotating the ruler, one can't rotate the ruler to the past-future direction. But relativistic effects do provide a way to determine the equivalence between length and time in spacetime. For example, one can measure c by measuring the velocity of light in water at rest and in water moving at velocity v. From the three velocities, the value of c can be obtained by rearranging the relativistic velocity-addition formula. Note that the length standard used to measure the three velocities is based on the speed of light in a vacuum, not c, so the measurement of c is a truly independent measurement. However, it is unfortunate that the length standard is based on the speed of light in a vacuum, and not on c, given that it is c that is about the equivalence of length and time in spacetime. In general relativity, the general metric is expressed succinctly as: (ds)2 = gpq xp xq How would a variable c even fit into this expression? And what do you think "ds" means in this expression? Bear in mind that regardless of what is used to define the standard of length, it will never be possible to determine the "true" value of that length. A length can be measured in terms of another length, but this ultimately leads to an infinite regress. And if a length is measured in terms of itself, it will have a definite value, but that value has no meaning.

Gravity.

All the same they simplify the math and leads to the correct answer. That depends on the connection. For a Riemannian connection, normal coordinates exist which simplify the proofs of identities. But for a general connection, for example if the torsion tensor is non-zero, then normal coordinates do not exist in general. Also, if one is using normal coordinates to simplify the proofs of Riemann tensor identities, then one also needs to include the proof of the existence of the normal coordinates themselves. Thus, in the end it may actually be simpler to prove the Riemann tensor identities directly without invoking normal coordinates. And while one is at it, one may as well prove the Riemann tensor identities for the general connection.

That's actually the point I'm making. It can't be completely random because then there would be no ability to control. But it can't be completely deterministic, either, because then there would be no free will.

In classical electrodynamics there are no magnetic monopoles. Mathematically, the divergence of the magnetic field is zero. This means that at all locations, there is no source of the magnetic field (unlike the case of the electric field for which the source at a given location is the charge density at that location). Equivalently, this also means that for every hypothetical closed surface, the net flux of the magnetic field through the surface is zero (unlike the case of the electric field for which the net flux through the surface is the total charge enclosed by the surface). A pole exists where there is a surface through which the net flux of the magnetic field is in one particular direction. But because there are no magnetic monopoles, there is always a balance of north and south magnetic poles on any closed surface.

And the notion of free will seems to rely on enough determinism to allow control but also enough randomness for there actually to be free will.

No, they're neurotransmitters. I did work them out a while ago (I actually have this album), and IIRC, the top-left is dopamine, the top-right is serotonin, the bottom-left is glutamic acid, and the bottom-right is part of an endorphin molecule.

So, is he going to bring back leeches?

Her favourite music is the 2017 Bubblemath album "Edit Peptide":

Normal coordinates can be used to prove Riemann tensor identities such as the second Bianchi identity, but they need not be used to prove such identities. I prefer not to use normal coordinates to prove such identities, but to prove them directly. Even though the Christoffel symbols are zero in normal coordinates, the partial derivatives of the Christoffel symbols are generally not zero and the Riemann tensor is generally not zero. The Christoffel symbols are not tensors whereas the Riemann tensor is a tensor. Thus, whereas the Christoffel symbols can be coordinate-transformed to zero at a point, the Riemann tensor in general can't be coordinate-transformed to zero at the point. The Riemann tensor may be defined in terms of parallel transport of vectors around infinitesimal parallelograms. Although the resulting change in the vector is itself infinitesimal, the Riemann tensor that is obtained as a result is not infinitesimal.

Two things: (1): Over cosmological distances, gravity-bound systems are but mere specks. (2): The standard FLRW model is just that... a model. It is a simplified approximation of the actual universe. However, it should be noted that it is superior to consider deviations from a simple model than to use a complicated model from the outset.

For one thing, there's the central limit theorem.

Google was reluctant to provide useful information about what chlorine dioxide powder is, but I did manage to find a Safety Data Sheet for a particular brand of the powder. It turns out that it is a mixture of sodium chlorite and sodium bisulfate. Given that these two react in solution to form chlorine dioxide, it is understandable why the powder should not be premixed in a small volume of water. https://horticentre.co.nz/wp-content/uploads/Safety%20Datasheets/Exstinkt%20Pure%20(Ixom)%20SDS.pdf

pfft

One problem is that G isn’t determined to a very high precision 6.67430(15)×10^-11 m^3/kg s^2 The limitations on that would affect any system relying on it. Yes. But what I said was a continuation of the hypothetical notion mentioned earlier of being able to measure G to an accuracy and precision comparable to that of h and c. Indeed, one of the reasons I said I don't know how to design the measuring instrument is because I don't know how to measure G to the required accuracy and precision. Bear in mind that the reason for replacing ΔνCs with G, apart from philosophical ideality, was to address the concern raised by @Killtech that the current definition of the second is based on an electromagnetic notion (the Cs atom). No, there is no such problem as the fundamental constant cannot be measured in this situation and therefore must be defined. This is fine because the constants - or more precisely the core physics they originate from - serve as the rulers to measure everything with. for example the speed of light together with the other constant allows you to construct a real photon emission which wavelength is fully determined by the constants and this base wave lengths servers as a ruler to compare any other real length to. For this we only need to know the defined values of the constants instead of measuring them. The definition via constants has the nice advantage that we have some freedom in constructing the ruler we use - yet all the different rulers constructed in this way will still agree (if the physical laws underlying them use are indeed correct). I take responsibility for the possible misunderstanding here. Even though the fundamental constants are defined to have definite numerical values, measurements of the dimensions still require physical access to the fundamental constants. Therefore, all the issues associated with measuring the fundamental constants in the past when the fundamental constants were measured still apply to the measurement of the dimensions in terms of the numerically defined fundamental constants today. In particular, the accuracy and precision of measurements of the dimensions is limited by the accuracy and precision of measurements of the fundamental constants even though they are not being measured in the same sense that they were in the past but as a standard of comparison. Why do you think that there is a "true" value of the fundamental constants? Yes, the Planck length is a definite interval of spacetime, but without a unit of length to compare it with, the Planck length can't be specified. And if the Planck length is the unit of length, then the Planck length has a value of 1, but its interval of spacetime remains unspecified.

From: https://xkcd.com/3073/

What NASA level computer did you use Why do you think such simulations require a lot of computing power?

Hmm, it could be but it would require some other constant to lose its definition. The unit of G is composed of units of time, length and mass. It makes no sense to compete for the first two, so its would compete with Plancks constant to define the Kilogramm by its value. As only the value of one of them can be defined, the value of the other becomes a derivative as a consequence. No. Considering the dimensions of the fundamental constants, [math]c[/math], [math]h[/math], and [math]G[/math], one has the following system of equations: [math]c = \dfrac{L}{T} \ \ \ \ \ ;\ \ \ \ \ h = \dfrac{M L^2}{T} \ \ \ \ \ ;\ \ \ \ \ G = \dfrac{L^3}{M T^2}[/math] Inverting this system of equations, one obtains expressions for the individual dimensions in terms of the fundamental constants: [math]L = \sqrt{\dfrac{h G}{c^3}} \ \ \ \ \ ;\ \ \ \ \ M = \sqrt{\dfrac{h c}{G}} \ \ \ \ \ ;\ \ \ \ \ T = \sqrt{\dfrac{h G}{c^5}}[/math] Therefore, specifying the numerical value of each of the three fundamental constants, [math]c[/math], [math]h[/math], and [math]G[/math], is sufficient to define the units of each of the three dimensions, [math]L[/math], [math]M[/math], and [math]T[/math]. Mathematically, it doesn't matter that none of the units are defined in isolation of the others. That is because the three fundamental constants are independent, and thus their expressions in terms of the three dimensions are invertible. However, there is the practical issue of measuring length, mass, and time in terms of the corresponding expression in terms of the fundamental constants. I'm guessing that because such an instrument would have to be able to measure the three fundamental constants, the same instrument would be used to measure length, mass, and time. However, I have no idea how to design such an instrument. [Note: If the LaTex above doesn't render, please Refresh this page]

And measles. Admittedly, I grew up at a time when pretty much every kid got measles, so I am also inclined to downplay the danger. But I have no issues with vaccination, so the measles I had as a child is no reason for the children of today not to get vaccinated.

I've simulated the Second Law of Thermodynamics and the Quantum Zeno Effect on an Excel spreadsheet.

Like when Volodymyr Zelensky met with the King shortly after Trump and JD Vance berated him in the Oval Office.

How is an atom a bound state of the field characterised by c? It's being used to define time. It should be noted that the choice of the particular atom and the particular transition is for technical reasons and not for anything that could be considered fundamentally theoretical. I'm quite sure that if the gravitational constant could be measured to an accuracy and precision comparable to the Planck constant and the speed of light in a vacuum, then it would also be defined to have an exact numerical value as the definition of the second.

There is a housing crisis in Australia, and this is being exacerbated by immigration. The fundamental problem as I see it is that there are going to be winners and losers regardless of what the government does. Increasing the supply of housing will reduce the cost of housing, which will be beneficial to those seeking to buy, but detrimental to those who have already bought. And even left-wing politicians may have a disincentive to implement a policy that goes against their own self-interest.

This is a questionnaire sent by the Trump administration to Australian universities receiving US funding: https://www.documentcloud.org/documents/25595847-questionnaire-for-us-research-partners/