KJW

I think it needs to be clarified precisely what a clock measures. A clock (specifically the part that physically responds to time) measures proper time along the spacetime trajectory (aka world line) of the clock. Ideally, a clock is not affected by any form of motion or gravity. This is a consequence of the principle of relativity, the principle that the laws of physics (and therefore the behaviour of clocks) are the same in all frames of reference. It should also be noted that, according to the equivalence principle, a local gravitational field behaves like an accelerated frame of reference. This means that gravitational time dilation is the same as time dilation in an accelerated frame of reference. It also means that freefall in a gravitational field is locally the same as an inertial frame of reference (btw, this means that special relativity is an important part of general relativity, not merely a precursor of it). A device that receives signals from a remote clock is not itself a clock. It is merely relaying to the observer of the device the measurement of proper time along the spacetime trajectory of the remote clock. Suppose the remote clock is ticking exactly once per second. It will tick exactly once per second irrespective of where it is or how fast it is moving. The intervals in spacetime marked by the ticks will be genuine one second intervals (I feel I can't stress this enough). Observing the remote clock involves null geodesics in spacetime from each tick of the remote clock to the observer, the time interval between the observed ticks being measured by a local clock. The interval between the ticks at the location of remote clock is exactly one second, the interval between the observed ticks measured by a local clock need not be one second. Both intervals are proper times at their own locations, but in no way is the interval between the observed ticks a measure of time at the remote clock. Nor is the interval between the observed ticks of the remote clock a measure of local time. What is coordinate time? Coordinate time is the value of a particular coordinate of a particular type of coordinate system. If spacetime is sliced into spacelike three-dimensional slices, coordinate time identifies each spacelike slice. The spacelike three-dimensional slices are usually considered to be defined by hypothetical observers whose spacetime trajectories are normal to the spacelike three-dimensional slices. The coordinate time may be the proper time for one particular spacetime trajectory. If the spacetime is stationary, then this coordinate system is naturally defined by the isometry between the spacelike three-dimensional slices. In the case of a black hole solution, the t coordinate corresponds to proper time at spatial infinity. If the spacetime has a Friedmann-Lemaître-Robertson-Walker metric (FLRW), then the t coordinate is the proper time everywhere (the age of the universe), but only for trajectories that are at rest relative to the comoving frame of reference.

Mrs Tilly likes spectral yellow but not RGB yellow.

It appears that one can "Like" by clicking the heart but not "Downvote" if someone has already upvoted or downvoted a post.

Around the turn of this century, I devised such a theorem. Basically, any dictionary based only on words must contain words that are either undefined or circularly defined. One way around this is for a dictionary to also contain pictures. In the case of defining a clock in terms of instructions on how to build it, one also avoids the problem associated with a dictionary based only on words.

Some time ago, I came up with the perfect definition of a clock. Note that the definition of time is that which is measured by a clock, so the definition of a clock cannot reference time. But one can define a clock without referring to time by providing instructions on how to build a clock. The instructions to build a clock is the definition of that clock.

We are always at a speed of zero relative to our own frame of reference. It should be noted that speed (or velocity) is always relative to something. However, the speed of light is always the same in all frames of reference.

I don't know what "opposite of the speed of light" means. However, (according to Wikipedia) the peculiar velocity of the Sun relative to the comoving cosmic rest frame is 369.82 ± 0.11 km/s towards the constellation Crater near its boundary with the constellation Leo.

Mrs Tilly believes in God but does not believe in religion.

When you refuse dialogue, it's only your loss, really 🤷‍♂️

Perhaps you can elaborate on how f(x) is continuous. It is clearly a discontinuous function to me.

@exchemist I've been looking at N-methyl-2-pyridone as an analogue of the N-substituted cytosine. The 1H-NMR spectrum has the following chemical shifts: H3 = 6.17 H4 = 7.34 H5 = 7.32 H6 = 6.57 HMe = 3.59 (https://www.chemicalbook.com/SpectrumEN_694-85-9_1HNMR.htm) Compare with benzene = 7.34 (https://en.wikipedia.org/wiki/Benzene_(data_page)) Compare with trimethylamine = 2.12 (https://docbrown.info/page06/spectra2/trimethylamine-nmr1h.htm) Compare with tetramethylammonium iodide = 3.207 (https://www.chemicalbook.com/spectrumen_75-58-1_1hnmr.htm) Compare with HMe of toluene = 2.32 (https://en.wikipedia.org/wiki/Toluene_(data_page)) Compare with HMe of methylcyclohexane = 0.858 (https://www.chemicalbook.com/SpectrumEN_108-87-2_1HNMR.htm) The chemical shifts of the ring protons of N-methyl-2-pyridone, being similar to benzene, do suggest a ring current associated with aromaticity. I also compared the methyl protons of N-methyl-2-pyridone to the protons of the methyl group attached to the uncharged nitrogen of trimethylamine and the charged nitrogen of tetramethylammonium iodide. However, this is complicated by ring current effects which led me compare the methyl protons of toluene and methylcyclohexane. On thing worth noting is that the oxygen atom of phenol and especially of the phenoxide ion is electron-donating to the 2, 4, and 6 positions. This is similar to the tendency for N-methyl-2-pyridone to be in the pyridone electronic configuration. Similarly, pyridine and especially the pyridinium ion is electron-withdrawing from the 2, 4, and 6 positions, also leading to the tendency for N-methyl-2-pyridone to be in the pyridone electronic configuration. However, I suspect that N-methyl-2-pyridone is still aromatic.

Given the resonance structures N–C=O <—> +N=C–O– , even with the deoxyribose attached the cytosine ring should still be aromatic (and flat).

For some reason, your LaTex is rendering for me immediately without hitting Refresh, but other LaTex I've looked at still requires Refresh.

Looking at the image in @studiot 's post, one thing that I see is notable is that whereas cytosine enolises to an aromatic hydroxy compound, the attachment of the deoxyribose to the nitrogen atom "freezes" the molecule in the non-aromatic keto form.

LaTex requires me to hit the Refresh button in order for it to render.

Why do you insist that the speed of light in a vacuum can vary? You seem to have a problem with defining its value as exactly 299792458 m⋅s–1. Would it be less of a problem to you if, instead of defining a specific value of the speed of light in a vacuum, the metre is defined such that the value of the ground state hyperfine structure transition wavelength of the caesium-133 atom is exactly 0.0326122557175 m?

No. But I do stay logged in (until I clear cookies, etc). Do you use a VPN?

Or a gauge freedom.

How is asserting that the value of the speed of light in a vacuum is exactly 299792458 m⋅s–1 any different from asserting that the value of the ground state hyperfine structure transition frequency of the caesium-133 atom is exactly 9192631770 s–1? The point is that defining any base unit of measurement involves asserting the exact value of some physical quantity. In the case of defining the metre, if one didn't assert that the speed of light in a vacuum is exactly 299792458 m⋅s–1, then one would have to assert that the length of some other physical notion has some specified exact value.

Yes and no. Actually, the gravity with which we are familiar is caused by time dilation, and the curvature of space plays no part in this. But the space surrounding the earth is curved. The Schwarzschild solution, which models gravity around an ideal non-rotating spherical object, requires the surrounding space to be curved for it to describe pure gravitation, even though it is only the time dilation which provides the familiar gravity. It is worth noting that the deflection of starlight by the sun is double that which can be accounted for by time dilation alone. It is the curvature of space which provides the additional half of the deflection. In general relativity, pure gravitation is described by the Weyl conformal tensor field, which has 10 independent components in four-dimensional spacetime. Thus, it is more complicated than the gravity with which we are familiar. Bear in mind that spacetime is the unification of space and time, and the notion of different frames of reference implies that one can't separate space and time. The mathematics of general relativity places space and time on equal footing, with the same formulae applying to both space and time equally.

Should be fixed now. I'll need to tweak it, since it's an old version of MathJax, but it should behave the same as the old system now. It was fixed but now it's gone.

Agreed. I thought this might be a preference option but couldn't find any way to change it.

There is no LaTex!

Hydrogen is always going to be released at the cathode (unless mercury is used as the cathode, in which case sodium is produced dissolved in the mercury). As for what's produced at the anode, whether oxygen or chlorine, I am also curious. I recall that in another thread, @exchemist said that both are produced, depending on the chloride concentration.