Wikipedia:Reference desk/Archives/Science/2024 March 30

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March 30

Visualisation of angular diameter turnaround

I wish to remake the xkcd diagram as per Talk:Angular_diameter_distance#xkcd_Graphics_of_Angular_Diameter_Turnaround but

seems to imply that up to z~1.5, corresponding to objects around 9.5 billion years old according to

objects appear larger with distance, counter to everyday observation. I presume that the object's distance is its age multiplied by c.

What's the mistake in my understanding? Thanks, cmɢʟee⎆τaʟκ 03:12, 30 March 2024 (UTC)

There are several distances like comoving and proper (also see observable universe) and in cosmology they can differ from each other by hundreds of percent. There's also an angular distance not a real distance where Euclidean geometry holds which goes backwards above a certain redshift. Sagittarian Milky Way (talk) 20:20, 1 April 2024 (UTC)

The traditional distance-size math can't work for far enough objects cause the Universe was so unexpanded in the past a small blob seen by microwave background radiation will look fucking huge. Sagittarian Milky Way (talk) 20:23, 1 April 2024 (UTC)

P.S.

The angular size redshift relation for a Lambda cosmology, with on the vertical scale megaparsecs.

has two graphs labelled "Reference Plot" and "Your Plot". On its file page, its English caption states "The red plot shows an incorrect angular diameter distance using a value for Hubble's constant without square rooting the expression for the density parameters." Why does the diagram need to show an incorrect graph? cmɢʟee⎆τaʟκ 03:21, 30 March 2024 (UTC)

The first plot shows the scale in kpc per arcsec (it is often better to write "arcsec" instead of a naked double prime). Up to $z\sim 1.5$, the same angle (say 1 arcsec) covers an increasing intrinsic size; conversely, the same intrinsic size (say 1 kpc) spans a decreasing angle, i.e. appears smaller with increasing distance. So this is as one would expect. For higher redshift, things become weird and objects start to appear larger again. I'd still like to see a convincing plot based on actual measurements — unfortunately, there are no good standard rulers out there (or I haven't paid enough attention). The last plot should really be deleted, "your plot" seems like some sort of experiment that the creator of the plot did. --Wrongfilter (talk) 07:34, 30 March 2024 (UTC)

A pair of physical properties, linearly related to each other by a physical constant only.

Here are five examples of such pairs, followed by a question:

1. A given radiation's energy, and the radiation's frequency, are two useful physical properties - linearly related to each other by the planck constant, i.e. $E=h\nu .$

2. The thermal energy, and the absolute temprature, are two useful physical properties - linearly related to each other (per one degree of freedom) by the Boltzmann constant, i.e. $E={\frac {k_{B}}{2}}T.$

3. A given radiation's wavelength, and this wave's temporal period, are two useful physical properties - linearly related to each other by the constant speed of light,.i.e. $\lambda =cT.$

4. A given radiation's energy, and the radiation's momentum, are two useful physical properties - linearly related to each other by the constant speed of light, i.e. $E=pc.$

5. A given body's energy, and the body's mass, are two useful physical properties - linearly related to each other by the constant sqaure of the speed of light, i.e. $E=mc^{2}.$

Besides these five pairs of useful physical properties, do you know of other pairs of useful physical properties - denoted by useful notation - and linearly related to each other by a physical constant (or by a combination of physical constants) only, which does not equal any pure number (e.g. 2 or $\pi$ and likewise)?

Note: By "useful" physical properties, I exclude new properties one can invent, e.g. products of values of useful physical properties, and the like. HOTmag (talk) 21:51, 30 March 2024 (UTC)

1, 3, 4, and 5 are just reducible to any two properties in special relativity and nonrelativistic QM that use the Planck constant and the speed of light. #3 in particular is the definition of any wave a priori. (There are important properties that you are missing in your description of #5: see mass–energy equivalence.) #2 meanwhile is derived from the a priori definition of temperature -- k_B could be considered a mental convenience.

Then again, I'm not sure if these a priori origins are precisely what you are getting at. Alternatively, you might be looking at constants that scale relations that are physical and not solely a priori derivations, such as the gravitational constant in F=GMm/r². Or you may be looking for derivations that reduce more complex relationships into simple functions of two variables, for which there are infinite possibilities; F=mg for example? [Edit: I'm excluding from consideration the natural derivation of SI units.] SamuelRiv (talk) 23:40, 30 March 2024 (UTC)

The relation F=GMm/r^2 does not satisfy my condition of there being a pair of properties. F=mg really contains two properties only, as required, but it does not satisfy my condition of there being a constant, because g is not a real constant: it changes as far as one moves away from the earth.

I'm not sure what you meant in your first paragraph. Could you give examples for your first sentence, or for the content in the parentheses - in your first paragraph? Re. the last sentence of your first paragraph: I don't exclude definitions, provided that the properties are useful ones, as explained in my last paragraph [I, too, am excluding from consideration the natural derivation of SI units]. HOTmag (talk) 04:29, 31 March 2024 (UTC)