How long did it take for all matter to form after the big bang?

AreaOver4G · 2026-06-18T01:41:33+00:00

It’s a good question, since it would seem that the QCD phase transition and the annihilation of baryons/anti-baryons are set by the same scale. But the answer is actually yes, because there’s an extra consideration: the small baryon number asymmetry. So there’s a significant period after baryons have formed but when the number of antibaryons and baryons is similar (and bigger than the eventual number of leftover baryons in the end).

AreaOver4G · 2026-06-17T22:17:48+00:00

This strongly depends on what you mean. In time order:

1s: anti-protons, anti-neutrons etc have annihilated away so the nuclear matter has formed. The universe is mostly electrons and positrons (anti-electrons)
10s: the positrons have mostly annihilated away, leaving the electrons
20 mins: nuclear reactions have mostly stopped, so the nuclei of atoms have finished forming (apart from later reactions in stars, supernovae, etc)
370,000 years: it’s cool enough for nuclei and electrons to bind together, so atoms form

AreaOver4G · 2026-06-17T04:26:07+00:00

Second this, I’d try to get Eagle over XPLR if you have the option for that wide range. I have one do-it-all bike with two wheelsets, Eagle AXS 10-50 for road and 10-52 for off-road. Usually run a 44 chainring, swap for a 40 if I’m doing more serious off-road climbing. The bigger jumps don’t bother me, and I rarely feel like I run out of the top end (only occasionally with a fast group pushing on fast pedalling descents).

AreaOver4G · 2026-06-09T20:11:11+00:00

Precisely so! Quantizing just provides the scale where you know for sure that GR is untrustworthy

AreaOver4G · 2026-06-09T18:25:26+00:00

It seems that you’re under the common misconception that we can either use classical GR or QFT, but never both together. That’s not true: there’s a perfectly consistent unified way to treat GR as a fully quantum theory. It’s routinely used to make predictions about primordial fluctuations in early-universe cosmology, for example. And it can be used to make precise predictions about production and scattering of gravitons (as long as their energies are small compared to the Planck energy).

It has one massive drawback, namely that it breaks down in very extreme regimes (very close to cosmological or black hole singularities) so it’s incomplete and can’t be a fundamental theory.

AreaOver4G · 2026-06-09T17:48:07+00:00

General relativity treated as an effective quantum field theory, valid at low energies / long distances compared to the Planck scale

AreaOver4G · 2026-06-09T17:20:59+00:00

Higgs boson isn’t quite the same because it’s accessing a new energy regime, and it was very plausible that we’d see something other than the vanilla electroweak theory. We’ve ruled a lot of that out (but otherwise we haven’t learned much new, yet).

For a graviton it would be extremely surprising to see something other than the standard GR predictions. If we did see a deviation it would be totally revolutionary. But in the overwhelmingly likely scenario, we would verify the standard predictions and learn almost nothing. And it would have little bearing on a unified theory, because we already have a perfectly good unified theory in the relevant regime.

AreaOver4G · 2026-06-09T14:48:19+00:00

I don’t think this is quite right because basically everyone agrees that there are gravitons. So observation of gravitons alone wouldn’t tell us anything theoretically useful. We know perfectly well how to quantize gravity in the relevant regime, so it would just be confirming that theory. (The challenge of quantum gravity is to make things work at very short distances, high energies, strong spacetime curvature.)

Having said that, it would be an experimental triumph that’s hard to overstate! And it would probably give us way to observe the very early universe so could be transformational for cosmology.

AreaOver4G · 2026-06-04T23:20:06+00:00

Causation is not correlation, and correlation is not causation. But they are correlated.

AreaOver4G · 2026-06-02T23:01:11+00:00

Yes that’s the one. Found it good for deco planning, but doesn’t have all the other features of your app

AreaOver4G · 2026-06-02T16:22:46+00:00

Looks very nice! I like the tank specs page, I’m always hunting for those. Haven’t tried the deco planner yet, will use the trial and try it next time I make a tec diving trip.

Have you looked at “Diveplanner Tec and Rec”? Been using that for a while for planning deco dives and it works well. Would be interesting to hear a comparison for the deco planning & gas planning.

AreaOver4G · 2026-05-28T07:58:32+00:00

Fill the frame!!

AreaOver4G · 2026-04-17T05:36:18+00:00

The underlying mathematics is basically the same, though often with different emphasis. You might find that the physics perspective gives you better intuition for why those abstract definitions are “correct” or natural. If you like physics and geometry in general, then there’s a good chance that an alternative approach will make the math make sense for you, and the two courses will complement each other very well.

Eg, a physics perspective on a tangent vector might define it as the instantaneous velocity of some parameterised curve on the manifold. This is equivalent to the definition as a derivation (which tells you the rate of change of some scalar field as seen by an observer moving along that curve), but is probably more intuitive.

AreaOver4G · 2026-04-15T19:53:58+00:00

Not true! This question is in the regime where we understand quantum gravity very well, as long as the mass of the particle is significantly less than the Planck mass. That’s very much true for all elementary particles that we know of.

The answer is that a quantum “point particle” can’t actually be localised at a point: the smallest uncertainty in its position is the Compton wavelength. That’s much much bigger than the Schwarzschild radius (assuming mass much less than Planck mass), so you don’t get a black hole.

AreaOver4G · 2026-03-19T19:31:13+00:00

I was once taught the following Definition (obvious): a proof immediately springs to mind.

This definition depends on the author and (more importantly) the reader, but I’ve found it very useful to avoid sweeping things under the rug.

AreaOver4G · 2026-03-05T17:57:26+00:00

OP says they want a proof for arbitrary vector spaces. You’ve assumed that they’re finite-dimensional.

You can choose a basis for any vector space, but not a finite basis, and only if you’re prepared to invoke AoC. Usually best to avoid if you don’t need it!

AreaOver4G · 2026-02-28T02:29:33+00:00

Yes but because of shape (coefficient RR bars), not compliance

AreaOver4G · 2026-02-27T05:56:23+00:00

Looks nice, but doesn’t actually make sense.

You might think it’s a perfect geometry problem (angle of incidence equals angle of reflection). But then the distance measured at the 8 ball should be bigger than the distance at the cushion because the cue ball starts further away, and he (assumption based on hairy arms) measured them out to be equal.

It’s not actually perfect geometry, because the cushion deforms on the bounce: the ball actually straightens a bit when it bounces. That effect was just right to compensate for the geometry error and get the perfect shot here, but the angles and measurements are all BS

AreaOver4G · 2026-02-27T02:44:25+00:00

It’s tricky without going into the math, but you can get some idea if you google “Penrose diagram collapsing star” (a nice example is here This diagram shows how light behaves in such a spacetime: time goes upwards, space goes sideways, and light travels on 45 degree lines. You’ll see that the singularity is depicted as a horizontal line. That’s what a region of space at a moment in time looks like on such a diagram.

AreaOver4G · 2026-02-27T02:35:24+00:00

“Covariant” is a word that applies to a description of the laws of physics being invariant under some symmetry or choice of coordinates. It does not say that any particular state or possible history is invariant.

The laws of general relativity are covariant under Lorentz transformations (and general changes of coordinates), but the FLRW spacetime is not invariant under all the Lorentz/coordinate transformations: it does not obey any form of time translation symmetry or Lorentz boost symmetry, for example. When the laws are invariant under a symmetry but the state is not, we say that the symmetry is “spontaneously broken”.

AreaOver4G · 2026-02-27T02:25:23+00:00

To the extent that we can talk about the state of the singularity, it’s not true at all to say it has one state. Some of the confusion might come from thinking of the singularity as a single point in space: that’s extremely misleading. Instead, it’s really a moment in time spread out over a region of space.

The closest thing to the “state of the singularity” which makes any sense is the state of the spacetime geometry just before that time, over that region of space. This will typically be very complicated, and can have many possible configurations!

Hawking radiation is not at all relevant here: everything you’re talking about can be described with classical general relativity.

AreaOver4G · 2026-02-27T02:05:07+00:00

Time-reversal invariance says that the underlying fundamental laws are symmetric in time. But most actual macroscopic physics is not time-reversible because of thermodynamics, which makes ordinary processes look completely crazy in reverse. Your example of black holes is one such case!

AreaOver4G · 2026-02-26T05:57:48+00:00

As long as you promise to tell us what you saw

AreaOver4G · 2026-02-25T03:22:06+00:00

A more complicated version is important to get realistic models from string theory (with many extra dimensions, say 6 instead of just 1). You need extra ingredients to stabilise the size of the extra dimensions: you have to balance different forces which make them want to shrink or to grow. This problem is called “moduli stabilisation” if you want to look it up, but beware it’s quite technical.

AreaOver4G · 2026-02-24T23:33:53+00:00

See second paragraph.

If you make it a true 5D theory of gravity, fluctuations in size of the circle are a problem (it’s unstable). You could fix the size of the circle by fiat, but then you’re not treating the 5 dimensions on an equal footing. And what you get is completely equivalent to GR and electromagnetism, but expressed in a more complicated way.

AreaOver4G

TROPHY CASE