MigL

In simple terms, intrinsic curvature implies there is no 'outside' dimensions embedding the curvature. Since there is no 'outside' you cannot 'see' a ship dropping below the horizon as your view is confined to the curved surface. The Earth's surface is extrinsic because you can go 'inside' the curvature by boring a hole between two points connecting the ends of an arc, or 'outside' the curvature to see the top of the mast of the ship dropping below the horizon. Not sur I agree. Global geometry is also determined by the mass/energy content of the universe, and this global curvature constrains possible topologies. As an example, a negatively curved universe can not close on itself, and has to be infinite. A flat universe can either be infinite or finite, as there are flat closed topologies like a flat torus. A positively curved universe has only closed topologies, like hyperspheres or toruses, available which are necessarily finite. If the universe is homogenous and isotropic, we may be able to use the local curvature of the observable universe as an indication of the global curvature of the universe, and all measurements indicate it is very nearly flat. That could mean the universe is finite but many orders of magnitude larger than the observable universe; much like the floors of your house are flat on a curved Earth, or it could actually be flat and infinite.

You're having problems imaging the topology of 4D space-time by comparing it to 3D or 2D topologies ? Welcome to the club. Mathematics, however, has no such limitations.

The 'block' universe is an interpretation. One of many, and the one you are choosing to use is called 'eternalism' and has many counter-arguments. See here for other interpretations

No paradox; classical and quantum mechanics don't mix. Black holes do not allow for the emission of anything, under classical considerations. Black Holes do have entropy, however, and so, an associated temperature. This temperature is barely above 0oK, and since the universe is currently at 2.7oK, BHs are actually net absorbers of mass/energy. It is only in the far future, when the universe has cooled below a BH's temperature that it will experience net evaporation due to Hawking radiation. Both Hawking radiation and the information paradox ( due to unitarity requirements ) are quantum mechanical considerations, and cannot be explained classically.

I don't know the mathematical motivation. The Physical motivation is the elimination of divergences in the perturbative corrections of Quantum Field Theory.

The temperature when the universe becomes transparent, and electrons can 'stick' to hydrogen nucleii, is basically the ionization temperature ( energy ) of Hydrogen. At higher temperatures atoms cannot bind, and you have a radiation filled plasma that is opaque like the Sun. As the present CMB temperature is 2.7oK , that indicates ( according to gas laws ) that the universe has expanded to over 1000 times its size since the recombination era.

As an extremely small mass ( compared to the mass of the Sun ) makes no difference whatsoever in Newton's equation, we can make that 'assumption' to ease the calculation. That doesn't mean light does not have the property of mass; it is massless, otherwise it could not move at c . And light is NOT energy, but it does have that property. Ooops. My mistake. As genady correctly points out above, a flat torus has no curvature, and even a 'regular' torus is only curved along one axis.

Yes, the topology depends on curvature. Obviously a universe with a scarcity of mass/energy would have negative, or flat curvature, and could not form a 'closed' topology like a hypersphere or a flat torus.

i) GR is not a 'complete' theory; while extremely accurate where applicable, it fails to make valid predictions in many cases, as it fails miserably when dealing with hi mass/energy and extremely short separations. ii) Gr does allow for closed timelike loops, which would enable time travel through the use of 'wormholes'. However, keeping those wormholes open requires the use of 'exotic' matter ( negative mass/energy ), which, as far as I know, can be harvested from immediately inside the event horizon of a Black Hole ( the 'counterpart' to Hawking radiation ), and may not exist or be realizable. See K Thorne's work. What does that tell you about my knowledge of the subject ?

Not that I have high regard for the 'logic' used in your argument, but I don't recall anyone saying that it was possible.

This is an aspect of the topology of the universe, and has nothing to do with bending of light by gravity. If the universe is 'curved', light has no choice but to follow the 'curvature; it cannot travel 'outside' as there is no outside.

And are combinations of 3 up/down quarks, in a 'cloud' of virtual gluons. All of which are fundamental and may have no size. So what composes the rest of the proton/neutron ? By that same definition, they would be empty also.

Yes that is what 'closed' implies. A positive curvature will always close on itself. This can be seen on the surface of a globe, where a ray of light following the curvature will come up behind itself. Different distances to the 'back of your head', however, may be seen in different directions depending on topology.

It is, actually, just that.

The distinction between 'empty space' and what we call elementary particles is not very clear, and depends entirely on your definition of empty space. Particles seem not to have any size, so by one definition, the atom is 100% empty space. By another definition, until we detect them, all particles are probability densities distributed throughout the atom, which then has no empty space. Ask a 'better' question.

IOW, Seth, the axis, or principal dimensions, do not change in any way,; the 'projection' of the interval onto the axis, or principal dimensions, is what changes. Singularities and infinities are essentially the same; a singularity is a point where an infinity arises. No one needs to consider the 'fade to gray', or any other kind of 'boundary' to the universe; a finite universe simply 'closes in' on itself, such that, if you 'looked' far enough away, you would 'see' the back of your head.

Say what ?

Nice example, Genady. And not to imply otherwise, but you only consider a linear scale factor as a function of time. And I'm sure you know of many functions f(x), that tend to infinity as x approaches a specific finite value. IOW, what if the scale factor is extremely non-linear ?with time

That's the difference between ''logical proof' ( as in made-up ) and experimental proof ( as in observed ). One of those can be purely delusional. We only 'know' reality by measuring, and measurements support relativity, not your incredulity. And every good physicist knows the distinction.

Not quite the same. Scientific theories have to fit observations, otherwise they are simply WAGs. If we have no observations, but simply varying definitions of an abstract concept, then ALL are WAGs. I don't often agree with S Hossenfelder, but in this case she makes some very valid points.

I'm 65 in about 3 weeks. Don't imagine my sperm count is very high.

One might say that the flow pulses of 'congestion' is an emergent property of the individual drivers/vehicles. And that reminds me ( of another video I watched to get my science fix during last week's 'sabbatical' ). Did we ever establish in the preceding 20 pages, the definition of 'free will' and whether it actually exists as such ? ( sorry to drag you back into this, Eise )

I remember when laptops used to 'burn' your lap. QCs will give you ( severe ) frostbite, and produce even more wasted power than bitcoin mining. Maybe after we finally get cheap fusion power ... I'm not worried about anyone breaking into my encrypted data for a long time to come.

Do we really need to worry about how the advent of quantum computing will affect any type of encryption just yet ??? Reality check ...

You must have gotten a lump of coal from Santa because you're still cynical and a little abrasive 😄 . Why not consider this a learning opportunity for all ? This property, energy, we define as the ability to do work, is essentially a property of the configuration of the system. Whether the system is moving gives us kinetic E and/or temperature, and its positional arrangement in any external or produced fields, gives potential E. I would add that 'intrinsic' energy, or mass, is only a property of fundamental particles, such as electrons, quarks and neutrinos. Most of what we normally consider 'mass' is tied up in various levels of binding energy ( molecular, atomic, nuclear and baryonic ) and is correctly identified as potential E, due to the positional configuration of the system. One could make the stretch that even elementary particles' intrinsic mass/energy is due to the configuration of the system as it results from the coupling to the Higgs field.