MigL

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.

You're right INow. As a favor to you, Iand in the spirit of the season, I will drop this, and show some good will towards other members. I just want my opinions to be treated the same as others, without the 'except'. We were discussing how my opinions were seen as justification for killing, yet others' were not, I guess because CharonY thinks there were no innocent children killed on Oct 7th. Merry Christmas. Will be back next week.

You're absolutely right. Of course that justifies breaking through a border, brutally killing 1400 people, and kidnapping several hundred more. See CharonY, I can extrapolate too.

I'm the one with the bad eyesight. Surely you must have seen the quote I included below my 'accusation'.

HaHa ! I guess if you have already convinced yourself of my guilt, it is easy to assume the worst about me. ( oops ! last time I said similar I got neg repped ) I have said many times there are plenty of guilty parties on both sides. But people, Israeli or Palestinian, are only responsible for the choices they, themselves make, not what others choose to do. And you have agreed with that. Yet some of us are clearly putting blame on one side only ... Yet I don't see you pushing back on String Junky assigning no blame whatsoever on some Palestinians who happen to be members of Hamas. He seems a little confused, as he thinks B Netanyahu is a member of Hamas. Maybe you should set him straight, or are you too busy chastising me for trying to provide a balanced view, and that the situation has gotten out of hand precisely because both sides refuse to take responsibility for their actions.

On the contrary, it means that in war , mistakes and accidents do happen. The 'fog' and all that ... But, if you don't have an open mind, and have already convinced yourself of someone's guilt, it is easy to assume the worst about them.

Here is a derivation ( some simple maths ) of the HUP as applied to a particle described by a deBroglie wave. Includes historical perspective and is well illustrated.