Genady

The answers to these questions should be independent of reference frame. Perhaps it would be easier to consider the scenarios in reference frame of one of the objects, i.e., where one of them is at rest.

One example of all three is thermal equilibrium.

Removing a boundary point is akin removing surface from water. It is possible to remove a very thin layer of water from the surface, but it is not possible to remove the surface and to leave the water without a surface.

But we are fine with loosely defined categories in real life.

I think, the no. 1.

OK, let's explore it. Let's assume that a line segment always has an end number. What happens when we remove that number? There are two possibilities: 1. It is impossible to remove a number from a segment. It is only possible to remove some open range of numbers, however small it is, but not one number only. One individual number is not removable. Or, 2. If one number is removed from a segment, what's left is not a segment anymore, but some other kind of object.

AFAIK, sufficient assumptions for CPT symmetry are: the Lagrangian is Lorentz invariant, local, Hermitian and normal ordered. Such Lagrangian is invariant when all spacetime signs are reversed and all particles and antiparticles are replaced.

Makes sense. Chemical camouflage to hide from creatures that sense the world mostly chemically. Visual camouflage to hide from creatures that sense the world mostly visually. Audio camouflage anybody?

Frankly, I don't know now what topic/concern is/are discussed. Is it something definite?

Unfortunately, this happens only for short term during psychotic episodes.

No, it is more than that. Just look at this book: Modern Classical Physics: Optics, Fluids, Plasmas, Elasticity, Relativity, and Statistical Physics by Kip S. Thorne (Author), Roger D. Blandford (Author) From the book description: This first-year graduate-level text and reference book covers the fundamental concepts and twenty-first-century applications of six major areas of classical physics that every masters- or PhD-level physicist should be exposed to, but often isn't: statistical physics, optics (waves of all sorts), elastodynamics, fluid mechanics, plasma physics, and special and general relativity and cosmology. Growing out of a full-year course that the eminent researchers Kip Thorne and Roger Blandford taught at Caltech for almost three decades, this book is designed to broaden the training of physicists. Its six main topical sections are also designed so they can be used in separate courses, and the book provides an invaluable reference for researchers. Presents all the major fields of classical physics except three prerequisites: classical mechanics, electromagnetism, and elementary thermodynamics

I don't think that having relative velocity constitutes a physical interaction. Maybe it does in some sense, but I am not familiar with such sense. In every meaning of physical interaction that I am familiar with, such a relation is excluded. E.g., interacting particles in QFT.

A new pic from friend: Trumpetfish

Imagine points on a plane which are vertices of a square 1x1 grid covering the entire plane. Find a shape with area < 1 such that it cannot be placed on the plane without touching at least one of these points.

Yes, they are. But they are not interactions.

I don't immediately see it. Could you elaborate?

I see independent differences (Dictionary by Merriam-Webster: America's most-trusted online dictionary😞 Socialize Conform

I think there are more things we know for sure, such as patterns of the redshift, CMB radiation and its patterns, gravitational lensing, elements content, evolution of features, etc.

Moreover, we never observe or measure real numbers. Unlike natural numbers - we can count - and rational numbers - we can break things.

If it was, the question did not mention it. Mathematics answers what has been mentioned in the question.

This is what you mean, right?

I think it is called mathematics.

Thank you. Yes, this is my understanding. Quantum fields represent / fit something out there (reality), like gazelles' legs represent / fit the terrain they live on.

It is proven in GR that homogenous isotropic space is unstable. It has either to expand or to shrink. Which one and for how long, depends on initial conditions. Why the initial conditions, aka Big Bang, were what they were, is unknown. The dark energy is inferred not to explain why space expands, but rather to explain why the expansion accelerates.

OK, if 'to conform' means 'to socialize' then it perhaps is in human nature. I disagree. From the statement, "for an athiest to not play golf, they first have to be taught what golf is" follows the logical conclusion, "as long as they were not taught what golf is, they play golf". The conclusion is wrong; as this conclusion is a logical consequence of that premise, the premise is wrong. So, in order to not play golf, they don't need to be taught what golf is. They just need not to play it.