From: PointedEars@web.de   
      
   [Thank you for having followed the Followup-To that I set.]   
      
   Bill Sloman wrote:   
   > On 14/02/2026 5:58 am, Thomas 'PointedEars' Lahn wrote:   
   >> Bill Sloman wrote:   
   >>> They can behave in very different ways. Mass can stay put. Energy   
   >>> tends to travel at the speed of light.   
   >>   
   >> Utter nonsense.  Mass and energy are quantities, not physical objects.   
   >   
   > Mass and en energy are quantities used to described the behavior of   
   > physical objects.   
      
   They are physical quantities; they are also properties that _we assign_ to   
   physical systems in order to describe them (not just objects; not just their   
   behavior, but also their _state_).   
      
   For example, if the quantum-electromagnetic field has an energy that is ℎ f   
   (or ℎ c/λ, or ℎ k c) above its ground-state energy (which is also its   
   zero-   
   point energy), then we say that there is a photon with frequency f (or   
   wavelength λ, or wavenumber k, respectively): the photon is the quantum of   
   that field (AISB).  The quantum-electromagnetic field is therefore also   
   called "photon field", and in quantum field theory we simply identify the   
   photon with that field.   
      
   > Those described mostly in terms of mass can stay put.   
      
   Objects with non-zero mass can be at rest in an inertial reference frame.   
      
   AIUI, objects with zero mass cannot, because at relative rest they would   
   have zero total energy (provided there is no associated potential energy),   
   and for us they would not be detectable -- which is equivalent to them not   
   existing then.  But (an important concept in particle physics is that)   
   existence or the happening of a process cannot depend on the choice of rest   
   frame: either an object exists in all rest frames, or a process can happen   
   in all rest frames; or it cannot exist or the process cannot happen at all,   
   respectively.  (This is e.g. how it is explained that a single photon cannot   
   vanish to produce a particle--antiparticle pair in perfect vacuum.)   
      
   > Those described mostly in term of energy travel at the speed of light.   
      
   No, you are confusing and oversimplifying things.   
      
   The energy--momentum relation of free particles in Minkowski space is   
      
     E^2 = m^2 c^4 + p^2 c^2,    (1)   
      
   where E is _total_ energy, m is mass, c is the speed of light _in vacuum_,   
   and p is the Euclidean norm of (linear 3-)momentum.   
      
   Under those conditions, the momentum vector of objects with non-zero mass is   
   given by   
      
     P = γ m V,   
      
   where   
      
     γ = 1/√(1 - v^2/c^2)   
      
   is the Lorentz factor, and V is their relative velocity.  Therefore, the   
   square of the momentum is given by   
      
     p^2 = P^2 := P ⋅ P = γ^2 m^2 V ⋅ V = γ^2 m^2 v^2,   
      
   where v is the relative speed (speed is the norm of velocity; the Euclidean   
   norm of a vector is equal to the square root of its scalar product with   
   itself).  Therefore, for those objects we can rewrite eq. (1):   
      
     E^2 = m^2 c^4 + p^2 c^2 = m^2 c^4 + γ^2 m^2 v^2 c^2 = γ^2 m^2 c^4.   
      
   Since γ is a function of v, this allows us to write more conveniently (what   
   I call) the speed--mass relation   
      
     v = c √(1 - m^2 c^4/E^2).   
      
   It follows that the closer the mass of an object is to zero, the closer the   
   speed of that object can approach c, and objects whose mass is *equal to*   
   zero MUST move at the speed c (in all inertial reference frames).   
   Conversely, for an object to attain the speed c (in all inertial reference   
   frames), its mass MUST be zero; or IOW, objects whose mass is not zero   
   *cannot* move *through* space at the speed c.   
      
     [I for one find it remarkable that this jumps out of the Minkowski metric,   
      with which eq. (1) can be derived, without any explicit references to   
      kinetic energy or forces.]   
      
   Notice that this basic fact is independent of how much total energy these   
   objects have; notice further that because the total energy depends on the   
   kinetic energy (and since mass is frame-invariant, in the absence of   
   potential energy not on anything else), for objects with non-zero mass it   
   depends on the chosen rest frame (is NOT frame invariant).   
      
   So it is a misconception and misleading to describe this as pertaining to   
   "Those [physical objects that are] described mostly in [terms] of energy".   
   *Every* object of physical inquiry has energy because that is something that   
   *we ascribe* to it.   
      
   >>>> Do photons attract one another? Do they bounce off one another?   
   >>> Crossed laser beams don't seem to interact.   
   >> They do if their energy is large enough.   
   >   
   > They could do if their energy were large enough.   
      
   Yes.   
      
   > I don't know of any experiments with actual lasers that have ever   
   > demonstrated the effect.   
      
   Fair enough.  To my knowledge photon--photon scattering is not studied by   
   crossing laser beams, but e.g. with light that is emitted by massive   
   electrically charged particles:   
      
      
      
   >>>> If you apply Newton's law of gravitation to photons, the force   
   >>>> will be enormous when they get in a close intersection. Wouldn't   
   >>>> that fuzz up images at cosmological distances?   
   >>>   
   >>> It doesn't seem to. The mass of most photons is pretty small,   
   >>   
   >> You could say that; it is *zero* :-D   
   >   
   > The mass-energy isn't zero.   
      
   Yes it is.  What is called "mass-energy" by some people (NOT physicists) is   
   the rest energy, the energy that a system has at relative rest.  It is given   
   by E_0 = m c^2.  Trivially, if the mass is zero, as with photons, so is   
   their rest energy or "mass-energy".   
      
   There is no other mass but that which was formerly called "rest mass" by   
   some physicists (not Einstein).  If you have learned something else, then   
   you have learned a concept that is obsolete, and has been considered   
   obsolete for at least 40 years now.   
      
   > We wouldn't be able to detect them if it were.   
      
   You are mistaken.   
      
   >>> and when they are travelling at the speed of light they don't   
   >>> interact for very long.   
   >>   
   >> Nonsense.   
   >   
   > More paradoxical that nonsensical/   
      
   No, it is just nonsense.  Photons can interact across a distance of ca. 13.8   
   Gly, as we can see in the Cosmic Microwave Background radiation.   
      
   The range of the electromagnetic interaction is infinite (in theory),   
   due to zero mass of its gauge boson, the photon.  See also:   
      
      
      
   >>>> Just asking.   
   >>> But not thinking at all.   
   >>   
   >> You, too, do not know what you are talking about.   
   >   
   > In your "expert" opinion.   
      
   Well, it would be hubris for me to claim that I am an expert in these   
   matters, but *I* have *actually* *studied* (Astro-)Physics, including   
   everything that I have written about above and before, at a real university   
      
   [continued in next message]   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)