About the maximal electrostatic potential energy U(r) of a pair electron-positron at rest with distance r
in [Relativity]
|
From: PD on 19 Jul 2010 14:59 On Jul 16, 2:16 pm, va...(a)icmf.inf.cu wrote: > I suppose we are all in agreement about the increase of U(r) with an > increase of r. Has U(r) a finite maximal limit value when r tends to > infinite? In case of positive answer, which is that maximal value? You may have heard in freshman physics that the zero point of potential is physically arbitary. In all interactions, the only thing that is important is the *change* in potential energy between initial and final states, and that number is independent of the overall scale. It is frequently customary to put U(r=infinity) = 0, so that all values of U(r) for finite r are negative. But this by no means required and many problems are more convenient to solve with a completely different choice. PD
From: PD on 19 Jul 2010 15:00 On Jul 19, 8:38 am, "Dono." <sa...(a)comcast.net> wrote: > On Jul 16, 12:16 pm, va...(a)icmf.inf.cu wrote: > > > I suppose we are all in agreement about the increase of U(r) with an > > increase of r. > > No, imbecile, the potential DECRESES with distance. No one agrees with > your idiocies. You may want to check your comment. The OP was asking about a positron- electron pair.
From: valls on 19 Jul 2010 17:38 On 19 jul, 12:11, dlzc <dl...(a)cox.net> wrote: > Dear va...: > > On Jul 19, 4:24 am, va...(a)icmf.inf.cu wrote: > > > > > > > On 16 jul, 15:13,dlzc<dl...(a)cox.net> wrote: > > > On Jul 16, 12:16 pm, va...(a)icmf.inf.cu wrote: > > > > > I suppose we are all in agreement about the > > > > increase of U(r) with an increase of r. Has > > > > U(r) a finite maximal limit value when r > > > > tends to infinite? > > > > r probably will tend to a maximum at r_U > > > (radius of the Universe, in a non-expanding, > > > flat Universe), and r_U may be a function of > > > time as well, in this Universe. If one of > > > the charges moves across the Rindler horizon > > > of the other... > > > > > In case of positive answer, which is that > > > > maximal value? > > > > That'll probably depend on when you ask. > > > But I'd think it will asymptotically approach > > > some value with increasing values of r. > > > Even using modern cosmology, you give only a > > naive answer. I was waiting a much more > > detailed answer, a quantitative one related with > > the electron known intrinsic constants. > > Then maybe you'll need to develop this answer yourself. > Sure. I will do it a little ahead. > > Maybe this is an open problem in today Physics? > > Finding the size of the Universe is, yes. > No, I refer only to find the finite maximal limit value considered for the potential energy. > > I found a very simple answer using only 1905 > > Relativity: > > Who cares about your insistence on 105 year old physics? Why did I > know you were going to drag this back to your old stomping grounds? > If you cant offer an adequate solution even using modern cosmology, it seems to me reasonable that you would be interested in knowing one that uses only 1905 Relativity. Anyway, it is a lot much simple to show the solution that to talk about its existence. Following 1905 Relativity (1905R), the maximal limit value for the potential energy of a pair electron-positron is 2 m_e c^2, where m_e is the today rest mass for the free electron. That value corresponds to the experimentally measured energy of the photons that result from the pair annihilation. The essential support is in a thread I opened some time ago. The title and the link are the following: Potential energy in 1905 Relativity http://groups.google.com.cu/group/sci.physics.relativity/browse_frm/thread/0ea5fc8334fa1353?hl=es# I found (many years ago) analysing the 27Sep1905 Einsteins paper in his historical context that The (rest) mass of a body is a measure of its (potential) energy-content. This is a particular case of his much general result about mass measuring energy. As the arbitrary additive constants characteristic of potential energies (managed by 1905 Einstein) all disappear in his final result (mass has not an arbitrary additive constant), this means that 1905 Einstein finds a unique natural zero for potential energies (even if not realizing it at all). And the potential field energy and the body rest energy is one and the same thing. > David A. Smith RVHG (Rafael Valls Hidalgo-Gato)
From: valls on 19 Jul 2010 17:56 On 19 jul, 13:59, PD <thedraperfam...(a)gmail.com> wrote: > On Jul 16, 2:16 pm, va...(a)icmf.inf.cu wrote: > > > I suppose we are all in agreement about the increase of U(r) with an > > increase of r. Has U(r) a finite maximal limit value when r tends to > > infinite? In case of positive answer, which is that maximal value? > > You may have heard in freshman physics that the zero point of > potential is physically arbitary. In all interactions, the only thing > that is important is the *change* in potential energy between initial > and final states, and that number is independent of the overall scale. > Well, you dont answer my question, but what you say is compatible with an infinite value for U(r) when r tends to infinite (any arbitrary additive constant doesnt change the infinite). Anyway, I consider more interesting the other alternative with a finite maximal limit value. I just address it in an answer to dlzc (David) in this same thread. I consider adequate to refer you to it, instead of repeating here my analysis. > It is frequently customary to put U(r=infinity) = 0, so that all > values of U(r) for finite r are negative. But this by no means > required and many problems are more convenient to solve with a > completely different choice. > > PD RVHG (Rafael Valls Hidalgo-Gato)
From: PD on 22 Jul 2010 14:58
On Jul 19, 4:56 pm, va...(a)icmf.inf.cu wrote: > On 19 jul, 13:59, PD <thedraperfam...(a)gmail.com> wrote:> On Jul 16, 2:16 pm, va...(a)icmf.inf.cu wrote: > > > > I suppose we are all in agreement about the increase of U(r) with an > > > increase of r. Has U(r) a finite maximal limit value when r tends to > > > infinite? In case of positive answer, which is that maximal value? > > > You may have heard in freshman physics that the zero point of > > potential is physically arbitary. In all interactions, the only thing > > that is important is the *change* in potential energy between initial > > and final states, and that number is independent of the overall scale. > > Well, you dont answer my question, but what you say is compatible > with an infinite value for U(r) when r tends to infinite (any > arbitrary additive constant doesnt change the infinite). Read what I wrote. U(r)=0 is quite finite. > Anyway, I > consider more interesting the other alternative with a finite maximal > limit value. I just address it in an answer to dlzc (David) in this > same thread. I consider adequate to refer you to it, instead of > repeating here my analysis. > > > It is frequently customary to put U(r=infinity) = 0, so that all > > values of U(r) for finite r are negative. But this by no means > > required and many problems are more convenient to solve with a > > completely different choice. > > > PD > > RVHG (Rafael Valls Hidalgo-Gato) |