We are in no way considering the same thing. Theory will give exact predictions if your assumptions are exact (this includes initial conditions even though that isn't really an assumption - you are assuming your measuring device measures perfectly?) Anyway, within the theory, assumptions are made which are approximately true, these are where errors build up - I know this. But that is not the same as what you were claiming.
Ok, in principle a theory will give exact predictions given the initial data, but we, scientists, don't usually know what these exact answers are. For instance, if I give you an arbitrary charge distribution and ask you to tell me what the electric field is everywhere, you can't do it if the charge distribution is crazy enough. You can write down the solution as an integral, but because you can't do the integral exactly you can't tell me what the exact field should be.
Aer: I swear Aer, you can be really dense sometimes. You misinterpreted again. Most physicists accept that thermal energy contributes to rest mass of a system of particles. You seem to claim they do not accept that. But you're wrong, as I explained.
I hate to 'support' Aer but i hate to hear your blabbering too. The nucleus (after alpha/beta decay) exited into a higher energy state emits gamma ray subsequently and comes down to a lower energy state. Is the rest mass of the nucleus different before and after gamma radiation? Does the energy that exites the nucleus add to its rest mass? As your habbit you might aviod these inconvenient questions too. Anyone else?
The following answer to a question regarding mass increase reflects the position I have held for a long time. I arrived at my conclusion after reading many high energy physics papers mostly from particle accelerator experiments. It deviates from Special Theory, regardless of the fact that many 'relativists' often proclaim particle accelerators 'prove' Special Theory to be true. "Mass m in the equation E = mc2 is equal to the rest mass (m0) times the factor gamma. Gamma has the value 1 when v = 0, and increases toward infinity as v approaches c. That is, the mass in E = mc2, which is clearly the mass the questioner is concerned about, does indeed increase as an object acquires energy due to motion = kinetic energy. E = mc2 clearly implies that, as total relativistic energy E increases, the total (rest and relativistic kinetic) mass increases correspondingly! It is this _total_ mass that has to be reckoned with when interacting with the object. For example, the mass of the electrons in the electron beam of a CRT increases due to the acceleration of the electrons toward the face of the tube. This factor has to be taken into account in designing the deflection system that scans the beam across the tube face. Likewise, the considerable increase of the mass of particles in particle accelerators has to be taken into account in the design of accelerators. Furthermore the answer to the question is not complete. There was also a 'be it kinetic, or otherwise?' The questioner should be informed that, yes indeed, it doesn't make any difference what form of energy is acquired by the object. Kinetic energy is only one possibility. Thermal energy and potential energy (of various kinds) also matter. For example, the binding potential energy between the constituents of the nucleus contributes significantly to the mass of the nucleus. It is precisely the liberation of this mass-due-to-binding-energy that is the basis of nuclear fission reactors and the atomic bomb! Answered by: Warren F. Davis, Ph.D., President, Davis Associates, Inc., Newton, MA USA" http://www.physlink.com/Education/AskExperts/ae121.cfm
Let me try to put one issue to rest, the vast majority of physicists do agree that all types of energy (mass, kinetic, thermal, electromagnetic, nuclear, etc) do contribute to gravity. Please see some of my earlier posts for references and explicit quotations to this effect by expert physicists in the field. However, Aer has made it clear that he is absolutely not interested in what physicists have to say on the matter. Note that this does not contradict the no black hole from fast moving particle result also accepted by physicists for reasons I also try to explain (but perhaps do so poorly).
Some figures: A neutron has a mass of 1.67492716*10^-27 kg A proton has a mass of 1.67262158*10^-27 kg An alpha particle has a mass of 6.64465598*10^-27 kg A simple calculation will reveal that the mass of tha alpha particle is less that the mass of 2 protons and 2 neutrons (its constituents), the difference is accounted for by the negative binding energy of the alpha particle. Suppose I ask you to close your eyes and I place an alpha particle in one distant region of space and 2 neutrons and 2 protons (separated so that they have essentially no interaction) in another distant region. The question is, can you tell the boxes apart purely by gravitational means? In other words, does the binding energy of the alpha particle actually contribute to gravity or not?
Physics Monkey, Good example for binding energy being part of rest mass of alpha-particle. Does the excitation energy of the nucleus form a part of its rest mass before it emits off that energy as gamma radiation and gets into lower energy state? Again, the question, whether the rest mass of the exited nucleus is different before and after gamma radiation?
I did not misinterpret anything! That is EXACTLY what I said. Now here is the part that you are too dense to understand - I am claiming that thermal energy will not contribute to the rest mass if kinetic energies do not contribute to gravity! Get it? I think you don't. No, I do not speak for them, my claims do not equal their claims!! You are about as dense as they come Please Register or Log in to view the hidden image!
I think I've made it clear that I don't care for flat out claims (the ONLY thing that has been presented in every post of this thread - and yes, I don't give a rat's ass about my own claims either, they are just claims to counter the other BS claims without proof).
Binding energy is negative energy. How might you propose that negative energy contributes to gravity? Is it anti-gravity? Anyway... The explanation of binding energy as "negative" is a bit convenient, I think the matter is much more complicated than that, but I am not aware of any explanation that goes deeper than just stating that the binding energy is negative. And don't be fooled by the likes of James R and others whom like to claim that slamming 2 particles together will magically produce 1 particle. No... that'll never happen - in actuality, you get the 2 particles exploding into multiple subcomponents.
I don't see exactly how binding energy being negative is "convenient"? Binding energy has a very precise meaning in a multiparticle quantum system. I must supply that energy to the alpha particle in order to break it up (of course, the process I use must be consistent with conservation laws). In this case I am breaking bonds made by the strong nuclear force. When I supply 13.6 eV to the electron in a Hydrogen atom to ionize it I am breaking bonds made by the electromagnetic force. Same basic idea, same precise meaning to binding energy. Also, yes I am suggesting that the binding energy lowers the gravitational contribution of the alpha particle from what it would be considered separately as 2 neutrons and 2 protons. The notion of negative energy or negative pressure is found in cosmological GR models involving dark energy etc.
Also, I am not being 'fooled' by James R. Recombination collisions are not imaginary and they occur many areas of the physical sciences. For instance, in Bose Einstein Condensates, the recombination of condensate atoms into untrapped and uncondensed molecules is a known loss mechanism in the condensate.
Don't be stupid like James R. You are talking out of both sides of your mouth (or you don't have any idea what you are talking about). The example you state is not in any way the same as what James R presented. What you are refering to with Bose-Einstein condensates is not an accelerated collision between two atoms, but rather it is the collapse of two atoms into each other due to attractive forces, not kinetic energy.
So, in effect, the binding steals from the rest masses of the neutrons & protons, not contributing to the gravity. Please Register or Log in to view the hidden image! Atoms combining to form molcules is different from combining into nucleuses. Even the condesation, as the kinetic energy within the atoms&nucleuses could not be made 0 since absolute 0K is unreachable, is not stable.
Aer, things always bind together because of attractive interactions. The atoms in a condensate still collide, it just so happens that the collision is relatively soft. However, if you insist on an example at high energies then so be it. Quarks are produced in high energy scattering events, but these quarks always recombine to produce hadrons. Not sometimes, not occasionally, they always recombine.
