I am not going to argue with you, since you are setting me up against Einstein, and then making it a cradinal sin to disagree with Einstein on certain points. Einstein was not God: He did make mistakes which he himself admitted. So let me try again:
Correct, but only when the electron is not bound within an atom or a material. It is also valid when the free electron is not moving and then it gives for a SOLITARY electron within its own inertial reference frame that e=m . This is the energy that a free electron has at the vacuum level. Thus, equation cannot give the energy when the electron has an energy that is less than its free energy: i.e. when e<m.
Exactly! But when you include these energies and calculate the energy of the electron to be e=m/ where m/ is smaller than m, then according to this equation the electron cannot have kinetic energy.
No Farsight is not doing this: This is what you people are doing: You are claiming that for an electron energy e less than m, the kinematic term p2 is still valid. We are saying that when the energy of an electron e is less than m, there can be no kinetic energy whatsoever: Just as Einstein has proved. The equation e=sqrt(p2+m2) does then not apply.
You are again projecting yourself, Sol and Ziggurat. It is really you who ignore experimental results that we all agree are correct. The fact remains that for a hydrogen atom with rest mass MH, formed from a proton with rest mass mP and an electron with rest mass me one has that:
No, that's not what I'm thinking of. Invariant mass varies. Surely you know this? Rest mass is a measure of a system's energy content when you're motionless with respect to it. A cannonball in free space has a greater rest mass than the same cannonball on the surface of the earth. That's because it has gravitational potential energy equivalent to the kinetic energy of a cannonball falling at 11 km/s. I'm not kidding about this. Think it through and do some research, see for example http://en.wikipedia.org/wiki/Mass_in_general_relativity and http://www.ncbi.nlm.nih.gov/pmc/articles/PMC336961/
I disike this approach because it suggests that the particle is something separate from its field. We made the electron in pair production, from an electromagnetic wave, an electromagnetic field variation. Now we've got a standing wave, a standing electromagnetic field. Call it something else if you like, but remember the wave nature of matter, we don't have some point-particle which is distinct from its electromagnetic field.
It isn't equal amounts because the electron plays the part of the cannonball while the electron plays the part of the Earth. The electron accelerates towards the proton nearly two-thousand times as much as the proton accelerates towards the electron. Discount the latter and it's the electron potential energy that's converted into kinetic energy then radiated away. Setting the dipole aside too, don't think that all the electromagnetic field energy has simply vanished just because there's no net electromagnetic force on a positron.
Do check it out though, it is important.
The amount of energy in a system that is at rest with respect to me. Divided by the speed of light squared of course.
I call it rest mass, but don't think that it's absolutely invariant. The mass of the cannonball in free space is greater than its mass on the surface of the Earth. It really is. You gave it kinetic energy when you fired it upwards at 11km/s, and this was converted into gravitational potential energy. In the cannonball. Conservation of energy applies.
To explain it to you. And Johan was talking about a light wave in box, which rather suggests that EVERYTHING here is moving fast.
I've already said that all energy is in the end dynamical. You know why a cannonball potential energy is converted into kinetic energy? Because the coordinate speed of light varies in a non-inertial reference frame. Kinetic energy at the subatomic level is transformed into macroscopic kinetic energy. The cannonball hits the ground, that kinetic energy is radiated away, and the mass of the cannonball is now less than it was.
I said It really isn't more energy Zig, it's less energy. That radiated photon proves it. It's that simple. Sol was banging on about the electron having positive kinetic energy despite and ignoring the mass defect.
I can't calculate it offhand. I could look it up and give you a calculation, sol will tell you that I'm no dummy, but I won't because it still wouldn't be enough. No calculation can get it across to you that kinetic inside the system is exhibited as the mass of the system, and the electron is such a system. You'll continue to think of the system itself moving and exhibiting kinetic energy whilst retaining an invariant mass.
Yes you have. This is the whole point Johan was making. The photon in the box doesn't have any mass. It has kinetic energy instead. The box doesn't have kinetic energy, it has mass instead.
You can't have your cake and eat it because it's double counting.
E=mc² is not some superficial relevance of relativity, Zig. Go and look at Einstein's 1905 E=mc² paper Does the inertia of a body depend upon its energy content which refers to a radiating body losing mass. The body loses kinetic energy. It loses mass. It doesn't gain kinetic energy and keep the same mass.
You construct two spin ½ particles out of a spin-1 particle in pair production. You split the incident photon over a nucleon to get an electron and a positron.
It isn't a problem. It's just chiral frame dragging, the electron is a bit like a roton in a BEC, and conservation of charge applies in pair production.
It ought to be good enough to get you interested. The electron isn't the same as a photon, but you can split a photon into two other photons with twice the wavelength. And you can annihilate the electron and the positron, which you made in pair production, to yield two photons. So think again about a photon in a box. Don't dismiss it along with 4π/nc^1½ and the depiction below just becuse it doesn't tie in with what you've been taught. Think of the proton as something much smaller, right in the in the middle. Remember there's no surfaces, so add more contours to fatten the torus to a near-spherical symmetry. Enjoy the pleasure of finding things out.
OK let us become more specific: As far as I could ascertain in text books the consistent picture is that equivalent means that when two competent (not an observer who will squash an anode into the surface of a diamond), equivalent observers do the same experiment without making any mistakes, they must get the same result: Do you agree with this?
In terms of my present knowledge I agree absolutely!
It has been very rare that Ziggurat posted anything on this thread that is relevant and correct. This is, however, one of those rare surprising occasions. He is correct: I claim that when there is a light wave within a totally enclosed resonant cavity, it must be a standing light wave that, like any and all standing waves, does not have any kinetic energy. Thus the light energy is now completely stationary energy: And stationary energy is rest mass energy.
Probably not, unless you're using some strange definition of "do the same experiment" and/or "get the same result".
As usual you are displaying your enormous ignorance when it comes to physics. If both observers do the SAME experiment within their respective inertial reference frames they must get the same result. This is what Einstein's first postulate means.
Sheesh Ziggurat, a massless photon doesn't have mass, it has kinetic energy. But confine it in a box and that system now has mass rather than kinetic energy. It's so simple and so rooted in the relativity of a radiating body loses mass that I cannot believe you don't understand this. And I'm frankly appalled that nobody has conceded that Sol's moving box is something different to a light wave in a box, which is what Johan referred to. The standing wave doesn't have kinetic energy because it's standing. It exhibits inertia instead of momentum. It isn't moving, but it still resists your attempts to change its state of motion, just as it did when it was moving through space at c.Ziggurat said:
I am glad to see we are in total agreement about standing light waves when light is confined. You cannot imagine what I went through on this thread for more than a year.