Meir Achuz

In SR, there are four dimensions x,y,z,t. There is the same symmetry for rotating between x and t as there is between x and y. Space and time cannot be independent units, any more than x and y can.

Anyone of those 3 units could be chosen as the single unit for calculation. As an example, if you choose cm as the fundamental unit, a lifetime may come out as 12 cm. If you want to know it in seconds you divide by the conversion constant 3\times 10^8 cm/sec to get 4\times 10^{-8} sec. It's just like if you get an answer in inches and want cm, you multiply by 2.54.

The idea that SI tries to block progress toward unification is correct, but this implementation is awkward. Elementary paricle physicists have been using "natural units" for over 50 years. The natural system has only one unit, which could be either distance, time, or energy. hbar and c are conversion constants used to change from one unit to another. Saviour's choice of S and T as two independent units violates the space-time symmetry of special relativity. Doing so makes simplicity complicated. If he doesn't unify space and time, how can he hope for unity?

I just noticed Martian's followup. I had just followed his advice before he gave it. NON meant nonsensical. It is impossible to get into the rest frame of a photon. I didn't read past that. Now I see that case A shows it is impossible. The rest makes no sense to me. Sorry

"Originally Posted by Edtharan The situation I am wondering about is a magnetic field perpendicular to the page (as in the first image) with two metal plates next to one another like this | |. the virtual electron/positron pair form between the plates and the magnetic field directs them to intercept each plate (the electron on one and the positron on the other). " A magnetic field could affect virtual particles, but a virtual particle could not hit a plate. The VP (not Cheney) is a mathematical artifice that can only be part of an intermediate state. It can never be a final state particle.

1. FDs are in 4-momentum space. There is no time, so nothing is going back in time. 2. Virtual particles cannot leave the diagram, while real particles do. A photon cannot decay into two real particles, because that process cnnot conseerve 4-momentum. 3. More photons could be prduced by just adding a photon to any lepton leg.

"My question is, is it sensical or non-sensical to use a photon reference frame to observe, using relativity, another photon?" NON

In a good conductor (\sigma>>\epsilon\omega), the magnetic field lags the electric field by 45 degrees. For any conductor, the lag will be something between 0 and 45.

The meter is not an appropriate unit for magnetic field strength. Are you thinking of the H field which has units of amperes/meter? Then (in the SI system) B(in Tesla)=4pi*10^{-7} H(in amp/meter).

Sorry, I meant a virtual image. That ray diagram is not only for a focal point. Its shows how the image of the object is produced.

The diagram at <http://www.optigone.com/m2000.htm> shows a ray diagram for how a real image of an object placed at the bottom appears just above the top hole.

My calculator agrees wilth you, but I would give each answer to 2 sf to agree with the sf of the relative velocity.

1. neutron --> proton + electron + antineutron. This is an example of "beta decay". 2. One inverse process is antineutrino + proton --> neutron + positron 3. Another inverse process, proton --> neutron + positron + neutrino, can only take place in some nuclei (called "proton rich"). This process cannot occur with an isolated proton because it could not conserve energy. 4. Another inverse process, proton + electron --> neutron + neutrino occurs when a proton in a nucleus "captures" an inner atomic electron.

There is no sharp transition, but the radiated power varies like the frequency squared and will be very small at low frequencies. Antenna efficiency also varies like frequency squared, so the observation of radiation goes like f^4.

Probably not. The copper slows down because of resistive energy loss, which doesn't occur for a SC. Also the Meissner effect means that the magnetic field would not enter the SC. Now, do the expt and prove me wrong.

You should use conservation of energy in the center of mass system. This leads to v=\sqrt{u^2+G(m+M)/2x}, which must be integrated to find x(t). This assumes v<<c, so SR needn't be used.

"it isn't a binomial expansion since the exponent is not a natural number." The binomial expansion works for the power -1/2, and for any real or complex number.

For z>>R>>L, the force ~1/z^4. Anytime z>> than anything else, the force is dipole-dipole and ~1/z^4. For L<<<R, and z<R, the force is the same as the electric force between two uniformly charged discs. F will be almost constant when z<<R, and then fall off slowly with z as it becomes comparable with R. The force can be calculated for z~R using a Legendre expansion.

"The force between two pairs of poles falls off proportional to the inverse fourth power of the distance between them. (The like poles repel and the unlike poles attract. The nearer poles exert stronger forces on each other than the more distant ones.) So, at large distances, the force between these two magnets should fall off proportional to the inverse fourth power of distance." If a web page is "proof", that is your proof. THEN: "Measure the force between a magnet and a steel washer on the balance. Notice that the dependence of force on distance is different. In particular the force drops off more quickly for the steel washer than it does for the magnet. The washer becomes magnetized when it is near a magnet. The magnetization of the washer falls off in proportion to the strength of the magnetic field from magnet. The magnetic field of the first magnet falls off as the inverse third power of distance, combined with the inverse fourth power fall off of the force between two magnets the resulting force falls off as the inverse seventh power. (However if the steel washer is not a perfect soft magnet, that is if it retains magnetization when removed from the presence of a magnet then the force will fall off somewhat more slowly than the inverse seventh power.)" That is NOT the force betrween two magnets, but between a magnet and a piece of soft iron. The point implied buy the site is the the induced magnetization of the iron washer depneds on the field of the magnet which falls off like 1/x^3, which is where the other power comes in.

"3) z>>L: F=6(MAL)^2/z^4, like the force between two dipoles. In between these regions, the force is more complicated, but can be treated using a Legendre polyomial expansion." A power series on the symmetry axis shows that the leadilng term at large x is 1/x^4. The Legendre polynomial expansion can extend this to all angles. This is done in many EM texts.

1/x^4

That is an interesting website. I have several comments to make: * They consider magnets with L~R, while I had L>>R. This means that only my case (3), with F~1/x^4 for large x, is appropriate for their magnets. For one case, they get a pull of 7.2# at 10" and 0.6# at 20". This is approaching a 1/x^4 fall off. * Their attraction does not equal their repulsion. This is because there is a demagnetizing effect with oppposing magnets that weakens the effective magnetization. I considered an ideal magnet for which the magnetization never changes. This gives equal push and pull. I don't understand why they still have pull>push at large distances where the demagnetization should not be effective. It may be that they used the same demagnetizing factor at large distances as at small distances. (Their ratio is a constant 5/3.) * At one point, they mention "The strength of a magnetic field drops off roughly exponentially over distance." But the standard formula they give is the same one I used. It gives a 1/x^3 dependence to the field at large x, leading to 1/x^4 for the force. I call 1/x^4 a "power law" dependence.