DQW

It doesn't take more than a small post-it note if you have a slide-rule or a century-old calculator... [math]26^7 \approx 8*10^9 ~ \implies 26^{78} \approx 26*8^{11}*10^{99} [/math] that took a calculator, but it could be avoided too (with bigger paper) [math]8^3 \approx 500 \implies 8^{11} \approx \frac{5^4*10^8}{8} \approx 8*10^9 [/math] [math]\implies 26^78 \approx 8*26*10^{108} \approx 2.1*10^{110} [/math] According to the Google calculator :

The Neel Temperature for Mn metal is 95K; it orders antiferromagnetically (AFM) only at low temperatures. Above this, it is a regular Curie paramagnet. A quick search gave me this hit : http://chemistry.anl.gov/ClusterStudies/images/Mnn-atom.pdf http://chemistry.anl.gov/ClusterStudies/SpectroscopicAndStatic.html If that's not sufficient I can find you a better reference later. Bulk Mn is AFM for a completely different reason than that which makes MnO, MnF2 and other such compounds AFM. The bulk metal is AFM because of the lattice parameter in the crystal being suitable for ensuring a non-negligible overlap between the valence electrons of nearest neighbor atoms in addition to exchange mediated by conduction electrons. This (first part) is explained thorugh the Direct Exchange mechanism, originally porposed by Heitler and London, (for simple diatomic molecules) and subsequently improved upon by Freeman, Watson (Phys Rev 124, 1439-1451 , 1961) and later (the second part was included and the ordering was) extended to metals by Stoner and others. Mn2+ based compounds are AFM because of Superexchange : hopping of the spin paired 2p electrons of the liganding anion (O2-, F-, etc) reduces energy due to delocalization; since the 2p electrons in a subshell are antiparallel, hopping is permitted (by an extension of Hund's First Rule) only if the neighboring Mn2+ ions are also spin-antiparallel - hence the ground state is AFM (note : that's a naive explanation, but it catches the essense of the mechanism very nicely). The reason manganese is called that, (the Latin origin is from magnes which essentially means 'magnetic') is because it was first extracted from the ore pyrolusite which is ferromagnetic. And yes, manganese can be made ferromagnetic too, by making it nanocrystalline, or in the form of thin films (and possibly in other ways too - I really don't know anything about that).

As do I !

The validity of performing a thought experiment lies in the fact that the scientific principles underlying the thought experiment are well established and supported by real experimental evidence. There is no new science in a thought ("gedanken") experiment, and hence no need for additional experimental support.

In general, no. HOwever, it does affect the rate at which temperature chenges. The time consdtant for thermal changes goes like C/K, where c is the heat capacity and K is the thermal conductivity (make sure the units of the ratio are those of time). The reason is obvious : it takes more heat to produce the same change in temperature, the greater is C (and hence it takes more time at a given heat transfer rate). The heat transfer rate itself depends only on temperatures, geometries and thermal constants whose units possess a factor of time in them : such as the thermal conductivity, the emissivity, the convective heat transfer coefficient, etc. It is unclear what you are talking about here. If the beaker is well insulated, one assumes that there is no heat loss out of the beaker, and energy conservation then tells us that the heat lost by the hotter liquid is gained by the colder liquid. So, as such there's onlt heat transfer between the two liquids in the beaker. To monitor the rate of heat transfer, one must combine the liquids without mixing and measure the time for thermal homogenization - for the temperature to become uniform within the liquid. As explained above, this will happen faster in the case where the heat capacity of the liquid is lower (pouring in hot alcohol). But this does not mean the the heat transfer is quicker too. In fact, since the time constant for temperature change scales like the the heat capacity, C, and so does the heat transferred, the time constant for heat transfer is actually independent of C. If that last bit wasn't clear, think of the rate of change, which is inversely proportional to the time constant. [math]\frac {d \theta}{dt} ~~\alpha~~1/C [/math] [math]\Delta H ~~\alpha ~~C \Delta \theta~~\implies~~\frac {dH}{dt}~~\alpha~~C \frac {d \theta}{dt} ~~\alpha~~C/C =1 [/math]

I apologise for my first post - it was uncalled for. I take back what I said.

CERN's Particle Adventure is a great page. And Hyperphysics does a nice job too, if you want to get straight to the point. There's also a very nice summary of the standard model here.

The path of an electron-positron pair in field-free vacuum is nothing like a spiral. You are likely picturing the spiral paths in a collider which result from the applied B-field and extending this picture to field-free space. Where have you made this "point". Your previous passage made no mention of a photon being similar to an electron. It merely spoke of spontaneous pair production and subsequent annihilation. If the idea is that an electron-positron pair becomes a pair of photons, then that is tantamount to saying that HCl is the same as water since HCl + NaOH becomes NaCl + water. Wait...any particle-antiparticle pair will annihilate to make photons, so how about "hydrogen atom = photon" ? Clearly, you seem to be talking about the Higgs field acting as the order parameter breaking the electroweak gauge symmetry during the early stages of evolution. It is possibly true (at least according to the current version of the standard model) that mass arises out of the interaction of a lepton or quark with the Higgs boson (which is yet to be detected). But could you please show me how a spinless boson mediates your proposed equality between a fermion (the electron) and a boson (the photon) ? And what does symmetry breaking have to do with particle-antiparticle annihilations ? And in fact, the electron is the same as a photon just as a cow is the same as a pencil - after all, they both are formed from the same stuff that emerged out of the big bang. But how is this relevant to the OP's ideas ? And I can name (and describe in terms of an order parameter) a phase transition that will convert water to ice and vice-versa. Can you please do the same for the electron and photon ?

Thanks for the advice ! If you know so much about "symmetry breaking" why did you not state that the freezing transition in water is itself a spontaneous breaking of a continuous symmetry. Surely this would have bolstered your case. Yet you did not state it...and you instead resort to "metaphorical examples" to resolve a physical question.

This is true. The superconductor goes "normal" in the presence of a field exceeding the critical field, Hc. In a Type II superconductor, there is an intermediate phase - the Abrikosov phase - bounded by two critical field curves : Hc1(T) and Hc2(T), where fields penetrate the bulk through lines known as flux vortices.

It is the other way around.

Paramagnetism and diamagnetism are extremely well understood, thanks to work done by people like Langevin, Curie, van Vleck, Pauli, Anderson and others.

If you don't stick to pure elements (why should you ?) the best permanent magnets are made of rare earth-transition metal intermetallic compounds. Look up NdFeB (popular name for Nd2Fe14B) and SmCo5. Some transition metal alloys are fairly good too : look up AlNiCo.

No it's not. Mn is antiferromagnetic.

Fe, Co, Ni, Gd are the only elements that are ferromagnetic at RT (Gd, on a cool day) Because they are different. Ferromagnetism comes from an exchange interaction between the electrons in the material. If the magnitude of the exchange interaction is large and positive, you have ferromagnetism. If it's large and negative, you have antiferromagnetism. If it's very small, you have neither.

The susceptibility of Bi is about -10^-4. It won't do jack. You know you can have a diamagnetic susceptibility as large as -1 - with a superconductor. But even with that, you are not creating a monopole effect. You will merely be changing the geometry of the field lines, for instance, forcing them to turn more tightly inside the body of the magnet itself.

That's only the force on a moving charge, not the force on a magnetic moment !

If you want to picture something, this is the best you can do : Imagine 4 cloudy lobes (shaped like very eccentric ovoids) sticking out of the central Oxygen atom and pointing towards the corners of a regular tetrahedron (centered on the Oxygen nucleus). Now pick 2 of these 4 lobes and stick a proton on the end of each one. Now pull these two lobes just a little closer to each other (reduce the angle between them from about 109 deg to about 104.5 deg). That's what your water molecule will look like. Each of these lobes corresponds to a pair of electrons, both sharing the same z-component of orbital angular momentum.

Supersolidity in He-4 is actually quite an exciting new discovery. See Moses Chan's paper from last year. Solid He is nothing new though. It is well known that He will freeze at high pressures. That He-4 will continue to be a BEC in the "solid" phase is what's interesting !

Besides the obvious technical difficulties, there's one theoretical problem that hasn't been mentioned yet : there's only one place on Earth where the local magnetic field points upwards - at the magnetic north pole.

The superconductor you bought is likely Yttrium Barium Copper Oxide , YBa(2)Cu(3)O(7), popularly known as YBCO. These are cheap and have a Tc of about 90K. If you cool a YBCO disk down with LN2 (77K), it should be able to stably levitate a suitable permanent magnet. Commonly used magnets are made from Nd(2)Fe(14)B (popularly called NdFeB magnets), and a little piece of one of these will levitate stably (not slip off) as long as the size of the magnet is smaller than that of the SC disc. If you want to levitate the SC over the magnet (and this is a little harder because you want the SC to be continuously immersed in LN2), make sure the SC is smaller than the magnet.

Time is not an observable in QM (like position is); it is merely a parameter. And it is not quantized either.

That's nonsense !