Science questions not worth a thread I: I'm a moron!

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So does mercury.
 
If the wettablity is high (i.e. theta is <90°) and the diameter is small you will get capillary action.
The wettability causes the liquid to have a contact angle theta because of the cohesion / adhesion forces of the interface. Now gravity will try to pull down the liquid in the tube opposing the surface tension (which is again caused by the liquid/air interface (and the resulting forces)). So it's a matter of intermolecular forces (Liquid-liquid, liquid-air, liquid-tube) working against gravity.

For H2O the wettability on glass is high so the meniscus is downward, for Hg the wettablity is low so the meniscus is upward, of course if you change the material of the tube the wettability (intermolecular forces of liquid-tube) might change.
 
ok big question . i've read a book about the history of physics since 1895 to 1970. Something i dont understand. Each important findings ends out with a great big formula . The long formula Schrodinger or Heisenberg comes out with give what ? the position of an atom, electron ? Is there anywhere where i could see the maths behind a formula, the development and final results ? cause after Newton's formula i dont understand nothing.
 
If the Earth had a set of rings (like the ones I posted in the demotivator thread in H&J) that was somehow permanent (or at least 'till the sun died), how would have life evolved differently?
 
ok big question . i've read a book about the history of physics since 1895 to 1970. Something i dont understand. Each important findings ends out with a great big formula . The long formula Schrodinger or Heisenberg comes out with give what ? the position of an atom, electron ? Is there anywhere where i could see the maths behind a formula, the development and final results ? cause after Newton's formula i dont understand nothing.

I find Wikipedia to be pretty robust on the topic. It's probably worth reading through a timeline. In school, it was explained to me that essentially there are three "ages".

1. Classical physics, which works until electromagnetic radiation is studied by
Planck and Einstein's early work are important here (e.g. photo-electric effect, Planck's law, Planck's constant). Try reading about "black body radiation" and "ultraviolet catastrophe".

2. Early quantum theory tries to explain the dual nature (wave and particle) of electromagnetic radiation that Einstein/Planck uncovers. That cumulates with Schrodinger and Heisenberg. Schrodinger's wave function does predict where an electron should "probably" be. Heisenberg basically points out that the amount of error in the equation means you can't have complete knowledge of an electron---you either know where it is or how it is moving directionly.

3. Modern quantum theory is then the fall out of Heinsenberg and Schrodinger's conflicts and the interpretations of it.

Overall, I find it's important to understand the history as a set of problems and partial solution, rather than convenient math.
 
ok big question . i've read a book about the history of physics since 1895 to 1970. Something i dont understand. Each important findings ends out with a great big formula . The long formula Schrodinger or Heisenberg comes out with give what ? the position of an atom, electron ? Is there anywhere where i could see the maths behind a formula, the development and final results ? cause after Newton's formula i dont understand nothing.

The Schrödinger equation describes the motion of particles. It has the same function as Newton's equations, but is more correct. For a large amount of matter it gives the same result as Newton's equations, but it also correctly describes the motion of very small particles like atoms or electrons. It has its shortcomings, as it doesn't include relativity, so there are other equations that are even more general.

If you really want to learn about the maths behind these formulas you should go for a physics text book that deals with this stuff.

I find Wikipedia to be pretty robust on the topic. It's probably worth reading through a timeline. In school, it was explained to me that essentially there are three "ages".

Not really. A lot of stuff that goes beyond classical mechanics was developed very quickly so it doesn't make sense to really speak of ages. It's more like there are different pictures or levels and you have to decide which is suitable for your problem:

1. Classical physics - anything that doesn't involve quantum physics or relativity
2. Special Relativity - for large objects with large speed
3. Semi-classical theory - treat the motion of particles with quantum mechanics but treat fields as classic fields
4. Full quantum theory - also quantize the fields
5. Quantum field theory - combine the full quantum theory with special relativity

The next step would be to combine all this with General Relativty, to get a full theory of everything, but there still is no theory to do this.

You cannot really say that these theories came one after another, but different fields had different needs and thus developed the theory that was best for their problems. For example solid state physics still mostly uses semi-classical theories, because if you have so many atoms it's already hard enough to do the semi-classical treatment.

1. Classical physics, which works until electromagnetic radiation is studied by
Planck and Einstein's early work are important here (e.g. photo-electric effect, Planck's law, Planck's constant). Try reading about "black body radiation" and "ultraviolet catastrophe".

And it also breaks down at high speeds, thus the need for Special Relativity.

2. Early quantum theory tries to explain the dual nature (wave and particle) of electromagnetic radiation that Einstein/Planck uncovers. That cumulates with Schrodinger and Heisenberg. Schrodinger's wave function does predict where an electron should "probably" be. Heisenberg basically points out that the amount of error in the equation means you can't have complete knowledge of an electron---you either know where it is or how it is moving directionly.

Actually, although it started with that, early quantum theory didn't really do much about electromagnetic radiation. It became more concerned with the wave properties of atoms and electrons. The real quantization of electromagnetic fields came later.

3. Modern quantum theory is then the fall out of Heinsenberg and Schrodinger's conflicts and the interpretations of it.

Huh? It was quickly shown that Heisenberg's and Schrödinger's theories were equivalent, so there wasn't really any conflict there. Modern quantum theory is the attempt to describe everything with quantum field theories.

Overall, I find it's important to understand the history as a set of problems and partial solution, rather than convenient math.

I agree. The math often came as a way to solve a certain problem and later people tried to interpret the math.
 
Thanks for the corrections, and sorry if I butchered your field. :) My learning of it only came as a drive-by intro to it while in an analytical biochem course. /lame excuse
 
i all know that guys. What i dont know is who the hell uses those formulas ? I mean in a system so small there is 'lets say a glass of water there are literally billions of atoms. nobody will use that formula to know where are every atom! and if one uses it, what for ? and what does it looks like ? all i see is a formula with letters. I dare anyone to fill it with real numbers!

but i'm a bit lost since people are saying schrodingers equations can describe planets...

what are the lowest number of equation (and which ones) possible to describe all physic phenomena

I thought there were only Einstein General Relativity, and any of the three possible quantum ones. (Matrix, Schrodinger and the other unusable one...)
 
The formulas are often used for simulations. E.G. for medical researches the coupling of enzymes to proteins is described by the wave functions of the single atoms. Also in material sciences the wave functions (and a lot of other formulas) are used for ab-initio simulations.
 
i all know that guys. What i dont know is who the hell uses those formulas ? I mean in a system so small there is 'lets say a glass of water there are literally billions of atoms. nobody will use that formula to know where are every atom! and if one uses it, what for ? and what does it looks like ? all i see is a formula with letters. I dare anyone to fill it with real numbers!

Well, for example I am using it: In my lab I can trap a single atom with a light beam, and the motion of that atom can be described by the Schrödinger equation. The Schrödinger equation is a bit too simple, though, so if I want to add interactions with the light in my model I need other equations.

For larger systems there are mainly two approaches. One was mentioned by GoodGame: If the particles are mostly independent on each other you can use statistical mechanics to describe the large system.

The other approach is used in solid state physics. There you use the symmetry of the crystals to get all the possible solutions for particles in that crystal.

In these cases you usually derive your model once from the basic quantum mechanical equations and then use that model. But if you do research on basic quantum mechanical systems, which took some time until it was possible, but is now possible, you really have to use the basic equations and put real numbers into them.

but i'm a bit lost since people are saying schrodingers equations can describe planets...

It can, but no one does it, because it would be way to complicated. What you can do is take the Schrödinger equation and simplify them by neglecting terms that are too small to make any difference. If you do that for planets you arrive at Newton's laws and those are easy to use on planetary motion.

what are the lowest number of equation (and which ones) possible to describe all physic phenomena

I thought there were only Einstein General Relativity, and any of the three possible quantum ones. (Matrix, Schrodinger and the other unusable one...)

I would say, two: The Standard Model Lagrangian and the Einstein field equations. But "possible" only means theoretically possible in this case, as there is no way to describe everything with those in practice. For practical problems you need to use simplified equations, like the Schrödinger equation.
 
That Lagrangian formula is huge. I guess its just a huge formula taking every formula of every fields.

Another question: is there a very specific size of matter where we have to switch from General relativity to Quantum ?

same idea with boltzmann statistic vs. Schrodinger. when do you switch

since Schrodinger equations can describe big objects, why can't we say physics are united under one field ? I tought the only missing part to unified theory was to unite Newtonian laws with quantum laws

thanks uppi for that great answer
 
That Lagrangian formula is huge. I guess its just a huge formula taking every formula of every fields.

Actually it's "just" the whole Standard Model of particle physics thrown together into one formula. The formulas other fields need should be derivable from these (again, at least in theory), because if you know how every particle and field behaves, you should be theoretically be able to calculate everything else.

It is quite ugly and that's why there a theoretical physicists who try to find a simpler equation that contains all that. So far they haven't been really successful, though.

Another question: is there a very specific size of matter where we have to switch from General relativity to Quantum ?

No, they're at the opposite ends of the scales. For very large objects you have to use GR, for very small objects you need QM. There is a very large intermediate regime, were both approaches simplify to Newton's laws of motion, so either one would work. However if you are in this intermediate regime, you should just use Newton's laws anyway. Why suffer all the trouble that GR and QM are, if the solution can be found easier?

same idea with boltzmann statistic vs. Schrodinger. when do you switch

You have to abandon the Schrödinger equation as soon as you're not able to calculate it anymore. Because this scales exponentially, this can happen very soon as you increase the number of particles. Depending on how much the particles interact, 10 particles can already be tricky. (If they don't interact much the number can be much higher though). But this is mainly limited by how big a supercomputer you can build.

If you can't calculate the Schrödinger equation any more, you need to find a good model, that neglects the parts that aren't important and describes everything you need. Statistical mechanics is one of those and you apply it, once the preconditions are met (particles behave all alike, there's enough of them to do statistics...)

Another way is to let a quantum computer do the calculation of the Schrödinger equation. Basically you use one controllable quantum system to simulate another (uncontrollable) quantum system. This could speed up the calculation, because the first system already follows QM and doesn't need any classical calculations. Here the limit is also around 10 particles at the moment, because it is hard to control a large quantum system if you don't know what it should be doing, because you can't calculate it.

since Schrodinger equations can describe big objects, why can't we say physics are united under one field ? I tought the only missing part to unified theory was to unite Newtonian laws with quantum laws

The problem is not so much replicating Newton's laws with QM, but rather explaining the extra effects of GR with QM. If you want a theory of everything you need to explain all the effects of QM and all the effects of GR. So far nobody has been able to come up with a theory that does that.

And then there is the problem that at extreme conditions (which we won't be able to generate for a long time), GR and QM actually contradict each other. So at least one of them must be wrong, possibly both. To resolve this issue is one of the holy grails of physics. But I wouldn't bet that the solution appears anytime soon.
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The problem is not so much replicating Newton's laws with QM, but rather explaining the extra effects of GR with QM. If you want a theory of everything you need to explain all the effects of QM and all the effects of GR. So far nobody has been able to come up with a theory that does that.

And then there is the problem that at extreme conditions (which we won't be able to generate for a long time), GR and QM actually contradict each other.
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what are extra effects ? what is left to find and is there a list somewhere? I find physics are a bit far from our reality given the power they are running particles accelerators. will it explain anything of our reality to find a new particle at an energy which was only available 3 minutes after the big bang and has never been seen since?
 
what are extra effects ? what is left to find and is there a list somewhere?

All the effects that can only be explained by General Relativity so far. For example, the bending of light by gravity, black holes and the weirdness surrounding them, time diletation by gravity, the orbit of Mercury around the sun.

And then there are even effects that have been predicted by GR but haven't been observed yet.

There probably is a comprehensive list out there, but at the moment I don't have one.

I find physics are a bit far from our reality given the power they are running particles accelerators. will it explain anything of our reality to find a new particle at an energy which was only available 3 minutes after the big bang and has never been seen since?

It depends on the field how far physics is removed from our reality. For example research on semiconductors can have very practical applications: Better computers, more efficient solar panels and so on.

Particle physics is indeed much further away from our experienced reality and practical applications of it a rare (but do exist). But it is necessary to understand our reality at a fundamental level. And even the particles they find at these high energies can be relevant to that: For example the Higgs boson, they're searching for at the Tevatron and LHC is (well, if it exists, which I am not entirely sold on) responsible for giving particles mass. And it's easy to imagine, that if particles had no mass, the world would be quite different.
 
Are there any exceedingly large list of primes freely available? I'm looking for a comprehensive list of primes or even psuedo-primes would be great from 2 to at least 10^15 preferably even higher. I'm hoping to find a pre-computed list so I don't have to waste compute time creating my own, and the Maple libraries of primes don't go nearly far enough.
 
I don't think so, it would compromise internet security.
 
Hmm maybe.

Try mathworld then.
 
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