Posts by Mike Hewson
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Watch This Space
Posted 11 days ago by Mike Hewson
Cool. There will be a lunar eclipse ( late afternoon DownUnda ) in two days. And on the 29th of this month an annular solar eclipse of which that we will also get a taste. As I'm roughly 100 miles off the centreline, I might get a few minutes of something. Again, weather permitting, I'll see what I can snap.
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Science book reviews & recommendations
Posted 13 days ago by Mike Hewson
Right, we have LIGO Magazine Issue 4 looking at the installation program for AdLIGO. I'd call it 'where the rubber meets the road' issue. Firstly :
... to prepare for the first observing run in 2015 with the Advanced LIGO detectors ....
... The first science data is expected to be from a 3 month run of the LIGO detectors in 2015 ...
which I find quite exciting! New data. My Precious. I think the articles might imply ( my wild guess only ) something for E@H in early 2016 ???? :-) :-)
Yes, that is another two years. But on the upside we will be more practised with our pipeline here by then. And I have more time to try to understand GR and tensors and stuff. :-)
There are high quality photos of the components from Livingston. Very optopunk equipment. They are going for modular arrangements called 'cartridges', I assume to ease the evolution of hardware upgrades down the track. There are certainly high order problems being addressed like differential heating of suspension wires due to stray light. Very detailed attention to particulate contamination.
The article on coatings demonstrates the importance of energy transfers at the very thin optical interface. Very high tech materials science, and very high chequebook too I'd say. DownUnda CSIRO got that contract ! :-)
Another article looks at the medium to longer term observational plans, plus linkages to EM astronomy. Plus how do you make a room clean - with the help of Mom and her sewing machine of course!
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Posted 14 days ago by Mike Hewson
What Matters About Antimatter
The first thing that you wil notice about antimatter is that there isn't any. Well not that you could see everyday or even every solar eclipse. Rare stuff and only fleeting if so. You either get lucky with some cosmic ray experiment or down at the local particle accelerator, and then on a good day.
Interestingly antimatter was predicted before it was found. How would you like to be the theorist who bagged that ? You fiddle with the equations, find a new solution, effectively predict an entire new class of objects and publish. Fortunately you are believed so the relevant observations are soon performed and bang, right on the money, there it is. Carl Anderson found the anti-electron, later dubbed the positron*, in 1932 just two years after the prediction.
Quite unlike this Higgs business where you have to wait until the other end of your own lifetime to disclose a result, after an enormous investment in time and money and other people's careers. Even then you don't see the particle, because it lives too short a time. What is detected are pieces of the Higgs Grenade that leaves shrapnel all over your shiny apparatus, so that by effectively reverse engineering one deduces what blew up. But while you might yearn for a Nobel in particle physics, what you really ought do is sell electricity to the LHC. In a gold rush : sell spades .... :-) :-)
We can thank Paul Adriene Maurice Dirac for the idea. He was quite obsessed with playing with equations, by his own admission this was how he discovered new laws. So there's a good pointer for the budding theoreticians out there. He is one of the giants of quantum mechanics, in the heady days when nearly everyone from Einstein on down was in the ruckus to sort out this new viewpoint upon the Universe. I have read some of his original papers ( I don't really follow them well though ), and I think when a certain square root is taken then you can have - as you know square roots do - two solutions. The positive one is the world we live in or specifically the electrons from Dirac's context of the day. The negative one is the elusive antimatter.
Some key points about antimatter :
- it's not a magical substance. Not even evil. Despite Star Trek the only place you'll go with antimatter at present is into oblivion. Sorry Trekkies ( yes, I have read Krause's The Physics of Star Trek ).
- it's successful existence prediction was due to following both Quantum Mechanics and Special Relativity to logical conclusion. It's a child of the union if you like and thus validated both when verified by experiment.
- it has the same rest mass ( a positive quantity** ) than the corresponding matter particle.
- it has the opposite electric charge when compared with it's matter counterpart. This includes the case of neutral particles ( as minus zero = zero ) eg. an antineutron is distinct from a neutron.
- it is deemed to have the same spin but opposite magnetic moment ( ie. while considering all the caveats in our spin discussions ).
- and yes they annihilate when they meet. This is the most famous property and also explains why antimatter is hard to keep around for long in a non anti-matter world. Carefully note that an anti-electron and an anti-proton won't annihilate. You'd might get an anti-hydrogen atom, say, if their mutual energy is such as to produce a bound state. Just like normal hydrogen***. So it's a particle that annihilates with it's given anti-particle that gives a burst of gamma radiation ( for example ) when they meet.
- neutral Bose particles eg. photons don't have antiparticles.
Or if you like, how would you know ? A photon isn't charged, nor possesses a magnetic moment. It does have spin, but we don't change that to flip over to antimatter. If a photon met an anti-photon ( which would hence be a particle with identical properties to the photon ) and they annihilated, you'd get errr .... two photons? :-):-)
Neutrinos are potentially squirrely here. Once neutrinos were hypothecated**** then their labeling was subject to 'making up the differences'. So if I wait for a neutron to decay into a proton plus an electron then the neutrino that I attribute the excess/uncounted energy is going to be labelled an electron anti-neutrino. That way I begin with a single matter particle ( the neutron ) and wind up with the same nett number of matter particles ( one proton plus one electron plus one antineutrino ).
More recently it has been established that the various neutrinos have a difference in rest masses. That especially means they can't all have zero rest mass. Ettore Majorana constructed the bit of theory that ought apply if a Fermion was it's own antiparticle. Does a neutrino have even a tiny magnetic moment? The basic experimental challenge here is that neutrino presence in any given instance is only ever deduced. You don't see a particle track or the like. What you do get is an inverse square reduction in neutrino attributable events with distance from a nuclear reactor, say. Or a directional dependence - even through the substance of the Earth - of what is deemed as neutrino captures ie. they come from the Sun. Across all suitable scenarios that deduction is consistent so far, thus I do believe in their reality. But to be pure the arguments are statistical and thus ultimately require enough interactions to get significance. More so the trouble if you seek a low-rate event.
After the positron we had to wait over a decade for others. In the 1950's that area of study boomed with ever increasing energy to pour into interactions. Back then you'd get new classes of behaviours like : throw two protons together and what came out was three protons plus a whole bunch of other stuff ( the particle 'zoo' ). One gag was that the discoverer of a new particle should not be awarded a Nobel Prize but a large fine.
Later came quarks, vector bosons and the like. But by then antimatter was always to be considered and a factor in symmetries to be obeyed. Or maybe not, as we will see. Next up :
Richard Feynman and The Switchback Road
* Language purists will then note that an electron should thus be called a 'negatron'. The correct reply to that is naturally : go and find your own particle, and then we'll talk names .... :-)
** But .... for that to make sense you have to agree that the momentum and the energy are negated relative to the sign of the mass ( plus you have to insist on probability densities being strictly positive ). Hmmm. Arrgh. Foofle. But if you then reverse the direction of time .... :-)
*** As far as we have discovered eg. the energy levels, ionization and all that. The positron/anti-proton system transitions using photons, which is what is measured.
**** Essentially to round out the accounting rules of particle physics. To conserve the conservation laws ! :-)
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Problems and Bug Reports :
Goodbye XP & What's best to do now?
Posted 15 days ago by Mike Hewson
You don't have to do anything necessarily. M$ have simply ceased to fix/fiddle with XP from now on. Your operating system still exists. Certainly if you were thinking of getting another computer, on other grounds, then the field is open. As with most things IT the choices depend upon what you might want to get up to.
By your remarks, what you may more urgently need is some effective security & browsing software.
[anecdotal] Personally I like Trend Micro for viruses etc, but opinions will differ, and like similiar software it has specific browsing protection. Around $50 AUD for a single computer for a year. Try here for a free examination of your system to see how screwed up it might be. [/anecdotal]
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Posted 16 days ago by Mike Hewson
Spin Addendum ( not essential )
You might wonder why Fermions are allocated 1/2 as their spin value. In what we have covered eg. Stern-Gerlach type measurements we are evaluating a magnetic moment. SG is magnetic device and so we sort the silver atoms as per it's magnetic properties, little magnets etc.
Now you may be familiar with an 'ordinary' moment - not as an instant of time, but a lever arm. So if I have a force acting at a distance from some deemed, or actual, pivot of rotation then I have a moment of force. For the purpose of creating a rotation about said axis then what matters is the component of a force at right angles to the line from the pivot. This has a sense in that if you reverse that component's direction the induced rotation ( if any ) will go the other way. This is also called torque and what a jolly good thing it is eg. when you select reverse gear on your car you are reversing the torque at the drive wheels. Some important points :
- a given torque is defined with respect to a given pivot. Change the pivot and the torque is different.
- a given torque is defined with respect to the point of application of the force eg. if you apply the force at the pivot point you won't get a rotation at all about that pivot.
- any force component along the line to/from the pivot will also not produce a torque, whatever else it's effects may be.
- of course the bigger the force, or the further away it is from the pivot, the larger the moment or leverage.
- deemed/actual. You are not always dealing with a rigid body of a mechanical type. The van Allen radiation belts surrounding the Earth are composed of ions from the Sun which have been corralled by the Earth's magnetic field to spiral around the magnetic field lines from pole to pole.
A magnetic moment is that which determines how much torque a magnet will feel in a magnetic field. You may notice that when you play with two ( macroscopic ) magnets there is a tendency for one or both to flip around in order to have them attract each other. We describe/define opposite magnetic poles as attracting, but we have an extra rotation here because of the nett effect including like poles repelling. Remember that you can't split a magnet to get the poles by themselves. Electric charges can be held apart singly eg. if you look at the pattern of electric field lines over the surface enclosing some volume you can deduce what charge & sign thereof lies within.
If you like the magnetic moment of a body is the ratio of the induced torque to the magnetic field producing said torque. This is typically modeled or quoted as linear in that for a given body doubling the field doubles the torque ie. the magnetic moment is a constant of proportionality.
For an electron the magnetic moment certainly seems to be a constant. Notwithstanding that one day we may be able to get up really really really close to an electron and discover it is not a point particle after all. Otherwise/until we are being a tad cheeky in supposing that it has some axis of spin, that there is some mass not sitting on the axis, so the electron has an internal angular momentum about such an axis, and because it has some not-on-axis charge then it has magnetic behaviour. So that's the mental model but it is really a macroscopic-to-microscopic analogy, and taken with a grain of salt it is useful ultimately because predictions agree with experiment. And spectacularly so in quantum mechanics.
So the electron's angular momentum has, via the magnetic aspect, a measurable component being 1/2 of h-cross. h-cross is Planck's constant ( typically annotated as h ) divided by 2*PI. h-cross may also be called the 'reduced' Planck's constant, where the upper stem of the 'h' is crossed horizontally when you write it.
[ Confusingly : authors sometimes call 'spin' the component you measure ( either magnetic moment or angular momentum ), and sometimes the full spin vector ( that you can't measure ). Or for that matter the quantum number ( dimensionless ) usually written as s, that is inserted into the relevant equations. ]
So an electron has h-cross/2 worth of angular momentum. Quite tiny in the everyday sense. Quantum mechanics says all objects will have their angular momentum some multiple of h-cross/2 ie. the measurable component as discussed. Even a Ferris wheel will have, like most macroscopic objects, such a property being some massive integer multiple of that. Like energy, our instruments are typically too crude to distinguish b/w [GAZZILLION * h_cross/2] and [(GAZZILLION + 1) * h_cross/2].
[ But beware with compound objects as we have to distinguish the intrinsic angular momentum of constituents from their orbital angular momentum, that being due to the whole particle whizzing around an atomic nucleus say. As there is a world of mathematical pain in that department we'll Let That Dragon Be. ]
The deeper connection with spin is related to the symmetry of wave functions under geometric and other transformations. Wave functions are those mathematical beasts that are used to represent quantum systems. For a spin-1/2 wave function you would rotate it twice around a full circle to get back to the same thing. Note that I've said we are rotating the wave function used to represent the particle. Whether you want to think of that as some 'real' physical rotation of the object is your pleasure, as discussed. What alters as you go around is the phase of the wave function, a directly unmeasurable quantity to be exact. However if you compare neutrons that are given a single full circle rotation - by traversing a certain magnetic field configuration - with their cohorts that didn't -> they interfere because you are measuring a phase difference. That difference shows up as to whether you detect neutrons at all in certain positions, so there is your experimental meaning of phase shifts. Much like what we do with the Michelson-Morley-Fabry-Perot type LIGO interferometers using photons.
Quantum mechanics is full of such mathematical or closely related statements like 'rotate the wave function'. No one actually has a direct visceral sense of the topic. A visceral sense is like being nailed back into the seat of a car if you rev up, drop the clutch and drag off into the distance. Human senses are at the wrong scale to instinctively know anything about the microcosm. For instance talk of the Higgs Boson/Field is replete with jargon very akin to the underlying mathematical model, with hands waving frantically if attempts are made to explain in 'real' terms. See all the rigamarole with discussing 'symmetry breaking' for instance ....
OK, that's four posts in as many days! Let's digest that for a while ..... :-)
( edit ) 4 posts in 5 days ... I just had to keep rolling on this, I would have lost the thread otherwise ....
( edit ) 'lost the thread' indeed ! I always do such lame puns. :-)
( edit ) Silly dufus, I didn't mention a key feature : torque induces a change in angular momentum. That's why the car's wheels rotate faster when you hit the go pedal. There is another moment here alas, the moment of inertia. That relates to the distribution of mass around the pivot/axis, and hence at least for rigid bodies ( where the innards don't re-arrange themselves, much ) is a constant of proportionality b/w a given torque and a given change in angular momentum. This is where the signs and directions of things matter eg. the car brakes will slow rotation.
[ I never know quite where to stop explaining stuff.... ]
( edit ) See ? I really can't help myself ....
because of symmetry arguments, electronic shell structure and of course further experimentation the magnetic orientation of the silver atoms is deemed to be due to that lone electron mentioned. Specifically it is not due to the orbit of that electron around the nucleus ie. linked to orbital angular momentum. The only explanation consistent with all findings is that is intrinsic to the electron.
To be exact 46 = 2 + 8 + 18 + 18 and so electron #47 is by itself in an s-orbital ie. spherically symmetric and thus nil orbital angular momentum.
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Posted 20 days ago by Mike Hewson
When is 1/2 not one-half ?
Answer : In quantum mechanics, always. :-) :-)
Try this construct in your mind. You have what is deemed a spin-1/2 particle. This is a type of Fermion, typical examples being electrons, protons, neutrons and their anti-particles. It has a single spin vector centred upon itself ( whatever that means ). But you can never measure the whole vector at once. You can only ever measure one component of the vector within 3D space, and if you do : from then on all history of measuring the spin components of the particle along the other two perpendicular axes is lost. You cannot make any verifiable statement about the full vector at any measurement instance ie. the 3 components along each of the three axes in 3D space.
So as in the Stern-Gerlach apparatus you have an axis to measure this spin against. That in particular means that the device sorts individual Fermions as per their spin values to produce some physically distinguishable results. Bung the spin-1/2 particles through and then choose to further examine one of the particle streams, call it 'up' for discussion. Let all the 'down' particles hit some detector/barrier ( hence being counted ) and thus take no further part in events. Run that first stage 'up' stream into, say, a 90 degree rotated SG apparatus so we now sort according to another axis now. It will split into two equal streams. Throw the 'left' stream away and only keep the 'right'. At this point, classically, you would now assert that you have two firm parts of the full vector so we could confidently label the stream as 'up/right'. Bung that through a third SG which is now rotated 180 degrees c/w the first and none should come through the lower most channel*. Right ?
Wrong. Epic fail. You get equal numbers going through either channel of the 3rd SG in the chain. Admittedly you have thrown away some fraction of the total that the gun originally emitted. But you have definitely not performed a progressive sorting along perpendicular axes, in order to reconstruct the original spin vector. Each time you measured along any one axis, the components along the other two were randomised.
Now you may legitimately object as to whether there is a 'true' vector of spin held by the particle as one of it's properties. After all that works perfectly for big objects, rotations/spins included eg. a Ferris wheel may have its angular momentum vector readily defined in 3D to the degree of accuracy of the measuring apparatus. For Fermions the hypothesis is that each of the components, when measured, has length '1/2', and so the total vector ( but un-measurably so ) has length SQRT(3/4) ie. the length across a cube of side length 1/2 from one corner to the diametrically opposite one. As per Pythagorus.
This careful thinking is consistent and works well to predict behaviours in the small. In deeper formulations of quantum mechanics this spin measuring rigamarole may be viewed as a variant upon Heisenberg's Uncertainty Principle. The three spin components are called 'conjugate' and thus can't be measured both accurately and simultaneously.
Ultimately it's one of those 'it is what it is' features of the universe with no clearer or better explanation. Which is why many have, and still do, rail against the logic of quantum mechanics but also have no improved program for experimental prediction. Upon this theory rests the production of an enormous amount of modern devices and machinery eg. no quantum mechanics -> no silicon chip. It's success is outstanding. Next up :
What Matters About Antimatter
BTW : top job if any of you have even vaguely followed me. For me at least, the rest of quantum mechanics is a relative doddle compared to this spin twaddle. David Bohm ( one of my legends of QM ) spoke of implicate order vs explicate order. What we see and measure is explicate. The underlying regularity is implicate. So if I do one of those tricky cutting sequences with folded paper then pull it out to display a line of people shapes holding hands then I have demonstrated implicate and explicate order. The challenge in physics is that we see the explicate order and have to deduce the folding and the cutting etc, and so uncover the implicate order. FWIW I do this sort of thing day in & day out as a medico. I call it 'alleged diagnosis' .... :-) :0)
* Using this demo set :
- 'random xz' for the gun spin orientation
- angle = 0 and 'up' for the first SG module
- angle2 = 90 and 'up' for the second SG module
- angle3 = 180 and 'up' for the third
and watch the splits go 50:50 for each stage ! :-)
Message boards :
Posted 20 days ago by Mike Hewson
Transition to the Spin World of the Small
Otto Stern and Walther Gerlach performed a landmark experiment in the early 1920's. First they set up two opposite magnetic poles in such a manner so that the space between them had a non-uniform magnetic field. That means that the direction and strength of the magnetic field would vary according to the particular position. The effect of that was such that any second magnet introduced into that region would feel a nett force to move it either towards or away from a particular pole - depending upon the magnet orientations.
Let's step away from history for a moment and use the above described setup for our own Gedankenexperiment. Get some magnets that are small enough to throw through that region between the poles, but not so small as to be anywhere near atomic or molecular size. That is, the magnets will contain very many atoms. Put it all in a vacuum, and for that matter do it away from planets and stars etc so that we can forget about gravity as well. Arrange matters so that a 'magnet gun' will toss the magnets through the inter-polar region, but in quite random orientations. Have a sticky wall on the other side so the magnets will stay put where they hit it. Let it rip for a while. What would you expect to see as regards the distribution of our magnets on the far wall?
Sensibly ( and correctly ) you will predict an even spread over some arc centered on the main magnets. You could do some math and relate, say, the speed of the little magnets ( hence the time spent within the strongest non-uniform part of the magnetic field ), the relative strengths of the big and little magnets etc, to the dimensions of the pattern obtained. A smooth spread.
You could repeat this entire procedure many times, while cleaning off the far wall in between runs. Gather up the magnets and reload the gun. In addition you could rig the magnet gun to spit them out in particular orientations. Then you could correlate some chosen orientation with a resultant wall position. With some practice I could nominate a spot on the wall, and you could set up the gun to group them closely on the wall where I indicate. Fun, huh? :-)
Back to Misters Stern and Gerlach. They used neutral silver atoms. These have atomic number 47, meaning they have 47 protons in the nucleus. Plus 47 electrons whizzing around. That's an odd number and a key point in what follows. They shot these atoms, with presumably random orientations, through the magnet gap. On a distal photographic emulsion they saw two bands, one 'above' or closer to one of the large magnet poles, and one 'below' and closer to the other pole. There were no hits at all in between those two bands. Further runs revealed that the stronger the magnetic field the wider the bands were. If the field strength was progressively reduced then the bands would gradually come together and merge in the middle.
Now what do we make of this ? Recall that at the time all the quantum stuff was just in formulation, very contentious etc. One approach ( Schroedinger ) predicted three separate bands and not two. Rather than retrace the confusion then, let's go for the modern view :
- an overall phrase used for this sort of result is 'space quantisation', which is a little misleading I think. It's not packets or blobs or cubes of space. Perhaps 'direction quantisation' is easier to swallow. The idea is that if you physically define a magnetic axis ( the magnetic gradient here, as opposed to some an arbitrary descriptive choice without physical definition ) then the small world ( aka quantum realm ) will notice that in special ways not seen with our much bigger magnets in the above Gendankenexperiment.
- we are sorting little magnets. Unlike a big magnet we can't grab a silver atom in each hand and test to see if some two-ness emerges with different 'ends'. Clearly using silver atoms has demonstrated a two-ness here, but what would an 'end' mean for an atom?
- since we got quite distinct piles of atoms on the far wall then each atom ought have, in the context of the specific apparatus, one of two magnetic orientations in order to land in either. One atomic orientation gets it to the top band, the other orientation puts it through to the other.
- because of symmetry arguments, electronic shell structure and of course further experimentation the magnetic orientation of the silver atoms is deemed to be due to that lone electron mentioned. Specifically it is not due to the orbit of that electron around the nucleus ie. linked to orbital angular momentum. The only explanation consistent with all findings is that is intrinsic to the electron.
- by extension then all electrons possess this intrinsic spin. The other 46 in a silver atom have pairings that negate their influence on the matter. The two-ness comes from two distinct orientations ( with respect to the gradient field ) of the spin of electron number 47.
- now you can have magnetic things going around in orbits producing measurable effects. You can define an orbital angular momentum in such cases and directly link that to some magnetic behaviour. Change the angular momentum and see the results vary. The rotor of your local AC power generation facility will show that in spades.
- does this mean that an electron really spins, like a little rotor? Two answers here :
(a) If it helps to think that way then do so. But do remember that you have in fact assumed that to be so.
(b) Who cares? We can never test that ie. the electron throughout all experiments performed to date either are, or may be deemed as, point particles. So do the math as per spin = 1/2 ( more on that later ) and get on with it.
My personal view : spin is a macroscopic word/concept applied to quantum objects. It works if done consistently. Next up :
When is 1/2 not one-half ?
( edit ) I found this great interactive demo of the Stern Gerlach experiment. Select 'random xz' for the spin orientation of the gun, and use only one magnet and you'll have the original setup. I love the sounds too. If you are bold you may add magnets, rotate the magnet modules with respect to each other, filter the spins at the gun etc. In effect you will retrace the variants on the original SG apparatus and so - if you dare - find stuff out. See whether or not your large scale intuition holds up! :-)
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Problems and Bug Reports :
Average credits declining - Can anyone explain?
Posted 20 days ago by Mike Hewson
.... the bulk of the power goes into producing unusable heat adding more entropy into an already disordered universe. (Sorry about that, but I do get a little carried away at times.) ....
Hey! Entropy rules! Our computers are merely heaters that calculate. :-)
[ However your name is now recorded on the list of those to blame in the far future when the Universe dies of it's Heat Death. ]
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Posted 21 days ago by Mike Hewson
So What Does Stay The Same If You Run Time Backwards ?
Suppose we had an more ordered collection of things and ran time backwards to get a less ordered arrangement. That would be the equivalent, time running forwards, to a less ordered arrangement going to a more ordered one. This is not impossible. It breaches no fundamental interaction laws.
Now when we say that entropy almost always increases with time in a closed system then : for each starting point ( earlier in time ) of some time interval that we are considering we can put that starting point as the ending point for an earlier interval. Et cetera. You can take this process as far as you like back to the Point of Confluence. Thus implying that entropy almost always decreases as time is reversed ( with the reasonable assumption that the entire Universe is a closed system ). In fact this is sometimes used as one definition of time. Well perhaps not what time is per se, that's a tad nebulous, but which is the 'forward' direction ie. that which entropy almost always increases in a closed system. The 'arrow of time' as per entropic reasoning.
A reminder about the 'closed' bit. My fridge/freezer cools down it's contents, thus making the position and momentum of the molecules of ice cream etc more orderly. But it is not closed. The working fluid of the fridge passes b/w what I may designate as the boundary of the interior of the box. The refrigerant is cooler than the box contents on entry, and leaves hotter than it was on entry. It takes energy out of the box. It is then compressed on the outside of the box, making it very much hotter and thus radiating heat to the room surroundings which at that time is cooler than the refrigerant. The fluid is then decompressed - typically via a nozzle in a process labeled Joule-Thompson throttling - and hence passively cools before entry to the box again. Rinse, lather, and repeat so cooling the fridge contents at the energy expense of operating a compressor. For which I contribute work via yet some other source to run eg. burning coal at a power station. So the decrease in entropy within the fridge is well outweighed by the increase in entropy down at the power station surrounds.
Now it may not seem, from descriptions that you read and hear about, that the early universe was more ordered than now but it was indeed so. That is because those microstates that we mentioned earlier have many degrees of freedom. So it's not just position - which is probably the first quality that you might think of when you think of orderly eg. ducks in a row - but speed/momentum, spin etc too. And each time particles are created you have more objects to count. So an atom in an excited electronic state has less entropy than the subsequent atom in it's ground state plus a photon zipping off in some direction. Or a photon of sufficient energy that annihilates to produce an electron and a positron.
Which brings us to spin and a property called parity. Parity is the idea that if you swap left for right, like a mirror does, then things stay the same. So parity is a type of symmetry in direction sense. Most screws in the hardware shop are 'right handed' - more by history than necessity - with the result that it will go into the wood, say, when you twist the screwdriver clockwise with your right hand ( as you see it from the head end of the right arm ). But what is your right hand ? It's the one on the opposite side of the body than the heart. Well most people's anyway.
Many years ago I got to meet and examine a man with dextrocardia. Literally that means the 'heart on the right'. It was in the run up to 4th year surgical finals, and we were kindly provided with volunteers to practise our physical examination skills. Or lack of them, for some. Then we would be asked questions in a mock, but very real feeling, format like the viva-voce we had to do later. This chap was the willing subject for a group of about twelve of us, myself included. We were not warned. We had lots of ideas : he'd ruptured his diaphragm in an accident and so his heart was displaced, he was born with a small liver but had a very diseased and enlarged spleen. Our lists went on, but no one got it. You see : all his internal organs were a mirror image of the Gray's Anatomy plan. If he got appendicitis you'd better go in on the left or be very surprised. Clearly this particular variation says alot about the physical development of people under the action of genes. The rate of this 'disease' in the population is one divided by some large Lotto number. Our instructor for the day wasn't worried that we'd fluffed it. Unless we were going to practise in the remote rural town the chap came from it very probably wasn't going to be an issue during our careers. He wanted us to believe what our senses told us. A very good lesson indeed and obviously quite memorable. For what it's worth a child was born with the same characteristics in the very same town. But two houses down the street ... :-)
Note that 'left' and 'right' are peculiarly human terms here. If our body plans were such to have a plane of symmetry horizontal through our midrift instead of vertical through the centre of our spine, then we might talk of 'up' and 'down' being the relevant names when discussing direction sense symmetries. Which is just a rotation, not a reflection, of the left/right choices above. Regardless, it is still true that our 3D spatial universe has two choices for 'winding'.
Magnetism. There is a deep connection b/w magnetism and winding sense. Beware. At one point in what follows we are going to leap from everyday well-viscerally-understood and demonstrated ideas to more nebulous and indirectly measurable ones. I will signal that transition.
Now you know that magnets have two different ends. These typically have the labels of 'north' and 'south', which is another historical/human precept like left & right above. No matter. The fact is that you can have two magnets and when mucking about with them note that in some configurations the ends push away and sometimes they pull in. You can actually feel that. Albert Einstein was given a compass when he was about ten years old and played with it alot. He describes thinking then about why it was that something could affect something else at a distance ( in this case the compass and the Earth ) without anything obviously in between. You can see where his later ideas about 'fields' were planted.
When electricity was discovered and/or defined it was found that magnetism related to it. In particular you could have a loop of wire, push a magnet in and out of the plane of the loop and electricity would flow in one direction around the loop, or the other. Or you could run a current through the loop and, depending on the setup, the magnet would either be attracted towards or repelled away. Notice carefully that with each arrangement there is a 'two-ness' occurring. A magnet movement in one direction would produce a current flow opposite to that when the magnet was moved the other way. A current in one sense would produce the opposite force on the magnet compared to the case when the current was reversed.
After much of this ( plus some work on definitions akin to north/south so that researchers could talk in common about what they were doing ) the idea of magnetism being a vector quantity arose. The mental/math construct to describe and visualise magnetism is as a vector field. For a given current along the wire the magnetic field vector is perpendicular to the vector defined by the current, and if you flip the current the field points in the exact opposite direction in 3D space. This geometry is precisely analogous to the winding senses of screws, and more generally the way rotations are dealt with mathematically. Hence the word 'spin' creeps into the language of the topic. After all : if you have some axis/line, then what locus/curve do you describe by requiring the tangent to said curve always being at a right angle to the vector to the axis? A circle of course. What directions do circles have? If you think of a circle as a type of line curved around on itself ( snake eating it's tail ) then you can go around one way or the opposite way. Clockwise or anticlockwise. Only two-ness applies. You label one way with respect to some standard eg. traditional clock behaviours, the other choice is given an opposite sense wording. With magnet ends you can use the planet eg. towards the cold part of the Earth where the stars rotate about a point directly above and there are bears but no penguins.
In the end it was the relative motion between the magnets and the wires that really mattered. You had to consider the orientation of your gear in 3D space, and within that the winding sense was needed. This was folded into a consistent framework which as you know has led to all manner of devices, especially those which generate current by wire movements near magnets to those that produce movements by running a current in a wire near magnets. Generators and motors that is.
So far this is classical electrodynamics. Enter Einstein and Special Relativity. If you take the static electric field around a charge and then transform it via SR's equations ( under relative motion that is ) you wind up with (A) a component like the static one, and (B) a new effect dependent on the relative velocity ( a vector ) b/w the charge and the traveling viewpoint. This second component has exactly the characteristics that we have assigned to magnetism. Magnetism is a relativistic effect. The two-ness ultimately derives from the fact that the relative velocity vector will indicate that you are either moving closer to something or are moving further away. Next up :
Transition to the Spin World of the Small
( edit ) Sharp punters will note that I have glossed over the cases where the geometry is such that no magnetic effects come into play. For instance where two current carrying wires are mutually perpendicular, the field from one does not affect the current in the other. But these are border cases of more general arrangements, parts of the parameter space where you flip from one option/behaviour in the two-ness to the other.
( edit ) Dextrocardia Man had no special medical problems on account of it. Levocardia rules presently for humans and indeed for many mammals to which such a descriptive scheme could sensibly apply. If dextrocardia were more common then we'd be dividing the human race into Dextrocardiacs and Levocardiacs as a matter of normal thinking ( we already do that anyway for preferred limb usage ). I think there's a good sci-fi novel in that ..... :-)
( edit ) So I guess you could label magnet ends, not as North & South, but Bear & Penguin !
( edit ) Whoops! I've been a tad unclear. You can of course use a screwdriver within your left hand, and while looking at the second hand of a clock sweeping around, follow that to drive the screw in. What I was meaning was that when the right thumb is uppermost then clockwise means you roll that wrist so that the thumb moves away from the central plane of symmetry of the human body.
Message boards :
Gravitational waves: have US scientists heard echoes of the big bang?
Posted 21 days ago by Mike Hewson
That's good. I liked :
".... Doug Neidermeyer, a cosmologist at the U.S. Military Academy in West Point ..."
Nice touch. :-)