Celestial Sphere

Mike Hewson
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[ Sorry for the break in the

[ Sorry for the break in the flow. Silly Season et al. The good news is that this post is a long one with plenty to think about! :-) ]

So Where & When Did The CMB Originate ??

Short answer : Everywhere. About 300,000 years after the Point Of Confluence.

Long Answer : Consider the hydrogen atom. It's the simplest atom possible. A single proton as the nucleus and one electron bound to it. There are other isotopes of hydrogen. Deuterium has a proton and a neutron in the nucleus. Tritium has a proton and two neutrons in the nucleus. They all have the same nuclear charge so any neutral atom of the hydrogen species has still only one electron. For what follows we'll consider plain & simple hydrogen with only the proton in the nucleus.

Well we say the electron is bound to the nucleus, but to be sure the proton is bound to the electron too. This is because they are attracted to one another. This is described by saying that they have opposite electric charges and that the electromagnetic ( EM ) force works with opposite charges attracting. Over a century ago classical electrodynamic theory predicted that the proton and the electron ought very quickly sit one atop of the other if they came nearby. Thus there would be no such thing as atoms. Then quantum mechanics came along and resolved that issue, and others, with the idea that they couldn't sit one upon another.

Hence there was a minimum of distance that they would be separated by and an energy level of interaction for the duo that would not be undercut. This is given the title of ground state. That state of the proton/electron combination is the 'quietest' behaviour that they have. The energy of the ground state is the first of a series of states with increasing energy. It's the lowest rung on an energy ladder. It turns out that, up to a point, there are distinct gaps between the levels. Also the gaps get smaller as you go to higher energies. It would be a weird sort of step ladder that has closer spaced rungs for the higher up steps, but that is the way it works for atoms.

Here's lies a key issue : 'up to a point'. There is a threshold level, called the ionisation energy where the stepping ends. Above that there are no discrete energy levels ie. there are still energy levels ( as high as you like without bound ) but also they are as close as you like. The proton and electron roam around separately, maybe interacting but not necessarily. Another word used for this is 'continuum' or 'free', as opposed to 'quantal' and 'bound'. An atomic energy level above ground state but not as far as ionisation is called an excited state*. Classical electromagnetism had the continuum behaviour all the way down to the electron sitting with the proton, and that energy would mathematically be at negative infinity. Quantum mechanics has stopped that sort of rot ... :-)

[ASIDE : mind you, the same problem currently exists with gravitational theories but we've haven't found a viable alternative yet. So the 'singularity' alleged to lie at the centre of a black hole is where everything that went into the hole sits one atop the other. If you know how to fix that issue, a Nobel Prize awaits you !! :-) ]

The energy gap from the ground state to ionisation is ~ 13.6** eV, where 'eV' means electron Volt. The exact definition of eV isn't important here. One eV is a fantastically small amount of energy in human terms, but more than 13.6 of them will split up any hydrogen atom into a free proton and a free electron. That's where the term 'ionisation' comes in, as we then have two ions ( charged particles ) where before there was a neutral body. Please note that it could take even less than 13.6 eV to ionise as the atom may be well up the ladder already ( ie. not in the ground state ) and thus nearer the top where the ionisation threshold is. So if you give an atom more than is needed to ionise it then any excess energy above is shared between the ions afterwards.

So that pretty much covers the generality of how a single proton and a single electron interact. Now let's throw in a third*** particle. A photon. The photon is the force 'carrier' for electromagnetism. In quantum mechanical terms EM is described as a field and the photon is the quantum of the field. It's hard to give an accurate everyday example to correspond with here. Perhaps think of the photon as like 'a cheque in the mail' and so representing money in transit b/w banking accounts. Something like that.

The photon can interact with either a proton or an electron when separate. Indeed when it does we usually describe and calculate as if the photon were first absorbed by the charged particle and then later emitted****. In that process both the photon and ion will change in energy. This is called scattering.

What if the photon encounters a hydrogen atom ie. a bound state of an electron and proton ? This depends on the energy that the photon has, and where upon the energy ladder the atom lies when the photon turns up nearby.

(1) The photon may fly on by. No particles change their characteristics. This is the 'nothing happens' interaction and is a legitimate outcome.

(2) The photon may be absorbed by the atom :
(a) This may ionise the atom and then the proton and electron go their own ways - we get a pair of ions.
(b) If it doesn't ionise - not enough energy to hop off the top of the ladder - then you are left with an excited atom.

(3) If the photon energy and a discrete gap to drop down through is just right, a photon going by will continue on but it also induces another photon to be emitted of the same energy and phase. This is known as stimulated emission and is the basis of lasers .....

Naturally the inverse processes can occur :
- A free electron may lose energy by emitting a photon and then become bound to a proton, thus forming an atom.
- An excited atom may emit a photon and by that energy loss go to a lower ladder rung, even down to ground state.

What has been described here also works for other atoms as well. The detail and complexity varies of course but we have the basic behaviour as above.

The cosmic relevance is as follows : some time after the Point Of Confluence the Universe consists of light nuclei and electrons and photons all whizzing around separately, banging into each other and whatnot ( a plasma ). Then things cool down - these particles lose energy - and so atoms may form. That changes the situation for the photons as well. That transition then gives us what we now call the CMB. Continuing this exposition next time :

More On CMB Electrodynamics

or

How Do You Settle Down A Bar Brawl ?? :-)

Cheers, Mike.

* Some sources/texts use terminology implying that it is the electron which is excited, the electron has energy levels .... etc when describing bound states like atoms. My preference is to ascribe to the atom in toto ie. the proton is there too !

** That 13.6 eV is effectively no different if there is an extra neutron or two in the nucleus. To be exact both a proton or a neutron have a property called magnetic moment related to the particle's underlying spin value. This means that even a neutron which has an overall nett charge of zero is still an electromagnetic player. If the atomic energy levels of hydrogen, deuterium and tritium are measured to high detail they will subtly differ, and more so the stronger any surrounding magnetic field.

*** Well I'm talking here of an 'actual' photon which may be subject to measurement. This contrasts with the 'virtual' ones which when assumed to be present ( though never seen ) round out the description ( see next note ). So a proton in company with an electron within an atom are presumed to interact via virtual photons. This is the price of having an accurate theory ! If you don't put these virtual guys in then you don't get answers that match with experiment.

**** For all interactions see the full Quantum Electrodynamics ( QED ) treatment with Feynman path integrals/diagrams. That describes the entire horror and very accurately indeed. What I am describing are so-called low order interactions which dominate the description.

I have made this letter longer than usual because I lack the time to make it shorter. Blaise Pascal

Mike Hewson
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More On CMB

More On CMB Electrodynamics

So hopefully you have firm the idea that for atomic energy levels :

- below a certain level you can only get specific discrete numbers with gaps in between.

- above the ionisation threshold the nuclei and electrons will separate and run free, giving and taking any particular energy you can provide.

Let's imagine a big ( magic ) box with transparent walls. Fill it full of equal numbers of protons and electrons and let things equilibrate. But make them all real hot, here defined as meaning that the average energy per particle is well above the ionisation energy of the hydrogen atom. This is why the box would have to be magic as that temperature would be well over 3000K and I don't know of any suitable material with transparent sides that would cope for long with that.

Anyway, in that scenario try to look through the box to see whatever might lie on the other side. You will fail as the plasma within will absorb any light at all. The ions - protons and electrons - are unbound and so will absorb and emit a photon of any energy. The plasma is opaque. It will be radiating light in the manner we have already discussed though. In fact you know of such a beast, as you see it everyday. But not at night. Yes the Sun is one whacking great ball of plasma*, as are all stars**.

Now let's imagine the temperature going down gradually. Initially not much will change, you still won't see through. But at around 3000K we begin to allow atoms to form as the protons may bind with the electrons AND the other particles that may knock into said atoms may not have the energy to ionise them. However in addition any photons that are about may not have the exact energy to cause a transition of the atom up to a higher level, because it won't provide a precise amount that fits a gap b/w ladder rungs. Photons are not 'half absorbed' in this situation, it's all or nothing. So the photon will fly on by ....

Most of them at least. Yes there will be some that do match some gap, absorption will occur and then re-radiation by steps down to ground state. These will be a small fraction of the total though. Hence for the most part the atoms ( hydrogen ) and the radiation ( photons ) will have de-coupled. Our box of material - now called a gas of atoms, not a plasma - will now transmit the vast majority of photons without alteration. The photons can travel quite an uninterrupted distance now and the contents of the box becomes transparent. You could see someone waving at you from the other side.

So for the expanding universe the question becomes 'when does this occur?' Current estimates put that around 300,000 years after the Point Of Confluence. It is not that all protons and electrons will suddenly and simultaneously form atoms. There will be a variation of energy around the average. Some less, some more. As that average ( read temperature ) decreases there will be a graded transition between most ions being free through to most having combined to form atoms.

The CMB as witnessed now are those very photons that first emerged during that decoupling era. Back then the photons had an energy corresponding to about 13.6 eV. The expansion of the Universe since has dropped that energy to way less*** than that, so the effective temperature of such photons is not the 3000K of the decoupling time but some 2.7K now. Next up :

So What Happened To The Photon Energy ?

Cheers, Mike.

* Yes the cooler outer layers can give specific spectral signatures of absorption of light at certain frequencies produced by the plasma beneath/behind, but the plasma emission per se is featureless. What we perceive to be the Sun's 'surface' ( photosphere ) is ~ 6000K.

** But I don't know of any poets that have looked at the night sky and then penned an 'Ode To Yonder Plasma Spheres' .... :-) .... nor is much said about lightning.

*** Below one thousandth of an electron volt.

( edit ) Oh. You settle down a bar brawl by capturing the energetic ones, then the rest can leave to go home ! Throwing bucket-fulls of water often helps too. :-)

I have made this letter longer than usual because I lack the time to make it shorter. Blaise Pascal

Mike Hewson
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So What Happened To The

So What Happened To The Photon Energy ?

The time of matter/radiation decoupling. Due to a much earlier phase in the Universe it turns out that for each proton or neutron there are about a billion photons ( or electrons, or positrons, or neutrinos as the weak nuclear force involves exchanges & reactions b/w all of the above ). The likely reason is that, due to an asymmetry in the forces at even higher energies, matter and anti-matter annihilated leaving a slight excess in matter. This deserves an extended explanation of it's own, so maybe later on .... :-)

Numerically what we call 'matter' was a very very slight contaminant within a sea of radiation. Still is. This is even without accounting for the Dark Matter/Energy business. So now we sit in a bath of low energy photons - the CMB - such that we wouldn't notice it unless we go looking, or fall over it like Penzias and Wilson did. Plus there is an immense number of neutrinos. You have no doubt heard of the statement that so-and-so many neutrinos pass through our bodies every second, but it is extremely rare that any one of them interact with us. This is true. For us they are hardly perceptible, and vice versa of course.

[ Universally we are in a very special place here on Earth. A place of complex structure at an interface of transit/transformation of low-entropy/high-energy photons ( from the Sun ) that become high-entropy/low-energy photons ( radiated from Earth into space ). Compared to the vast bulk of the Universe we are a mind-boggling ultra small probability deviation from the average. Well away from equilibrium. Any random sample of the Universe will overwhelmingly produce a blob of vacuum with some particles whizzing through. ]

Now gravity is always relevant on any sufficiently large scale. We may ignore it for, say, atomic and sub-nuclear stuff but it determines the behaviour of the entire universe. It always attracts, and whether you choose to describe using Newton or Einstein, it is true that separating things with mass/energy costs energy ie. it takes energy to separate things apart. Like throwing a rock into the air it will gain height at the expense of kinetic energy. That is one way to view the decrease in energy of the CMB photons : they lose energy and thus go to lower frequency and longer wavelengths because they are all 'climbing out' of the common gravity well.

Another way to think of this is the 'oven' getting bigger. There is an upper limit to the wavelength of any radiation that is within such a cavity ie. it can't exceed the size of the cavity. As the cavity enlarges so does the maximum possible wavelength, hence the frequency and energy is lower per 'resonant mode' or photon.

Note that the energy has not been lost. It has been converted to a different form that is labelled as 'potential'. Should the Universe ever contract back again onto itself then such potential energy would convert back. Indeed that reduction in energy per photon also applies to those other distant objects we have discussed, the supernovae on the 'other side' of the Universe say. The full treatment/description is thus more than simply a Doppler type effect. It's a GR thing ultimately .... because while it is velocity related for sure, the Universe has also become significantly bigger while the photons were in transit for a substantial fraction of the age of the Universe. However you attribute it this redshift is around 1120, meaning that the Universe has expanded by about that factor during the time it took the CMB photons to get here. Or the Universe was about 1/1120th as old when produced. I say 'about' as the full math isn't linear on that one.

Now those CMB photons represent an ongoing reception of information from a steadily expanding edge to our 'known Universe'. You can think of it as a moving surface going away from us. It is not a 'flat' surface but rather a thin spherical shell, geometrically having a near side and a far side of slightly different radii*. Recall that the change in state that produces the CMB is a progressive process, not instantaneous, as the average particle energy goes under that magic 13.6eV. At each moment we see the plasma to gas transition of successively further ( distant in space and earlier in time ) volumes of space. This is homogeneous and isotropic ( ignoring special local factors ). Meaning that if we were 'over there' at any part of the Universe that we are just receiving CMB photons from today, then we would see the same type of radiation from here arriving too as a new 'image' of the distant Universe. The kicker is that 'here' and 'there' were once the same spot, or only slightly displaced, many moons ago. Indeed long before there was a Moon! :-)

Actually why don't we go for the throat and consider nucleosynthesis, where did the protons and neutrons come from etc ? This is equivalent to considering the whole Universe as like a particle accelerator, very much where particle physics meets astronomy. Next up :

Carpe Jugulum !!

Cheers, Mike.

* The closer face of the shell - smaller radius and not as far back in time from our point of view - corresponds to a snapshot of the time when the phase of atomic transition was ending and most energies were clearly below 13.6eV. The far face of the shell - larger radius and hence further back in time as we see it - corresponds to the time when the phase of ionisation was ending and atoms were starting to form to any perceptible degree. Neither is really at an exact distance/time though. WMAP puts a range of 115,000 years as the width of this time interval ie. from 382,000 years to 487,000 years after the Point Of Confluence. This corresponds to a difference in redshift b/w those surfaces of about 80, both being up around the 1100 mark. Like most descriptions of smooth and gradual processes one can endlessly argue about artificial lines or markers delineating definitions, dichotomies ( one side or the other ) etc. You could view the thin shell as being an onion like enclosure of a series of shells b/w the given radii/times. Each onion layer being a earlier sample of a plasma->gas transition surface as you go further away/earlier. The key feature is that the Universe does what it does, human invented definitions be damned ! :-0

( edit ) Addendum : '.... One approach to defining entropy is to say that it is a numerical measure ( typically involving logarithms ) of the number of microstates per macrostate. Because the numbers are typically horribly large then using logarithms gives briefer notations.... '

Actually the main reason for using logarithms in the definition of entropy is to make it additive when we combine systems. Each microstate in one system can be associated with each microstate of another, so when two systems are combined the total number of microstates multiply. Logarithms ( = exponents to some base ) conveniently translate multiplication of numbers into addition of their exponents ...

( edit ) If you divide the temperature 'then' ( 3000K ) by the temperature 'now' ( 2.7K ) you get ~1100. This is no fluke. For equilibrium E = kT ( Boltzmann ) and E = h*frequency ( quantum mechanics for photons ), so temperature goes like photon frequency, in turn going like the inverse of photon wavelength. So the temperature of the CMB goes like the reciprocal of the size of the Universe.

I have made this letter longer than usual because I lack the time to make it shorter. Blaise Pascal

Mike Hewson
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Carpe Jugulum We are going

Carpe Jugulum

We are going to have to lurk in some esoteric areas of physics now. We need to talk, at a pretty 'high' intellectual level, about the topic of symmetry. It might be best to seat yourself in the role of having a constructor set for physical laws, and considering how things might be in the universe if we only changed one or a few key properties. So I don't mean matters like if we did or not call Pluto a planet, or moved it closer/further to/from the Sun by a few million km. We are going to talk of how the entire cosmos would work if we flipped some basic rules. We will discover that nature is not fundamentally symmetric, or can only be so if we phrase our descriptions in a certain way. Let's begin with what I think is the most difficult one to get your head around, then the rest will be easier ! :-)

We have already indirectly touched upon one of these symmetry questions, that of what happens when time is reversed. We have talked of entropy in the context of the rule that 'in an isolated system : as time increases then entropy almost never decreases'. That's a true statement as far as we know, but as laws go it is also highly annoying. I don't mean it's irritating because you can't spontaneously stuff the contents of an egg back inside because you've broken the shell after dropping it on the floor*. It is annoying because :

- it expresses an inequality, and

- it is a probabilistic statement

Thus if you have a collection of things, then the configurations of those things that we will call 'ordered' is normally a vanishingly small fraction of the total ways of arranging them. If you like regularity is mathematically in an extreme minority compared to non-regularity, for really anything you might want to consider. Here I am equating the ideas of regularity/structure/order in their 'natural' meanings without getting too mathemagical at you. Now put in some other stuff :

- nature's conservation laws ( energy, momentum etc ) allow unhindered 'transit' between all microstates ( = specific arrangements ) that adhere to total conserved quantities ( energy, momentum etc ).

- nature encourages transit b/w microstates simply because there are 3+ dimensions to our universe and quantum mechanics yields an imprecision at a very detailed scale. It's like the old joke that refers to freak accidents - you couldn't do it twice if you tried. At a very high level of resolution our force laws do not permit indefinite static structures, they will eventually yield change. The vacuum will bubble and pop regardless. Virtual particles arise, and when they do some 'tunnel through barriers' and hence states change eg. nuclei decay. We don't really know why that is true. But it is.

Quote:

[ASIDE] As an illustration, take what is the expression for the amount of energy in a beam of light at a certain frequency 'f' ( a laser for example ) :

E(f) * ( + 1/2)

where E(f) is how much energy a single photon contains at a particular frequency, this is Planck's constant 'h' times the frequency ( ignoring a famous trigonometry factor ) :

E(f) = h * f

which one can calculate exactly. But means : how many photons ( so that's an integer ) will I find if I measure it ? It is called an 'expectation' value, the 'photon number operator', an average if you like, because QM says you won't necessarily get the same number for each measurement upon similiarly prepared light beams. Sometimes you might get 1002 say, then 996, or 998 or ..... but for a given 'starting' beam state then over a series of measurements you'll get some value ( all else being equal etc ).

But the real issue is : what is the '1/2' doing there ? It represents the 'vacuum fluctuation', or how much nature chooses to stuff you about by if you want to go around the district counting** photons. One half is precisely midway b/w zero and one, which places the total beam energy exactly b/w that which is ascribed to one integral number of photons and the next. The 1/2 is irreducible***. The ultimate form of ambivalence b/w a full NO = 0 and a full YES = 1.

Now what if we have a 'beam' which has no 'real' photons at all ie. empty space ? Then on average you will have a half photon's worth, but any particular episode of measurement will either record one photon or none at all. Over many measurements the cases ( detection or not ) will converge to a 50:50 split. Isn't that just nasty ? It is this sort of crap that really pissed Einstein off, and you can see why .... :-) :-) [/ASIDE]

Next up :

So What Does Stay The Same If You Run Time Backwards ?

Cheers, Mike.

* For some reason this is the requisite example to quote in entropy explanations. Shattered eggs haven't been observed to be the focus of converging energetic processes ( sound waves etc ) that reassemble shells with separated yolk and egg-white neatly inserted, that then leap upwards back into your hand.

** And when you count photons, or measure any beam property at all there will always be some other corresponding property - called a conjugate variable - the measurement of which will be disturbed because you did that. Plus you can't swap the time order of performing the measurement of two conjugate variables and get the same circumstance. This leads to the various forms of the Heisenberg Uncertainty Principle.

*** While with 'squeezed light' you can park the vacuum fluctuations in different 'quadratures' of the beam, the total beam noise can't be suppressed.

( edit ) Whoops. I should add that if you do see one of those virtual photons springing spontaneously out of the vacuum then energy is still conserved. There must be some other process occurring to balance the energy books, which we will discuss later. It's just that I'm focusing on describing the photon counts here.

( edit ) Yep, I know what you're thinkin', you are waiting for a better punchline. But no, you just get that 1/2 ( at a minimum, other factors only worsen the uncertainty ) .... it just is.

( edit ) Sorry, couldn't resist :

Quote:
..... I know what you're thinking. "Did he fire six shots or only five?" Well, to tell you the truth, in all this excitement I kind of lost track myself ...


from Dirty Harry's Guide To Quantum Mechanics :-) ;-0

I have made this letter longer than usual because I lack the time to make it shorter. Blaise Pascal

Mike Hewson
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So What Does Stay The Same If

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.

Quote:
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.

Quote:
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

Cheers, Mike.

( 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.

I have made this letter longer than usual because I lack the time to make it shorter. Blaise Pascal

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Transition to the Spin World

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? :-)

THE TRANSITION

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 ?

Cheers, Mike.

( 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! :-)

I have made this letter longer than usual because I lack the time to make it shorter. Blaise Pascal

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When is 1/2 not one-half

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)

Cheers, Mike.

* 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 ! :-)

I have made this letter longer than usual because I lack the time to make it shorter. Blaise Pascal

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Spin Addendum ( not essential

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 ..... :-)

Cheers, Mike.

( 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 ....

Quote:
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.

I have made this letter longer than usual because I lack the time to make it shorter. Blaise Pascal

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What Matters About

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.

Quote:
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.

Quote:
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 ).

Quote:
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

Cheers, Mike.

* 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 ! :-)

I have made this letter longer than usual because I lack the time to make it shorter. Blaise Pascal

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Richard Feynman and The

Richard Feynman and The Switchback Road

This is a Feynman diagram :

Time is along the vertical axis going from earlier to later, and all three spatial axes are compressed to the horizontal direction. He invented this visual shorthand as a way of summarising cases to be covered when performing 'path integrals'. Not a literal representation but a type of graphic memo describing any essential happenings. Down there at small scale in the quantum domain really weird stuff happens that one can't explain with macroscopic/human scale intuition. Basically when you don't intercept the paths of particles you can't actually state what path they took, but even worse their nett behaviour is only consistently explicable by assuming that a given single particle to some degree takes each of all the possible paths. Believe or not. But when that is held to be true the predictions from theory are outstandingly accurate.

For this diagram electron paths are in blue, positron in red, and the wavy purple ones are gamma ray photons. The lower right shows a gamma being converted into an electron/positron pair. The upper left shows an electron/positron pair annihilating to produce a gamma. This is time symmetric, as you will see if I rotate the diagram :

so the words are upside-down, but now time progresses from the future into the past as you go up the page. Let's now ignore the gammas and the time direction, and focus on the switchback aspect alone :

Switchback is a term used often to describe roads or train tracks that reverse direction several times, as a steep grade is traversed say. Feynman originally envisaged this as looking down from a bombardier's position in a plane, through the bomb-sight as the landscape scrolled by underneath. Let's imagine doing that while we fly from the lower part of the diagram going upwards. So one would see :

- a road ( electron ) on the left, then

- another two roads would appear ( V2 ) on the right side, three in all now ( electron, positron, electron ), then

- the two left most roads disappear ( V1 ), so we are left with one road ( electron ) on the right.

V1 and V2 are vertices which are places and times ( both on the diagram and in the real world ) where something happens, other than mere propagation of a particle. He wasn't the very first to state this, but here's the magic Feynman conclusion : you could legitimately consider a positron as an electron traveling backwards in time ( which is why I omitted arrows for the particle tracks ). From the stance of accounting b/w V1 and V2 the charge transfer, spin etc there is no difference. A positive current going one way is the same as a negative current going the other. So the diagram is 'really' of a single electron where the gammas get emitted at the vertices to 'turn it around' ( in time as well as space ), hence momentum etc are conserved too.

Someone ( whose name I forget ) even hypothecated that the reason why all electrons have the same characteristics is because there is really only one electron ( in all of space and for all time ) rattling back and forth through spacetime, weaving through all electron event vertices. Go figure .... :-)

Quote:
If it helps think of a transaction b/w bank accounts. The people I owe money to will view me as a debtor whereas for me they are my creditors. Reconcile by addition to one account and subtraction from the other. While highly unorthodox, you could do this with cheques for negative amounts - issued by a creditor and presented to a debtor - and get the same result. Subtracting a minus is an addition !! :-)


In any case : apart from whatever is 'really happening', this demonstrates crucial symmetry in physical laws. Extend this argument to the other particles. Now with the apparatus of quantum mechanics :

- swapping matter for anti-matter is called C-symmetry ( Charge )

- swapping left spin for right is called P-symmetry ( Parity )

- reversing the direction of time is called T-symmetry ( Time )

To the best of our knowledge nature adheres to CPT symmetry which is a combined statement : IF you swap matter anti-matter AND trade all spins right left AND run time backwards THEN it all works exactly the same as the untransformed case. Specifically the probabilistic predictions of QM are unaltered. That is not to say that the symmetries are necessarily separately respected. That's why we will discuss next up :

The Weak Force = The Symmetry Breaker

Cheers, Mike.

I have made this letter longer than usual because I lack the time to make it shorter. Blaise Pascal

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