Quantum, Light and Stuff

Alex
Alex
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Wow, what an efford to answer

Wow, what an efford to answer my question! Thank you very much for that!

Indeed, I had a picture with three crafts in mind and was a little bit surprised finding this IFO. The arrangement you explained ist not visible at the first sight, it looks more to be in the same plane as the 'triangle'.

I hope to find more infos about the arrangement over the weekend; it's a very interesting stuff.

Cheers,

Alexander

Mike Hewson
Mike Hewson
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Just to be crystal clear Alex

Just to be crystal clear Alex : with Earth bound IFO's please distinguish b/w the arms of each IFO ( and how they respond to a gravitational wave, a study in itself ) versus the arrangement of the IFO's around the world ( thus attempt at source localisation in the sky, given certain responses from IFOs in some set ). My graphics are only referring to Earthbound IFOs and what might be deduced from the behaviour of some group of them. In this matter I have not shown the Earth holding the IFO's in some fixed relationship.

The LISA Pathfinder has a single 35cm 'arm' within itself. It's not going to measure any gravitational wave that passes by. Ever. To do so would require at least another arm, because the nature of gravitational waves is to effectively distort lengths in perpendicular directions to different degrees. Hence the Earthbound IFO's sense the difference in light's behaviour between the arms. So a particular IFO is a transducer of spacetime strain to photon flux. A microphone for instance is a transducer of air pressure fluctuations to electric current.

So that is why the original LISA design had three arms each some millions of kilometers long. The Pathfinder is only testing the technology, especially the capability of the craft to remain 'hovering around' the test masses that are within cavities inside the craft, at either end of the 'arm'. While this sounds weird, the LISA craft is largely shielding the test objects from all non-gravitational influences that are about. Once in proper operation the craft doesn't even touch the masses, because the wee thrusters etc move the craft to keep it that way ! Thus the masses will only be subject to gravity and thus in 'free fall', which in this case means in orbit within the solarsystem.

Above all, don't worry if you haven't caught all this. You are not the only one that struggles .... :-)

Cheers, Mike.

( edit ) All the zig & zag with the lasers in the Pathfinder is known as 'path folding', something that the LIGO's also do.

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

Mike Hewson
Mike Hewson
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Now, where were we ?

Now, where were we ? :-)

Light Polarisation II

Here is a classical ( pre quantum mechanics ) view of light as a propagating wave :

which portrays light of a single frequency/color. Firstly you will note that it has a vector ( arrow with length and direction ) indicating which way it is going. If you look at the top right of the figure the purple dot is the arrow tip looking right at you, so the light is coming 'out of the screen' at you. There are two other arrows at right angles to each other and also to the propagation vector. These are labeled as electric and magnetic fields.

The electric field vector, for instance, tells me which way a wee-wee-little positive electric charge would move, if it was there. So if I was an electron and that light wave came upon me I would move about in response to the forces generated upon me by those electric and magnetic fields. That would 'soak up' the energy in the fields, so to speak, but I would re-radiate further electric & magnetic fields because I have become an accelerated charge. Certainly if I, as an electron, were otherwise unconstrained then that re-radiation would occur at the same frequency and the light propagates onwards*.

The quantum transition is to view the electric field as proportional to the number of photons. In everyday life this is typically very, very many so if I add or subtract a few photons from the light streaming through my office window right now then I am not going to notice. Even a really good photo-detector will fail to track that variation of a few photons out of trillions of trillions. An electron in the vicinity of an oncoming photon will have a chance of interacting eg. absorbing the photon and then emitting it again. To absorb a photon in QM means that the photon is destroyed, and the energy it had is added to the electron's. Emission is the reverse where the photon is created by taking energy from the electron.

This is an example of quantum field theory which describes all manner of quantum interactions, of which there are variants available ( and still being refined ) for all forces bar gravity. For a photon/electron interaction as above you would use quantum electrodynamics which my hero Richard Feynman, plus Sin-Itiro Tomonaga and Julian Schwinger, received the 1965 physics Nobel.

So you can have an electron field for instance which is in all of space. Most places in the universe will have a zero** value for this field and hence no persistent electrons. I say persistent as one can have temporary, fleeting electrons. If one thinks of the field as like a bank with an energy balance then brief withdrawals can occur ( electron/positron creation ) provided repayment ( electron/positron annihilation ) happens before Heisenberg notices***. Which he won't if the product of the amount of energy borrowed and the duration of the loan is below Planck's constant. These virtual particles do not have to have the 'book value' for their mass/energy equivalents, as their persistent cousins do, but the heavier they are the shorter they live !

Cheers, Mike.

* Well, that is the base case to build upon for all other variants. I won't be teaching all of classical electrodynamics here! :-)

*** One model for the Higgs mechanism ( that produces inertia - resistance to change of motion - for some particles of non-zero rest mass ) involves two Higgs fields. One field is at zero value everywhere, the other is at a non-zero value everywhere but neither produce particles if undisturbed. If a weak nuclear force particle moves about it won't notice the Higgs fields differences below a certain distance ( the range of the weak force ), but the particle is impeded or suppressed for longer distances due to interaction with these fields. The reasoning is moderately complex and involves the idea of an internal symmetry which is allowed to operate for high energy scenarios ( high = particle kinetic energy comparable to rest mass equivalent ) but is diminished/eliminated for low energy ( low = particle kinetic energy much less than rest mass equivalent ) situations. This is the origin of the phrase 'symmetry breaking' in Higgs explanations. It means that at low energies the weak force vector bosons acquire an extra degree of freedom, or mode of wiggling if you like, that in a sense consumes energy to run. That reduces their kinetic response to energy input ie. increases inertia, which can be interpreted as a mass amount. Now the weak force vector bosons are involved in many other processes, so their mass ( however generated ) comes into play and hence indirectly sets the kinetic response of many other particles. That's why the Higgs is said to set the masses of fundamental particles.

[ With quantum field theory as is currently understood/enacted the extra wiggling must not occur at high energies because then theory would predict probabilities greater than one. Something cannot happen more than always ! :-)]

*** My wife used to work in the foreign exchange branch of a bank during the heady 80's. A junior accountant came to work one day in a really good expensive sports car. Further investigation revealed he had recently bought a house worth ten times his yearly income. Silly man. He was the last out of the branch each night and the first in every morning. Each evening he would transfer money from one of the bank's holding accounts ( typically containing millions ) to one he opened in a fake name but controlled by himself, then lend that on the overnite money market. He would make a few grand in interest per nite, and then put back the original amount in the morning. I guess if criminals were perfectly clever then we would have no use for jails ... :-)

( edit ) 'One model for the Higgs mechanism ...' : I think it is worth declaring that The God Particle is an utterly pointless media myth, a veritable semantic bushfire more or less accidentally started by Leon Lederman and his publisher. The Higgs mechanism refers to that symmetry breaking as a general requirement for reconciling low and high energy weak force boson characteristics within the framework of quantum field theory. A Higgs field is a specific field entity within some model created under quantum field theory framework, and as noted there may be several. A Higgs particle is a lump of one of the aforesaid Higgs fields, and being the sort of particle that has spin zero ( ie. integral value ) is thus a Higgs boson. There may be several varieties. Peter Ware Higgs is one of at least a dozen researchers working on that area of quantum field theory in the 1960's and since. Mr Higgs freely grants the contributions of others to the area of theory now named under his moniker, and he quite dislikes the 'God' label as likely causing religious offense to others ( he is an atheist ).

( edit ) 'set the masses of fundamental particles ...' to be precise this would be masses as assessed in the relatively low energy realm that we live. A hard thing to get one's head around is that very many everyday things, like the character of physical laws, can actually morph to other versions when things heat up. Here lies the meaning of 'grand unified theory' or how does matter in the universe behave when temperature is extreme eg. The Big Bang. Especially how, or indeed if, the four forces we deem as separate merge to an identical description at a pretty unbelievable energy scale. Merge means that a photon would operate identically to a gluon, or a weak force boson, or a graviton for that matter. Each of those force intermediaries would be indistinguishable in characteristics or effect at some insanely high temperature.

Of course, whether resolving such questions matters a rat's nadger for the man in the street ( who is paying for it ) is an important question. A main reason why the US Superconducting Supercollider project augured in was not simply parochial state politics but envy from other science craft groups at the disproportionate high funding received by particle physics enterprises. Some high energy physicist ungraciously labelled the congressional decision to stop SSC funding as 'the revenge of the C-grade students'.

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

tullio
tullio
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The birth of quantum

The birth of quantum electrodynamics is narrated by Freeman J. Dyson in his book "Disturbing the universe". He could not receive a Nobel prize since only three people can receive it (see the case of Nicola Cabibbo, of Cabibbo angle fame).
Tullio

Mike Hewson
Mike Hewson
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Yup, Freeman deserved better.

Yup, Freeman deserved better. He was the only guy who succeeded in demonstrating the equivalence b/w Schwinger's mind-numbing rigor, Feynman's freewheeling diagrammatic approach and Tomonaga's efforts.

To date there is still an unresolved issue of mathematical rigor in the theory. Indeed a wee spot of poison in QFT generally. It has to do with convergence of infinite sums, and is generally mumbled about and glossed over because : Dammit, it works! A finite sum is always independent of operand order. So if I go to the supermarket, put a ( finite ) number of things in the trolley and then go to the checkout for totaling and payment, then the order of scanning and addition to a running sub-total is irrelevant ( in the absence of arithmetic error ). I ought still owe the same amount regardless of any sorting of the items.

Now the trouble is that infinite sums are not actually sums. An infinite sum is a statement about a process of forming successive approximations. Each approximation is a finite sum. We seek a particular number ( casually called the 'infinite sum', more precisely the 'limit of the series' ) for which all bar a finite number of approximations are inside any arbitrarily small neighbourhood of that number. In rough terms that means we can get as close as we please to the limit by choosing a good enough approximation. Examine this pattern :

1 + (-1) + 1 + (-1) + 1 + (-1) + ......

where the ellipses '....' mean 'and so on without any stopping'. What ought the 'infinite sum' be here? Try this grouping :

[1 + (-1)] + [1 + (-1)] + [1 + (-1)] + ...... = 0 + 0 + 0 + ......

that 'should' wind up as zero. However with this grouping :

1 + [(-1) + 1] + [(-1) + 1] + [-1) + 1] + ...... = 1 + 0 + 0 + 0 + ......

so that would be an infinite sum of 1 then ? Right ? Well, no. Could I do this :

(-1) + [1 + (-1)] + [1 + (-1)] + [1 + (-1)] + ...... = - 1 + 0 + 0 + 0 + ......

giving a total of minus 1 ? I could even stretch it to produce :

1 + 1 + 1 + ...... (-1) + (-1) + (-1) + ...... = ??

So that's 'the sum' of plus infinity with minus infinity ? AArrgh we are just getting worse. The problem is that the sorting or sequence of presentation of the terms matters. We need some confidence that a given effort at successive approximations will indeed get closer to some 'true' value, and that approximations with more terms will ( generally ) be closer than those with fewer terms.

In the process of normalising with QM these limits arise. We have to normalise to ensure that probabilities lie b/w 0 and 1 inclusive. As mentioned some event cannot happen more often than always, nor less often than never. Thus if we cannot normalise in QM then we have no hope in predicting.

Back to QED and the like. We might as Feynman put it 'sweep infinity under the rug' by choosing to present operands ( read : expressions derived from Feynman diagram variants ) in a certain order, so that equally 'difficult' terms cancel. But how do we know, because we cannot simply assume, that the limit result would be the same for any other ordering ?

Re-normalisation is much the same gig, except that we seek to put a bound on the size of the error between a given finite approximation and the 'true' value. We renormalise in order to ignore high energy ( equivalently small distance ) events. Say, because we're just after everyday stuff and not the Big Bang. It's a way of saying : let's not go to infinity, let's stop at some chosen small distance scale, let's just accept a good guess for the sum of all those extra infinite terms ie. hoping they are too small to worry about even though we may not really know what they will do. While the mathematicians will crack it over this fudging, the test in physics is prediction ie. Dammit, it works ! :-) :-)

Cheers, Mike.

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

Mike Hewson
Mike Hewson
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I haven't forgotten this,

I haven't forgotten this, it's just that I'm having an issue or seventeen with my web hosting provider for illustrations etc.

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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