Quasi Periodic Oscillation -

AgentB
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Every now and then something comes up i had never heard of.

QPO - Quasi Periodic Oscillattion

and
ESA studying matter close to a black hole

I wondered if E@H type approach could be used to detect these oscillations.

Mike Hewson
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Quasi Periodic Oscillation -

Firstly the wiki entry is a straight word-for-word lift from this book.

Quasi periodic is a term for rhythmic but not quite, or alternatively random with regularities. Neither fish nor fowl ! :-))

The idea is that some transient phenomena has some repeating features. In general this comes under the rubric of 'chaotic systems'. Chaos here does not mean the traditional literal idea of totally random. It means 'sensitive dependence upon initial conditions', roughly that even slight changes of state at one point in time doesn't lead to slightly different states much later on. In essence the system state becomes absolutely unpredictable in the long term, which is important if you want to know if some aspect will thus repeat ( ie. be periodic ). Such systems are often subject to driving from effects which would alone produce contrary behaviours.

A classic and well studied chaotic system is single water drops falling from a faucet. I kid you not ! The competing effects here are gravity to pull the drop down with surface tension opposing. Typically one gets pretty regular timing of drop separation but with rather intense detail amongst detail discovered with closer inspection and variation of conditions.

In the black hole case at the inner part of the accretion disk the competing effects are gravity dragging material in vs 'abrasion' within the material. A good rough analogy is stuff going down a plughole that 'glugs' a fair bit and thus what goes into the pipe below may do so in a semi-rhythmic fashion. But that will stop after a while, or some other different temporary pattern will emerge.

Cheers, Mike.

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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Also rotation of material

Also rotation of material delays its descent into the hole ie. the Moon keeps falling to Earth but never hits 'cos it goes around. That inner accretion disk material needs to loose angular momentum and this is a highly interesting area of study. Some models posit that by magnetic effects the inner material interacts with stuff further out to achieve that. So roughly speaking material moves into the BH while the angular momentum ( a conserved quantity in the entire system exclusive of GW's etc ) moves out.

In answer to your question : with the relevant templates and good data you can pick up any signal via the Fourier stuff etc. At a guess I think QPO's would require a massive jump in capacity from our current capability @ ~ 2 TFlops. But the history of computing estimates is littered with like statements that some technological advance* shatters, so who can say ? :-)))

Cheers, Mike.

* In fact E@H itself is an advance of that type !

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

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RE: Also rotation of

Quote:
Also rotation of material delays its descent into the hole ie. the Moon keeps falling to Earth but never hits 'cos it goes around...


Errr...

Two points of order:

1:

Sure enough, the moon is in free-fall in the Earth's gravity well but it is not falling "towards" the Earth. (Due to the present trajectory of the moon, it continually misses impacting the Earth);

2:

Is not the shape of the distorted gravity field for our rotating Earth adding energy to the Moon to fling the Moon ever further away...?

Keep searchin',
Martin

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RE: the Moon keeps falling

Quote:
the Moon keeps falling to Earth

On a slightly larger scale, there is a rather interesting brain bender with the observation that:

The direction of acceleration for our Earth is different from the direction for where we see the Sun's light arrive from.

That is, we orbit a point that is significantly away from where we see the Sun.

Keep searchin',
Martin

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AgentB
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RE: In answer to your

Quote:
In answer to your question : with the relevant templates and good data you can pick up any signal via the Fourier stuff etc. At a guess I think QPO's would require a massive jump in capacity from our current capability @ ~ 2 TFlops. But the history of computing estimates is littered with like statements that some technological advance* shatters, so who can say ? :-)))

It struck me that there was some symmetry between the QPO glugging analogy and the GW chirps.

Mike Hewson
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@ Martin : the moon falls

@ Martin : the moon falls from the trajectory it would have taken in the absence of the gravitational attraction to the Earth.

It is tidal effects due to asymmetries upon the Earth's surface ( movable water masses ) which imparts a force upon the moon that moves it gradually away over a very long time scale.

The 'speed of gravity' and the speed of light are one and the same, so the instantaneous acceleration of the Earth is in the apparent direction of the Sun at said moment.

@ AgentB : There is a chap called Mitchell Feigenbaum who pioneered the study of what is now formally entitled as 'chaos theory'. He began this when working for Los Alamos labs where it was suggested he study instability and turbulence. The relevance then was the manner of atomic explosions. Here the opposing influences ( to be juggled/tamed for a 'good' bomb ) were the chain reaction rates when things are close together vs the energy released which separates things. Can one hold stuff together long enough to maximise the nuclear reactions before you then spray vast amounts of energy over the countryside ? Mitchell wasn't directly involved in weaponising per se though.

Any how he picked up on earlier work by a meteorologist Edward Lorenz who discovered the difficulty in making even general predictions in simple mathematical models because of the limited representation of numbers in digital systems, that often causes a truncation that matters down the track. The major surprise there was the lower significance digits that get discarded can really lead to quite different behaviours. For example if I rounded to 0.19835 rather 0.19834 then the first truncation gives me a wildly oscillating system some 10000 iterations later, whereas the latter truncation yields stability 10000 operations down the track. This is the butterfly that zigs instead of zags, later causing a freak storm on a distant continent gag ( which is a neat meme rather than a truly accurate analogy ).

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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RE: @ Martin : the moon

Quote:
@ Martin : the moon falls from the trajectory it would have taken in the absence of the gravitational attraction to the Earth.


Indeed so, and that is a very neat concise description. Very nicely in a form that avoids trying to untangle my thoughts earlier trying to describe how the acceleration imparted to the moon by the shape of the gravitational field around the Earth is balanced by the change in momentum and potential energy that the moon follows that then shapes the path of its orbit...

OK, you win on the Fermat/Pascal criteria for concise descriptions :-)

Quote:
It is tidal effects due to asymmetries upon the Earth's surface ( movable water masses ) which imparts a force upon the moon that moves it gradually away over a very long time scale.


An important effect is that the Earth rotates faster than the moon orbits, and so the misshapen gravitational field 'drags' the moon around faster...

Hence, the Earth's rotation slows gradually as the moon is dragged around to a faster orbital velocity into an ever higher orbit (and hence further away from the Earth).

There must become a time whereby the Earth has slowed to make the moon geosynchronous, or the moon becomes so far flung that the tidal effects are so small as to have negligible effect and to thence no longer perturb moon...

Quote:
The 'speed of gravity' and the speed of light are one and the same, so the instantaneous acceleration of the Earth is in the apparent direction of the Sun at said moment.


Errr...

Where we 'see' the sun to be, is not necessarily where it actually is at any particular instant. Our view is significantly skewed by the Earth's orbital velocity... Where we see the sun to be is not where we feel the sun's gravitational influence. (The solar system barycentre is not always within the solar sphere, however, that is not the effect I'm teasing you with here ;-) )

Is there not a significant problem in assuming a 'speed of gravity'?...

Do we not need an infinite speed for gravity to keep galaxies together?... Otherwise, how do all the stars 'know' where all the other stars are so as to be influenced in the right direction?

Then also there is the very interesting question of what effect the speed of light has for the propagation of 'changes in gravity' for how that might skew orbits...

For further thought. Any simulations for that?

Keep searchin',
Martin

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RE: RE: The 'speed of

Quote:
Quote:
The 'speed of gravity' and the speed of light are one and the same, so the instantaneous acceleration of the Earth is in the apparent direction of the Sun at said moment.

Errr...

Where we 'see' the sun to be, is not necessarily where it actually is at any particular instant. Our view is significantly skewed by the Earth's orbital velocity... Where we see the sun to be is not where we feel the sun's gravitational influence. (The solar system barycentre is not always within the solar sphere, however, that is not the effect I'm teasing you with here ;-) )

Is there not a significant problem in assuming a 'speed of gravity'?...

Do we not need an infinite speed for gravity to keep galaxies together?... Otherwise, how do all the stars 'know' where all the other stars are so as to be influenced in the right direction?


Surprised noone has picked up on this...

The effect I'm describing is that of "aberration"...

From a quick duck-duck, the best example describing this is "The Speed of Gravity - What the Experiments Say":

As viewed from the Earth's frame, light from the Sun has aberration. Light requires about 8.3 minutes to arrive from the Sun, during which time the Sun seems to move through an angle of 20 arc seconds. The arriving sunlight shows us where the Sun was 8.3 minutes ago. The true, instantaneous position of the Sun is about 20 arcs seconds east of its visible position...

And yet... There is no 20 arcs seconds of aberration measured for the direction of acceleration for our Earth orbit. Space and time are already distorted by the distribution of mass in our solar system and for our galaxy (and for the entire universe?)...

Quote:
Quote:

Then also there is the very interesting question of what effect the speed of light has for the propagation of 'changes in gravity' for how that might skew orbits...

For further thought. Any simulations for that?


By 'changes' I mean the continual repositioning of mass... Should not such changes require a propagation delay to be 'felt' elsewhere in our universe. Should not such a lag perturb orbits?...

Keep searchin',
Martin

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Mike Hewson
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Well done lads ! You have

Well done lads ! You have correctly retraced the conundrum as it existed before Einstein's relativity but after the speed of light was found to be finite. I mean that nicely : you have taken classical assumptions and pushed them to their logical conclusions and thus have discovered the true bother underneath that. The "propagation of 'changes in gravity'" is exactly what Einstein's GR is all about. Alas there isn't an intuitive fall back for us humans, indeed it leads to conclusions in contradiction to findings. So when phrases like :

Quote:
The true, instantaneous position of the Sun


are used one has ( unknowingly perhaps ) mixed measurements made in different reference frames without accounting for propagation delay. Hence the trouble. You cannot insist upon absolute 'truth' in measurement detail. All comments must be ascribed to some pre-agreed basis that includes light speed. We might use some God's Eye view/perspective to help encompass some scenario in our heads, to draw diagrams and construct equations and whatnot, but that will be a classical default. Because our brains work that way. We absolutely need to use an extra layer of cognition above that to correctly describe the universe as it actually occurs. You chaps are not stupid, not at all. You are chewing on the very thing at the core of relativistic descriptions.

The short answer is that one can only speak with consistency under all circumstances if one agrees to quote times & places using a special type of mapping. By mapping I mean an entire measurement system that creates a record of events for us to use when conducting & analysing observations. That system is not classical. In relativity that system is labelled 'an observer' but merely as a convenient shorthand. So when I say :

Quote:
The 'speed of gravity' and the speed of light are one and the same, so the instantaneous acceleration of the Earth is in the apparent direction of the Sun at said moment.


.... I have hidden much. Sorry. The 'said moment' is with respect to a clock located at whatever earthly measuring position you had chosen ie. precisely where you are chatting about the acceleration and the Sun's image. In turn that clock must be one partaking in an observer frame ( as above ), if we choose to reconcile with what might have occurred elsewhere in the universe. At the Sun in this instance ( where we may at our pleasure approximate to first degree as a mass point, and ditto for Earth ).

Now classically ( eg. Newton ) the universe was an instantaneous entity. You might take a while to ride your horse to town, but all the basic forces then known were not propagation constrained. There were observable things that could be delayed due to interactions and thus for example, the concept of refractive index ( a velocity ratio ) explained the bending of light wave fronts at a boundary. But then they didn't think of light in force terms. That epiphany was only when Maxwell disclosed that electromagnetic oscillations sped away from source at a speed - golly gosh - exactly the same as light. Coincidence ? No via Occam. Ole Romer had by then put a very good figure on light speed by watching the variation in occultation times of Jupiter's moons as measured on Earth.

So that is roughly where you chaps are at, and I really do mean that in all politeness. Light is speed constrained but what about gravity ? So what is the way out of this. I can't unpick/tweak the threads in your heads as a personal service and we don't need to anyway. In detail that involves several careful semesters at University level, with a more than annoying mathematical content, but I'll throw about some broad brush strokes shall I ? Let's put history aside for the moment and consider what makes best sense and agreement with present understandings. The 'modern' view. Anyone for a mini tute ? :-)

{ up next .... }

Cheers, Mike.

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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SpaceTime Mapping

SpaceTime Mapping 101

Spacetime is an unfactorable entity. Please consider it as existing in and of itself, unified, continuous and without any underlying roots/stratum/basis. Just is. Humans may overlay some convenient descriptive systems upon it, but spacetime was there long before we turned up. So this is not an anthropic view. There are an infinite number of possible systems one can use for that purpose. They are called 'observers' when really we mean a structured data collection facility.

 

Quote:
So not a walking/talking bipedal ape variant then. Certainly not some bloke sitting at a coordinate origin with a pair of binoculars watching the universe pass him by. Turtles could have invented GR if they'd had enough fingers ! Perhaps they already have and are ( slowly, carefully ) moving on to better things. Who can say ? ;-))

To achieve success - especially to avoid conundrum/contradiction - that observation facility has rules in it's preparation. In preparing any particular scheme we insert light propagation delay during construction to thus become an intrinsic feature of a single given system. Saves us getting caught out later. The rules for system construction are the same for all instances. When we have finished, as it were, studying some scenario with a system we may then go around ( or signal otherwise ) to collect up all the various relevant readings to make sense of whatever happened.

KEY POINT #1 : the time of some event/happening is that of a clock sitting at the event when it occurred. The fact that we may examine a record of said event sometime later on is interesting, but doesn't change the definition of what we mean when we say : so-and-so happened at this place and time.

spacetime_event.jpg

.... kindly burn that principle into your brainstem. If you don't then relativity won't make any sense.

We haven't yet got around to comparing or relating findings as recorded in one scheme in terms suitable for another. That's an extra task after we have made all the systems we choose to deal with. One observer ( remember to read 'suitably prepared data collection system' whenever I use that word from now on ) may compare notes, as it were, with another but only provided we have understanding ( which is where some complexity in maths lie ) when translating from one to the other.

 

Quote:
There are two 'types' of relativity. The Special and the General, so named because the second theory is a generalisation of the first. Of course we can then say the first is a specialisation of the second. Initially Einstein wanted the term 'Invariant Theory' but was talked out of it. It became 'Special Relativity'. Albert wanted to emphasise commonality rather than differences. But there you go, it happened that way and it stuck.

There are two types of observers ( sometimes also called 'frames' ). Inertial and non-inertial. I'll first deal with the easier of the two, inertial frames. There are many equivalent ways to express this inertial idea. I begin with the concept that is most immediately relevant here :

KEY POINT #2 : all inertial frames must measure the speed of any particular photon as 3 x 10^8 m/s { in MKS units & in a vacuum }

Now we had to add "in vacuo" so that the photon is unimpeded in flight ie. not bounced around etc so that the path length is increased by such interactions. We just want an uninterrupted transit, a 'straight line'*. Now there are two important implications here for this principle.

Firstly the speed of light is constant within any frame. This will be used to setup the frame itself especially the synchonisation of clocks at different positions. This is how we insert light propagation delay into the definition of the 'ruler' that we will use to make measurement claims. If in some calculation we only use that ruler ( or one derived from it ) then we automatically have the light propagation business in hand and conundrums won't arise in purely relativistic analyses. That's also a hint to not mix paradigms ....

photon_transit1.jpg 

The second is the clue for comparing measurement values between inertial frames, as we must have agreement on transit speed for a single photon. This will yield the various transform equations that give ( in gorrible algebraic detail ) the exact manner of how to reconcile records, of the same studied phenomena, from two different inertial frames. That is, as two different observers measure the same photon the exact numbers ( in the respective event records per frame ) will differ but that ratio distance/time will be the same for both :

photon_transit2.jpg 

Each observer will have their own private, independent system of measuring gadgets. Clocks and distance markers from respective origins. Each will have a set of four numbers ( three for length and one for time ) recorded for the endpoints of the photon flight.

So you can see that not alot of this is intuitive ( about the only thing that is would be speed = distance / time ). The inertial frames are those discussed and managed in Special Relativity. If no gravity is about ( or we assume is negligible ) then spacetime is mapped as above, also known as Minkowski spacetime. Hermann Minkowski was earlier a teacher of Einstein, when they butted heads a few times also, and later he picked up and formalised the mathematics of Special Relativity with geometric language. Einstein didn't like that approach but came around later, indeed realising that geometric thinking would be very useful for including gravity effects. Hermann died ( too ) young of appendicitis at 44 years old.

Cheers, Mike.

* You could, for an inertial frame at least, assert that a 'straight line' is defined by the path of a photon in a vacuum ! :-)

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

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