Questioning Gravity
Hi J,
-Interesting grav frequencies range from DC (static acceleration) to the "sonic barrier(s)" of mechanical detectors. There are noise bands associated with material thermal harmonics. The gross harmonics of the detector also impose a band gap spectra.
You raise an interesting question about piezo crystal length and signal amplitude.
-Imagine stacked cystals as little batteries holding a charge. Voltage increases with serial units as does the weight of stacked acrobats in 1G. A single large crystal should act as you suggest.Orginally ('93) we had daydreamed a, say, forty foot long stack of, say, foot long crystals.
-Compared with a short crystal, a long crystal will be less thermally noisy and offer more working current to measure.
-Other factors to consider are crystal aspect ratio which may trade-off current for directionality.
-and scaling vs. molecular bond strength. The larger things are the weaker they act- so an elephant's bones are thickly proportioned compared to a mouse. Thus a phased detector or emitter array of microcrystals might out perform a single large (exploding) crystal. Imagine a chip tiled with quartz discs, built up in layers. One could bidirectionally "image" gravity.
-Mock Up Device- I'm looking for conductive adhesive to glop electrodes onto the crystal ends. David Deming made some cool dielectric ring mounts for the rocks on hand. Somebody in this town has tiny super sensistive transistors that can be externally attached to a macro device. Any submicron transistor might do...we've got millions, we just can't get to them!
-We need to run some numbers to quantify the potential for piezo grav detectors vs. existing resonant mass detectors. We need the constants for quartz under given pressure and temperature as well as operational values for "single electron" transistors. Also we need to know the directionality curve of piezo molecules of various aspect ratios in a given orientation to a grav emitter.
Have you heard the Cold Fusionesque buzz over the recent superconducting antigrav announcements? Its a very exciting revolution, if true.
-later...
-ds
------------------------------
I met your cousin the other day. he talked me out of the stupid hole
I dug myself into regarding detecting gravity.
Some more practical questions -
what frequency would gravity waves operate at?
Do you expect better sensitivity from longer crystals, or is the
response of a crystal to stretching more like proportional to
percent change in length?
If the latter is the case, then a longer crystal I dont think would be more sensitive-
lets say you had two crytals, a long one and a short one , both being
pulled by the same gravity - the long one would stretch more than the
short one, in proportion to the ratio of the lengths, but the percent
change of length (the change in length divided by the total length)
would be the same for both I think. Then the crystals would give the
same voltage out. Unless the response isnt proportional to % change.
But I think voltage out must be proportional to % change.
Anyway a longer crystal would be more directional I suppose.
After sa'turd'ay I will have time to work on such things (big honkin test done then)
if you are still intrstd in pursuing.
-------------------------------------------------------------------------------------
To: santos@88net.net
Subject: crystal consciousness
Cc: rutman@zilker.net
have been slogging through an IEEE standard on piezoelectricity.
Am trying to find what voltage to expect from a source
that changes the LIGO bar by 2*10^-7 meter
'barium titanate' is oft mentioned as having high piezoelectricity.
Got the quartz data...looks good.
Fused quartz is amorphous and non piezo while crystaline is piezoactive but, lacking data, I thought the two materials might share other properties. Your definitive reference data makes such assumptions unnecessary.
Once we have a handle on the sensitivity deficeit of a single detector, as proposed, we can postulate a large baseline array to meet the ful requirement.
-ds
>> The internal thermal noise of the gravity wave detector test masses depends
>
>I took a good class where one of the experiments my partner and I did was to
>measure thermal noise and shot noise - but like you said a while ago in
>jest, steeping everything in liquid Nitrogen is probably the best way.
>How does LIGO work, do you know>
>
>> A possible microscopic model for the loss mechanisms in fused quartz is
>> presented.
>
>Okay, whoa! Why did they think of fused quartz too? I wonder if they
>are doing the smae thing?
>
>Yyou were totally right about voltage being additive with length -
>I was confounded by voltage compounded
>
>I bet theres places around that have old silicon crystal-making equipment-
>for some reason I was just reading about the making of silicon chips by
>the
>growth of
>extremely pure but long crystals, with imperfections measured in
>billionths -
>they did it
>by melting along a line, moving slowly up the length of the crystal, and
>blowing the imperfections
>ahead of them on the path as they move along
>and this was in the seventies, so there may be places that have such things
>in semi-modernized garb, 5 years old maybe.
>It would then be possible to substitute quartz (Si02) for Silicon,
>possibly by adding two moles of oxygen for every mole of Silicon.
>Actually that prabably wouldnt work - youd need to react the Oxygen with
>the Silicon without exception, by mixing the two in a reaction vessel
>and separating the Si02 from the unreacted O2 and Si and Si0 and Si03 and
>Si2 O3 and whatver the #@ else grows up in such environs
>using 'standard methods'.
>
>Ok , so youd need to have pure Si02 instead of pure silicon, which is the
>problem
>we started out with, but the goal was to fix that problem, so by getting
>somewhat
>impure
>Si02, the method of strip sublimation will form a highly pure crystal,
>with the
>imperfections brushed to one end, except the first thing i read on it was
>that crystals so formed are called fused quartz and are inappropriate for
>uses
>of
>piezoelectricity. Maybe that is no longer true; the source saying such fuzed
>quartz was inappropriate was people assuming that quartz of that
>perfection
>couldn't
>be formed, and this source (I left you xeroxes that may have the
>year
>when it
>came out) might be out of date. Laters
> jeremy
>
Re: gravity amplitude
Yes, we know sensitivity is currently hopeless, and therefore an interesting challenge.
Unfortunately for LIGO the laser schemes have severe problems such as noise in the mirrors and can't be pointed at will. They will achieve far less than theoretically optimal sensitivity. If their instrument points toward the earth on one end it may be swamped by internal magma noise. If we aim our instruments at a tangent, toward the horizon, and use arrays, we may yet be in a game that no one is likely to win soon.
It would be worthwhile to explore achieving arbitrarily high Q in piezo by active cancellation and distributed arrays.
Raw crystal size is a factor. A monster (5 ft) crystal only needs to shuttle a single electron to and from the quantum transistor, at a rate just above mean probability, to amount to a signal.
Even with an "inadequate" sensor, in principle, given a large enough data set (eons?), quantum spikes, and sufficient wavelet or fourier crunching, gravity signatures are there to be found.
I enjoy thinking that we revolve not just about earth's center or the sun, but also around the galactic center, which revoves around a cluster and so on, so in some real sense we ourselves are entrained to the vastest gravity scales. Even if just our body were floating by itself in space it would follow these motions. Personal Celestial gravity detection:What's so hard about that ;^) ?
Even if LIGO wins the solution race we may happen upon some useful concepts, even chasing a lost cause.
Until we have numbers on our scheme for comparison, and then ruthlessly optimise our design, I'll maintain goofy optimism.
-ds
>Dave, I think the problem of sensitivity may kill us -
>from what I've read the LIGO fellows are using
>a 2 mile long beam (~4 Km), which is going to contract and
>cause interference in their laser beams - so I figure
>if they use light of wavelength 2*10^-7 meters (200 nm,
>2000 Angstrom) and they're hoping for a contraction
>of one wavelength, that's a percent change of something
>like 2*10^-7 meters / 4 km = 5*10^-11, which may be
>way undetectable by peizo. I'll try to get a better
>picture of piezo response as a funct. of length change
>tomorrow at the PAM library.
> jeremy
>
>
To: santos@88net.net
Date: Tue, 14 Jan 1997 10:43:23 -0600 (CST)
Cc: rutman@zilker.net (Jeremy Rutman)
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Modulus of elasticity of cast aluminum = 5*10^11 Dynes/cm^2
Modulus = Force * length of rod / (cross sectional area * length of
deformation)
If length of deformation = 2000 Angstrom (10^-7 meter)
length of rod = 1 Km (10^3 Meter)
cross sectional area (guess) = 10cm^2
Then the force = 10^-19 dyne = 10^-24 Newton
If (if memory serves) the piezoelectric const. is about
10^-12 Coulomb/Newton, then we'd have 10^-36 Coulomb
if we had a 1Km crystal - which unfortunately is less
than 1 electron as theres something like 10^19 electrons in
a Coulomb of charge
Perhaps if we adjust the "precharge" on the crystal to where an electron "rides the fence" of jumping from crystal to transistor it will start to "quantum tunnel" back and forth in period with the AG (alternating gravity) signal. Given supremely low noise this effect might overcome the grim calculation you made.
Also, a large array of smaller crystals will amount to a large virtual crystal and any true detector, however weak, will show a greater probability of "quantum flux" that occaisionally pops the signal above the sensitivity floor.
The modulus of quartz is presumably much less than aluminium, at least at room temp.
What physical event is your grav signal value based on?
-ds
>Modulus of elasticity of cast aluminum = 5*10^11 Dynes/cm^2
>Modulus = Force * length of rod / (cross sectional area * length of
>deformation)
>If length of deformation = 2000 Angstrom (10^-7 meter)
>length of rod = 1 Km (10^3 Meter)
>cross sectional area (guess) = 10cm^2
>Then the force = 10^-19 dyne = 10^-24 Newton
>If (if memory serves) the piezoelectric const. is about
>10^-12 Coulomb/Newton, then we'd have 10^-36 Coulomb
>if we had a 1Km crystal - which unfortunately is less
>than 1 electron as theres something like 10^19 electrons in
>a Coulomb of charge
>
>
To: santos@88net.net (David Santos)
Date: Tue, 14 Jan 1997 14:47:00 -0600 (CST)
Cc: rutman@zilker.net (Jeremy Rutman)
In-Reply-To: <199701142042.OAA12012@mail.88net.net> from "David Santos" at Jan 14, 97 02:42:10 pm
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> Perhaps if we adjust the "precharge" on the crystal to where an electron
> "rides the fence" of jumping from crystal to transistor it will start to
> "quantum tunnel" back and forth in period with the AG (alternating gravity)
> signal. Given supremely low noise this effect might overcome the grim
> calculation you made.
>
> Also, a large array of smaller crystals will amount to a large virtual
> crystal and any true detector, however weak, will show a greater probability
> of "quantum flux" that occaisionally pops the signal above the sensitivity
> floor.
Ok, if we actually had a single-elctron transistor going then youre right
actually youre right in any case, no matter how much noise is riding on
a true signal, enough detectors/long enough time will reveal the mad truth
> The modulus of quartz is presumably much less than aluminium, at least at
> room temp.
Yes, from the crystal modulus you could find out
how much the crystal would stretch
> What physical event is your grav signal value based on?
>
> -ds
I'm cribbing from the LIGO project , guessing that whatever it is
they're trying to detect is going to smush their rod by a laser
wavelength
>
> >Modulus of elasticity of cast aluminum = 5*10^11 Dynes/cm^2
> >Modulus = Force * length of rod / (cross sectional area * length of
> >deformation)
> >If length of deformation = 2000 Angstrom (10^-7 meter)
whoops lost the 2, 2000A=2*10^-7m
> >length of rod = 1 Km (10^3 Meter)
> >cross sectional area (guess) = 10cm^2
> >Then the force = 10^-19 dyne = 10^-24 Newton
> >If (if memory serves) the piezoelectric const. is about
> >10^-12 Coulomb/Newton, then we'd have 10^-36 Coulomb
> >if we had a 1Km crystal - which unfortunately is less
actually this is independent of crystal length i beleive -
amt. of charge is prop. to force only
> >than 1 electron as theres something like 10^19 electrons in
> >a Coulomb of charge
at any rate we know my calculation has gone bad somewhere
since an electron microscope moves its tip by subatomic lengths,
so subatomic smushings should give readable signals.
I'm sure somebody somewhere makes these things - I
think Ill look up the guy at Boston U in the
article i was reading
GRAVITAS
Based on odd clues I think that SC components are required to overcome parasitic resistence and impedence on the (big long) circuit shorting (a tiny electron!) across crystal. If we design in a monopole/ground mode this may not matter as much.
At any rate adding SC should be easy enough (LiqNitr)and we want to chill anyhow.
Found lost quartz file, got new SEM file. Lets offer el SEM GuRu planefare/party to lighten our task. NO telling how fucked up our SEM is after sitting-on-cinderblocks for a decade.
A mere "+/- kilometer long crystal" (meaning array) based on your back-of-envelope calculation is good news, I say. We can design it. Some folks could even afford it. A planet size crystal would have been scary.
It seems one might pass LIGO, etc., as a later model starship may overtake a relic ship in reaching a star. It would be fun(ny) to sign on all the Keys of Enoch crowd as a cutting-edge self-funding gavtelescope net, each with a small gizmo to maintain.
note- the proposed cosmological binary neutron source Period needed- faster better.
recap- ultra low noise, powerful filtering/big sample (Curious, what's Fourier transform problem size record?), and vast time-correlated highly directional arrays will suffice.
~ds
In contemplating a "Superconducting Tunneling Electron Piezogravscope" (STEP), a superconducting ground plane could gather electrons from the end of the crystal and conduct them to a nanoneedle which would be carefully moved close to the quantum transistor(s). A SEM would no doubt fry a chip so we couldn't just supervise the connection of components. Squid supervision might work. We could use the SEM and its fine mechanical stage to calibrate assembly, then , without the electron beam we reproduce the motion with the circuitry. Cooling complicates things.
No doubt local chipheads know the right way to rig this.
I'm shortly starting to pump crystals with high V AC.
Impedence would still be a consideration in SC, if I am not mistaken so geometries are important.
It just occured to me that a piezocrystal's Q might best be manipulated from its opposite end with less potential interference with the delicate sensing end. The active damping of noise harmonics problem should be considered in light of the acoustic speed barrier and target period.
-ds
Predicting certain effects secondary to time dialation due to acceleration is simple. In the case of a mechanical watch, acceleration causes greater "rolling friction" in the watch and the watch would be slowed, much as a vehicle is more slowed by rolling friction when loaded. Firing a watch from a cannon, short of destroying it, would clearly tend to cause it to pause.
What Bill is saying can be put more simply- If you watch a clock and accelerometer in tandem you can calculate relativistic effects. Stated that way, I disagree that it requires particular "clever"ness.
Bill's comment about piezo echoes our engineering take on the problem of gravwave detection.
Bill, can you point us to any piezo based grav research? Weber's original notions included piezo. The net is dominated by amorphous resonant masses and laser beams as antenna schemes.
Our current working concept calls for a time correlated network of chilled giant (>1 meter long) natural quartz crystals with quantum dot/single electron transistors fabed on to the ends ("Superconducting Tunneling Electron Piezograviscope" (STEP)). Massive signal filtering (long sampling, heavy crunching) could, in principle, extend sensitivity to high arbitrary values based on a notion of probalistic "quantum spikes", occuring even in instruments calculated to be too insensitive for direct detection.
Bill, please critique this notion. How do you think this concept compares with the mainstream?
Thanks,
-dave santos
>
>> --------------------------------------
>> recip: bjt@riemann.usno.navy.mil
>> subj: Gravity Q&A;>> namefrom: jeremy rutman
>> from: rutman@zilker.net
>> source-level: bs. physics
>> review: special relativistic effects are observeable not to any
>> particular observer but only is relative from one to another. If I look
>> at my watch it will always look to me like it runs normally. Only someone
>> in a different frame sees it as slow Same for length. Now you are trying
>> to detect the effect of what i may be thinking of wrongly as a region of
>> temporarily increased relativistic effects.How can you hope to measure
>> any effects at all if your rulers and clocks are also experiencing the
>> effects of the wave? --------------------------------------
>>
>
>You do it by being clever, and by realizing that there are other forces at
>work besides gravity. The others are much stronger, and can overcome the
>effects of the spacetime distortions. Certain objects will
>"ring like a bell" when hit by a gravity wave. If the detectors do not
>ring, then the detectors will detect the residual effects. One could use
>pressure sensitive crystals, piezoelectric crystals, to measure the
>movement. Things like that. It is still not easy to do, and there have
>been no confirmed sitings of gravity waves.
>
>
>
>
>Gravitation Theory Group
>University of Maryland
>College Park MD USA 20742
>> Predicting certain effects secondary to time dialation due to acceleration
>> is simple. In the case of a mechanical watch, acceleration causes greater
>> "rolling friction" in the watch and the watch would be slowed, much as a
>> vehicle is more slowed by rolling friction when loaded. Firing a watch from
>> a cannon, short of destroying it, would clearly tend to cause it to pause.
>
>Ok, that answers it.
>acceleration is detectable. the gravity waves are not
>waves of 'special relativity' (which deals with relative velocity,
>not acceleration) they are waves of acceleration (general relativity)
>which is always detectable if only in the pit of your stomach.
Gravwaves do involve special relativity in that there are velocity differentials sweeping thru the system. Simple accelerations are easier to detect, however.
>hard-thing-to-think-about-for-the-day
>if i'm falling in a free-fall elevator then I
>can't detect it. so you can only feel (detect)
>gravity when you're not freefalling. we're not
>freefalling on the earth since we push against
>that which causes the gravity. But can we detect
>(and i mean directly - think about tidals later)
>the pull of the moon, since it seems we freefall in its pull?
>if we are in freefall for every gravsource but earth,
>is it true that acceleration is detectable as i claimed?
>(i think the thing about the watch is that every point
>is accelerating at the same rate, nobody is pulling
>against their neighbor, so no effects)
Freefall, at best, only postphones detection. Imagine freefalling thru a torus; passing to the other side the decceleration is proprortional to the masking of freefall. Plus, as one starts freefall toward a gravity well, acceleration is felt (less if terminal velocity, as in freefall in an atmoshpere is achieved). Actually, a sensitive enough accelerometer will always show suspicious changes in coursing a gravwell field. This is the slingshot effect used by planetary probes.
>
>> What Bill is saying can be put more simply- If you watch a clock and
>> accelerometer in tandem you can calculate relativistic effects. Stated that
>> way, I disagree that it requires particular "clever"ness.
>
>> Bill's comment about piezo echoes our engineering take on the problem of
>> gravwave detection.
>
>yeah that's pretty cool that theres so many hints that this is the
>way to go.
Yes, it is cool that piezo is not ruled out, and no one seems to be working it like the South Austin Gravity Hackers' Club.
>
>> Bill, can you point us to any piezo based grav research? Weber's original
>> notions included piezo. The net is dominated by amorphous resonant masses
>> and laser beams as antenna schemes.
>>
>> Our current working concept calls for a time correlated network of chilled
>> giant (>1 meter long) natural quartz crystals with quantum dot/single
>> electron transistors fabed on to the ends ("Superconducting Tunneling
>> Electron Piezograviscope" (STEP)). Massive signal filtering (long sampling,
>> heavy crunching) could, in principle, extend sensitivity to high arbitrary
>> values based on a notion of probalistic "quantum spikes", occuring even in
>> instruments calculated to be too insensitive for direct detection.
>>
>> Bill, please critique this notion. How do you think this concept compares
>> with the mainstream?
>>
>> Thanks,
>>
>> -dave santos
hi,
Whose are the included quotes below?
Re. Lost Xeroxes, if you mean the quartz constants, they are in the file, which was lost from sight for a short time.
I've consulted a cryogenics guru on home brew insulation. Our aluminized mylar (for blimps), in a multi layered sandwich with foam sheeting, should take us to low K. Mylar holds up at low K, the metal is a good radiant barrier(s), and the foam slows conducted heat. We need superconducting electronics supplies, not just for low signal resistence, but to avoid electical heating within cold chamber.
Draft Abstract is a good start. We could make an unordered list of all relevant concepts, order it according to precedence, then convert to a well styled narrative.
The quartz etching note is suggestive. One concept needing mention in abstract is the hypothetical sensitivity advantage of using giant natural crystals. Synthetic crystals are probably not made in such large sizes and would have to be aggregated more for a given sensitivity. Vast arrays of micro crystals favors manufacturing, and the trade-off needs study.
-ds
>Here's a calculation of tidal force (difference in gravity
>bet near and far sides of the earth from the gravitating object)
>>rEarth
> 6.371e+8
>#ths is all in centimeters, seconds, grams type units
>>rOrbitofEarth
> 1.4957e+11
>>rOrbitofMoon
> 3.8e+10
>>SecondsPerYear=60*60*24*365
>>
>>SecondsPerYear
> 3.1536e+7
>>
>>rOrbitofEarth=1.4957e+13
>>rDistanceToStar=c*SecondsPerYear
>
>>#This is for a star 1 lt year away
>>rDistanceToStar
> 9.454254899e+17
>
>>1/(rOrbitofMoon-rEarth)^2 - 1/(rOrbitofMoon+rEarth)^2
> 4.646875041e-23
>>1/(rDistanceToStar-rEarth)^2-1/(rDistanceToStar+rEarth)^2
> 3.015682909e-45
>>tidal(x)=1/(x-rEarth)^2-1/(x+rEarth)^2
>>
>>tidal(rDistancetoStar)
> 3.015682909e-45
>>tidal(rOrbitofMoon)
> 4.646875041e-23
>>tidal(rDistanceToFarStar)
> 3.015682912e-51
>#this last is for a star 100 lt. years away.
>
>I found an excellent crystals book but my xeroxes have mysteriously
>disappeared so I'll need to get it again - the guy says if you
>put some kind of acid on a crystall it'll start getting eaten away into
>mountainous lanscapes and that this reveals sections of opposite
>handedness! that there's lefthanded and righthanded sections in most
>crystals,
>living side by side, and i guess you tell the difference by the way they
>reflect light or something. Also quality quartz crystal is grown in big
>underground vats at 1000 atmospheres pressure, at 1mm a day.
>
>
Is there, even in theory, such a thing as a homogenus grav field? This would have to be a steady state universe where mass is perfectly distributed, but quantum nature forbids such "perfection". The detector would have to have zero extent also, or tidal gradients would exist.
>Imagine an object in free fall in an
>homogenous gravity field: every material
>point in the object experiences the same
>acceleration; thus no two points in this body
>experience any relative motion. No bodily
>contraction or expansion occurs; if our
>object was a spring scale, it would not
>stretch; similarly, any device intended to
>locally* determine whether an acceleration
>was occuring or not, would necessarily fail
>to do so. For example, our compounded
>trajectory around the sun, through the milky
>way, and around the universe, cannot be
>locally felt or manifested; we are freely
>falling through this path, and (to the extent
>that the fields involved are homogenous) no
>two points accelerate any differently from
>one another, thus no forces are felt within
>or by any objects travelling with us on our
>trip through the universe.
>
>Non-local measurements, as of an orbit
>against a background of 'fixed' stars,
>suffice, to reveal gravitational effects, as
>will local measurements made in an
>inhomogenous field. The inhomogenous field
>causes a relative acceleration between
>various points of a material body, so for
>example, a spring can be stretched or
>compressed due to the difference in
>acceleration between its various points.
>Inhomogenous fields can be either tidal
>effects of static fields, or due to different
>'heights' along a travelling gravitational
>wave.
>
>The greatest relative acceleration a
>gravitational field or wave can impart to two
>points of a body is the difference between
>the highest peak of the field and its lowest
>trough. Continuing with the notion of a wave
>passing through the local region, this left-
>right (x-axis) distance between highest and
>lowest points** is one half the wavelength of
>the wave in question. Thus detectors made to
>measure gravitational waves due, for example,
>to astronomical phenomena of period 500 Hz,
>will optimally be of a length
>L=wavelength/2=c/(2*500)=3*10^5 meters=300Km.
>Detectors made smaller than this length will
>feel stretchings less than the maximum
>possible; the smaller the detector, the less
>of an effect can be measured. Higher
>frequency waves are thus from a practical
>point of view easier to measure, as are waves
>of greater amplitude. Greater amplitude can
>be had from greater accelerations in the
>body/ies causing the wave. In the case of
>stellar wave-sources one has no control over
>frequency or amplitude save that of the
>choice between various stellar objects; if
>one could create a terrestrial gravitational
>wave source of great enough amplitude and
>high enough frequency, then in theory one
>could detect gravitational waves without the
>impracticalities of Kilometer-scale
>detectors.
>The piezoelectric crystal (Santos) provides a
>felicitous solution to the generation and
>detection of (necessarily high frequency,
>high amplitude) gravitational waves. Direct
>coupling of electrical potential to
>acceleration is achieved through the
>piezoelectric and converse-piezoelectric
>effect; piezoelectric crystals are capable of
>sustaining great accelerations and thus
>creating high amplitude waves; the frequency
>and thus wavelentgh are controllable and
>tunable; the distance between source and
>detector can be minimized (avoiding the
>deleterious signal attenuations caused by
>detection at stellar distances); the
>relatively weakly-coupled off-diagonal
>crystal coefficients mean the crystal is a
>directional source and detector to better
>than one part in 10 (ratio of pickup along
>other axes to measurement (z) axis).
>
>next section - numbers
>find max. acceleration ever attained with
>piezo (or maybe 1/2 of it for economics)
>calculate wave amplitude due to this
>acceleration, given crystal's size
>find how wave attenuates as it travels -
>1/r^2? 1/r?
>at any rate, find acceleration imparted to
>detector at given distance
>Piezoelectric constants can relate
>acceleration to voltage
> P=ex=sigma=sufrace charge, e=1.2C/m^2,
>x=strain=change in length/length
>
>
>=percent change in length
> x=dE ,d=piezo strain coeff.
> -x=sX s=compliance coeff
> -X=cx c=strain coeff
>(stress=c*strain=force/area)
> need relation of acceleration to stress.
>F=ma, stress=F/area, but what to use for m?
>find voltage due to above accel.
>find noise voltage
>noise in conductor: avg(v^2) =4RkT df
>where R=resistance of cond., k - boltzman's
>const, T=temp, df=freq. range
>formula goodto order 10^11 Hz
>
>
> *Without recourse to measurement of
>trajectory
>**in the direction of the long axis of the
>crystal, which has the greatest coupling;
>coupling from perpendicular directions is
>reduced by the factor of {off-diagonal matrix
>element/on-diagonal matrix element}
>
>possibly useful quotes
> "This assumption of exact physical
>equivalence makes it impossible for us to
>speak of the absolute acceleration of the
>system of reference, just as the usual theory
>of relativity forbids us to talk of the
>absolute velocity of a system..." (A.
>Einstein, On the Influence of Gravitation on
>the propogation of light, 1907")
>
>"Now let us imagine that each of the bodies (
>has been surveyed by means of measuring instruments
>at rest relatively to itself, and let the surface of S1
>prove to be a sphere, and that of S2 an ellipsoid of revolution.
>Thereupon we put the quesstion - What is the reason for this difference
>in the two bodies? No answer can be admitted as epistemologically
>satisfactory, unless the reason given is an observeable
>fact of experience." a.einstein, the foundation of the gen. theory of rel.
>annalen der physik, 49, 1916.
>
Yeah, copping a simulator from a graphics filter is cool. 3D graphics renderers, which compute light paths (refelection and absorption, but likely not bending and interference)would work to make some pretty simulations.
For a roll-ones-own I was thinking of a semantic net ordered as matrix dimensions where a grav signals interact like LIFE simulations. This could be done most sleazily (almost just a simulation of a simulation) as Web table input, client pull/server push, using animated GIF eyecandy (The operative notion is that mere HTML and a suffiently rich file structure can constitute a Universal Turing Machine).
'been thinking about temporal drift within an oscillating crystal...standing nodes age faster than rapidly moving parts...Does this history change the crystal's properties? Heat/stress effects have to be addressed in the model.
>I was thinking about a simulator for gravity propogation; i can do the program
>and output a raster of numbers, but i dont know jack about windows programming,
>if you know how to take a picture (raster) of bytes and put it in a pc window i could
>do it for the pc.
>There's a pretty good related effect in photoshop ; if you use the 'gradient' tool to make
>a radial gradient, then set it 'darken only' and make some more radial gradients,
>they run into each other like the fields of two masses running into each other and adding up.
>sort of.
>
To: santos@88net.net
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Subject: Welcome to gravity
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> Is there, even in theory, such a thing as a homogenus grav field? This would
> have to be a steady state universe where mass is perfectly distributed, but
> quantum nature forbids such "perfection". The detector would have to have
> zero extent also, or tidal gradients would exist.
You're right, that this is entirely hypothetical - I was calryfiying
for myself that one can only measure inhomogeneities. Analogous to
measuring voltage where the only thing that you can measure is the difference
between two points and not the 'absolute voltage' of a given point - its always
the difference between that point and another. The numbers section needs work but
it looks like a pretty straight path through the thicket. In particcular
there's a question i am having about converting the acceleration that one end
feels away from the other, into a force; F=ma but i am confused on what to
use for m.
I was thinking about a simulator for gravity propogation; i can do the program
and output a raster of numbers, but i dont know jack about windows programming,
if you know how to take a picture (raster) of bytes and put it in a pc window i could
do it for the pc.
There's a pretty good related effect in photoshop ; if you use the 'gradient' tool to make
a radial gradient, then set it 'darken only' and make some more radial gradients,
they run into each other like the fields of two masses running into each other and adding up.
sort of.
===
Sender: owner-gravity@zilker.net
Precedence: bulk
Reply-To: gravity@zilker.net
Subject: force calculation from known acceleration
If a material is given some arbitrary acceleration
profile over one particular
dimension, the average acceleration in that
direction is the value of an integral
over "a dot nhat" where nhat is the unit vector in
that direction, divided by the
interval over which you are integrating. For the
simple case of acceleration that is linearly increasing
in the x direction
the average acceleration is
1/2m((xmax)^2-(xin)^2)/(xmax-xmin)
where xmax is the final point in the x direction, and
xmin is the inital point, these two points demarking
a line in the x-direction**, and m is the rate
of increase in acceleration with increasing x.
In particular for a=0 at x=0, and a maximum accel.
of 1000g, over a region (crstal) of some length l, the
average acceleration is half the maximum acceleration,
or 500g. The average force thus exerted is
1/2 amax*mass of crystal, as long as relativistic speeds
have not been reached. At an acceleration of 1000g it
takes .5 c/a seconds before you are at half the speed of
light (where relativistic effects reach 11.5 percent),
or .5 (3*10^8m/s)/(10000m/s^2)=1.5*10^4 seconds.
Unknown to me - maximum accel acheivable for crystal-
why not limited only by voltage reachable
Do we need to approach c for gravitational
wave to be generated?
**which is the leg of a triangle-on-rectangle whose
area is represented by the expression 1/2((xmax^2-xmin^2))
Sender: owner-gravity@zilker.net
Precedence: bulk
Reply-To: gravity@zilker.net
Subject: force calculation from known acceleration
If a material is given some arbitrary acceleration
profile over one particular
dimension, the average acceleration in that
direction is the value of an integral
over "a dot nhat" where nhat is the unit vector in
that direction, divided by the
interval over which you are integrating.
For the simple case of acceleration that is linearly
increasing from 0 in the x direction
the average acceleration is
1/2 Amax
In particular for a maximum accel.
of 1000g, the average acceleration is half the
maximum acceleration, or 500g. The average force thus
exerted is 1/2 Amax*mass of crystal, as long as
relativistic speeds have not been reached. At an
acceleration of a it takes .5 c/a seconds before you
are at half the speed of light (where relativistic
effects reach 11.5 percent),
or 1.5*10^4 seconds.
If we operate at 60 Hz then speeds reach
Amax*2/(60*Pi) which is gonna be super un-relativistic,
exact calc later when im on my mac
fyi i'm using the factor called 'gamma' as my measure
of relativistic effect - gamma(v)=1/(sqrt(1-v^2/c^2),
lengths and times get multipled or divided by the gamma
factor to give the length as measured in frame moving
w.r.t. that in which obj is stationary.
Unknown to me - maximum accel acheivable for crystal-
why not limited only by voltage reachable
Do we need to approach c for gravitational
wave to be generated?
To: gravity@zilker.net
From: santos@88net.net (David Santos)
Subject: Re: corrected calc
Cc: robotman@ecpi.com
Sender: owner-gravity@zilker.net
Precedence: bulk
Reply-To: gravity@zilker.net
Grav waves are generated at any acceleration and so are relativistic
effects, although, at slow accelerations, are currently too weak to be of
experimental signifigance.
The "speed limit" of quartz is the thermal barrier where molecular bonds are
unable to hold against accelerations. A conjecture is that a hi frequency AC
signal can allow atoms to jiggle within their bonds at higher accelerations,
but this is only doable on a nano scale due to the need to locally pump the
crystal lattice. Still, atoms boil off at some point.
A useful model is to consider acoustic waves as a special case of heat- a
sharp blow to a stone cleaves it with precise thermal energy and the stone
scarcely heats, while a diffuse "hot knife" would be very wasteful of btus
to do the job. If we control gavity in high amplitude pulses we achieve a lot.
A vast phased array of nano piezo morphs can generate coherent grav waves,
but is a hairy fab, big budget excercise. Fortunately, to detect low
frequency cosmic grav waves, a single large crystal "sees" the signal
thoughout its mass at (almost) the same time, so a single electrode
suffices. Suitably placed multiple electrodes on a big crystal, or an array,
can determine phase angles.
Given temporal effects, etc., maybe we're inventing the Crystal Ball ;^)
(Ignore the last statement).