Relativity observed at a small scale

Bikeman (Heinz-Bernd Eggenstein)
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Mike Hewson
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Relativity observed at a small scale


Yeah! Amazing! ( We were just talking about this in another thread ) Using a clock to measure distance and speed ... Einstein would be grinning ear to ear. :-)

I was quoting a ( differential ) GPS unit as potentially able to elicit this effect, but you'd get a much higher degree if you could lug one of these around. They're aiming to improve down to 1cm in distance.

Oh my goodness! One second in 3.7 billion years .... so we meet at about the origin of life on this planet ( replicating molecules or whatever ), go our separate ways - wait for the atmosphere to have gaseous oxygen etc - then later meet at the NIST lab saying " ..... where have you been? " :-)

This could certainly change the slant on the phrase "sorry I'm running late ....." :-) :-)

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: ... Using a clock to

Message 99767 in response to message 99766

Quote:
... Using a clock to measure distance and speed ... Einstein would be grinning ear to ear. :-) ...


OK, so we have timepieces precise enough to measure Earthly gravity gradients...

Does this mean that we can now directly test Einstein's equivalence principle for gravity and acceleration?

Does this also mean that we no longer need to be ignorant of our state in a gravitational field assuming there is a measurable gravity gradient?...

There must be some good scope for new tests and proofs in that!

Keep searchin',
Martin

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Mike Hewson
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RE: Does this mean that we

Message 99768 in response to message 99767

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Does this mean that we can now directly test Einstein's equivalence principle for gravity and acceleration?


As the EP is a limit argument ( smaller & smaller space and time intervals ), then yes.

Quote:
Does this also mean that we no longer need to be ignorant of our state in a gravitational field assuming there is a measurable gravity gradient?...


Errr .... I've always known which way was down. Try dropping something. :-) :-) :-)

Seriously, yes, as ( provided the clocks are not malfunctioning ) then an equal rate of time passing when separated puts the magnitude of the gravity gradient below some measurable threshold. After all if you slide one clock along the bench top, and not raising/lowering it in what we think is up/down direction, then both will read the same rates, yes? However .....

While we can effectively probe the nearby space by comparing the two and wind up with a measurable vector/grad field, this too partly depends on the history of the clocks. If one of them spends time sitting 'upstairs' and running faster, then upon returning 'down' it will return to the previous rate as the 'ground floor' one - but not so as to cause the time values to agree ( the ground floor clock will read an earlier time ). For that, the travelling clock would then have to go 'downstairs' for a while, running slower than the ground floor counterpart before returning to get the time values to agree. Well it would, if you 'timed' these excursions right! :-)

So I suppose you could have a series of out & back transits of one clock in a given direction ( with respect to the other ), noting the differences with each trip, in order to map the field gradient. You could reset each clock to equal time values before each trip if the 'absolute' values worry you. You see, to be precisely true to The Relativities' scheme of time measurement you'd have to bring the clocks back together for comparison purposes OR have a pre-arranged synchronised rods n' clocks lattice ...... this is another way of saying that moving the clocks apart ( which requires accelerations ie. stops & starts ) alters their time rates.

This is why the original SR schema of clock synchronisation across distances uses light signals to correlate separated clock settings, so that one needn't assume anything about the behaviour of clocks while in motion. One can match the rates of separated clocks ( and all clocks are separate from one another because two can never occupy the same space at the same time ) by a succession of synchronisations. If two are set at 'midday' in the usual Relativity way, and then later require an adjustment of one because a synchronising signal reveals discrepancy, then one can deduce a rate of variance - so many seconds per hour or whatnot - and so by fiddling with one or other clock's rate-setting mechanism cause ( by degrees and trial ) successively better agreement at later synchronising attempts.

For those who are confused by this, please don't despair! Try remembering Einstein's definition of time - "that which is measured by clocks" - to avoid esoteric discussions of 'meaning'. At least by having an operational program to follow one can remain self consistent. One significant problem is that natural language doesn't readily accommodate such descriptions. Our everyday, and from birth, situations don't encompass noticeable relativistic scenarios. Which is why it is anti-intuitive. There's a self referential aspect to phrases like 'time going faster' alas ..... :-(

Cheers, Mike.

( edit ) One could ask the question as to how can we define the time for spatial co-incidence using macroscopic objects, using a differential technique, given that one can't actually meld one into another? After all if they are aiming to measure as little as one centimeter accuracy, then how big/little can a clock be to do that? You are now potentially talking of time differences within the substance/extents of the clock itself now! For a particle interaction in an accelerator setup say, you'd talk of back-tracking from detectors to somewhere in the beam line - the collision vertex. I'd argue for a similiar limiting process. Do these measurements ( differential clock rates ) along a specific line but at varying distances. Project the results to zero displacement for that direction, even though one never measured at zero. Repeat for all directions of interest. Compare the deduced zero values from all these directions. I'm trying to answer the question, in practice, of how to " ..... bring the clocks back together for comparison ....".

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

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RE: RE: Does this also

Message 99769 in response to message 99768

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Quote:
Does this also mean that we no longer need to be ignorant of our state in a gravitational field assuming there is a measurable gravity gradient?...

Errr .... I've always known which way was down. Try dropping something. :-) :-) :-)


And in space, or in a free-falling elevator, noone can hear you scream... :-p :-)

Quote:

Seriously, yes, as ( provided the clocks are not malfunctioning ) then an equal rate of time passing when separated puts the magnitude of the gravity gradient below some measurable threshold. ...

While we can effectively probe the nearby space by comparing the two and wind up ...


I thought we'd moved a long way away from the old metal coil spring things! ;-)

Bad puns aside... Time interferometry?...

I wonder if a laser gyroscope could be modified...

Keep searchin',
Martin

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Mike Hewson
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When we talk of clocks,

When we talk of clocks, observers et al we are really meaning any measurable physical process. We nominate one aspect of a situation as reflecting quantities we find of interest. No electron runs around being labelled as 'mine' or 'yours'. We can choose to partition the universe into sets of particles, some of which are 'clock-ish' for instance. Alot of texts about relativity ( & physics generally ) don't emphasise this arbitrary nature of selection of subsets of the contents of the universe. So we don't really need to have Kaptain Klingon scoot past in a spaceship at near light speed to demonstrate time dilatation. A muon shower from a cosmic ray hit in the upper atmosphere will do just as nicely ( extended decay half-life as viewed from the ground related to high speed ).

Laser gyroscopes are in effect performing an integration upon lots of little accelerations. So you mark your position and velocity as the submarine leaves harbor, go underwater for a few months and the laser array becomes a highly accurate inertial platform. In contrast to the moon shots where star field alignments were regularly required en route and after critical manouevres. In between such calibrations, accelerations are integrated to velocities and integrated again to displacements. Radio timing to and from Earth also played a role, particularly the moment of (un)masking of line-of-sight transmission as they emerged/went from/to the other side of the moon. Prior to the first landing Neil Armstrong, quite correctly as it turned out, was fairly worried about 'platform drift' : inaccuracies sneaking in as time progressed due to mechanical limits upon the gyros. He detected early on in the descent that they were arriving early at certain landmarks ( or moonmarks? ) which implied that they were going to land 'long'. Partly this was due to ignorance of the gravity field nearby the moon - non uniform concentrations of mass - and partly from inertial platform inaccuracy. Strictly the 'inertial platform' is the time dependent three axis dynamical set of position, velocity and acceleration. His timely acknowledgment of this became crucial when the chosen landing site was found to be strewn with rocks on closer inspection ..... and what a cool guy he was in handling all of this. And Buzz banged out the numbers to him in an even monotone and watched the alarm panels .... :-)

So what do I need in practice to be able to call something a clock without getting stuck in self referential circles? Ultimately it's a gut thing I reckon :

- an a priori expectation of regularity, whatever that really means.

- utility to align or calibrate with other clock-ish constructs. That way I can relate 'a clock tick' to 'one orbit of the moon' for instance.

- simple reproducibility ie. I have a prescription for duplicating clocks such that when they appear to vary we could attribute that to environment/circumstance rather than error or intrinsic variance of the clock. This implies that 'identical' clocks can be made to march together when co-located.

There may be other useful criteria. I also had thought of 'time interferometry' ( great minds think alike and fools never differ ) and have come up with a gedanken type of setup and process that doesn't involve too much high technology :

Firstly, have any of you done timing adjustments to a camshaft or distributor for the old style car ignition electrics? Well, back in my day, you had ( by various names like 'dynamometer' ) a stroboscope which would flash to illuminate a flywheel in synchrony with a spark plug firing. The flywheel would have a mark on it and a corresponding mark on the engine block to indicate 'top dead center'. This means that when the marks are lined up a certain piston would be at the geometrical top of the stroke. By rotating the base of the distributor one could advance or retard the spark with respect to this point in the four stroke cycle. You would see this stroboscopically ( which 'edits' the motion to reveal a specific but recurring event ) by the timing mark on the flywheel 'moving' with respect to the engine block mark - clockwise or anti-clockwise depending. [ By the way if you advance the timing right it'll run a tad rough when idling but it just purrs in the power band. ] So strobes are good for relative timings.

The second element in my scheme is a metronome. This is a spring driven upside-down pendulum adjusted in period/frequency by moving a weight along and back of the shaft which is the oscillating arm. Click-clack, click-clack, click-clack ...

The third element is the sextant of old. It's basically a monocular optical system which overlies two images from separate directions. One will be looking at the horizon, the other at an object like a star. As this is generally on a moving deck it is hard to keep things still when you want. All you need to do is adjust the internal angle of the sextant so that for some moment the star appears on the horizon. You then read off the angle from a scale and that is the elevation or whatnot of the star above the horizon. The Apollo guys used more modern versions to give angles between the Earth/Moon and some obvious stars, pop this into some pre-computed table and out comes your position ( with respect to Earth and Moon, a key matter of interest ).

Putting these all together I make a bunch of metronomes which I carefully calibrate to run at the same rate ( at my length co-ordinate origin ) when their little shaft weights are set to some position. I place these clones at points of displacement nearby or distant that are of interest ( so I have a system of length defining rods as well ). I now get a sextant to co-align image pairs of these metronomes ( images which are suitably enlarged if one is more distant ) and fire a shutter to open briefly so as to view the other metronome arm image when the shutter triggering metronome arm image is at a particular position. The images are viewed and compared at one place mind you.

Do I now see the other metronome arm at some constant position in it's swing?

If yes, then the two clocks are in effect running at the same rate.

If no, but the other metronome arm is advancing in position, then that metronome is running faster than the metronome that fires the shutter.

If no, but the other metronome arm is retreating in position, then that metronome is running slower than the metronome that fires the shutter.

( lets ignore issues of 'aliasing' - one strobe period picking up several frequencies - as that can be solved by doubling and halving of the shutter/strobe frequency, then seeing what happens. )

Metronome pairs that vary in rate, and compared over a long time, will wax and wane with their relative stroboscopic arm positions. I could count how many shutter firings it takes for a faster/slower metronome to return to an arm position equal to the other. This counts how many whole cycles it takes to be out of phase by one cycle. If it takes 2000 per 1, then the rate is different by 1 part in 2000 ( 0.05% ). That is : one metronome has click-clacked 1999 or 2001 times for the other one click-clacking 2000 times. I'm describing the equivalent of heterodyning of radio signals by the way.

Now I can map the nearby spacetime/gravity-field by noting which pairs of metronomes do what. One very useful metronome is at ground zero right next to me, but I can still do separated pairs neither of which is that one. This process fulfills all prior relativity timing schemes, I've just given an elaborated example. Note that even if I assume there is no delay between the sighting of a metronome arm position and the firing of the shutter to then note the position of the other metronome arm, the rate comparison is still valid as I don't care for any absolute phase. For a given pair I can cross check by swapping which metronome fires the shutter, so I swap observation of which metronome I deem faster/slower ( and invert any phase lag due to my apparatus for that matter ).

I'd thank Fizeau ( ? ) for the strobe/shutter idea as he used it to estimate the speed of light some time ago.

Cheers, Mike.

( edit ) I could for example place a laser behind each metronome arm, so that the beam is briefly occluded when the arm swings in front of it. This 'chops the beam' and the fall and rise in intensity at a distant point I could use to trigger a shutter.

( edit ) Whoops, I should have emphasised that the metronome's arm swing is basically determined by the wound spring mechanism and the moment of inertia of the rate adjusting mass at a given position along the arm. If the gravity gradient from other bodies across the dimensions of the metronome is small compared to that which spans the extents of the field you want to measure then the absolute value of acceleration due to gravity at any specific point is not a problem. If you like the metronome will run the same rate regardless of which way is 'down'. You could swivel them in place and this makes no practical odds for the comparison between metronome sites. But if it worries you, one could always include a series of rate comparisons at different orientations for each pair of metronomes ..... that would sort it!

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

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RE: in a free-falling

Message 99771 in response to message 99769

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in a free-falling elevator, noone can hear you scream... :-p :-)

Keep searchin',
Martin

Actually at my old work we could her the lady scream all the way to the bottom when she fell into the elevator shaft! She had pried the doors open and jumped out only to lose he balance, due to her high heels we think, and fell back into the partially open shaft, dieing from the sudden stop at the bottom. Apparently she had been stuck in one for many hours many years prior and decided it was not going to happen again. ;-)))

tullio
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A rather difficult but

A rather difficult but interesting paper from "Nature communications":
Quantum interferometric visibility
Tullio

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