# Pullin: most accurate clock possible

1. Jul 17, 2004

### marcus

Pullin et al have an article addressing the question
what is theoretically the most accurate clock one can build
to measure intervals of time less than a certain $$\inline T_{max}$$

If the clock must be able to time intervals as long as, for example,
$$\inline T_{max}$$ = 1 billion years
then how finely can such a clock discriminate
what is the smallest $$\inline\delta T$$ difference in duration that it
can detect?

initially they employ an argument of Salecker and Wigner
and they proceed to observe that to make the Wigner clock distinguish more finely one needs to make it more massive, but not increase the size, and so
if one tries to make the clock more and more accurate eventually it will collapse and become a black hole, which is after all very good because that is the best kind of clock anyway
It is a fine argument and you should probably read it in the original
Pullin et al paper
http://arxiv.org/hep-th/0406260

now if the clock has to last a billion years then it must be a black hole that will not go and evaporate sooner than that, so this lowerbounds the mass and upperbounds the ringing vibration frequency and lowerbounds the $$\inline\delta T$$

so the discrimination of the clock is bounded by the lifetime duration of the clock.

In fact the formula for the best possible clock is very sweet.

$$\inline\delta T$$ is simply going as the cube root of $$\inline T_{max}$$

this is in natural units, understandably, so a billion years is 5.855E59
So if we want to know how fine time differences we can discriminate we just take the cube root of that number and get 8.366E19

this is an incredibly short interval of time. what a wonderful clock!

After all a second is 1.855E43
so this $$\inline\delta T$$ that the clock can distinguish is over 20 orders of magnitude briefer than a second. It is E19 and the second is E43.
-------------

I decided I would get a really long-lasting Pullin clock, one that will last for 100 billion years
so $$\inline T_{max}$$ is 5.855E61

then the discrimination or "tick" of the clock is 3.88E20

this is still over 20 orders of magnitude smaller than a second
--------------

obviously these people are making very good clocks so I thought I should advise everyone about it

http://arxiv.org/hep-th/0406260

the paper is actually by Rodolfo Gambini, Rafael Porto, Jorge Pullin
but Pullin is the name I recognize because he edits the American Physical Society newsletter on gravity and quantum gravity and such. So I call it Pullin et al, for short

Last edited: Jul 18, 2004
2. Jul 17, 2004

### rayjohn01

Thats fascinating -- but I did not realize they could time black hole rotation
or otherwise time it -- what signal does it give , i'd like to look out for it.

3. Jul 17, 2004

### marcus

black hole vibration modes

it is all theoretical work, sometimes with computer simulation used

Probably 20 or 30 papers have been published so far on it

you can find the papers by searching with the keywords

"Quasinormal vibration modes" and "Black Hole"

Two of the famous papers in this subject are by two harvard guys who sometimes used to post at PF
Lubos Motl
Andy Neitzke

Maybe you know all this and are just kidding.

It is crazy to talk about picking up black hole vibrations as if it were a real possibility at this stage in human history.

But if one is going to design the theoretically most accurate possble clock that could theoretically ever be constructed by any civilization then one has to consider such extreme cases

even if you had a stable oscillator in front of you that was doing 1020 cycles per second
how would you make a phaselock loop and a counter and stuff to use such a high frequency oscillator to measure time? this is not in our civilization
it is the theoretical limit of precision of time itself

Last edited: Jul 17, 2004
4. Jul 18, 2004

### marcus

rayjohn01 pardon my sometimes mistrustful nature. i thought you were kidding. Yes, agreed! It is really fascinating.

the fascinating thing for me is that time itself has a fundamental inherent imprecision.

Also, if you are still around, I want to make the point that this is another one of those places where the Planck units or natural units make things nicer.

when thinking of a long period of time, yet still not the age of the universe, one wants to say something like "1 billion years"

But an earth year is not such a neat interval in planck time unit terms
In planck time units it is 5.855E59

So to make the example cleaner, why not say simply that the
$$\inline T_{max}$$ = E60

we'll say the longest period time we want the clock to measure is simply E60 planck units of time. (in earth year terms it is about 1.7 billion years)

then the cube root of E60 is simply E20

to take the cube root you just have to divide the exponent by 3
the cube root of 1060 is 1020

so the finest possible precision of the clock, the "tick" of it, is E20 planck time units.

(that happens to be still smaller than human instruments can distinguish, since a second is about 23 orders of magnitude greater, so this is very
'theoretical' but the fact remains that any real clock has limited precision and this is a fundamental universal limit---or so Pullin and friends find)

If you look at the Gambini Porto Pullin paper you will see I am just
using their equation (1) on page 1.
http://arxiv.org/hep-th/0406260

5. Jul 18, 2004

### marcus

It is a basic premise of Quantum Theory that only what can be measured has meaning.

this is also a scientific premise too---things have to have an operational definition if you are going to talk about them

so if you are going to talk time it has to be something that is defined operationally as result of some measurement

Gambini Porto Pullin find out a fundamental fact about time, that it is intrinsically imprecise. I will say this in natural units---in Planck time unit terms---to make it simpler to say:

If you want to measure intervals as long as E60 then the precision you can measure them with (the "tick") has to be at least E20

you cant hone it down any finer than E20

that is already so fine we cant tell, but the point is that any clock
has a finite lifetime and a finite precision.

--------

Gambini Porto Pullin derive a subtle consequence from this inherent imprecision of time.

All information dies.

there is a universal fundamental rate that all information gradually fades out.

this rate can be called the "Louisiana rate" because Pullin lives in
Louisiana
or perhaps can be called the "Montevideo rate" because Gambini is living in Montevideo, or wherever I dont remember at the moment.

it is a very important rate, at which all information dies, and they calculate it and it should have a name---so maybe it is too silly to call it the Louisiana rate and one should say "the GambiniPortoPullin" rate of dying of information.

this rate, if it is for real, kicks the tail of the Black Hole Information Paradox.
(you can read what they say about that in the paper cited)

6. Jul 18, 2004

### rayjohn01

No Kidding

Hi Marcus
I realize the theoretical nature of what your saying but on that footing I had some queries
a) what exactly was ticking so to speak I think you went on to say vibration rather than rotation.
b) You must have a way of reading the clock -what do you read i.e. how does this motion communicate to the external world is this in the form of gravitational waves?
Does the ticking depend on the hole history i.e. what happens if more matter is drawn into it , I know the horizon expands but are it's modes of movement somehow isolated from this or are you assuming that the device is already isolated in space.
IF it can communicate outwards the timing information is there a way in which the reverse happens i.e. info ( say gravity waves) induce timing alterations.
Even neutron stars altho' highly stable show drifts sometimes erratic changes as tho' the internal structure has modified , I understood that a modern view of holes is not quite so adamant about a conceptual singularity
perhaps indicating structure.
It always appears that the perfection of theoretical performance ( witness ceasium clocks) is never actually achieved through some influence and as accuracy increases the influences can be smaller.
I just wondered if such considerations had been included in the theory behind it. Ray.

7. Jul 18, 2004

### marcus

I think you are right---in the form of gravitational waves.
Since i am not the authority, just someone watching the experts at their play, I have to go back to the papers of Sakar Hod, Lubos Motl, etc and look to see what they say.

I will get links to some of those papers. There have been so many about BH vibrations by now it is a bit daunting to wade thru.

I could be wrong (and others around PF might know more) but I think their idea (Hod, Motl, and the other BH vibration people) is that the BH gravitational field is a rigid structure like a bell and that it has "ringing" frequencies.

If that is right then to build this crazy-sounding extreme Louisiana clock you would put a gravity-wave detector outside a black hole to pick up the ripples, and hook a counter to that.

then you would have to drive the vibrations somehow because the hole is constantly losing energy carried off by radiation----it is hard for me to imagine, maybe you have to have an outside source of gravity waves to agitate the black hole with, and drive its resonance----maybe you have to periodically feed a bit of mass into the hole.

since there is a big danger of being wrong I will go to arXiv now and
search "quasinormal mode" and "black hole" and try to find a link that
makes it more explicit what is vibrating and how one might use the vibration as one does other oscillators.

neat stuff, if a bit strange

8. Jul 18, 2004

### wolram

By Marcus.
Gambini Porto Pullin derive a subtle consequence from this inherent imprecision of time All information dies.
I maybe confused Marcus, but this implies that distinct energy levels
can not be maintained, I have just read some about "crispy states",
part of QM i think, and this seems relative to BHs and the ultimate
Clock, then again i could be up that gum tree

9. Jul 18, 2004

### marcus

here is a recent PhD thesis
that may provide a good bibliography and save me the trouble
of assembling one----PhD thesises often can serve as a guide to the literature

http://arxiv.org/gr-qc/0404093

Quasinormal Modes and Gravitational Radiation in Black Hole Spacetimes
Vitor Cardoso
PhD thesis, December 2003.

"Black holes play a fundamental role in modern physics. They have characteristic oscillation modes, called quasinormal modes. Past studies have shown that these modes are important to our understanding of the dynamics of astrophysical black holes. Recent studies indicate that they are important as a link between gravitation and quantum mechanics. Thus, the investigation of these modes is a timeliness topic.
Quasinormal modes dominate almost every process involving black holes, in particular gravitational wave emission during, for example, the collision between two black holes. It may be possible to create black holes at future accelerators, according to recent theories advocating the existence of extra dimensions in our universe. It is therefore important to study in depth the gravitational radiation emitted in high energy collision between two black holes in several dimensions, and also to make a theoretical study of gravitational waves in higher dimensions.
In this thesis we shall make a thorough study of the quasinormal modes of black holes in several kinds of background spacetimes. We shall investigate the gravitational radiation given away when highly energetic particles collide with black holes, and also when two black holes collide with each other. Finally, we shall study the properties of gravitational waves in higher dimensions, for instance, we generalize Einstein's quadrupole formula."

Wait. This thesis is 200 pages. It will be too long to download, especially if one only wants the bibliography from it, for access to the literature.
I will look for something else.

10. Jul 18, 2004

### marcus

11. Jul 18, 2004

### marcus

dont worry, just pretend all the time that the good old QM that we know and love is 100% true and believe that the pure state of being in some particular energy level can last indefinitely

having a peaceful orderly mind is far more important than being a stickler for finicky detail

the nice thing is that the rate GambiniPortoPullin are talking about is so slow that it takes tens of billions of years for anything untoward to happen-----as a rough guess we will never notice that time-evolution is not perfectly information-preserving. The Universe is deterministic and if you did really use a rubber then the girl will definitely not get pregnant.

Please dont be confused about this! It is an effect that is so slow that it is as good as not happening. It just happens to resolve a theoretical puzzle having to do with the evaporation of black holes (which is another of those extremely slow things, if we are talking about ordinarysize non-microscopic holes)

Theoreticians are like this, they create some baffling difficulty and make noise about it (using plenty of metaphors) and then they invent something else equally baffling that solves the problem. Maybe someday a special home will be made for them on one of the Channel Islands, or in the Hebrides, where they can be happy and not bother anyone.

Last edited: Jul 18, 2004
12. Jul 18, 2004

### kernelpenguin

I'm new to this...

Could someone tell me what the shortest possible time period is and how it was... 'invented'? And what does it define or what defines it? Is it the smallest possible time it takes for the smallest possible thing to happen?

And did anyone else think of Pratchett's "Thief of Time" when reading this thread? :uhh:

13. Jul 19, 2004

Staff Emeritus
Thief of time is a great book. There are just tons of good time travel stories.

14. Jul 19, 2004

### wolram

kernelpengui
Could someone tell me what the shortest possible time period is and how it was... 'invented'? And what does it define or what defines it? Is it the smallest possible time it takes for the smallest possible thing to happen?
------------------------------------------------------------------------------------------------------------------
I thought the Plank unit 5.391*10^-44s, the smallest meaningful to us

15. Jul 19, 2004

### marcus

many people do seem to have the hunch or opinion that this unit
marks the timescale below which we will never be able to measure
or that we will never be able to detect a difference in time intervals
that small

I never saw a proof that it is a sharp cutoff, or that the right quantity is exactly that and not half that much or 2 pi times that much. the arguments about this are kind of vague AFAIK.
Vague arguments are not necessarily bad or useless.

When a lot of people share an intuitive hunch and have some plausible reasoning (even if not exact and rigorous) to back it up, that can be, for me anyway, something to take seriously.

I share the belief that the planck timescale (or somewhere down around there) is apt to turn out to be a realm of new physics. but I can't say exactly what that means.

Probing brief time intervals is more or less the same as probing high frequencies------as short wavelengths go with high energies----and using the most familiar methods it would seem well-nigh impossible to ever get to planck scale (energy, frequency, etc) in order to probe things at that scale. If one relies on the fashionable means of the 1960-1980 era, namely bigger and bigger accelerators, one would never get there. Not on this planet anyway. But humans are ingenious and will no doubt find other means besides routine "high energy physics" to explore nature at that Planck scale.

I still dont have a clear idea of what it means to say Planck time is the "smallest meaningful" or "smallest measureable" time interval. Maybe someone else has a clear-cut operational meaning to give for this.

16. Jul 20, 2004

### wolram

Marcus, would it be correct to say that in theory every unit of time is
devisable,? Time seems so different to other dimensions", But the original
question asked, "for something to happen", could this be an infinitely small
time?

17. Jul 20, 2004

### marcus

Wolram, you answered kernelpenguin's question the right way, I think. He said
You said the planck time unit is 5.39E-44 sec.

that does it.
It is the only candidate fvor "the smallest time it takes for the smallest thing to happen"
It has been around for 100 years, with people gradually beginning to suspect that is what it is. But nobody knowing for sure.
So you told him what the unit was. Thats about all anyone can say.
I just got excited by your mentioning that, and felt moved to give my own perspective on it.

It is a really neat time interval and we should look at the formula for it sometime.

18. Jul 20, 2004

### NateTG

Shortest measurable time segment

In the first half of the 20th century, Heisenberg came up with the Heisenberg Uncertainty Principle, which relates to quantum theory, and indicates, among other things that the maximum precision which time can be measured is related to:
$$h \leq \Delta t \Delta E$$
Where $$h$$ is plank's constant, $$\Delta t$$ is the precision of time measurement, and $$\Delta E$$ is the precision of the energy measurement.
As the time interval gets smaller, the energy involved gets larger, so, if we assume, for a moment that we're using the mass of the universe, we get
$$\Delta t \geq \frac{h}{M_u}$$
as the smallest conceivable measurement of time - this is approximately $$10^{-90}$$ seconds.

I believe the $$10^{-44}$$ figure is calculated using the plank length, and the speed of light.

19. Jul 20, 2004

### marcus

the mass of the observable universe keeps increasing all the time as light reaches us from farther and farther away.
the mass of the universe may well be infinite, or it may be finite, but it is utterly unknown to us, we can only say it is at least this big, at least as big as the mass of what is so far observable., but there is no indication that it is not much much bigger

but suppose we knew the mass of the universe, how would you proposed to design an instrument that used the mass of the universe to measure some small intervals of time?

oops, have to go. well, so far i dont understand your post Nate