# Quantum time

1. Mar 28, 2005

### wolram

Is it correct to think that, in QG at a fundamental level there is no
time evolution , and 10-40 seconds is the smallest measurable time
period? I have looked at various papers, and it seems that even though
10-40 seconds is the smallest time unit ,many "Timeless events", can
occure beyond this limit.

2. Mar 28, 2005

### setAI

10^43 operations per second- any smaller time unit is meaningless because all quantum parameters in the universe are "frozen" in their states until the next flop- the universe is essentially static frames of Hilbert-space configurations which flop 10^43 times a second- there could not be any continuous time in a discrete space with a speed limit [c]- the time quantization would automatically be established by the propagation of information at c from one planck-area to the next- any "less" time and all the planck-areas in a space would be identical to the moment before- therefore no change/motion/time would have occurred-

basically: quanatized space [planck length ~10^-35 m] divided by the maximum speed of possible changes in the space [c= ~10^8 m/sec] = quantized time [~10^-43 sec]

Last edited: Mar 28, 2005
3. Mar 29, 2005

### marcus

I agree with setAI that the usual approximate figure figure for the planck time is 10^-43 second

so I would ask your question over again in the same words except with a time interval that is a thousand times smaller, namely 10^-43 second instead of 10^-40 second.

it is an interesting question and one concrete thing to ask is

Could a clock be built that ticks 10^43 times a second?

Is there a limit on how fine a clock you can build?

Eugene Wigner asked this question (he was a nobel-grade physicist of the mid 20th century) and wrote a paper about it. You are in good company.

Rodolfo Gambini wrote a paper last year where he tried to improve Wigner's result.

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

he found that there was a limit on how fine a clock you could build if you wanted it to run for some definite time. If you insisted on the clock LASTING a while then that limited your choices. Very fine clocks that tick a lot per second (so you can measure very fine time differences) do not, according to Gambini, last very long. He proved a formula about it.

I just saw another argument that you cant measure distances finer than planck length. (when the lightwavelength gets too small the light collapses to make a black hole). It goes along with not being able to measure distance finer than planck that you cant measure time finer than planck.

maybe a clock that ticked faster than planck would collapse to make a black hole.

I guess I generally agree with setAI except I dont know that space and time are made of discrete bits. It is sufficient that there are physical limits on how fine you can MEASURE and that has the same practical effect as if the world were discrete (but it isnt theoretically the same thing)

Last edited: Mar 29, 2005
4. Mar 30, 2005

### wolram

But what is a clock? only in quantasised time , is time limited to a finitley
small division, why can time not be smooth and have no divisions? I find
it difficult to imagine a "timeless", period, where events occures, but none
preceede the other.
please exuse spelling as my checker is defunct.

5. Mar 30, 2005

### marcus

I didnt say time is not smooth.

I didnt say time is broken up into bits.

I do think that there are theoretical limits on how precisely and reliably we can measure it.

the bunch of theory called "quantum" is very much about the limitations on measurement-----like the heisenberg trade-off between measuring position and momentum (there's a limit on how accurately you can pin things down).

6. Mar 30, 2005

### marcus

distance can be smooth
spatial extent can be smooth and not broken into "bits" of length of some definite size

and yet even tho it may be continuous, nature may impose limits on how accurately we can measure it

suppose you have a cylinder cavity and you want to use a lightwave to measure the length. you count the humps of the wave, or the nodes, from one end to the other

(actually people do determine distance very much like this, with a standing wave or some other wave as a kind of "ruler" and the nodes as the nicks on the ruler)

you drive the measuremtn to be more and more precise by using a wave that is shorter and shorter wavelength, you keep jacking up the frequency or the photon energy of the wave to get higher precision. What is the limit?

the limit is gravitational collapse

when you have increased the frequency up to where the wavelength is shrunk down to Planck length, then there is so much energy concentrated in so small a volume that the light energy collapses to a black hole.

it is a theoretical calculation. it gives a theoretical limit on how fine you can determine length

It doesnt say that space is "broken up into little bits". it doesnt say that it is or that it isnt. space might be smooth continuum or it might not.
let's not overstep what we can reasonably say

what we can say is there are limits on our ability to measure length, to how fine we can determine it

7. Mar 30, 2005

### marcus

same with time

a clock is just a steady frequency
or a stable oscillator what you measure duration of other stuff with
by counting the humps,

it is like you measure the length of a cavity by a standing wave "ruler"

clocks also have a black hole type limit

that is what Gambini described in that paper. I think it is a good one.

and 1958. there is a paper by him in 1957 and another by him and Salecker in 1958, and last year Gambini, whom I respect highly, was hard at work continuing the line of thought Wigner initiated in 1957. that is a kind of quality

Last edited: Mar 30, 2005
8. Mar 31, 2005

### wolram

By Marcus
you drive the measuremtn to be more and more precise by using a wave that is shorter and shorter wavelength, you keep jacking up the frequency or the photon energy of the wave to get higher precision. What is the limit?
----------------------------------------------------------
I agree our measuring methods must have a limit, but it is interesting to
speculate about the finness of time and if it has a reality in sub micro
states and if plank time is a meaningful measure.

9. Mar 31, 2005

### marcus

limitations on what and how fine one can measure are at the heart of quantum theory

as I guess you know this----that one of the famous interpretations of QM is that if you cannot measure something (even in principle) because of some quantum mechanical limitation then it is meaningless to ask about it

something like that. probably I am saying it wrong

for instance, if you cant tell which slit the electron went thru, if the experiment is set up so that even in principle there is no way of knowing, then you cannot say it went thru one or the other

we really need someone else to tell us about this, it is about the Interpretation of QM------the Born Interp., the "Hidden Variables" interp, etc.

without getting into complicated issues, the core feature of any quantum theory is there are two separate entities the Observer and the Other thing, and a quantum theory tells you what the Observer can and cannot observe, what he can know and not know, if he measures one feature of the thing then whether he can go and measure some other feature (like position and momentum), how one measurment affects another, possible outcomes of measurment (spectra), probabilities, uncertainty.
the reason every quantum theory has a hilbertspace is that it is a convenience for representing uncertainty inherent in what one system can know about another.

when you "quantize" a classical theory you introduce some mathematical paraphernalia like a hilbertspace that can represent essential LIMITATIONS ON KNOWLEDGE and especially limitations of a fundamental kind on how precisely things can be measured.

the curious thing is, nature seems to want us to do this, because when you introduce the gear representing uncertainty the theory calculates better numbers. singularities are removed. everything works better

the hydrogen atom can exist because nature insists on a certain leeway of uncertainty. you'd think that the electron would spiral right down and stick to the proton. but she doesnt like that because then you'd be too certain about where the damn thing is. it is only nature's insistence on vagueness that keeps us all alive.

(this is what they realized IIRC in 1925 or so: quantizing explains the stability of the hydrogen atom, a famous moment in history. it had worried people)

adding an intrinsic indefiniteness to the picture makes it more realistic (better numbers, fewer paradoxes)

a major philosophical issue, ever since 1925, has been this: if you can't measure something for some fundamental reason, then does it make any sense to ask which way it is? if you cant tell, should you ask?

if you can't measure finer than planck, then does it make sense to ask whether something is 1.1 planck units long or 1.2 planck units long.
Maybe it is "both and neither" the way the electron goes thru "both and neither" slit(s).

Last edited: Mar 31, 2005
10. Mar 31, 2005

### wolram

The laws of nature seem to have been" forulated", to limit human
progress, they restrict us to sub ligh speed travel, how much mass
energy can be put in one place, how far we can see both micro and
macro, i just wonder if any of these are real bounderies, or if they
are a veil that maybe lifted one day, to say it is meaningless to speculate
on something that is unkowable is correct, but it is a brick wall to us
humans, but maybe someone will come along with a wrecking ball one
day and free us from our shackles.

11. Mar 31, 2005

### marcus

bars become rungs

12. Mar 31, 2005

### marcus

that's pretty decent writing wolram.
what appears at one time to bar progress might on another day become part of the ladder
I cannot answer the implied question, of course

Last edited: Mar 31, 2005
13. Mar 31, 2005

Staff Emeritus
I have to say that in some ways the advanced theoretical physicists speak with forked tongues. On the one hand they characterize relativity, both special and general, as "effective theories", essentially large scale/low energy approximations to some unknown more general theory. On the other hand they are punctillious about building in the Lorentz transformations into their new physics just as it were truly the undelying theory that Einstein originally thought it was.

There are cracks in this wall, and I don't mean crackpots! Marcus has noted the work in Doubly Special Relativity, and though wormhole physics is looking more and more unlikely (both Visser and Susskind have recently written against wormhole and space warp FTL), all hope is not yet gone. Maybe Something Will Turn Up, as Mr. Micawber used to say. (See Marcus for chapter and verse).

14. Mar 31, 2005

### marcus

Shamefully, I dont know my Dickens :uhh: