# Is time quantized?

Haelfix
Yes, I also find that quite awesome. There are so many things that make string theory fascinating that I can't help feeling there must be something there that Nature has used. It's possible that it's not the case and that it will turn out that string theory has no relevance to the real world (or maybe we will never find out) but it is so amazing that it's worth exploring further, IMHO.
As I learn more about it, I also feel that its almost guarenteed to be something related to the real world. If for no other reason, that it outputs nonperturbative information (or has a duality) with various field theories that most assuredly are of physical interest. Whether its the full shebang of gravity, or just a good description or dual of some sector thereof, I of course do not know.

But to say that it is a spacetime vector index implies a non-trivial relation between these (since they transform under a specific way under "Lorentz transformations of the ambient space") . This is the part that I don't quite understand. Do you see what I mean?
Mmm... Lorentz symmetry isn't much different from O(n) symmetry, and O(n) symmetry isn't hard to get accidentally. Having two of "something" and if each one of those "somethings" have quadratic interactions, then you automatically have O(2) symmetry.

xristy
Gold Member
Did you see any errors in Schiller?

Only one slight issue, he kinda demolishes... all of physics at the Planck scale. How valid is this paper?
I didn't see anything that seemed in error. He is simply going step-by-step through pretty uncontroversial physics and arriving at what I would say are rather obvious conclusions. I think the paper is interesting because it rather simply lays out the nature of the discreteness at the Planck scale without having to engage in advanced speculation.

Fra
I guess the meaning of emergence of spacetime is itself ambigous. Emergent from what? There seems to be more than one way to implement this. Also the meaning of background independence can be interpreted at will.

I think the simplest meaning of background independence simply means that it's not satisfactory to consider dynamical spacetime as perturbations around a non-dynamical background because the decomposition is ambigous.

One can also consider a dynamical background as evolving in a larger space of spaces. But then if the space of spaces is non-dynamical we have just moved the background one level. I still find this unsatisfactory.

From the information point of view, background independence should mean starting with a "random" or at least "minimal" prior structure. With structure I count also forms of the actions. To start with a structure, and given dynamical principles, but random information about the states. Then of course things will seem to emerge out of nothing. But then the fact that the framework itself contains implicit priors is ignored. This is the problem I'd like to see solved.

It's often innocent to ask a question, and then say "I have no idea what hte answer is" - I have no information. But the fact that a specific question is asked, implies some information IMO.

/Fredrik

xristy
Gold Member
I guess the meaning of emergence of spacetime is itself ambigous. Emergent from what? There seems to be more than one way to implement this. Also the meaning of background independence can be interpreted at will.
...
I think that Smolin in arxiv.org/abs/hep-th/0507235, The case for background independence, gives "...a careful statement of what physicists mean when we speak of background independence."

X

Fra
Yes I've read that paper by Smolin some time aog and it contained some good reflections.

"I would now like to broaden the discussion by asking: Does the relational view have implications broader than the nature of space and time?"

This relational and background talk isn't just about spacetime, it can be deeper than that.

It's common to not consider the dynamics of the theory itself as part of physics. The dynamics of the theory is at some level constrained to some sociological level in the scientific community. But if we consider how a particle views the world, then everything must be physical, including it's evolving view (theory). If you reflect over this, and add this to the relational views then I would like a deeper analysis than what I can see coming from say the string framework.

/Fredirk

xristy
Gold Member
I was motivated to simply clarify that the technical phrase "background independent" doesn't need to be taken as arbitrary or particularly ambiguous.

This relational and background talk isn't just about spacetime, it can be deeper than that.
I agree that a relational principle fully applied is about much more than spacetime -- unless by spacetime we understand that to be all there is, i.e., configurations thereof.

Without straying too far afield, it is worth noting that Rovelli in arxiv.org/abs/quant-ph/9609002, Relational Quantum Mechanics, applies a relational principle to other than an a priori background.

Ultimately there is no background and figure only relationality, but that isn't what the OP was asking about.

X

Fra
I was motivated to simply clarify that the technical phrase "background independent" doesn't need to be taken as arbitrary or particularly ambiguous.

I agree that a relational principle fully applied is about much more than spacetime -- unless by spacetime we understand that to be all there is, i.e., configurations thereof.

Without straying too far afield, it is worth noting that Rovelli in arxiv.org/abs/quant-ph/9609002, Relational Quantum Mechanics, applies a relational principle to other than an a priori background.

Ultimately there is no background and figure only relationality, but that isn't what the OP was asking about.
I think we agree.

Yes, I guess what I tried to add to the thread (my motivation ) is to suggest that to in order to try to answer what the OP really asked (clearly noone can, but we can reflect over it and what strategy we need) might require broadening the questions asked.

I agree this isn't what the OP asked, but then again, maybe in the quest for the answer these questions should be asked? :shy:

/Fredrik

xristy
Gold Member
It's common to not consider the dynamics of the theory itself as part of physics. The dynamics of the theory is at some level constrained to some sociological level in the scientific community. But if we consider how a particle views the world, then everything must be physical, including it's evolving view (theory). If you reflect over this, and add this to the relational views then I would like a deeper analysis than what I can see coming from say the string framework.
This is a bit puzzling.

Evidently by dynamics you mean how a group of physicists go about developing a theory. If so, I would certainly agree that isn't considered a fit subject for what physicists usually construct theories about.

Does the talk of "how a particle views the world" mean something like "how a particle (whatever that is relationally) interacts?"

In this context it isn't clear to me what is meant by physical beyond simply saying that the conceptual frame of reference of talk about particles is usually what we could call physical.

Smolin, Rovelli, Loll and their colleagues certainly seem to be working toward a deeply relational analysis of fundamental physics.

xristy
Gold Member
Yes, I guess what I tried to add to the thread (my motivation ) is to suggest that to in order to try to answer what the OP really asked (clearly noone can, but we can reflect over it and what strategy we need) might require broadening the questions asked.
I referenced Schiller's paper specifically to provide, in an informative manner, an affirmative answer to the OP's question: Is time quantized?. It seems clear that based on the physics we know from experiment, time is quantized. There may not be an agreed upon theory that neatly ties up how to make sense of the quantization, nonetheless all the evidence is that it is indeed quantized.

Developing that theory will undoubtably require broadening the way in which questions are asked, specifically adopting a relational stance to the questions themselves.

X

Fra
This is a bit puzzling.

Evidently by dynamics you mean how a group of physicists go about developing a theory. If so, I would certainly agree that isn't considered a fit subject for what physicists usually construct theories about.

Does the talk of "how a particle views the world" mean something like "how a particle (whatever that is relationally) interacts?"

In this context it isn't clear to me what is meant by physical beyond simply saying that the conceptual frame of reference of talk about particles is usually what we could call physical.

Smolin, Rovelli, Loll and their colleagues certainly seem to be working toward a deeply relational analysis of fundamental physics.
I think it's puzzling too, I was just making a loose associative reflection between these two scenarios:

- A scientific theory interacting with it's environment, where the theory is responding and changing to feedback. Clearly the interaction properties of the theory with the environment would be expected to be in part unpredictable, and in part related to the scientific method. The laws of dynamics in this context is closely related to the scientific method itself. Basically this is a kind of "ai thinking". Beeing non-specific to traditional physics. Here the focus is not a matter of never beeing wrong. Learning means gambling and experimenting, but survival also means we need to gamble clever. Random gambling may mean death. Random gamblers will not be selected in evolution.

- A "particle" interacting with the environement. Here the interaction properties are governed by the "laws of physics". In this picture, the laws of physics are not dynamical. They are fixed. In the case they disagree with experiment, we usually think that they are wrong. And not as much attention is given on the dynamical revisions of the laws themselves. So either the theory is right or it's wrong.

I guess what I was after is, where does the scientific theory live or manifest? Zurek said that what the observer is, is indistinguishable from what the observer knows. I like that wording.

Scientists are nothing but systems interacting with it's environment, right? What determins the interaction properties of a scientist - or a collection of scientists? Surely there are softly predictable patterns although complex, when you add the human aspects. The scientist respects the scientific metod. Why? Probably because the scientists that don't, aren't too commonly observed :)

Could we gain any insight by making this reflections, and nothing that in one abstract sense one major difference between say and atom and a scientist is a massive difference in complexity. What's the "scientific method" of a particles sujbective responses? And could this help us rethink our way of analysing physical the scientific method in physics, to "improve it"?

/Fredrik

Purely a thought. Since the energy is quantized and therefore matter is quantized, is it possible for time to be quantized?
The short answer is no. More precisely, Pauli's theorem (1926) asserts that a selfadjoint time operator is incompatible with a Hamiltonian with spectrum bounded from below. Hence impossible.

What about defining time as the reading of a clock? After all, reading a clock is a physical experiment that should follow the laws of QM. I never understood this until I read Rovelli's paper on partial observables, http://arxiv.org/abs/gr-qc/0110035 . A real experiment consists of two measurements, one detector A and one clock t. The partial observables A and t can not separately be predicted by the theory, only the complete observable A(t). Only complete variables correspond to selfadjoint operators.

If we have two clocks T and t, then T(t) and t(T) are complete observables and subject to quantum fluctuations.

arivero
Gold Member
The short answer is no. More precisely, Pauli's theorem (1926) asserts that a selfadjoint time operator is incompatible with a Hamiltonian with spectrum bounded from below. Hence impossible.
What I like of this answer is that it uses exactly the startpoint of the opening post:
Purely a thought. Since the energy is quantized ...

Of course, the energy spectrum of single-particle relativistic quantum mechanics is not bounded from below. But I'm going to read up on Pauli's theorem since it seems rather interesting. It seems there are a number of assumptions that might not apply.

Haelfix
The nogo proof of a time operator, at least that I know off is pretty much identical to Dexters post here, eg a 3 liner:

Like with the position operator, people fudge with this and try to enlarge the hilbert space in some way, etc etc (with not very satisfying or compelling results)

Fra
What about defining time as the reading of a clock? After all, reading a clock is a physical experiment that should follow the laws of QM. I never understood this until I read Rovelli's paper on partial observables, http://arxiv.org/abs/gr-qc/0110035 . A real experiment consists of two measurements, one detector A and one clock t. The partial observables A and t can not separately be predicted by the theory, only the complete observable A(t). Only complete variables correspond to selfadjoint operators.

If we have two clocks T and t, then T(t) and t(T) are complete observables and subject to quantum fluctuations.
The conceptual distinction between partial and complete observables by Rovelli is interesting but I am not sure if I find it satisfactory. I will read the article more carefully. I was able to skim the two first pages before I fell asleep last night.

My first impression would be that the difference is not distinct, rather a matter of degrees. I'm not sure if he means deterministically predictable probability (like in standard QM) - if so, I personally don't think there exists any fundamentally complete observable at all, but that's just me.

Also, it seems the partial observables may still have an a priori probability to be observed.

So I'd instead like to think in terms of relative degrees of predictability, like in different degrees of confidence in the probability measure. Partial, and complete observables of Rovelli might fit in as extremes in that picture, but there seems to be a domain in between, where partial observables are also "partial predictable" in the sense that their probability is not deterministically evolving.

I'll try to read that paper later.

/Fredrik

Fra
I associate to conditional probabilities.

If q is a parameter measured, t is a clock-variable measured, one can consider.

P(q|t), P(q) and P(t)

Now if the function P(|) was known and certain rovelli's reasoning would make sense to me, but P itself must be supported somewhere. And the most obvious place I can imagine is the the observers microstructure. And here I think the information capacity of the observer somehow constrains P.

The information capacity of the observer might also constrain the meaning of the intersection of q ant t as events. The memory size, means that the probability of an intersection must somehow depend on what data is retained? I think this decision is part of equilibration with the enviroment.

Since $$P(q|t) = P(q \wedge t)/P(t)$$

I can't accept the heuristic use of probability theory in this context. IMHO at least a part of the problem is the physical meaning of probability. People always tend to avoid it. I think of this as beeing processes taking place and beeing coded in the observes internal microstructure.

/Fredrik

Also, it seems the partial observables may still have an a priori probability to be observed.
Sure. Partial observables may be observed, but only complete observables can be predicted.

I find it useful to think about observation as the answer to a question. For a pendulum, we have two partial observables: the pendulums position A and time t, which correspond to the questions:

A - what is the position of the pendulum?
t - what is time, i.e. the reading of my clock?

We can answer these questions by observation, but our theory can not predict the answer. What can be predicted (probabilistically in the quantum case, and we need to know the system's state) are the complete observables:

A(t) - what is the pendulum's position at time t?
t(A) - what does the clock show when the pendulum is at A (modulo whole periods)?

Only complete observables are subject to quantum fluctuations and correspond to self-adjoint operators. A partial observable like time serves to localize an experiment and is a c-number parameter. The complete observable that you could build out of a single partial obserable would be

t(t) - what does the clock show at time t?

which is clearly not quantized.

Fra
Sure. Partial observables may be observed, but only complete observables can be predicted.
In the way Rovelli explains it, I understand what he means. Ie. he somehow argues that complete observables are relative. This makes sense. It's not too far from the idea that that conditional probability are more fundamental than absolute ones, and that all "real" observables must be conditional - that sort of makes alot of sense to me. It seems also very much inspired by GR. But there is more to it (I personally think this is good stuff, but I think it's not all the story)

What I like to question is the physical basis for this distinction. What does predict mean? I assume that with prediction Rovelli doesn't not refer to a guess. I think he refers to a deterministic prediction. And when that fails, he tries to restore determinism by instead imagining a probability space and then deterministically "predicts" the probability.

There is something with this that doesn't smell right to me. My first objection is that the distinction between a guess that later turns out wrong and a confidence deterministic prediction that is dead one, is defined in the future. Also if we consider probability distributions we furthermore need statistics to determine the distribution.

So in this view there is no solid ground for the probability space. At least not that I can see.

Don't get me wrong, I like Rovellit and I started reading his book some time ago and I like his sentiment behind the relational QM! but further up in his reasoning he looses me. And I think it's related to this.

I like to see explicitly the observer also brought into this reasoning. So instead of talking about P(a|b) and think that P is given, I like to think in terms of P(a|b|O) where O refers to the observer, and in a sense one can imagine each observer to implement his own measure P, and instead objectivity of this measure is emergent. But I don't think deterministically emergent. And evolution of observers then conicides with an evolution of measures P.

The problem now is how to end the sequenct P(a|b|c|d|...). I think the solution to this may be the observers complexity (related to info.capacity and "energy" "mass"). Since the measure lives in the observer, there may be a natural "cutoff" here, that can be physically motivated.

Only complete observables are subject to quantum fluctuations and correspond to self-adjoint operators. A partial observable like time serves to localize an experiment and is a c-number parameter. The complete observable that you could build out of a single partial obserable would be
I am somewhat hesitant to take the standard QM formalism too seriously in the context of trying to extend the theory. I think a review of the foundations will bring more clarity on this, and on the process we call "quantization". There is alot of stuff beneath the standard QM formalisms that I think should be relaxed, and therefor I expect possible tweaks to the conclusive reasoning based on standard QM. Therefore I don't feel confident using that as a tool of reasoning in this extended context.

/Fredrik

Fra
I see a connection here to a generalized sense to background dependence, and the concept of ad hoc splitting of the dynamica background into a fixed background and a dynamical perturbation.

Consider P(a|b) vs P'(a|b')

IMHO the decompositon P(|):s and b's seems to lack physical basis unless supplemented with more arguments.

b effectively makes a parametrisation of the measures of a.

/Fredrik

Prior to replying to your question ~ some relative Background Knowledge for you.
An advanced understanding of the 'formula' for gravity, has been developed by a United Kingdom research team during 1994-2008. Vital aspects have already been validated, by some of the most prestigious research organizations known to the scientific community. Preparation of Section One to a three-part presentation headed ' The Theory of Everything ', will present quantum gravity and its derivatives.
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Found it, thanks.

As I understand the "deltas"

Kronecker is discrete,
Dirac is continuous,

for time in signal processing.