Is Time Quantized? Exploring Theories and Possibilities

[Tachyonie]

Purely a thought. Since the energy is quantized and therefore matter is quantized, is it possible for time to be quantized? Are there any theories to would support that idea? And perhaps, if time is quantized then what about space (as in space we move in) itself?

 

[peter0302]

The real question is "is spacetime quantized" and the answer is no one is sure yet. If you have ever heard of "First Quantization" and "Second Quantization" then you'll appreciate that spacetime would be the "Third Quantization", a major evolution in quantum theory (Second Quantization refers to QFT, the quantization of fields). It would, one hopes, unify QM and General Relativity, which has not yet been done.

 

[Tachyonie]

Yes I ment spacetime sorry, I just couldn't remember how to phrase it properly.
Thanks, Ill try to google the "Quantizations"

 

[peter0302]

Wikipedia usually works great for this stuff too! The articles tend to be extremely accurate.

Also I'll add my own two cents on all of this - while energy clearly comes in small packets that we call quanta, and spin and charge are also quantized, the vast majority of physical quantities remain continuous values. The energy spectrum of photons is completely continuous, as is momentum, kinetic energy and everything derived from it, and, as far as we know, spacetime coordinate. No one really knows what it would mean to quantize spacetime. Is every possible physical location a point on a discrete grid like pixels on a computer monitor? What would that mean for SPECIAL relativity, let alone General Relativity? These are all unanswered quesitons.

 

[Fra]

This is related to the question of what the physical basis of time really is, and what the physical basis of quantization really is.

The usual way quantization is treated is often either fairly heuristic, or arbitrarily axiomatic by starting with a classical model and then quantize it. And the resulting models have been succesful, but nevertheless it's easy to get a feeling of lack of deeper understanding.

I personally don't see clearly how a continuos state space would be distinguishable from a discrete state space. Because any real observer are likely to have a limited observational resolution. I personally see the continuum in most of our models as a mathematical model. Ie. the continuum isn't necessarily physical. Then one might argue that if the continuum is indistinguishable from a discrete model, there are mathematical ghost degrees of freedom that lack physical basis. Therefore i would rather like to replace the description with the equivalence class of models that allows both continuous as well as discrete spaces.

But my gut feeling is that I have hard time to appreciate the concept of a physical continuum, from the point of view of information capacity. Sure one can imagine that there may be a continuum and I as a simple observer can only see a part of it, but then it means I can not keep the reference to the larger structure. Any kind of larger theory would violate the information constraint where the theory lives. In this sense, one might imagine time as relative change to be discrete relative to an outside observer. However, how would the observer himself be able to judge wether what he sees is discrete relative to some larger construct that he are unable to imagine?

/Fredrik

 

[padremo]

My understanding is that there is no such thing as 'empty space'. Space is the collection of particles (and virtual particles) which are constantly being created and annihilated. in that sense, spacetime is quantised.

 

[Fra]

The way I think of spacetime is that it serves the purpose of a relation. Suppose that emergent relations, form spacetime. And the emergence is so that locality is optimized so to speak.

Then the question is still what is a relation in a physical context? Does there need to be a physical basis for the relation too? Or does it make sense to consider mathematical relations with unbounded complexity? I think not. I personally think the measurement problem is part of this. If we have two observers, observing things. Then we claim that there exists a deterministic relation between the observers. Who is observing this relation? And how is objectivity handled?

/Fredrik

 

[genneth]

The understanding of spacetime seems to be deeply divided between people who understand GR and people who understand the Standard Model. You will get different answers from the two camps. People who understand both are few and clever enough to not comment

 

[xristy]

another view on quantization

I think that Christoph Schiller's paper: http://arxiv.org/abs/gr-qc/9610066" is a pedagogically nice treatment of the issue of spacetime quantization - as well as energy and so on.

 

[padremo]

The understanding of spacetime seems to be deeply divided between people who understand GR and people who understand the Standard Model. You will get different answers from the two camps. People who understand both are few and clever enough to not comment

Surely no-one understands both (or either for that matter) :-)

 

[lbrits]

String theory is one framework in which spacetime emerges as a low-energy, long-distance description of a quantum system. Now, it might not be our universe, but there is a place in which the quantization of spacetime can be understood.

In any event, you can quantize an ordinary relativistic point-particle where the particle's proper time is the thing conjugate to the Hamiltonian. In that case, the spacetime coordinates x^\mu are all operators on a Hilbert space, and all the delicacies of quantum mechanics follow. You can always choose a gauge, however, in which x^0, or any other linear combination, is diagonal. In that gauge, x^0 behaves simply as an ordinary number, and one is not normally aware of it being an operator.

 

[nrqed]

String theory is one framework in which spacetime emerges as a low-energy, long-distance description of a quantum system. Now, it might not be our universe, but there is a place in which the quantization of spacetime can be understood.

Really?!?

It seems to me that the staring point of any string theory action is a string propagating through a background spacetime. The spacetime is here to start with, it does not emerge from the theory!

 

[lbrits]

Really?!?

It seems to me that the staring point of any string theory action is a string propagating through a background spacetime. The spacetime is here to start with, it does not emerge from the theory!

Unfortunately that is a common misconception. One normally starts with a particular background and quantizes around it. But while it appears that there is a background in which the strings move, from the point of view of the string there is merely a scalar field X^\mu(\sigma) propagating on it's 2D worldsheet. "Background" fields like the metric make their appearance as coherent states (due to other strings) on this 2D conformal field theory. There are other fields living on this CFT, namely \psi^\mu as well as various ghosts, so how are they to be interpreted as embedding functions? They are too weird to have such an interpretation, and it is better to think of "classical" string theory as some Riemann surface with a particular conformal field theory living on it.

From what I understand (for open strings at least), you can start with a CFT with a spacetime type X^\mu, and continuously move to another vacuum, by a process known as Tachyon condensation, in which this field disappears (no more spacetime). So spacetime is merely an excitation in the theory, i.e. a "space-filling D-brane". But it is just one state, and there are other states which have to be very bizarre indeed.

If this hasn't convinced you, all known "string theories", or known string vacua, are dual to each other and to something that has an 11D supergravity low-energy limit. So here you have a number of 10D string theories (states) and they can be mapped to something with 11 dimensions. If the number of dimensions isn't even fundamental, then spacetime itself is on shaky ground =)

 

[nrqed]

Unfortunately that is a common misconception. One normally starts with a particular background and quantizes around it. But while it appears that there is a background in which the strings move, from the point of view of the string there is merely a scalar field X^\mu(\sigma) propagating on it's 2D worldsheet. "Background" fields like the metric make their appearance as coherent states (due to other strings) on this 2D conformal field theory. There are other fields living on this CFT, namely \psi^\mu as well as various ghosts, so how are they to be interpreted as embedding functions? They are too weird to have such an interpretation, and it is better to think of "classical" string theory as some Riemann surface with a particular conformal field theory living on it.

From what I understand (for open strings at least), you can start with a CFT with a spacetime type X^\mu, and continuously move to another vacuum, by a process known as Tachyon condensation, in which this field disappears (no more spacetime). So spacetime is merely an excitation in the theory, i.e. a "space-filling D-brane". But it is just one state, and there are other states which have to be very bizarre indeed.

If this hasn't convinced you, all known "string theories", or known string vacua, are dual to each other and to something that has an 11D supergravity low-energy limit. So here you have a number of 10D string theories (states) and they can be mapped to something with 11 dimensions. If the number of dimensions isn't even fundamental, then spacetime itself is on shaky ground =)

Fascinating. Thanks for those details.

I am always confused because it seems that at some point people switch from a description in terms of a 2D theory to a description in terms of strings/branes moving in some target space and it's never clear to me how/why the transition is made.For example, couldn't one describe everything in terms of a 2D field theory, without ever talking about an ambient spacetime? Is it necessary to view the string as propagating through a target space? Or is it just a convenient but completely unnecessary step?


But then, what do they mean when they say that certain excitations on the worldsheet correspond to spacetime fermions? On the worldsheet, there are scalar fields and fermioninic fields. From the 2d worldsheet perspective, what does it mean to have an excitation that corresponds to a worldsheet fermion? The mu are simply scalar fields, they are not coordinates. It sounds as if this would imply that the fermion fields are dependent on the scalar fields from the point of view of the 2D CFT??

And what is a brane in that case if you keep the point of view of the 2D worldsheet. Again, the X\mu are scalar fields, not coordinates.

Thanks again. Sorry for the simple-minded questions

 

[lbrits]

Well the worldsheet field-theory has scalars X^\mu(\sigma, \tau) and fermions \psi^\mu(\sigma, \tau) and ghosts. These fields admit mode expansions in terms of creation and annihilation operators. The 'states' of the string then are found by acting on the ground state \left|0\right\rangle by these creation operators. Note that the creation operators also carry a Lorentz vector index, so creation operators always add 1 to spin. On the other hand, the zero-modes of the \psi^\mu(\sigma, \tau) in the Ramond sector obey the Dirac algebra, and so the ground state, which obeys p_\mu \psi_0^\mu \left|0\right\rangle = 0, is a representation of that algebra. In other words, the ground state of the string is a spinor. When I say "state" here, I don't mean quantum state. Or I should say, "first quantized" state. But first quantization is a lie we tell undergrads =)

This picture is known as the RNS model. There is also the Green-Schwarz model, which has manifest spacetime spinors but worldsheet supersymmetry is hard to see, and this model is hard to quantize. They are equivalent, however.

Back to your first question. You can do everything from the worldsheet point of view. Things like string scattering amplitudes can be written completely in terms of the worldsheet CFT. I think you can also describe branes using what's called "boundary states" on the CFT. But this is too microscopic to be able to handle big calculations. So, starting with your CFT, you figure out what the spacetime fields look like and how they behave to whatever order in quantum perturbation theory you like. Then you solve those equations like classical equations, because that is easier to do...

It's a bit like trying to solve fluid dynamics by talking about individual atoms. A gnarly task indeed.

 

[Schrodinger's Dog]

The simplest answer and therefore the least scientifically rigid is that time is relatively quantised by us, as it involves the orbital period of the sun, the moons phases, the energetic emissions of caesium amongst other things. Not of course the answer you want, but none the less yes it is and might not and might be depending on how you define time. I've been reading too much philosophy I think. Quantized:

1.to subdivide (as energy) into small but measurable increments.
2.to calculate or express in terms of quantum mechanics

 

[nrqed]

Well the worldsheet field-theory has scalars X^\mu(\sigma, \tau) and fermions \psi^\mu(\sigma, \tau) and ghosts. These fields admit mode expansions in terms of creation and annihilation operators. The 'states' of the string then are found by acting on the ground state \left|0\right\rangle by these creation operators. Note that the creation operators also carry a Lorentz vector index, so creation operators always add 1 to spin.

Thanks again, this is very very interesting stuff.

Before discussiong your other points, let me ask you about what you said above. the index mu is a Lorentz vector index. By this here we mean a Lorentz transformation in the target space, right? But if, for the sake of the discussion, we keep everything from the point of view of the 2D CFT, there is no ambient space so this is a purely internal symmetry, correct? But this symmetry is a Lorentz symmetry so it's kind of strange. From this point of view (of the 2D CFT), this is imposed by hand or does it follow from some consistency condition?

Or maybe I am completely missing the point.

Thanks again

 

[lbrits]

Yes, there are other string theories or CFTs where the "target space" is, for instance, the group SU(N), and these are called sigma models.

Anyway, in the sector that the 2D CFT is free (i.e., non interacting), each field living on it will cause an anomaly to appear that (seems to) break conformal invariance. It contributes a number to the trace of the energy momentum tensor (which needs to be zero for conformal invariance to hold). Generally commuting fields add to this number while anticommuting fields subtract from it. So as soon as you add one field to your CFT, you'll need to add another to cancel the anomaly.

I think an arbitrary (but probably not the most general) free CFT will have some # of commuting scalars, some # of anticommuting scalars (ghost), some # of commuting spinors (ghosts again) and some # of anticommuting spinors. These fields are all representations of the 2D poincare group, so that's why we pick them. You can then pick these numbers so that the anomaly vanishes. I believe the solutions are 26 commuting scalars and no anticommuting spinors, 10 commuting scalars and 10 anticommuting spinors, and some really funky solutions which I don't know much about (N = 2 and N = 4 worldsheet supersymmetry, for those who are keeping track).

So in a sense, the Lorentz symmetry is sort of along for the ride. If you write an action

S = \int\!d^2\sigma\, \sum_i \partial_\alpha \phi^i \partial^\alpha \phi^i

then this is the action of some number n of scalar fields. But you get an SO(n) symmetry for free. There are some important subtleties why the metric happens to be SO(n-1, 1) rather than SO(n), and I'm not quite sure I understand these, (it has to do with Weyl invariance), but that's another story.

 

[nrqed]

Yes, there are other string theories or CFTs where the "target space" is, for instance, the group SU(N), and these are called sigma models.

Anyway, in the sector that the 2D CFT is free (i.e., non interacting), each field living on it will cause an anomaly to appear that (seems to) break conformal invariance. It contributes a number to the trace of the energy momentum tensor (which needs to be zero for conformal invariance to hold). Generally commuting fields add to this number while anticommuting fields subtract from it. So as soon as you add one field to your CFT, you'll need to add another to cancel the anomaly.

I think an arbitrary (but probably not the most general) free CFT will have some # of commuting scalars, some # of anticommuting scalars (ghost), some # of commuting spinors (ghosts again) and some # of anticommuting spinors. These fields are all representations of the 2D poincare group, so that's why we pick them. You can then pick these numbers so that the anomaly vanishes. I believe the solutions are 26 commuting scalars and no anticommuting spinors, 10 commuting scalars and 10 anticommuting spinors, and some really funky solutions which I don't know much about (N = 2 and N = 4 worldsheet supersymmetry, for those who are keeping track).

So in a sense, the Lorentz symmetry is sort of along for the ride. If you write an action

S = \int\!d^2\sigma\, \sum_i \partial_\alpha \phi^i \partial^\alpha \phi^i

then this is the action of some number n of scalar fields. But you get an SO(n) symmetry for free. There are some important subtleties why the metric happens to be SO(n-1, 1) rather than SO(n), and I'm not quite sure I understand these, (it has to do with Weyl invariance), but that's another story.

Ok. I can see the SO(n) symmetry popping out for free (as long as the scalar field are non-interacting). The issue of getting an SO(n-1,1) invariance instead really intrigues me but we could talk about this later.

But what about the wolrdhseet fermion fields. Is there a simple way to see why they should carry a spacetime index mu? Why would they have to come up in such a representation if we look at things from the point of view of the 2D theory?

 

[Haelfix]

String theory is fairly dynamical, in the sense that the ambient space where you put a metric into start (rulers and clocks) is free to evolve. The gravitons and various topological events interact and then backreact on the weak field Nu (which is varied in the action) and this can lead to new backgrounds.

Of course the calculations are done mostly on the worldsheet (and interactions thereof) but there is nothing stopping you from retransforming out of that picture.

Of course sometimes that's a hard calculation, and afaik people are only able to get explicit closed form answers for special simplified cases (sometimes you can guess the new answer based solely on consistency criteria)

The real issue is what do do when the full background metric g cannot be separated into weak field approximations (eg curvature is strong). Thats an open and active field of research, and the procedures are involved.

 

[lbrits]

Ok. I can see the SO(n) symmetry popping out for free (as long as the scalar field are non-interacting). The issue of getting an SO(n-1,1) invariance instead really intrigues me but we could talk about this later.

But what about the wolrdhseet fermion fields. Is there a simple way to see why they should carry a spacetime index mu? Why would they have to come up in such a representation if we look at things from the point of view of the 2D theory?

Well, you could call the index of the fermions something else, like i. The point is that there are a number of them, (for anomaly cancellation purposes), and in the case that there happen to be 10, we might as well call the index \mu as well.

 

[Haelfix]

Incidentally, the derivation of Einsteins equations is derived from the vanishing of the one loop beta functional of the sigma model or analagously as the weyl invariance of the effective action.

I find that pretty neat.

 

[dst]

I think that Christoph Schiller's paper: http://arxiv.org/abs/gr-qc/9610066" is a pedagogically nice treatment of the issue of spacetime quantization - as well as energy and so on.

Only one slight issue, he kinda demolishes... all of physics at the Planck scale. How valid is this paper?

 

[nrqed]

Incidentally, the derivation of Einsteins equations is derived from the vanishing of the one loop beta functional of the sigma model or analagously as the weyl invariance of the effective action.

I find that pretty neat.

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.

 

[nrqed]

Well, you could call the index of the fermions something else, like i. The point is that there are a number of them, (for anomaly cancellation purposes), and in the case that there happen to be 10, we might as well call the index \mu as well.

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?

 

[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.

 

[lbrits]

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]

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]

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]

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 no one 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]

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]

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 no one 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

 

[Thomas Larsson]

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]

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 ...

 

[lbrits]

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:

https://www.physicsforums.com/showthread.php?t=113311

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

 

[Thomas Larsson]

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 a lot 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 a lot 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

 

[lbrits]

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.
RobertGWS. Senior Partner.

Time to unsubscribe from this thread!

 

[Coin]

Time to unsubscribe from this thread!

Off topic-- how do you do this? I have been wondering for a long time if it is possible to unsubscribe from a thread you have posted in.

 

[lbrits]

If you're logged in, click on the "thread tools" button near the top. Do a page search if it's hard to see.

 

[Coin]

If you're logged in, click on the "thread tools" button near the top. Do a page search if it's hard to see.

Found it, thanks.

 

[Dcase]

As I understand the "deltas"

Kronecker is discrete,
Dirac is continuous,

for time in signal processing.