Why time is not an observable in quantum theory?

[Dickfore]

Nonetheless, time is relative. Different observers can measure different values of time using similar (identincally built) instruments. I don't see an irefutable reason against the idea of time being one of the basic observables of a quantum system and consequently considering a linear, unbounded, self-adjoint operator with fully continuous spectrum in the mathematical formalism.

Actually, in non-relativistic mechanics, time is invariant.

 

[Careful]

Indeed. This kind of physics is discussed in specialized papers, not in in the textbooks. Why? Because it may lead beyond the existing quantum paradigm.

I don't know why you think this would imply the existence of a time operator. I mean physical clocks are simply material configurations and all you have to do is to define a suitable coarse grained observable and clock state in order to get away with this. You may naively feel that this cannot be done, but there is no contradiction whatsoever in any scheme which incoorporates classical gravitation (through semi-classical laws). In contrast to what most people think, all this does not imply that gravitons as quantum particles cannot exist. Nobody has ever succeeded to make sense out of these quantum spacetime ideas (including you) simply because one cannot make them ''consistent'' (see my previous post). First of all, it appears you have to give up either translation or Lorentz invariance (of the vacuum) and second, it's just philosophical balderdash (I know mathematicians have more the tendency to think that not being so dismissive of such ''nonsense'' is a sign of intelligence, but it really is not). Now, this may be too harsh for your refined taste ... but I actually want to make a bet that these naive ''ideas'' will never succeed. I agree however that conventional QFT is insufficient but not in *this* way.

 

[Fredrik]

What I understand from your reply is that the model you describe converges to a situation where space cease to exist when t=0.

It doesn't include t=0, and space shrinks to a point in the limit t→0.

You may argue that having that point t=0 has no significance to physical world. However it may give a clue to the reality of nature.

How could it, when it doesn't change the predictions of the theory?

 

[arkajad]

I don't know why you think this would imply the existence of a time operator.

I didn't say so. What I say is that "time of an event" (the kind of event needs to be specified precisely) is an observable (can be measured), but it can not be represented using the textbook "observables" of QM. Yet it can be discussed theoretically and the theory can be compared with experiments if we go beyond the textbook wisdom. If you search - you will find many papers published on this subject.

 

[rpt]

It doesn't include t=0, and space shrinks to a point in the limit t→0.

Point is a mathematical definition. I would call that a situation where space cease to exist.


How could it, when it doesn't change the predictions of the theory?

It does not change the already existing preditions of the theory.
But it does an additional prediction that you ignore.
"Everything is emerging from emptiness - a condition where there is no space and time"

 

[Demystifier]

But what happens when we want to measure "time" of an event, not a wave. Physical waves surely don't have "time", but events do, i.e. a decay of a particle.

A possible answer is given in the paper I've linked there. In short, "events" correspond to Bohmian pointlike particles, which have well defined positions in space and time.

 

[rpt]

Sorry that my comment
"Point is a mathematical definition. I would call that a situation where space cease to exist."

appeard inside Fredriks quote in post 35. I didn't know how to use the "quote" function.
Now I know :-).

 

[Careful]

I didn't say so. What I say is that "time of an event" (the kind of event needs to be specified precisely) is an observable (can be measured), but it can not be represented using the textbook "observables" of QM. Yet it can be discussed theoretically and the theory can be compared with experiments if we go beyond the textbook wisdom. If you search - you will find many papers published on this subject.

I totally disagree, why would one be able to measure something like a time coordinate or a space coordinate as a matter of fact? I mean I have no trouble in making a physical clock, preparing the state and making a clock reading, but why should one interpret this as the time of an event? Those (t,x) coordinates mean nothing. I do not need to know my place in space and time, the only thing I am aware of is that my clock readings go forward and that I interact consciously with my neighbors and they are conscious too. I am not sure if we speak about the same thing here but coordinate time never ever can be measured by any experiment. It seems like you are simply adding some observable to the theory which has no basis in microscopic physics (ie, the material that constitutes the clock) and which you want to interpret as a clock reading. Did I get that right? If so, that would be completely unphysical.

All such ideas come from taking old fashioned quantum theory seriously which you shouldn't. We advanced to QFT and that theory offers a completely different point of view (albeit you still can construct here a nonlocal Newton Wigner operator - nobody would argue that it corresponds to a physical measurement!). The inadequacy of Bohm de Broglie theory for QFT (there really is no acceptable scheme for particle creation) really shows that such ideas belong to the stone age.

Similarly this shows that quantizing GR in the standard way does not make sense. Moreover, I have no idea of what successful program you would be talking about ... for example all these kappa-Minkowski like ideas are still in their infancy and have not obtained sufficient maturity yet to give a full spacetime interpretation to the algebra (and they would all face the philosophical problems I mentioned).

 

[arkajad]

I totally disagree, why would one be able to measure something like a time coordinate or a space coordinate as a matter of fact?

Coordinate is not an event. Detector click (in response to, say, "a passing electron") is an event. We observe the detector and we find that when it clicks it is located at a certain place and it clicks at a certain time. Then clicks again. We make notes of the coordinates of these events. We also know detector's construction (or many small detectors making a big detector) to some degree. The detector can move along a certain trajectory. We register its clicks, we get a series of spacetime coordinates in a given frame of reference. We want now our theory to be able to provide us with a process that simulates what we have observed.

Ordinary QM does know how to do it, but there are ways to extend the standard QM so that this can be done and that the theory can be compared with experiment.

 

[Careful]

Coordinate is not an event. Detector click (in response to, say, "a passing electron") is an event. We observe the detector and we find that when it clicks it is located at a certain place and it clicks at a certain time. Then clicks again. We make notes of the coordinates of these events. We also know detector's construction to some degree. The detector can move along a certain trajectory. We register its clicks, we get a series of spacetime coordinates in a given frame of reference. We want now our theory to be able to provide us with a process that simulates what we have observed.

Ordinary QM does know how to do it, but there are ways to extend the standard QM so that this can be done and that the theory can be compared with experiment.

No we don't : we simply observe that a detector clicks, *period*. The moment we watch our clock after we have observed it to click, we are already too late. All we have is a series of conscious moments stored in our brain and all we can do is make at theory which makes such series of events probable given our ''awareness moments''. I think you confuse very two basic things which is something like space-time awareness and *measuring* of space and time. And space-time awareness does not imply that you know where you are in space and time, it just means you 'know' you are somewhere 'now' and all other stuff in the universe is neither in your observable past or observable future.

I don't understand your last point at all: you say ordinary QM is ok, but you still want to extend it?? For what then? If it is not broke, don't fix it.

 

[arkajad]

No we don't : we simply observe that a detector clicks, *period*.

We do not have be present there. The detector can have the the automatic clock mechanism. It registers the time of the click. It is like when you observe earthquakes. Earthquake is a big event. It is characterized by a place and a time. We are analyzing statistics of earthquakes. Quantum earthquakes are similar - but on a smaller scale. Nothing prevents you to from getting a time series from a Geiger counter.

 

[Careful]

We do not have be present there. The detector can have the the automatic clock mechanism. It registers the time of the click. It is like when you observe earthquakes. Earthquake is a big event. It is characterized by a place and a time. We are analyzing statistics of earthquakes. Quantum earthquakes are similar - but on a smaller scale. Nothing prevents you to from getting a time series from a Geiger counter.

Well even that is not true... all I know is that this detector with a clock produces two series of numbers, it doesn't mean that I actually know how these numbers came to being. I can at best make a model which makes such list probable as well as the fact that when I look I observe the detector in this state. The detector is by no means characterized by a universal place and time, all that counts for the detector is its own (quasi) local reference frame and the particles coming in. Universal time and space are just additional concepts which have a reality in asfar they allow for the physical theatre to arise. I cannot make any strict retrodictions about the past giving all assumptions I put on the detector. All I can do is assume boundary conditions upon the physical environment and test those by making future experiments hoping that the latter would remain stationary in some imaginary global timeframe. But I can never - ever measure them (since doing so would actually change the environment)!

It's a bit like what happens in social talk: if I am not there and actually hearing everything which has been said by whom and at what moment. Then the only thing I have is hear-say; nothing more nothing less (this is an important principle in court btw).

 

[arkajad]

Well even that is not true... all I know is that this detector with a clock produces two series of numbers, it doesn't mean that I actually know how these numbers came to being.

That's your problem. Nevertheless you have two series of numbers that came out of a certain coupling between the detector and the system that caused these records.

I can at best make a model which makes such list probable as well as the fact that when I look I observe the detector in this state. The detector is by no means characterized by a universal place and time, all that counts for the detector is its own (quasi) local reference frame and the particles coming in. Universal time and space are just additional concepts which have a reality in asfar they allow for the physical theatre to arise. [QUOTE}

Again, it's your problem. The detector does not care about "universal time and space". It just does it's job.

I cannot make any strict retrodictions about the past giving all assumptions I put on the detector. All I can do is assume boundary conditions upon the physical environment and test those by making future experiments hoping that the latter would remain stationary in some imaginary global timeframe.

Why anything should remain stationary? Nothing in reality is exactly stationary. We can't help it. That's how life is.

 

[Fredrik]

"Everything is emerging from emptiness - a condition where there is no space and time"

That isn't a prediction. A prediction says something about results of experiments. This is just an additional axiom added on top of the theory, an axiom that doesn't change the theory's predictions or add any new ones. So it's like adding an invisible blue giraffe that doesn't interact with matter to Newton's theory of gravity.

 

[Careful]

That's your problem. Nevertheless you have two series of numbers that came out of a certain coupling between the detector and the system that caused these records.

I can at best make a model which makes such list probable as well as the fact that when I look I observe the detector in this state. The detector is by no means characterized by a universal place and time, all that counts for the detector is its own (quasi) local reference frame and the particles coming in. Universal time and space are just additional concepts which have a reality in asfar they allow for the physical theatre to arise. [QUOTE}

Again, it's your problem. The detector does not care about "universal time and space". It just does it's job.



Why anything should remain stationary? Nothing in reality is exactly stationary. We can't help it. That's how life is.

I don't see what my problem is, *you* have a problem in the sense that you want some measurement of time playing a fundamental role in quantum physics. There is no such thing of a kind and I see really no physical necessity for quantum theory to be pushed in that direction.

Your last comment is somewhat 'silly' in the sense that we assume boundary conditions to remain stationary all the time! For example, when I measure neutrons and I get some twisted statistics, I do not assume that some unikely phenomenon such as invisible high energy, localized gravitational waves entered my laboratory and knocked my neutrons systematically to another place. I just draw the conclusion that I was unlucky and do the experiment again.

So, given the fact that there is an intrinsic uncertainty upon a time registration by a clock (where the uncertainty is defined with respect to the time scale of other physical processes in nature, not with respect to some absolute time), why do you want to assign a coordinate system to those detector readings? There is no way to know when is when, all you do is imagining that when the detector clicked you were looking at the sexy lab assistent. But you never measure that. Perhaps, we are talking next to each other, but I see no way why clocks should play a fundamental role in quantum physics.

 

[arkajad]

I don't see what my problem is, *you* have a problem in the sense that you want some measurement of time playing a fundamental role in quantum physics. There is no such thing of a kind and I see really no physical necessity for quantum theory to be pushed in that direction. to another place.

"[URL
Measurement of the Single-Photon Tunneling Time[/URL]

http://www.springerlink.com/content/g57t53414812v4wr/"

http://arxiv.org/abs/1006.0117"

http://en.wikipedia.org/wiki/Time_of_arrival"

http://www.gap-optique.unige.ch/Publications/PDF/qutritQIC.pdf"

http://www.quantumphil.org/wheeler.pdf"

This may give you an idea as to what to what other people are interested in.

 

[Careful]

"[URL
Measurement of the Single-Photon Tunneling Time[/URL]

http://www.springerlink.com/content/g57t53414812v4wr/"

http://arxiv.org/abs/1006.0117"

http://en.wikipedia.org/wiki/Time_of_arrival"

http://www.gap-optique.unige.ch/Publications/PDF/qutritQIC.pdf"

http://www.quantumphil.org/wheeler.pdf"

This may give you an idea as to what to what other people are interested in.

Could you just tell me in 10 lines how you would define a time operator? This would be much more efficient and perhaps then I would take a look, I really don't have so much time to read just anything other people find interesting (and I am not sure whether we are not saying the same thing in another way).

I just watched the time of flight concept on Wikipedia: this is a rather meaningless as a fundamental concept, I must say. I mean it is great in practice, but it should not play any role in basic physics. This is old fashioned special relativity, general relativity thought us otherwise.

 

[rpt]

That isn't a prediction. A prediction says something about results of experiments. This is just an additional axiom added on top of the theory, an axiom that doesn't change the theory's predictions or add any new ones. So it's like adding an invisible blue giraffe that doesn't interact with matter to Newton's theory of gravity.

How can it be an axiom?
We didn't start there. We ended up there based on the theory we developed.
So is it inccorrect to say that its a use of the theory to predict (understand) a condition where measurements cannot be made due to physical limitaions as you mentioned in one of your previous replies.

 

[arkajad]

There is no such a thing as "time operator" (well, there can be, but its physical meaning would be rather obscure). But there can be such a thing as "tunneling time", or "time of arrival", or "time of event", where the particular "event" is defined as an irreversible transition time for a given detecting device. These things are being measured in the labs and they are being discussed theoretically using several alternative approaches. "Time of arrival" is conceptually rather simple, so this concept is a good point to start with. You may like to search Google for this term together with the keyword "quantum".

 

[Careful]

There is no such a thing as "time operator". But there can be such a thing as "tunneling time", or "time of arrival", or "time of event", where the particular "event" is defined as an irreversible transition time for a given detecting device. These things are being measured in the labs and they are being discussed theoretically using several alternative approaches.

Ok, I see what you mean, but such observables are all nonlocal... I don't see why such things would be interesting from a fundamental point of view. For example you don't really measure the time that an electron hits the detector, depending upon the size and where it hits and how fast the response is, we get a registration somewhat later by our clock. So what precisely is the theoretical debate? Is it concerning the details of the detector or the environment, the state of the particles or what? I don't see what the fundamental issue is here. It is an interesting question to ask, but I don't see the fundamental relevance... this is certainly not what the original question was about.

 

[arkajad]

Ok, I see what you mean, but such observables are all nonlocal...

You would have to define "observable". You would have to define "nonlocal". A measurement never takes place at one point and at one time. The measuring device always occupies some finite region of space, and it reacts only after a certain amount of time when coupled to any system outside. If this is what you call "nonlocal", then all real measurements are nonlocal. So what? Physics can deal with such kind of "nonlocalities". But they are called local. Nonlocality comes into being only when spacelike separated systems can influence one another in a statistically significant way.

 

[Careful]

You would have to define "observable". You would have to define "nonlocal". A measurement never takes place at one point and at one time. The measuring device always occupies some finite region of space, and it reacts only after a certain amount of time when coupled to any system outside. If this is what you call "nonlocal", then all real measurements are nonlocal. So what? Physics can deal with such kind of "nonlocalities". But they are called local. Nonlocality comes into being only when spacelike separated systems can influence one another in a statistically significant way.

Right, so my question is do you guys define an observable from first principles when discussing this? About your interpretation of measurement: well we really don't know that, do we? We have no idea what a measurement even *is*, all we know is what it does: it reveals a number. Anyway, this is a deep question which I feel should not be adressed on a forum. So yeh, I do not know an answer to that issue right away, it seems to me there are distinct possibilities here. Also, we are not going to debate about something as silly as a definition. But you did not answer my question: why would such observables be of fundamental importance to quantum mechanics? So, if you don't like the word observable: you measure either arrival times or time differences, so what should this tell me about the fundamental laws?

 

[arkajad]

Well, we do know what a measurement is. We measure things all the time. We know aht events are. They happen all the time.

Why some type of measurements are of fundamental importance to QM? We do not know whether they will be of fundamental importance in the future or not. And we do know that they were for a long time neglected, theoretically and experimentally. That is why they are interesting. Perhaps something new is lurking there and perhaps not. We will never know if we do not research. That is why more an more people are looking into this business, when new techniques of making measurements become available.

 

[Fredrik]

How can it be an axiom?
We didn't start there. We ended up there based on the theory we developed.

That's not what we did. I described the steps involved in finding a spacetime that's consistent with general relativity. Then I said that if we add another point to this spacetime, it wouldn't be a manifold. That would make it inconsistent with general relativity, which says that spacetime is a manifold (more precisely: a smooth 3+1-dimensional Lorentzian manifold with a metric that solves Einstein's equation). So to include that additional point in the theory, you have to make it an additional axiom. (That would make it a different theory, by my definitions). Since it doesn't lead to any new predictions, or change any of the predictions of general relativity, it's just like an invisible blue giraffe.

So is it inccorrect to say that its a use of the theory to predict (understand) a condition where measurements cannot be made due to physical limitaions as you mentioned in one of your previous replies.

I don't understand that sentence. You're saying something about the time before atoms had formed and no measuring devices could exist. What about it?

 

[Careful]

Well, we do know what a measurement is. We measure things all the time. We know aht events are. They happen all the time.

Why some type of measurements are of fundamental importance to QM? We do not know whether they will be of fundamental importance in the future or not. And we do know that they were for a long time neglected, theoretically and experimentally. That is why they are interesting. Perhaps something new is lurking there and perhaps not. We will never know if we do not research. That is why more an more people are looking into this business, when new techniques of making measurements become available.

Of course we don't : it is not because we do something all the time that we know what it is. It would be like saying that we know God to exist because we have given him a name. We also do not know what physical events are: actually this is an open question in noncommutative spacetime approaches. It is not because we idealize an event to a point that we have understood it. I thought that as a mathematician, you surely would appreciate those points.

Yeh, perhaps there is ... my ''guess'' is that QM might fail for more advanced double slit experiments with massive particles.

 

[dextercioby]

No -- that's why I said "it seems to me...". :-) I looked at quant-ph/9908033 (assuming that's one of the papers you meant?),
but that was a while ago and I forget what I concluded about it.
I'll go take another look...

Cheers.

To add more confusion to this thread when it comes to its coherence, I would add (or probably repeat myself when writing) that there's a real pitty that the approach to QM based on RHS hasn't been pushed significantly deeper. And here I don't mean some new results for a theory that's 85 years old, but I mean at least translating all very well known textbook examples (take Fluegge's problem book) and applications into this rigorous distributional language. The simplest model I could come with right now would be the 1D finite potential. Or was it done and I don't know. Then I would have loved to see models in 2D and in 3D, of course...

EDIT: I just realized that I'm not the only one diverting from the original topic...

 

[rpt]

That's not what we did. I described the steps involved in finding a spacetime that's consistent with general relativity. Then I said that if we add another point to this spacetime, it wouldn't be a manifold. That would make it inconsistent with general relativity, which says that spacetime is a manifold (more precisely: a smooth 3+1-dimensional Lorentzian manifold with a metric that solves Einstein's equation). So to include that additional point in the theory, you have to make it an additional axiom. (That would make it a different theory, by my definitions). Since it doesn't lead to any new predictions, or change any of the predictions of general relativity, it's just like an invisible blue giraffe.

Fredrik,
I know, that I shouldn't say things without fully dunderstanding general relativity and related mathematics. I am telling things based on what you explained to me, to further clarify things for me. I will explain why I said so.

You said FLRW solution gives (+ve curvature) family of 3-sphere as a solution to space-time. Then you said requiring that Einsteins relation satisfing this spacetime results in a relation that relates the parameter defining the 3-sphere and its radius.

I thought the 3-sphere that results at t=0 which is a point does not violate what you said above. I interpreted it as the limiting case of the solution. If we talk about gradients of surfaces in the model (which also exist in limiting sense) why do not include this point as a one which complies with the theory without having additional axioms. At this point there is no space so it does not need any coordinates to describe anything. It just that we include this point in the solution space becase it does't violate the theory. Why does it violate the definition of space-time manifold? Is it not continuous and homogenous?

 

[strangerep]

[...] I looked at quant-ph/9908033 [...] but that was a while ago
and I forget what I concluded about it.

Now I remember... the paper is full of heavy functional-analytic
argument and requires lengthy (re-)reading and sustained concentration.
The author works with unbounded operators in ordinary Hilbert space,
and therefore has to be very careful about domains of definition for
(powers of) the unbounded operators. I doubt that I'll sort it all
out properly in my own mind anytime soon. :-(

there's a real pitty that the approach to QM based on RHS hasn't been pushed
significantly deeper. And here I don't mean some new results for a theory
that's 85 years old, but I mean at least translating all very well known
textbook examples (take Fluegge's problem book) and applications into this
rigorous distributional language. The simplest model I could come with right
now would be the 1D finite potential. Or was it done and I don't know. Then I
would have loved to see models in 2D and in 3D, of course...

Well, any example that uses Dirac bra-ket formalism with
distribution-valued inner product, etc, is secretly using RHS.
But going "deeper" requires significantly heavier math.

In his textbook, Ballentine presents RHS early as the "natural" setting
for QM, but it is rarely mentioned in most of the subsequent chapters, iirc.

Rafael de la Madrid has made some attempts to expose RHS to a
larger readership -- though he limits the heavy math to keep
the papers accessible to that readership. If you look through
his papers via Google Scholar, you find a couple where he treats
the 1D potential example.

I just realized that I'm not the only one diverting from the original topic...

Yeah, we should stop.

 

[rpt]

If what I am saying makes any sense,
The credit should go to Fredrik who explained me beautifully what is the mathematical representation of space-time in general relativity in few lines in very simple language.
I only tried to make an interpretation of what the model may be telling us.

 

[DevilsAvocado]

"Why "time" is not an observable in quantum theory?"

rpt, you did observe time outside quantum theory?? What does it look like!? I’m dying of curiosity!

(joking friendly )