Understanding Time and Clocks in Relation to Observers

[Fra]

A simple question, but I wonder how different people think of this wrt internal vs external clocks.

It's been argued rightfullly that a satisfactory formulation of a measurement theory that is to be consistent with gravity (I use this word intead of QM, to not confused current QM with a future understanding which may, or may not deform it) must somehow be formulated by an inside observer. Ie. an observer that is subject to the same issues as any other physical system. External or classical observers are simply an idealisation.

The same applies for "clocks".

But what does this mean? This is where my question comes in. I see two options.

If we described the clock as a part of the system we study, so as to get proper "relational" time, then what about the evolution of relations? They still evolve with respect to another kind of time - which conceptually we can think of as "cosmological time" without necessarily confusing it with the same term in the standard model.

Clearly this "cosmological time" does not in the same way correspond to a "clock time". But the question remains how to understand it their connection.

It's not enough as I see it to do like Pullin and Gambini to observe clocks part of the system, because this observation either implicitly makes use of a larger complex context, or ensembles.

This ultimately boils down to the problem of time as in getting rid of time by considering relational notions only, but one must not forget that relations also involve in the general case, and this "cosmological time" can not be reduced in the same way without assumptions of equilibrium in the state of relations. And then this assumptions needs at leat some level of argument to be acceptable?

/Fredrik

 

[Thomas Larsson]

My viewpoint is heavily influence by Rovelli's work on partial observables, with a twist.

In general, we have one observer equipped with two detectors A and B. The observer makes a set of simultaneous readings (a_n, b_n); for simplicity, I assume that the corresponding operators A and B commute. Dynamics in a generalized sense is a correlation between these readings.

In particular, it may happen that detector B is a clock. Then b is time (a c-number), b_n is the time of event n, and A(b) describes the time evolution of the operator A. But the situation is symmetrical, so A could be a clock instead, and B(a) would then describe the time evolution of the operator B. Or it may happen that neither A nor B is a clock, but we may still be able to find some pattern in the pairs (a_n, b_n). This is a genuine generalization of the notion of dynamics as time evolution.

In field theory, we instead have operators A(x,t) which also depend on space. To recover that situation, detector B must measure spacetime locations, b_n = (x_n, t_n). So B could be a clock plus a rod, or a GPS receiver. Note that reading a GPS receiver is a completely local experiment. In order to interpret the result as meaningful spacetime coordinates, GPS satellites must be present and working properly, which amounts to a non-local assumption. However, even if the satellites are malfunctioning or absent, we can still read off detector B locally. Even if b_n is no longer a useful spacetime coordinate, the pairs (a_n, b_n) may still have meaningful dynamics in the generalized sense.

My philosophy deviates from QFT in one respect. In QFT, the coordinates (x,t) are partial observables which can be observed but not predicted. In the setup above, the observer's space coordinate can be predicted, because any physical observer has some dynamics x(t). In particular, a physical observer has some mass M, and the result of any observation depends on M.

There are two limits where we can ignore M. QFT is a theory of small objects, which means that the observer's (inert) mass is effectively infinite. GR is a theory of large objects, which means that the observer's (heavy) mass is zero. IMO, this is the key problem of quantum gravity: QFT and GR makes incompatible assumptions about the observer's mass. It also makes me dubious about results from semi-classical gravity, since you could easily sneak in some inconsistent assumption about M when you take the hbar -> 0 limit.

 

[Fra]

Hello Thomas, thanks for sharing your thinking on this.

For the purpose of discussion and elaboration I have some questions on your view.

My viewpoint is heavily influence by Rovelli's work on partial observables, with a twist.

In general, we have one observer equipped with two detectors A and B. The observer makes a set of simultaneous readings (a_n, b_n); for simplicity, I assume that the corresponding operators A and B commute. Dynamics in a generalized sense is a correlation between these readings.

I think you are fast here. You start by I presume and inside view here? Then, you talk about operators, so you must picture a state space, like hilbert space. Is this evolving or static? If it's evolving, then there is an additional time except for B - right? If it's not evolving, then how can the inside observer make the conclusion that there exists an eternal fixed state space?

QFT is a theory of small objects, which means that the observer's (inert) mass is effectively infinite.

I agree. This is closely related to, but a different angle to, when Smolin says that the notion of timeless law only makes sense when we study small subsystems. Ie. where the context(the observer) is infinitely complex(massive) relative to the system in question.

This completely fails when one considers cosmological style models, or open systems.

GR is a theory of large objects, which means that the observer's (heavy) mass is zero. IMO, this is the key problem of quantum gravity: QFT and GR makes incompatible assumptions about the observer's mass. It also makes me dubious about results from semi-classical gravity, since you could easily sneak in some inconsistent assumption about M when you take the hbar -> 0 limit.

I agree this is a problem, but I'd like to see hear you elaborate the other questions before I comment more on this, since they are related to me.

I fully share your view that the mass of the observer is a key here, but I think I see it differently. To me, the significant part is the complexity of the observer that can be used for representations of it's state. This means that infinite mass measn infinite information, and zero mass means that there is not enough complexity to even encode and represent all the operators we are used to in the inside view. This is why I think we are lead to an "open system" which leads to undecidability and must be treated by an evolving scheme.

/Fredrik

 

[meopemuk]

It's been argued rightfullly that a satisfactory formulation of a measurement theory [...] must somehow be formulated by an inside observer. Ie. an observer that is subject to the same issues as any other physical system. External or classical observers are simply an idealisation.

The same applies for "clocks". But what does this mean?

In my opinion, this question can be answered only after clarifying a more philosophical question: what is physics? and, more generally, what is the role of science?

One possible answer is that physics (and science in general) must provide a comprehensive description of the entire world, which includes descriptions of the physical system, observer, measuring apparatus, clock, and distant galaxies all on equal footing. If this is the case, then, indeed, it seems that quantum mechanics in its present form is not adequate.

However, there is also a different point of view. According to this approach, the goal of physics (and science in general) is to describe and predict results of measurements performed in well-controlled experiments. Once the theoretical prediction is made, it should be possible to arrange an experimental setup in which this or that prediction can be confirmed or rejected. Statements/predictions that cannot be verified by experiments simply do not belong to physics. They should be regarded as unscientific and left to either philosophy or religion.

So, any valid physical statement is always associated with a well-defined experimental setup. Any experimentalist knows exactly how his setup is arranged, i.e., what is the observed physical system, what is the measuring apparatus, and where is the clock from which he gets the time readings. There are well-defined boundaries between these three components. In this logic it becomes completely natural that in quantum mechanics there are different means to describe the physical system, the measuring apparatus and the clock.

The (state of the) physical system (i.e., the object that is observed in the experiment) is described as a vector in the Hilbert space specific for this object. The measuring apparatus is described as a Hermitian operator in the same Hilbert space. The clock reading is described as a numerical parameter.

Of course, this description is not complete and not comprehensive. The separation lines "physical system" / "measuring apparatus" / "clock" depend on the particular experimental setup. But there is nothing wrong with that. As I said above all objective knowledge about the world is experiment-dependent. The idea that there is some "true" knowledge which is independent on the particular experimental setup is in direct contradiction with the "scientific method".

In conclusion, I would like to say that the seemingly cumbersome QM formalism with its different treatments of the physical system, measuring apparatus and clock is not so bad after all. In fact, this formalism matches perfectly the way we obtain information about the world in observations and measurements. The annoying "incompleteness" of QM is not worse than the "incompleteness" of the scientific method itself. For a more complete and satisfying "knowledge" one should go to the church or mosque.

Eugene.

 

[Fra]

Thanks Meopemuk for adding your thinking. This was exactly what I wished for with this thread, to expose different reasonings and bring it up for discussion.

The idea that there is some "true" knowledge which is independent on the particular experimental setup is in direct contradiction with the "scientific method".
...
The annoying "incompleteness" of QM is not worse than the "incompleteness" of the scientific method itself. For a more complete and satisfying "knowledge" one should go to the church or mosque.

I agree here. Since I suspect you thouhgt otherwise, my hidden point here is not at all to raise the old Einstein-like objections to the incompleteness of QM. The implication of my view is rather than the world is MORE incomplete than the formalism of QM allows for.

So, any valid physical statement is always associated with a well-defined experimental setup.
...
The (state of the) physical system (i.e., the object that is observed in the experiment) is described as a vector in the Hilbert space specific for this object.
...
In fact, this formalism matches perfectly the way we obtain information about the world in observations and measurements.

I think your visions works fine for typica particle physics experiment, when the subsystem-massive-context assymetry is valid. And when the preparation phases of the experiment can be "hidden" in the context without problems.

But to consistently infer the hilbert state space with certainty from actual interaction history and consider this as a physical process and not just an external deduction, one must assume that the context of the observer is large enough to somehow relate to an infinite history to conclude what the state space is with certainty. This idealisation works fine for the mentioned subsystem approach, where both state spaces and "timeless" laws can be distinguished.

But what about when the subsystem abstraction fails, ie. in cosmological models? Does that mean you consider that to fall outside science, just because we are unable to establish a timeless statespace? I think it's true that we loose predictability here, but lack of perfect deductions doesn't mean excellent inductions won't perform well.

Note that "cosmological models" doesn't just refer to traditional cosmology, it can also refer to an arbitrary inside view, which must be treated with "cosmological logic" - ie. the system we observer is an open system and all we have is a limited assessment made through an event horizon. This can also have strong impacts not only on normal cosmology but also on the unification work, when inside views are acknowledged.

/Fredrik

 

[Fra]

Maybe if we look at a smaller key question to illustrate the problem I see.

The (state of the) physical system (i.e., the object that is observed in the experiment) is described as a vector in the Hilbert space specific for this object. The measuring apparatus is described as a Hermitian operator in the same Hilbert space.

If we demand this to be a statement resulting from a scientific method, and thus be a result of an interaction history we may call "experiments", then how can the observing system (observer, apparatouses, rods etc included) make an inference and establish what the state space of this system in question is? And how can this observer know that this space will not change with time?

If he can't, is the abstraction of a timeless objective statespace even justified in a fundamental description of physics? (in any other way than as an effective description in special cases where the space changes neglectable as compares to the change of the information living on the space)

The idea that the statespace can only increase but never decrease and thus one could always picture an "ultimate" statespace fails if one requires this information to be physical and encoded by a real physical system. Then wouldn't each observer merely see a truncated state space, wher no single observer can get a birds view of this because it would violated the information bound of the observer, if we believe that no physical system can encode infinite amount of information.

I just wonder in the light of this, would we benefit from a new way of thinking here, or not?

To say tha the fixed state space, fixed evolution laws etc accurately describes what we see is not something I can agree with in general. This is what smolin called the "Newtonian scheme" in his philosophical perimeter talk on the reality of time and evolutio of laws. But in despite of the name it doesn't refer to classical mechanics, it rather just refers to the notion of timless statespace, and timless laws.

I think his argument against this old scheme is clear, what makes it still doubtful is that he does not show another way, to give doubtes an alternative.

Perhaps, we need to actually see how to do it better, before we can admit that the current abstraction is flaw? To find a replacement before tossing the old?

/Fredrik