Time operator, or Time eigenfunctions

[RUTA]

"I don't follow how this argument proves that time is fundamentally different from space."

Here is how I differentiate these concepts:

Space – the construct of true multiplicity from apparent identity. “I have two hydrogen atoms in this jar.”

Time – the construct of apparent identity from true multiplicity. “The person typing this is the same person who introduced Relational Blockworld.”

 

[meopemuk]

I don't follow how this argument proves that time is fundamentally different from space.
Certainly, in the laboratory, we can only note correlations (in Rovelli-esque meaning),
but surely this also applies to position? Consider the original Rutherford scattering
experiments, where he had some assistants sitting in a dark room recording the position
of flashes on a screen (within a system of grid regions on the screen). If one removes the
particle source, the screen is still there and the positions of various grid regions on that
screen still exist as references. In this sense, we can still "measure position" even if there's
no physical experimental system in the lab. I don't see how this is fundamentally from
"measuring time" by looking at one's watch, except perhaps in how the watch's reading
advances continually while we watch it.

Hi strangerep,

I would like to disagree with your statement "If one removes the
particle source, the screen is still there and the positions of various grid regions on that
screen still exist as references. In this sense, we can still "measure position" even if there's
no physical experimental system in the lab."

To "measure position" you need to measure something, i.e., a physical systems. Without the particle source you cannot realistically measure anything. Unless there happens to be a speck of dust on the screen. Then you can say: "Oh, the position of this dust particle is x". Without physically present electrons, alpha-particles, or dust particles you can perform measurements only in your imagination.

Even when you don't have any physical system/particle in your lab, the screen (for measuring positions) and the clock (for "measuring" time) are still fundamentally different. In this situation, you don't get any useful physical information from the screen (it does not perform any measurements), but you still get "time measurements" from the clock. I put "time measurements" in quotes, because they are not measurements in the usual sense of this word: they are not applied to any specific physical system. Time is simply an attribute of your experimental setup - a numerical parameter.

The situation changes once you turn on your scattering machine and begin to receive flashes from particles on the screen. Then you collect physically meaningful data about real physical systems - particles. You can say: "particle 1 had position x1", "particle 2 had position x2", etc. These measurements involve interactions between physical system (particle) and the measuring apparatus (the screen). They tell you something about particle properties. That's why we call particle position an observable.

Clock readings are not affected by the presence/absence of particles in your experiment. The clock keeps ticking at the same rate independent on what are the states of particles hitting the screen. So, clock readings cannot be called "observables". Their "measurements" do not involve interaction between a physical system and a measuring apparatus. They remain a parameter, which simply labels everything that occurs in the laboratory at each specific time instant. So, it would be incorrect to say that "particle 1 had time t1". The correct statement is "particle 1 had position x1 when the laboratory clock showed time t1".

So, from their operational meanings, "time" and "position" are very different beasts. One should be careful not to mix them (like apples and oranges) in the same 4D Minkowski continuum. This does not undermine relativity. As Wigner (1939) and Dirac (1949) showed long ago, one can build a perfectly relativistic quantum theory without invoking the concept of the 4D Minkowski space-time. In this approach, time is a numerical parameter and position is an observable with its Hermitian operator.

 

[deferro]

Time doesn't really exist in quantum mechanics (also not in classical physics).

But, it does exist when we see a quantum state, or measure momentum classically.

Quantum time has a different ruler, since events evolve under an exponentiated time (the momentum operator that evolves a state).
In GR time and distance are equivalent, but "in the large"; in QM time and distance are exponential, but singular. Or, there is a unitary time and distance measure in QM, there is a variable but approximate (d-approximated) time/distance measure in GR; the ratios are fundamentally ruled by different constants (gauges).

This leads to the conclusion: "large time and space are smooth but approximate; small time/space is exact but chaotic."

ed:
I'd like to expand on this; Seth Lloyd et al. effectively introduces the 0 + 1 statistical measure of states in QM as a potential; 0 is a ground state for a quantum, 1 is the potential state (in future time). These are bounded by Dirac brackets, or bra-kets. These are 'simply' placeholders for the 0 + 1 -> 0,1 evolution in exponentiated time of the state.

Then $$e^{i\phi}$$ is 'against' 1, observer o is always present or in the now, "looking at 0"; so that $$\phi$$ is = {}, the empty set.
So that, the momentum operator evolves the 1, or unitary state in exponential quantum time. The $$\phi$$ of GR is gravity or gravitational potential. QM's empty set of states is not gravity or 'gravitational time'. Mass is the connection.

 

[strangerep]

Space – the construct of true multiplicity from apparent identity. “I have two hydrogen
atoms in this jar.”

Time – the construct of apparent identity from true multiplicity. “The person typing this is the
same person who introduced Relational Blockworld.”

Do you mean this paper: quant-ph/0503065 ?

 

[strangerep]

Hi Meopemuk,

I would like to disagree with your statement "If one removes the
particle source, the screen is still there and the positions of various
grid regions on that screen still exist as references. In this sense,
we can still "measure position" even if there's no physical
experimental system in the lab."

Hmmm. Yet another case where I was already absolutely certain that
saying it that way would get me into trouble, so I'd better try and
clarify what I was thinking. I'll do so in the context of your
explanation...

To "measure position" you need to measure something, i.e., a physical
systems. Without the particle source you cannot realistically measure
anything. Unless there happens to be a speck of dust on the screen.
Then you can say: "Oh, the position of this dust particle is x".

Agreed. Although,... strictly speaking,... you can only say "I saw an
event flash within some region (x,y) on my position reference grid."

Without physically present electrons, alpha-particles, or dust
particles you can perform measurements only in your imagination.

Yes, but this is partly where I should have been clearer. See below.

Even when you don't have any physical system/particle in your lab, the
screen (for measuring positions) and the clock (for "measuring" time)
are still fundamentally different. In this situation, you don't get any
useful physical information from the screen (it does not perform any
measurements), but you still get "time measurements" from the clock. I
put "time measurements" in quotes, because they are not measurements in
the usual sense of this word: they are not applied to any specific
physical system. Time is simply an attribute of your experimental setup
- a numerical parameter.

But the position grid is also an "attribute of the experimental setup"
-- a set of numerical parameters. If you didn't have a memory, you
wouldn't realize that the number on the clock face keeps changing.
Similarly, if you couldn't move your head or refocus your eyes,
you wouldn't realize that there are multiple position grid regions.

The situation changes once you turn on your scattering machine and
begin to receive flashes from particles on the screen. Then you
collect physically meaningful data about real physical systems -
particles. You can say: "particle 1 had position x1", "particle 2 had
position x2", etc.

Strictly speaking, you can only say "there was a flash at position
x1", etc, and you can record these observations in a spatial sequence
(on paper) that correlates with your mental sense of time progression.

These measurements involve interactions between
physical system (particle) and the measuring apparatus (the screen).
They tell you something about particle properties. That's why we call
particle position an observable.

If we write down not only the grid position where a flash occurred, but
also the reading from our local clock, why is the time reading less
physically significant than the grid reading? In both cases, we're
correlating an event (flash) with previously established reference
systems (a position grid and a clock).

Clock readings are not affected by the presence/absence of particles
in your experiment. The clock keeps ticking at the same rate
independent on what are the states of particles hitting the screen.

But the position grid also continues to exist in the absence of
flash events.

So, clock readings cannot be called "observables". Their
"measurements" do not involve interaction between a physical system
and a measuring apparatus. They remain a parameter, which simply
labels everything that occurs in the laboratory at each specific time
instant. So, it would be incorrect to say that "particle 1 had time
t1". The correct statement is "particle 1 had position x1 when the
laboratory clock showed time t1".

Actually, I think both statements are not quite correct. I'd prefer
to say "an event occurred at lab grid position (x,y) when the
lab clock showed time t", and so on.

I.e., since we're recording not only the grid position of an event but
also the clock reading, why should the clock reading not be considered
an observed number associated with the event, just as the position grid
reference is also a number (or pair of numbers) associated with the
event?

So, from their operational meanings, "time" and "position" are very
different beasts. One should be careful not to mix them (like apples
and oranges) in the same 4D Minkowski continuum. [...]

I agree that time and position are different, and that 4D Minkowski
space is little more than a (problematic) carrier space for certain
Poincare representations. My objection against relegating time
to a lesser status than position is more to do with the role of
both position and time in parameterizing observed events.

 

[p764rds]

I think a present moment is more likely than a continuous time stretching back to the 'big bang' (if there ever was one!) because there is too much information to store in the universe to roll back time by reversing clocks. A computer cannot reverse its clock either - there is no store of data of what happened in the past - it would be too much data & too difficult to implement that).

So, the ideas of going back to the big bang that are fashionable at present are IMO plain wrong.

 

[meopemuk]

I.e., since we're recording not only the grid position of an event but
also the clock reading, why should the clock reading not be considered
an observed number associated with the event, just as the position grid
reference is also a number (or pair of numbers) associated with the
event?

I agree that time and position are different, and that 4D Minkowski
space is little more than a (problematic) carrier space for certain
Poincare representations. My objection against relegating time
to a lesser status than position is more to do with the role of
both position and time in parameterizing observed events.

I am not saying that time has a "lesser status" than position. I am saying that it has a different status. Yes, a full characterization of the measurement must include the record of both particle position and the time shown by the laboratory clock at the instant of measurement. However these two pieces of information have very different physical meanings. Position measurements depend on the state of the measured system, its dynamics, properties, etc. This is true also for all other genuine observables that are associated with physical systems: momentum, energy, etc. In quantum mechanics all these observables have Hermitian operators associated with them.

On the other hand, time "measurements" are completely independent on the state of the physical system, on what type of system is being studied, and whether any system is present at all. Laboratory clock is simply ticking at a constant rate. Time is kind of universal ideal parameter that should be simply attached to each and every measurement as a label. In other words, time is not an attribute of the physical system. Time is an attribute of the measurement.

Time truly stands alone, and I don't see how it can be fit into the category of observables. There are other numerical quantities in physics, which, like time, are not really observables in the quantum-mechanical meaning of this word. The dimensionality of space (3) is one of them.

Let me give you this (almost absurd) example to make my point more clear. Suppose that in your lab you happened to measure that a particle has position (x,y) on the screen, and that's all you got from your experiment. You have obtained a physically valuable (though miniscule) information. For example, your experiment tells you that there is at least one particle in your corner of the universe. If you are persistent enough, possibly you can even publish this result in Phys. Rev.

Now suppose that you've "measured" time t. This doesn't give you any meaningful information about the physical world. By itself, it is completely useless.

 

[Demystifier]

In order to "measure time" you just need to look at your watch.

Likewise, in order to "measure space" you just need to look at your meter stick.

By the way, in the paper I have pointed out that such a symmetric treatment of time and space in QM is in agreement with experiments, because such a treatment explains the rule that the squared transition amplitude is the transition probability PER UNIT TIME. How would YOU explain that rule?

 

[meopemuk]

Likewise, in order to "measure space" you just need to look at your meter stick.

I don't know what you mean by "measuring space". In physics we are measuring positions of particles or other physical systems. But we are not measuring "times of particles". Instead, we are recording times at which measurements (of true particle observables) were made.

By the way, in the paper I have pointed out that such a symmetric treatment of time and space in QM is in agreement with experiments, because such a treatment explains the rule that the squared transition amplitude is the transition probability PER UNIT TIME. How would YOU explain that rule?

I am far from saying that time is irrelevant in physics (some people do say that). There are plenty of important physical quantities (like the transition probability per unit time), which involve time in their definitions. I am only saying that time has a unique and separate status in experimental physics. Time is different from observables like position or momentum. It would be better if our theories reflected this simple fact, rather than mixed time and position in one ill-defined 4-vector.

 

[RUTA]

Do you mean this paper: quant-ph/0503065 ?

Yes, but RBW really has no substantive bearing on the post -- I was just hard pressed to identify a past version of myself uniquely :-)

 

[p764rds]

Yes, but RBW really has no substantive bearing on the post -- I was just hard pressed to identify a past version of myself uniquely :-)

Block universe paper:
http://arxiv.org/ftp/quant-ph/papers/0503/0503065.pdf

I think too, that there is a simultaneous quantum states reference frame that is probably a single non-relativistic frame (as in paper quoted above). This *must* be so if instantaneous quantum entanglement correlations are what indeed is happening. - A *better* view IMO, is that quantum entanglement correlations perceive no separation - then no entity needs to travel at infinite speed for correlation to work.

In the observable real world (so to speak) then an underlying quantum 'present moment' would need to be transformed algorithmically to SR, GR and relativistic frames to exist in our 'real world'. The quite trivial reason for this, is to maintain a logical causality model for the universe. In a field model of the universe where information has a maximum speed, even a computer 3D world program would need to do this or the causality of what is happening (eg infinite gun speeds) would not work and a large universe fleld model program would crash.

Lets take three real world events in sequence A to B to C with consistent, workable causality assumed, this could not be transmitted at infinite speed in an 'observable world' (because causality could fail).

But if A, B and C were entangled quantum states and observation of A disentangled B and C then this would occur without sequence A to B to C, rather A to B and C at the same present moment. It would have to be infinite or alternatively (and IMO better) they are not separated from each other by space or time. We could not have A disentangles B then C. It must be at the same time, so speed must be infinite (or not states separated).

If the three particles were photons traveling at the speed of light away from each other then one photons state observation would need to 'catch the other two' and not sequentially, so it would have to be at 'infinite speed' or *better* IMO assume they are not separated at all - as far as quantum states are concerned that is.

 

[RUTA]

p764rds writes, "If the three particles were photons traveling at the speed of light away from each other then one photons state observation would need to 'catch the other two' and not sequentially, so it would have to be at 'infinite speed' or *better* IMO assume they are not separated at all - as far as quantum states are concerned that is."

In our Relational Blockworld interpretation we assume, basically, that QM is simply a spatially discrete QFT so there is no screened-off particle moving through space from the source to the detector. Detector clicks are part of the detector, but "things" are constructed from relations (not ever smaller "things") and the click evidences a relation co-constructing the source and the detector. We're using a path integral formalism over graphs to model this approach:

http://xxx.lanl.gov/abs/0903.2642"

Essentially, the path integral approach is based on the fact that “the source will emit and the detector receive” (Feynman, 1965); per Tetrode, "the sun would not radiate if it were alone in space and no other bodies could absorb its radiation" (Tetrode, 1922).

Using this approach you can do quantum physics in 4D spacetime, i.e., configuration space is just a computational device with no ontological significance.

I'll stop there. That's probably more than you wanted to know :-)

 

[ZapperZ]

I will remind everyone involved to try and limit references to only peer-reviewed publication. Other than the BTSM forum and the high energy physics discussion, the rest of the physics topics must either used established physics or peer-reviewed papers, not preprints or manuscripts. If any of these arXiv manuscripts have been published, please include its exact citation.

Zz.

 

[RUTA]

I will remind everyone involved to try and limit references to only peer-reviewed publication. Other than the BTSM forum and the high energy physics discussion, the rest of the physics topics must either used established physics or peer-reviewed papers, not preprints or manuscripts. If any of these arXiv manuscripts have been published, please include its exact citation.

Zz.

“Deflating Quantum Mysteries via the Relational Blockworld,” W.M. Stuckey, Michael Silberstein & Michael Cifone, Physics Essays 19, No. 2, 269 – 283 (2006), quant-ph/0503065.

In case you're not allowed to read arXiv papers unless they're published, you'll have to skip the arXiv reference in my previous post with our latest results, but you can check out the RBW path integral formalism at:

“Reconciling Spacetime and the Quantum: Relational Blockworld and the Quantum Liar Paradox,” W.M. Stuckey, Michael Silberstein & Michael Cifone, Foundations of Physics 38, No. 4, 348 – 383 (2008), quant-ph/0510090.

How's that?

 

[ZapperZ]

“Deflating Quantum Mysteries via the Relational Blockworld,” W.M. Stuckey, Michael Silberstein & Michael Cifone, Physics Essays 19, No. 2, 269 – 283 (2006), quant-ph/0503065.

In case you're not allowed to read arXiv papers unless they're published, you'll have to skip the arXiv reference in my previous post with our latest results, but you can check out the RBW path integral formalism at:

“Reconciling Spacetime and the Quantum: Relational Blockworld and the Quantum Liar Paradox,” W.M. Stuckey, Michael Silberstein & Michael Cifone, Foundations of Physics 38, No. 4, 348 – 383 (2008), quant-ph/0510090.

How's that?

That's fine. All we require is the the exact reference. That way, any member can do a citation index on any references if he/she so wishes.

Zz.

 

[p764rds]

“Deflating Quantum Mysteries via the Relational Blockworld,” W.M. Stuckey, Michael Silberstein & Michael Cifone, Physics Essays 19, No. 2, 269 – 283 (2006), quant-ph/0503065.

In case you're not allowed to read arXiv papers unless they're published, you'll have to skip the arXiv reference in my previous post with our latest results, but you can check out the RBW path integral formalism at:

“Reconciling Spacetime and the Quantum: Relational Blockworld and the Quantum Liar Paradox,” W.M. Stuckey, Michael Silberstein & Michael Cifone, Foundations of Physics 38, No. 4, 348 – 383 (2008), quant-ph/0510090.

How's that?

Having read the references here's my thoughts:
Quoting “Reconciling Spacetime and the Quantum: Relational Blockworld and the Quantum Liar Paradox,” W.M. Stuckey, Michael Silberstein & Michael Cifone, Foundations of Physics 38, No. 4, 348 – 383 (2008), quant-ph/0510090.:
"dynamical reality is only a proper subset of a spatiotemporally contextual reality given globally" Then a 'spatiotemporally contextual reality' would be something like an quantum / information space that communicates with a dynamic reality and maybe even creates it.

The sequential aspect of causality viewed as a manifestation required in a 3D model, where in order to move (at all) from one coordinate to another, a sequential process is needed. Otherwise it would be impossible to traverse even 1D yet alone a 3D space. An ordered, lorentz covariant sequence is required to move from a position x1 to a postition x2 (in a time t). I see it almost as a design problem to be overcome.

This sequence of traversal events (kinematic motion) must be Lorentz covariant and relativistic to avoid causal and logical conflicts - an annoying necessity necessary in a field model of the universe - even a computer 3D program would require this to avoid emabarrasing crashes in a field model 3D virtualization (eg robot fires laser at mirror and kills himself at the same time that he shoots, also, even relativity problems would occur).

The plausibility of a pure physical 3D space within nothingness has to be questioned, because a 3D space is essentially a mathematical construct waiting for a mathematical implementation.
A 'real physical space' situated in nothingness has logical difficulties (what holds it up - its empty, where are its boundaries - its empty, etc). IMO - impossible.

But, a 3D space is very easy and efficent when constructed from data. e.g. a 3D computer virtual world where arrays (processors love them!) are very efficent algorithmic structures for manipulating 3D space.
Information needs no real physical 3D space to exist itself, nor has it any mass, and is at least a candidate to be able to construct a 3d universe space in what we understand as 'nothingness'.

Instant correlation between entangled quantum states no matter where in physical 3D space lends support and offers at least a possible mechanism to instant entanglement phenomena.

I ask if the above named papers are an accepted viewpoint and to what extent?

 

[RUTA]

Having read the references here's my thoughts:
Quoting “Reconciling Spacetime and the Quantum: Relational Blockworld and the Quantum Liar Paradox,” W.M. Stuckey, Michael Silberstein & Michael Cifone, Foundations of Physics 38, No. 4, 348 – 383 (2008), quant-ph/0510090.:
"dynamical reality is only a proper subset of a spatiotemporally contextual reality given globally" Then a 'spatiotemporally contextual reality' would be something like an quantum / information space that communicates with a dynamic reality and maybe even creates it.

The sequential aspect of causality viewed as a manifestation required in a 3D model, where in order to move (at all) from one coordinate to another, a sequential process is needed. Otherwise it would be impossible to traverse even 1D yet alone a 3D space. An ordered, lorentz covariant sequence is required to move from a position x1 to a postition x2 (in a time t). I see it almost as a design problem to be overcome.

This sequence of traversal events (kinematic motion) must be Lorentz covariant and relativistic to avoid causal and logical conflicts - an annoying necessity necessary in a field model of the universe - even a computer 3D program would require this to avoid emabarrasing crashes in a field model 3D virtualization (eg robot fires laser at mirror and kills himself at the same time that he shoots, also, even relativity problems would occur).

The plausibility of a pure physical 3D space within nothingness has to be questioned, because a 3D space is essentially a mathematical construct waiting for a mathematical implementation.
A 'real physical space' situated in nothingness has logical difficulties (what holds it up - its empty, where are its boundaries - its empty, etc). IMO - impossible.

But, a 3D space is very easy and efficent when constructed from data. e.g. a 3D computer virtual world where arrays (processors love them!) are very efficent algorithmic structures for manipulating 3D space.
Information needs no real physical 3D space to exist itself, nor has it any mass, and is at least a candidate to be able to construct a 3d universe space in what we understand as 'nothingness'.

Instant correlation between entangled quantum states no matter where in physical 3D space lends support and offers at least a possible mechanism to instant entanglement phenomena.

I ask if the above named papers are an accepted viewpoint and to what extent?

In answer to your last question, RBW is a relatively new interpretation of QM having been first introduced at Bub's 2005 annual conference, New Directions in Foundations of Physics. It also survived a screening at Price's 2005 conference, Time-Symmetric QM, among others since, of course. It has been published in Physics Essays, Foundations of Physics, and Studies in History & Philosophy of Modern Physics (v39, No. 4, 736 – 751 (2008)). I would say the interpretation has been properly vetted. Is it widely appreciated? Not at all. Bub said it took him three epiphanies to "get it" and he would have to spend a week lecturing to grad students on each one to teach it, so it's not widely understood.

I greatly appreciate your reading the Foundations paper and responding to it here. I would say from your response that we failed to communicate the adynamical nature of our approach. We're suggesting that space, time and "things" (entities that "move from coordinate x1 to coordinate x2" in your response, for example) are to be co-constructed in a mutually self-consistent fashion. Spacetime and things do not exist independently of one another, so discussion of 3D space as an entity in and of itself (as I infer from your response) is meaningless in our interpretation.

We believe we need a new approach in the formulation of QM to properly convey our interpretation, thus the path integral approach over graphs. This is widely used in QFT of course (e.g., lattice gauge theory) and in fact we're suggesting QM be viewed as a spatially discrete QFT of sorts; it's a little more complicated than that, as you know from reading the Foundations paper. In that paper, we presented the temporally continuous, spatially discrete 2-source amplitude, assuming it's well-behaved at the boundaries. We have, since publication of the Foundations paper, solved the fully discrete two-source amplitude over a graph of N nodes with exact boundary conditions (where it is not well-behaved, the differential operator has a zero eigenvalue) by restricting the path integral to the the row space of the discrete differential operator, which also contains the discrete source vector, in order to avoid singularities. Our interpretation justifies this restriction. That paper (the arXiv shown earlier) is only under review, so we're not allowed to say anything more about it here :-)

Thanks again for your response. Perhaps you should email me if you've more questions.

 

[p764rds]

I greatly appreciate your reading the Foundations paper and responding to it here. I would say from your response that we failed to communicate the adynamical nature of our approach. We're suggesting that space, time and "things" (entities that "move from coordinate x1 to coordinate x2" in your response, for example) are to be co-constructed in a mutually self-consistent fashion. Spacetime and things do not exist independently of one another, so discussion of 3D space as an entity in and of itself (as I infer from your response) is meaningless in our interpretation.

We believe we need a new approach in the formulation of QM to properly convey our interpretation, thus the path integral approach over graphs...

I was saying that 3D space as a 'real physical entity' has certain illogicalities from a point of view that it may (and everything in it) be constructed from information rather than fields, particles etc. But that is only my opinion, not an accepted fact.
What appealed to me: in your words " space, time and "things" are to be co-constructed in a mutually self-consistent fashion".

Or are you saying that "path integrals over graphs" could be used and certain boundary conditions have been solved - aspects of QFT that needed addressing (and would not interest me personally)?

 

[Belzy]

Time doesn't really exist in quantum mechanics (also not in classical physics).

Well put, Time does not exist independently of the life/being that notices it. See anthropic (or man-related) principle.

 

[p764rds]

Well put, Time does not exist independently of the life/being that notices it. See anthropic (or man-related) principle.

'Something that notices' would be a von neumann-like entity. For example a computer, an animal brain, a human brain, an insect brain. This is a data area with an area to process the data. Usually inputs and outputs too. They need something to push the data through i.e. some type of ticking clock. IMO the universe is one itself. But 'a thought' is a mechanical entity rather than something ethereal. It could probably best be described as 'made from' information.

 

[RUTA]

I was saying that 3D space as a 'real physical entity' has certain illogicalities from a point of view that it may (and everything in it) be constructed from information rather than fields, particles etc. But that is only my opinion, not an accepted fact.
What appealed to me: in your words " space, time and "things" are to be co-constructed in a mutually self-consistent fashion".

Or are you saying that "path integrals over graphs" could be used and certain boundary conditions have been solved - aspects of QFT that needed addressing (and would not interest me personally)?

We're trying to change the notion of "things in spacetime" as you imply by "and everything in it," to the notion of a unified "raumzeitmaterie," spacetimematter, as Weyl put it. It would truly make no sense to talk about space, time or things independently of one another. That's why we employ the path integral formalism over graphs. We're not trying to address formal issues in QFT, but certainly the formalism must bear on them ultimately.

Essentially, instead of starting your story with "things" located relative to one another in space and asking how their spatial organization will change (causal dynamics via differential eqns), you construct a picture of what you mean "things" involved in some phenomenon, which REQUIRES notions of space and time, and compute a probability amplitude for the occurance of that phenomenon (spatiotemporally holistic view per path integral).