Time operator, or Time eigenfunctions

[JohnSimpson]

"Time" operator, or "Time" eigenfunctions

We seem to define hermitian operators for momentum, position, energy ect., but we don't really talk about a "Time" operator, or "Time" eigenfunctions. What does time mean in standard quantum mechanics, and why is it different than the above dynamical variables?

 

[Bob_for_short]

Fortunately, it is not necessary. The other operators are sufficiently numerous and are already complicated to deal with.

Bob.

 

[meopemuk]

We seem to define hermitian operators for momentum, position, energy ect., but we don't really talk about a "Time" operator, or "Time" eigenfunctions. What does time mean in standard quantum mechanics, and why is it different than the above dynamical variables?

Yes, time is really a special quantity in quantum mechanics and in physics in general.

Momentum, position, energy, etc. are attributes of physical systems. You can say "momentum of the particle is p", "position of the particle is x", etc. meaning that these are measured properties of the given particle. However, you cannot say "time of the particle is t". It is more accurate to say "when particle observable was measured, the laboratory clock showed time t". So, in fact, time is an attribute of the laboratory, observer, or the reference frame. For this reason, time is not an observable, and there is no point to introduce an "Hermitian operator of time". It is quite natural to represent time by a simple numerical parameter, as it is done in both classical and quantum mechanics.

 

[mn4j]

Time features prominently in the definition of both Energy, and momentum operators.

 

[t_siva03]

since time is relative for each observer, I think it can only be considered in the context of sequences of events because all observers should agree that event A occurred before event B etc. We do not have a better concept of time currently.

 

[workmad3]

meopemuk is I believe correct for standard quantum mechanics, and this is why quantum mechanics doesn't mesh with relativity. With special relativity, every particle should have it's own time coordinate as it's in 4d spacetime. This produces problems with the standard equations though (such as negative energy states).

As such, general quantum mechanics treats time differently. I believe quantum field theories such as QED have an approach that is more in keeping with special relativity, but not general relativity.

 

[workmad3]

since time is relative for each observer, I think it can only be considered in the context of sequences of events because all observers should agree that event A occurred before event B etc. We do not have a better concept of time currently.

According to relativity, you can't actually make this statement :) Two observers could actually observe 2 events occurring in different orders. Look up the concept of 'simultaneous spaces' for more detail. In this respect, as with all others in 4d spacetime, time is no different from space and the ordering of events changes depending on your current position in spacetime, in the same way that ordering of items in space can change depending on your current position in spacetime.

 

[Demystifier]

There is a way to treat time in QM on an equal footing with space:
http://xxx.lanl.gov/abs/0811.1905 [accepted for publication in Int. J. Quantum Inf.]

 

[meopemuk]

meopemuk is I believe correct for standard quantum mechanics, and this is why quantum mechanics doesn't mesh with relativity. With special relativity, every particle should have it's own time coordinate as it's in 4d spacetime. This produces problems with the standard equations though (such as negative energy states).

As such, general quantum mechanics treats time differently. I believe quantum field theories such as QED have an approach that is more in keeping with special relativity, but not general relativity.

I disagree that the special role of time violates relativity. True, this special role is inconsistent with the 4D spacetime. However, there is a different (more general) view on the principle of relativity, which does not require the existence of the 4D Minkowski spacetime continuum. This view is based on the supreme role of the Poincare group (Lorentz group + space and time translations) as the group of transformations between different inertial observers. Then fully relativistic quantum mechanics can be formulated in terms of unitary representations of the Poincare group in the Hilbert space. 4D spacetime is not needed for that. This theory was first developed by Wigner in 1939. In 1949 Dirac extended this approach to interacting systems as well. The same approach is applicable to quantum field theories. The best reference is Weinberg's "The quantum theory of fields" vol. 1.

It is true that in QFT quantum fields are formulated as operator functions \psi(x)on the Minkowski "spacetime". However, there is no reason to identify this abstract 4D continuum with physically observable position and time. In fact, arguments x of quantum fields are used as integration variables when operators of observables and the S-matrix are calculated in QFT. So, there is no trace of x in final results that can be compared with experiments.

 

[Fra]

However, there is a different (more general) view on the principle of relativity, which does not require the existence of the 4D Minkowski spacetime continuum. This view is based on the supreme role of the Poincare group (Lorentz group + space and time translations) as the group of transformations between different inertial observers.

I personally think this logic is still problematic, to be used as a design principle.

It basically reduces the observer frame to an arbitrary gauge choice, total lack of physical significance. Only the relations between the choices, manifested by the symmetry transformations that generates all possible choices, are considered physical.

I see no other escape than that the process of actually inferring how different observers or gauges relate, must take place relative to an observer. If it doesn't, then one maintains some realist view of this symmetry.

I guess either one thinks that's fine, or one doesn't. This is fine as an effective framework, but I think this logic aren't going to be very viable when it comes to finding a more coherent framework for QG.

The spacetime realism is removed, but instead we have a symmetry realism, or what I've seen philosophers also call structural realism. I have to agree it's a step in the right direction, but it's far from home.

/Fredrik

 

[Count Iblis]

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

 

[Fra]

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

There is a standard logic, by which this is usually meant, but there is I think nevertheless I think an open question wether this is an appropriate foundation for a scientific model, because no matter how we argue, various forms of time still fails to go away. I think it's fair to say there are good arguments on both sides.

Here is an interesting talk by Lee Smolin.

On the reality of time and the evolution of laws
"There are a number of arguments in the philosophical, physical and cosmological literatures for the thesis that time is not fundamental to the description of nature. According to this view, time should be only an approximate notion which emerges from a more fundamental, timeless description only in certain limiting approximations. My first task is to review these arguments and explain why they fail..."
-- http://pirsa.org/08100049/

There isn't much doubt that Smolin well understands the standard arguments for that time isn't fundamental, as argued by several people. But he still points out that things are not that easy.

I don't think Smolins talk reflects on all details in the best possible way but it's a start that may provoce some new questions. No offense, but I personally think if someone consider his questions just philosophical baloney, they probably missed the points. It's easy to dismiss his arguments on a first reflection, but the more you think about it, there is something there.

/Fredrik

 

[t_siva03]

With special relativity, every particle should have it's own time coordinate as it's in 4d spacetime.

How does one define that time coordinate? For example muons, are particles created in the atmosphere by cosmic rays falling constantly to Earth at around 200,000 miles per second. Since muons move so quickly with respect to the laboratory reference frame, time passes slower in the muon reference frame than in the laboratory rest frame. The muon's internal time coordinate makes sense only in the context of comparing to another reference frame. In and of itself, I don't think one can define such a time coordinate according to relativity at least.


Thanks for pointing out simultaneous spaces, a mind boggling concept!

 

[p764rds]

How does one define that time coordinate? For example muons, are particles created in the atmosphere by cosmic rays falling constantly to Earth at around 200,000 miles per second. Since muons move so quickly with respect to the laboratory reference frame, time passes slower in the muon reference frame than in the laboratory rest frame. The muon's internal time coordinate makes sense only in the context of comparing to another reference frame. In and of itself, I don't think one can define such a time coordinate according to relativity at least.


Thanks for pointing out simultaneous spaces, a mind boggling concept!

Correlated states of entangled particles 'ignore' SR and GR and lose their entanglement simultaneously.

 

[naturale]

In SR time is a dimension, but to define a relativistic clock, that is to obtain the physical property of time, one need to suppose periodicity. This periodic aspect of the time dimension could be at the origin of the quantum phenomena.

Even for light particle such as the electron, the periodic dynamics (the intrinsic period related to the Compton scale) are to fast to be observed, about 10^-22 sec, and the system appears to have aleatoric behavior. Only resolving time scale smaller that this intrinsic periodicity the time observable make sense, beyond this resolution there is the possibility to describe QM in terms of classical waves.

 

[p764rds]

In SR time is a dimension, but to define a relativistic clock, that is to obtain the physical property of time, one need to suppose periodicity. This periodic aspect of the time dimension could be at the origin of the quantum phenomena.

Do you mean something like a minimum 'clock tick' (periodic-like) is similar to a quantum state change, or something like that? What is your idea?

 

[naturale]

Not exactly, it is something coming from the old formulation of QM (de Broglie, Bohr, Sommerfeld, Einstein ...). The frequency v of a field gives the energy of the quanta E = h v. But, there is more, imposing periodicity T = 1/ v you actually get the correct energy quantization E_n = n h / T . Changing reference system there is a variation of the time interval T which gives the correct dispersion relations for the energy levels E_n, ecc ... . In this way one finds many many deep analogies with QM.

 

[p764rds]

Not exactly, it is something coming from the old formulation of QM (de Broglie, Bohr, Sommerfeld, Einstein ...). The frequency v of a field gives the energy of the quanta E = h v. But, there is more, imposing periodicity T = 1/ v you actually get the correct energy quantization E_n = n h / T . Changing reference system there is a variation of the time interval T which gives the correct dispersion relations for the energy levels E_n, ecc ... . In this way one finds many many deep analogies with QM.

Correct dispersion levels? Can you expand on that? Are you talking about the Von Neumann / Birkhoff Quantum Logic?
http://en.wikipedia.org/wiki/Quantum_logic

 

[naturale]

A quantized field has an (ordered) energy spectrum E_n = n h / T, because it is like a quantum harmonic oscillator with periodicity T. But you get the same energy spectrum imposing a periodicity T to a wave. The allowed frequency are v_n = n v where v is the fundamental frequency T= 1/ v. Now, if the field has mass M, according to SR the period T change to T' = T / \sqrt{p^2 + M^2} so the energy levels has the relativistic dispersion relation E_n = h n \sqrt{p^2 + M^2}. This quantization is the one you get from the usual QFT. But you can obtain commutation relation or the Schrodinger eq as well. That is assuming periodicity as a principle you get quantization.

 

[elect_eng]

We seem to define hermitian operators for momentum, position, energy ect., but we don't really talk about a "Time" operator, or "Time" eigenfunctions. What does time mean in standard quantum mechanics, and why is it different than the above dynamical variables?

I was taught that time is just an independent parameter in standard QM. This is explicitly stated in "Modern Quantum Mechanics" by J.J. Sakurai.

Time is fundamentally different from dynamic variables in that the later are functions of the former. Although there is no time operator associated with measuring the time-state of a system, there is a time evolution operator which allows the description of how the state of a system changes with time.

I probably did not say that in the strictly correct way, but hopefully it makes some sense.

 

[naturale]

I was taught that time is just an independent parameter in standard QM. This is explicitly stated in "Modern Quantum Mechanics" by J.J. Sakurai.

Time is fundamentally different from dynamic variables in that the later are functions of the former. Although there is no time operator associated with measuring the time-state of a system, there is a time evolution operator which allows the description of how the state of a system changes with time.

I probably did not say that in the strictly correct way, but hopefully it makes some sense.

In the ordinary (Hamiltonian) formulation time appears as an "independent parameter", but in the covariant (Feynman) formulation of quantum mechanics time is a "dynamical variable". However, also in this formulation the quantum time is not exactly the relativistic time. In the latter case SR is invariant under time inversion. The former case, because of the close analogy of the path integral with a partition function, time appears as statistical time which arrow is fixed by the second principle of thermodynamics. These incongruences seems to be solved assuming time as a microscopically and dynamically compact dimension.

 

[p764rds]

There's a kind of flat-space-quantum-state-correlation time that is simultaneous everywhere. It does not need to hold to SR and GR because no information is being transmitted (no causal problems). How? Take 5 entangled particles anywhere in our spacetime universe. When their state correlations collpase that happens at all 5 points simultaneously regardless of what the clocks say on the respective laboratory benches. They are all at the same moment as though they were not separated at all. IMO its a more fundamental time than einsteins spacetime.

 

[Demystifier]

Has anybody noticed my post #8?

 

[CPL.Luke]

I did it was an excellent paper, however it concluded on a sour note, with the time eigenstates not being physical. in reference two of that paper however the author demonstrates pauli's proof that time is not an operator, and then makes his way around the problem. I'm surprised that the paper "quantized time" hasn't been given more notice.

 

[p764rds]

I did it was an excellent paper, however it concluded on a sour note, with the time eigenstates not being physical. in reference two of that paper however the author demonstrates pauli's proof that time is not an operator, and then makes his way around the problem. I'm surprised that the paper "quantized time" hasn't been given more notice.

Yes, quantized time seems reasonable to me. There seems to be a lot of debate about time -
in entanglement there seems to be a simultaneous time (ie a 'present moment' rather than spacetime relative times) that correlated states understand. Is this concept used in QFT?

 

[Bob_for_short]

Look, when we go from Classical Mechanics to Quantum Mechanics, we factually go to a wave mechanics with the energy quantization as an eigenvalue problem (consider waves in a box, for example). There is no need to quantize the time in such a wave mechanics.

Bob.

 

[Halcyon-on]

Look, when we go from Classical Mechanics to Quantum Mechanics, we factually go to a wave mechanics with the energy quantization as an eigenvalue problem (consider waves in a box, for example). There is no need to quantize the time in such a wave mechanics.

Bob.

The same quantization can be obtained by imposing periodic BCs in time, that is the time is in a (temporal)box with length T=h/E being E the energy of the quanta.

 

[Demystifier]

Look, when we go from Classical Mechanics to Quantum Mechanics, we factually go to a wave mechanics with the energy quantization as an eigenvalue problem (consider waves in a box, for example). There is no need to quantize the time in such a wave mechanics.

Yes, but relativity suggests that time should be treated on an equal footing with space. So if there is a space-position operator, there should also be a time-position operator.

 

[RUTA]

There's a kind of flat-space-quantum-state-correlation time that is simultaneous everywhere. It does not need to hold to SR and GR because no information is being transmitted (no causal problems). How? Take 5 entangled particles anywhere in our spacetime universe. When their state correlations collpase that happens at all 5 points simultaneously regardless of what the clocks say on the respective laboratory benches. They are all at the same moment as though they were not separated at all. IMO its a more fundamental time than einsteins spacetime.

You've 5 events in M4 labeled as "simultaneous" but they do not occupy a single hypersfc, so what do you mean by "simultaneous?" Proper time for all is the same at these events? That would seem problematic since it suggests a worldline and you can't have worldlines for screened-off entities (right?).

 

[meopemuk]

Yes, but relativity suggests that time should be treated on an equal footing with space. So if there is a space-position operator, there should also be a time-position operator.

If there is time operator, then it should have eigenstates. So, there should be, for example, a state in which an electron is "localized" in time at t=0. Then the probability of finding the electron at t<0 or at t>0 is zero. This seems to contradict the charge conservation law.

 

[p764rds]

P764RDS: Quote
"There's a kind of flat-space-quantum-state-correlation time that is simultaneous everywhere. It does not need to hold to SR and GR because no information is being transmitted (no causal problems). How? Take 5 entangled particles anywhere in our spacetime universe. When their state correlations collpase that happens at all 5 points simultaneously regardless of what the clocks say on the respective laboratory benches. They are all at the same moment as though they were not separated at all. IMO its a more fundamental time than einsteins spacetime."

Ruta:
You've 5 events in M4 labeled as "simultaneous" but they do not occupy a single hypersfc, so what do you mean by "simultaneous?" Proper time for all is the same at these events? That would seem problematic since it suggests a worldline and you can't have worldlines for screened-off entities (right?).

No, no worldlines here:
There is no proper time needed for the 5 decorrelation events. Proper time is irrelevant here. Also:
1) Do not need to obey the laws of physics as in einstein's SR. These are quantum state correlations and not laws of physics in the normal sense.
2) The speed of correlation knowledge (not speed of information!) is infinite - not finite as in light/gravitons information maximum speeds. Because of the instantaneous nature there is only one reference frame - its a kind of Newtonian/Galilean type of frame. Not Riemann or Minkowski.
3) The proper time is unknown and not needed.
4) The simultaneous decorrelations of entangled quantum states between separated entangled particles or a 'present moment' is required.
5) The speed of 'correlation knowledge' is infinite in this model (a *better* view is: there is no perceived separation between the correlated states of entangled particles (hence simultaneous) Note: The particles themselves obey normal SR, GR and reference frame physics, its only the correlated states we are concerned with)

 

[RUTA]

"There is no proper time needed for the 5 decorrelation events. Proper time is irrelevant here. Also:
1) Do not need to obey the laws of physics as in einstein's SR. These are quantum state correlations and not laws of physics in the normal sense."

The detection events occur somewhere in spacetime, regardless of QM, so what do you mean by "simultaneous" if not in the context of spacetime?

 

[Demystifier]

If there is time operator, then it should have eigenstates. So, there should be, for example, a state in which an electron is "localized" in time at t=0. Then the probability of finding the electron at t<0 or at t>0 is zero. This seems to contradict the charge conservation law.

As explained in the mentioned paper, one should make a difference between kinematics and dynamics. The kinematic time operator exists and it does have eigenstates - delta functions in time. However, such wave functions do not satisfy the standard wave equations of motion, so eigenstates are "unphysical" from the dynamical point of view. If, for example, tachyons existed, then time eigenstates would be dynamically physical, while space eigenstates wouldn't.

But the main point is the following. Kinematics should be defined BEFORE the dynamics. In this sense the time operator exists, because the operators belong to kinematics, not dynamics.

 

[meopemuk]

As explained in the mentioned paper, one should make a difference between kinematics and dynamics. The kinematic time operator exists and it does have eigenstates - delta functions in time. However, such wave functions do not satisfy the standard wave equations of motion, so eigenstates are "unphysical" from the dynamical point of view. If, for example, tachyons existed, then time eigenstates would be dynamically physical, while space eigenstates wouldn't.

But the main point is the following. Kinematics should be defined BEFORE the dynamics. In this sense the time operator exists, because the operators belong to kinematics, not dynamics.

Hi Demistyfier,

your paper is based on an (unproved) assumption that time and space "should be treated on an equal footing". In my opinion, this contradict the physical meanings of the notions "time" and "position". Position is a property of a particle (or any other physical system). That's why we call it "observable" together with momentum, spin, energy and other observables. However time is not a property or attribute of the particle/system. In order to "measure time" you just need to look at your watch. This value does not depend on the physical system that you are observing. You even may not have any physical system or particle in your laboratory - and you can still "measure time". So, "time" is not an observable in the usual sense.

 

[strangerep]

Position is a property of a particle (or any other physical system). That's why we call it "observable" together with momentum, spin, energy and other observables. However time is not a property or attribute of the particle/system. In order to "measure time" you just need to look at your watch. This value does not depend on the physical system that you are observing. You even may not have any physical system or particle in your laboratory - and you can still "measure time". So, "time" is not an observable in the usual sense.

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.

 

[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.