A Question about the empirical evidence of time

[Maxila]

I want to put this thread in the right context. After reading a plethora of physics literature for many years I have no doubt the people with advanced degrees in physics who work on this stuff are much smarter than me. I don’t believe my observations haven’t already been considered and dismissed for good cause however; the connections and dismissal are not apparent in the volumes of literature I’ve read. This has left me with nagging questions to which I seek answers? I accept there may be unobservable dynamics of the related phenomena that are not translatable to the observable outcomes however; I do try to put empirical evidence, logical progression, and methodical reasoning ahead of enigmatic solutions, and I am able to put aside intuition where evidence indicates differently. It’s why I am so disturbed by my observations and the lack of literature or answers concerning them. Below is a brief description of what I believe is an accurate assessment of facts and observations. I don’t believe I’ve made speculative assumptions but please correct them if I have.I believe most people would agree that in the broadest sense time represents change. I also believe if we asked the question, what is the cause of change; most physicists would agree that fundamentally observable change necessitates (and results in) *energy changing position (*energy in a broad sense from particles to matter). All clocks I’ve studied including atomic cesium clocks base their time output on some increment (a piece) of motion [I can provide the functional details with references for Cesium clocks if needed]. While motion is defined as a change in position per time, the time standard itself is an increment of motion. Just as the phenomenon being measured for a mass standard is a quantity of energy, it seems apparent the phenomenon (and quantity) of the time standard is an increment of energy’s change in position (motion). What has necessitated us to pass over this simple empirical evidence that time is a measure of energy’s change in position, in lieu of our current enigmatic view of time?

 

[Dale]

all clocks I’ve studied including atomic cesium clocks base their time output on some increment (a piece) of motion [I can provide the functional details with references for Cesium clocks if needed].

This is not correct. Please provide the reference that leads you to believe this and explain what part of the reference you are interpreting as implying this.

 

[Maxila]

All clocks I’ve studied including atomic cesium clocks base their time output on some increment (a piece) of motion [I can provide the functional details with references for Cesium clocks if needed]

This is not correct. Please provide the reference that leads you to believe this and explain what part of the reference you are interpreting as implying this.

NIST Cesium clocks keep time by adjusting a microwave frequency derived from a quartz oscillator to the resonance frequency of the Cesium atom. As the Cesium atoms pass through a microwave cavity a detector is used to produce a feedback signal that continually tunes the quartz oscillator (from which the microwave frequency is being derived) in a way that maximizes the number of state changes (florescence of the Cesium atoms).When the maximum number of state changes is reached the quartz oscillator is locked and standard output frequencies are derived from it.

Maximum florescence determines that the microwave frequency is tuned precisely, which in turn was derived from (and used to tune) the quartz oscillator that provides the output frequency of the clock. < (increments of energy's motion)

"Very accurate clocks can be constructed by locking an electronic oscillator to the frequency of an atomic transition." http://hyperphysics.phy-astr.gsu.edu/hbase/acloc.html

All time and frequency standards are based on a periodic event that repeats at a constant rate. The device that produces this event is called a resonator...
Fundamentals of Time and Frequency, Michael A. Lombardi, National Institute of Standards and Technology, 17.3 Time and Frequency Standards http://tf.nist.gov/general/pdf/1498.pdf

"Those atoms whose atomic state were altered by the microwave signal emit light (a state known as fluorescence). The photons, or the tiny packets of light that they emit, are measured by a detector."

"This process is repeated many times while the microwave signal in the cavity is tuned to different frequencies. Eventually, a microwave frequency is found that alters the states of most of the cesium atoms and maximizes their fluorescence. This frequency is the natural resonance frequency of the cesium atom (9,192,631,770 Hz), or the frequency used to define the second." http://www.nist.gov/pml/div688/grp50/primary-frequency-standards.cfm

Fundamentals of Time and Frequency, Michael A. Lombardi, National Institute of Standards and Technology
17.3
Cesium Oscillators http://tf.nist.gov/general/pdf/1498.pdf

"Those atoms that changed their energy state while passing through the microwave cavity are allowed to proceed to a detector at the end of the tube. Atoms that did not change state are deflected away from the detector."

"The detector produces a feedback signal that continually tunes the quartz oscillator in way that maximizes the number of state changes so that the greatest number of atoms reaches the detector. Standard output frequencies are derived from the locked quartz oscillator (Fig. 17.12)."

 

[SlowThinker]

All clocks I’ve studied including atomic cesium clocks base their time output on some increment (a piece) of motion
...
What has necessitated us to pass over this simple empirical evidence that time is a measure of energy’s change in position, in lieu of our current enigmatic view of time?

The time it takes for an excited electron to fall to the base energy level, does not involve any movement, at least as far as my understanding goes. It's not very useful in constructing accurate clock, but in theory can be used to measure time.

Also I'm not sure what you're actually proposing, but consider the fact that the time seems to go at very similar speed throughout the universe, even if there is no or weak connection between various parts. For example, we don't see one star burning twice as fast as another (of the same mass). Does your concept of measuring time with movement explain, why this is so?

 

[Dale]

NIST Cesium clocks keep time by adjusting a microwave frequency derived from a quartz oscillator to the resonance frequency of the Cesium atom. As the Cesium atoms pass through a microwave cavity a detector is used to produce a feedback signal that continually tunes the quartz oscillator (from which the microwave frequency is being derived) in a way that maximizes the number of state changes (florescence of the Cesium atoms).When the maximum number of state changes is reached the quartz oscillator is locked and standard output frequencies are derived from it.

Maximum florescence determines that the microwave frequency is tuned precisely, which in turn was derived from (and used to tune) the quartz oscillator that provides the output frequency of the clock. < (increments of energy's motion)


Fundamentals of Time and Frequency, Michael A. Lombardi, National Institute of Standards and Technology
17.3
Cesium Oscillators http://tf.nist.gov/general/pdf/1498.pdf

Reading your referenced material I can see how you would get the impression. An atomic clock does not base its time output on an increment of motion. There is certainly motion involved in the clock, but the time output is based on an increment of energy.

Think about a pendulum clock. The time output is based on the periodicity of the pendulum. There are also a variety of gears and springs and other moving parts that are important for the practical implementation of the clock. But the thing on which the time output is based is the pendulum, not those other parts.

In an atomic clock there are many "gears and springs" several of which involve motion, but the "pendulum" is the hyperfine transition which is an increment of energy not motion.

 

[Maxila]

All clocks I’ve studied including atomic cesium clocks base their time output on some increment (a piece) of motion [I can provide the functional details with references for Cesium clocks if needed]

...For example, we don't see one star burning twice as fast as another (of the same mass). Does your concept of measuring time with movement explain, why this is so?

The concept I outlined is not a predictive theory it is only a logical thought progression of empirical observations. We already have great predictive theories that address the rate at which a star burns. My post and questions revolve around, how I may have erred in those empirical observations, or even if empirically correct why can’t that understanding of time be applied to those existing theories?

 

[SlowThinker]

The concept I outlined is not a predictive theory it is only a logical thought progression of empirical observations. We already have great predictive theories that address the rate at which a star burns. My post and questions revolve around, how I may have erred in those empirical observations

But what is that observation? You only say that moving things move. I can add that moving things keep their speed.
But if time was defined by movement, nothing would prevent one star aging twice as fast as another star, since nothing moves between them. That's why we need a stronger definition of time, one that explains why all stars age in the same way.
Can you clarify, what exactly are you trying to say?

 

[Maxila]

But what is that observation?...
But if time was defined by movement, nothing would prevent one star aging twice as fast as another star, since nothing moves between them

I think I see how you may have interpreted my statements differently than I intended. I didn't mean to imply time is defined by movement, this may seem a subtle difference however; what I said was empirically I've observed time to be a measure of movement. Trying to put that in proper context, just as mass is a measure for a quantity of energy, time appeared to be a measure of energy’s change in position (movement). Our theories define how energy behaves relative to its mass and movement.

When I contemplated the time relationship to the empirical change I could observe or imagine, it always appeared time accounted for energies (any energy meaning particles to matter) motion which was the cause of that empirical change. That is what I am questioning here, are there errors in that contemplation or why may it be unworkable with our theories? My assumption is that this has already been considered and excluded for a reason, yet I find no reference to it in literature I've read?

 

[Dale]

empirically I've observed time to be a measure of movement.

That is not correct. Velocity is the measure of movement.

 

[Mister T]

What has necessitated us to pass over this simple empirical evidence that time is a measure of energy’s change in position, in lieu of our current enigmatic view of time?

I think you are missing a fundamental distinction. That distinction is between objects that occur naturally and properties that are invented by humans. Energy, position, and time are human inventions. We invent them in an attempt to be able to understand and predict how naturally-occurring objects behave. They are properties of objects.

Energy can't change position. Objects have energy. Objects have position. We can change, or observe a change in, an object's position. And that change in position might be accompanied by a change in energy. And it may be accompanied by a change in time.

We arrange objects (or observe objects already arranged) in such a way that a change in their position can be compared to another arrangement of objects' change in their position or energy. Then we compare those objects and use the comparison as a way of measuring what we call time. For example, the hand of a clock makes 24 revolutions while Earth rotates once relative to the sun. When we can observe those two things happening in a repeatable way we declare it to be a good way to measure time. When we notice discrepancies we look for better ways of doing it.

 

[pervect]

The concept I outlined is not a predictive theory it is only a logical thought progression of empirical observations. We already have great predictive theories that address the rate at which a star burns. My post and questions revolve around, how I may have erred in those empirical observations, or even if empirically correct why can’t that understanding of time be applied to those existing theories?

If you are saying that the concept you are outlinging doesn't make physical predictions, I would agrre. I'm not sure I follow what you mean by "emperical observation", but to me the lack of physical consequences imples that you are basically arguing about philosophical issues. I don't happen to agree with what I can understand of your philosophy. While I could go into some more specifics as to where I disagree with your philosophy, I'm not sure its worthwhile. If we are all agreed on the physical predictions, that is as much agreement as can be reasonably expected.

 

[Maxila]

If you are saying that the concept you are outlinging doesn't make physical predictions, I would agrre. I'm not sure I follow what you mean by "emperical observation", but to me the lack of physical consequences imples that you are basically arguing about philosophical issues. I don't happen to agree with what I can understand of your philosophy. While I could go into some more specifics as to where I disagree with your philosophy, I'm not sure its worthwhile. If we are all agreed on the physical predictions, that is as much agreement as can be reasonably expected.

I don't believe I have brought any philosophy into this. What I have done is look more deeply at one aspect of physical change from, fusion, to aging, to the position of objects in our universe. I think we can agree everything is comprised of energy in one form or another, and the dynamics that predict and explain those changes are explained in theories like QM and GR. What I have concluded (right or wrong) is the time aspect always seems to define the change in position of those energies and forces? While I am questioning and asking about that conclusion, I don't believe any aspect of it is philosophical.

 

[Maxila]

Think about a pendulum clock. The time output is based on the periodicity of the pendulum. There are also a variety of gears and springs and other moving parts that are important for the practical implementation of the clock. But the thing on which the time output is based is the pendulum, not those other parts.

I don’t follow how you arrive at the conclusion each apex of a pendulum swing is not an increment of its motion?

In an atomic clock there are many "gears and springs" several of which involve motion, but the "pendulum" is the hyperfine transition which is an increment of energy not motion.

What has caused you to conclude from the NIST documents they make any direct measurements of the energy in the hyperfine transition? They only discuss detecting the number of photons emitted from the transition.

Excerpts from the previously linked documents:

"…the microwave signal in the cavity is tuned to different frequencies. Eventually, a microwave frequency is found that alters the states of most of the cesium atoms and maximizes their fluorescence…."

"….Those atoms whose atomic states were altered by the microwave signal emit light (a state known as fluorescence). The photons, or the tiny packets of light that they emit, are measured by a detector…"

"…The detector produces a feedback signal that continually tunes the quartz oscillator in way that maximizes the number of state changes so that the greatest number of atoms reaches the detector…"From NIST FAQ (How Clocks Work 3rd paragraph): http://www.nist.gov/pml/div688/timekeeping.cfm

If the correct frequency can be generated to make the atoms change, then that frequency can be counted or divided down and compared. In this case, the generated frequency is the 'tick

what I said was empirically I've observed time to be a measure of movement.

That is not correct. Velocity is the measure of movement.

Velocity is a change in position per time; you can see the reasoning will be circular if time is accounted for by the increment of a change in position of some other energy or object, i.e. a quartz crystal, Earth rotation, etc. In such a case those things are a measure of energy's movement; velocity will be a movement in relationship to their measured movements.

From the previous NIST links:

"All time and frequency standards are based on a periodic event that repeats at a constant rate. The device that produces this event is called a resonator. In the simple case of a pendulum clock, the pendulum is the resonator. Of course, a resonator needs an energy source before it can move back and forth."

 

[Nugatory]

"All time and frequency standards are based on a periodic event that repeats at a constant rate. The device that produces this event is called a resonator. In the simple case of a pendulum clock, the pendulum is the resonator. Of course, a resonator needs an energy source before it can move back and forth."

The text that you've underlined is what happens when we use English to describe something that isn't easily written in natural language. There is no shortage of resonant systems in which nothing physical moves, but it is very hard to describe in English how these systems change from a state described by one point in phase space to another, and then return to the initial state, without using words like "move back and forth". (I managed it in the previous sentence, but it took me several tries and the wording is still awkward - it would have been far easier to have written $\phi(t)=e^{i\omega{t}}$ and then point out that $\phi$ isn't the position of anything).

Consider that some of the more interesting resonant systems around are quantum mechanical in nature, and in these nothing has any identifiable position so it makes no sense at all to talk about something in the system "moving".

It is true that most of our measuring instruments have to move some reasonable macroscopic object just so that we can read them. But that's just a matter of how we like to see measurement results presented... The cesium atom that measures the passage of one second is going through its hyperfine transitions without anything moving.

 

[russ_watters]

There are other predictable processes that do not involve movement; radioactive decay is one commonly used as a clock.

 

[Le Cucu]

Wait a second, but in case of radioactive decay, isn't something moving away from nucleus which just decayed?

 

[Nugatory]

Wait a second, but in case of radioactive decay, isn't something moving away from nucleus which just decayed?

Yes, but that's not what we're using to measure time here. We're just looking at the transition from "undecayed" to "decayed", and the motion or not of the decay products is beside the point.

 

[Le Cucu]

Yes, but that's not what we're using to measure time here. We're just looking at the transition from "undecayed" to "decayed", and the motion or not of the decay products is beside the point.

Well, I was just trying to follow OP idea for sake of discussion. The transition is happening with movement of both nucleus and outbound particle/photon.
Same happens with aging stars or black holes, or any other physical object.

 

[Mister T]

I think we can agree everything is comprised of energy in one form or another,

I don't agree. I don't even agree that that assertion makes sense. Energy is a property of everything, but those things are not comprised of energy. Some things, like electrons for example, might be fundamental particles. Fundamental in the sense that they have no internal structure, so in that sense to say they are comprised of anything is nonsense. They do have some properties, though. Like a magnetic moment, a mass, and yes, an energy.

What I have concluded (right or wrong) is the time aspect always seems to define the change in position of those energies and forces?

The measurement of time involves changes.

While I am questioning and asking about that conclusion, I don't believe any aspect of it is philosophical.

It is entirely philosophical. It is one thing to understand physics, or any other science, but it is quite another thing to understand the philosophy of that science. Many college professors teach a science and know very little of the philosophy of that science. When students ask them questions about that philosophy, perfectly valid and highly relevant questions by the way, they are totally puzzled by them.

 

[Dale]

I don’t follow how you arrive at the conclusion each apex of a pendulum swing is not an increment of its motion?

Sorry, I must have been very unclear. I agree that a pendulum clock measures an increment of motion, specifically the cyclic back and forth motion of the pendulum.

What I am trying to show is the distinction between the motion on which pendulum clocks "base their time output" and the motions which are incidental. The pendulum motion is essence of the clock. It is the thing that is used as the frequency standard in a pendulum clock.

There are also other motions, such as weights or springs, and gears and hands. Those motions, however important for the practical design of the clock, are not the frequency standard.

In an atomic clock there are many motions which are important for the practical function of the clock, but they are all of the incidental kind. In an atomic clock the essence of the clock, the frequency standard, is the hyperfine transition. Unlike a pendulum, the hyperfine transition is not an increment of motion.

 

[Dale]

What has caused you to conclude from the NIST documents they make any direct measurements of the energy in the hyperfine transition?

I never understand what a "direct measurement" is supposed to mean. Usually it seems to be used as an excuse to ignore valid data that you don't like.

What is measured is the frequency of the radiation corresponding to the hyperfine transition. The hyperfine transition is a transition between two energy eigenstates. It is therefore reasonably described as an increment of energy. It is not a transition between different velocity or position eigenstates. It is therefore not reasonably described as an increment of motion.

From the previous NIST links:

"All time and frequency standards are based on a periodic event that repeats at a constant rate. The device that produces this event is called a resonator. In the simple case of a pendulum clock, the pendulum is the resonator. Of course, a resonator needs an energy source before it can move back and forth."

This poor wording is the reason that this thread has not been closed down previously. Your initial misunderstanding was reasonable in light of the document. However, a poor wording is not a license to promote personal speculation, particularly after your misunderstanding has been corrected.

Do you understand that the frequency standard of an atomic clock is the cesium hyperfine transition?

Do you understand that the hyperfine transition is a transition between two energy eigenstates?

 

[Maxila]

The text that you've underlined is what happens when we use English to describe something that isn't easily written in natural language

I understand this was an area of concern before I made the post. In this thread there are already disagreements as to the meaning of the words written. I assume my perceived observations are likely not compatible with unobservable phenomena for valid reasons I wanted to learn about.

Yet for me the logical progression is looking at empirical evidence first, understand if observations of time as a measure of energy’s change in position are even valid for phenomena that are entirely observable? Obviously I haven’t been able to come up with an invalid example myself. I’d like to work through the empirical analysis before moving on to accept a more enigmatic explanation.

It is true that most of our measuring instruments have to move some reasonable macroscopic object just so that we can read them... The cesium atom that measures the passage of one second is going through its hyperfine transitions without anything moving.

That may be the case but we don’t observe it directly. The cesium clock’s time measuring functions are outputting a microwave frequency, detecting a quantity of photons (as the microwave frequency is tuned to the hyperfine transition), and using that feedback to tune a quartz crystal which in turn is tuning the output microwave frequency. The photons emitted are certainly moving a specific length (its wavelength) within a speed (c), as is the quartz crystal as it distorts and emits an electron after each distortion cycle. What is observed and output by the clock is an increment of those motions. Even simple math shows that as time being measured as length/c = t and when stepped down the distortion of the quartz crystal t is the proportional movement as a ratio of that distance/velocity. In other words the apparent (to me) measurement and output for t is the proportional relationship of length to change of position as λ/c = t = x/v = ƒ output of the clock (I hope my simple math correctly showed the time relation to the actual motion ?)

It begs the question can we come up with an example of direct observable change that is void of any change in position of its components or energy where t is not merely the proportional relationship of x/v change observed?

 

[Maxila]

I don't agree. I don't even agree that that assertion makes sense. Energy is a property of everything, but those things are not comprised of energy. Some things, like electrons for example, might be fundamental particles. Fundamental in the sense that they have no internal structure, so in that sense to say they are comprised of anything is nonsense. They do have some properties, though. Like a magnetic moment, a mass, and yes, an energy.

Your right, my statement was too sloppy when you consider point particles. Do you think it would have been more accurate to say; "everything that can be observed physically has a measurable energy"? What I've tried to contemplate is if energy changing position in some manner is always necessary for observable change? I have seen examples that QM has conditions where that is not the case but I don't think those changes are directly observable?

 

[Mister T]

Your right, my statement was too sloppy when you consider point particles. Do you think it would have been more accurate to say; "everything that can be observed physically has a measurable energy"?

It at least makes sense. I don't find it particularly meaningful, though. For example, for some things you can measure their energy and get zero. And anyway, the amount of energy that something has can often be chosen to be any value you like and it's only changes in energy that have physical significance.

Yet for me the logical progression is looking at empirical evidence first, understand if observations of time as a measure of energy’s change in position are even valid for phenomena that are entirely observable?

Perhaps you could give us an example (some empirical evidence) of energy changing position. As I've said repeatedly in this thread such a thing is not sensical. An object (for example a speeding bullet) can have a position. And it can have energy. And the position and energy can change. And you could even devise a way to make a clock out of it for purposes of measuring time. But it's the bullet, not its energy, that changes position. I have no idea how you would go about coming up with an empirical method of defining position of an energy.

Note that the bullet's position and energy are both frame-dependent. You can find a frame of reference where the bullet's position is zero, it's energy is zero, or both, or neither. And despite all that there will still be frames of reference where you can, and others where you couldn't, use the bullet as a clock (a device for measuring time).

 

[SlowThinker]

It begs the question can we come up with an example of direct observable change that is void of any change in position of its components or energy where t is not merely the proportional relationship of x/v change observed?

I gave that example earlier in this thread. An excited electron (such as in a laser) returns to its base state, with certain probability every second. A photon is emitted in the process, but that's after the electron returns. No movement happens while the electron is at the higher energy level.
How does your concept deal with a probability anyway? If you want to say that an electron circles a nucleus certain number of times and then returns to the base state, that's not how quantum world behaves. An electron is not moving around the nucleus at all.

Also your understaning of the atomic clock seems to be wrong to me. Photons and atoms are moving in the clock, but it's not used to measure time. They simply carry information among splitter and amplifier.

 

[Dale]

understand if observations of time as a measure of energy’s change in position are even valid for phenomena that are entirely observable? Obviously I haven’t been able to come up with an invalid example myself.

The cesium hyperfine transition is not a measure of energy's change in position, as you are well aware by now.

 

[Dale]

Besides the clear counterexamples presented already, the other problem with this approach is that it is fundamentally mistaken.

Suppose that we did not know any QM and suppose that the only clocks we knew how to build were pendulum clocks. So, according to this line of reasoning time would be a measured using an increment of motion.

However, even for a pendulum clock it is not true that the thing being measured is the motion. If you take two identically constructed pendulum clocks and swing one by 1° and the other by 2°, then the increment of motion has doubled, but the frequency has not changed. So even though there is more motion, what is measured is the same time.

Similarly, a pendulum (or any other frequency standard) also has volume, and mass, and color, and price. But none of those things are what is measured in the clock.

 

[Maxila]

Usually it seems to be used as an excuse to ignore valid data that you don't like.

Please don’t accuse me of this; that is a common and often ingrained trait of human nature that I abhor. I go to great lengths to police my thoughts in that regard. I make every effort to try and follow where facts lead (not where I’d like them to). If my statements are wrong, it is likely due to lack of intellect or knowledge, I can accept that.

I never understand what a "direct measurement" is supposed to mean.

In the case of the cesium atoms change in energy states, my reference was we don’t observe the atoms electron gaining and losing energy “directly”; we observe the photon emitted when the electron goes back to its lower energy state.

Do you understand that the hyperfine transition is a transition between two energy eigenstates?

Yes

The cesium hyperfine transition is not a measure of energy's change in position, as you are well aware by now.

Yes, and I didn't mean to imply that if I did.

Do you understand that the frequency standard of an atomic clock is the cesium hyperfine transition?

Yes, as I understand it is the microwave frequency of the photon discharged from that transition. We only appear to have a disagreement with the clocks function in relation to the transitions role in it.

The clock tunes its output microwave frequency to create the transition (as the atoms fall through a microwave cavity). The tuning of that frequency is controlled by a quartz oscillator that is in a feedback loop with a detector counting the photons from the atoms that change states. When the microwave output is exactly in tune to the transition frequency the quartz oscillator is locked (as determined by the photon detector).

In the clock, the role of the transition is only observing we have a maximum number of atoms changing states by detecting the photons they emit. That’s how we determine the microwave output frequency is tuned to the transition frequency. The clock does not observe or measure the frequency or energy of the photons emitted from the transition.

Suppose that we did not know any QM and suppose that the only clocks we knew how to build were pendulum clocks. So, according to this line of reasoning time would be a measured using an increment of motion.

However, even for a pendulum clock it is not true that the thing being measured is the motion. If you take two identically constructed pendulum clocks and swing one by 1° and the other by 2°, then the increment of motion has doubled, but the frequency has not changed. So even though there is more motion, what is measured is the same time.

Similarly, a pendulum (or any other frequency standard) also has volume, and mass, and color, and price. But none of those things are what is measured in the clock.

I believe the simpler math for time-motion relationship can answer that. In that math the time component is a ratio of length per change of positon. In my reply to Nugatory, the example for the relationship of the microwave motion, to time, to the quartz motion, to the output frequency, I tried to show as λ/c = t = x/v = ƒ (microwave motion = time = quartz motion = output frequency). For the pendulum example you gave I hope it is correct to write the relationship as x/v = 1 = 2x/2v. What I want to convey is that if the ratio of length to change in length is the same, the time interval is the same, x and v are only a proportional ratio for t. In other words t represents the increment of motion in proportion to length and velocity. (When I thought of time and space (length) in this way, for me, it made the concept of space-time axiomatic, as inseparable parts of a single phenomenon.)

 

[Dale]

The clock does not observe or measure the frequency or energy of the photons emitted from the transition.

Of course it does. That is the whole purpose of the entire clock. Everything in the clock is part of doing exactly that. In fact, everything you described in your most recent post describes the process of measuring that frequency.

For the pendulum example you gave I hope it is correct to write the relationship as x/v = 1 = 2x/2v.

It is not even close to correct. When x is maximum v is 0 and when x is 0 v is maximum. And as I said earlier doubling them does not change time although it changes the "increment of motion".

This is a forum for education on mainstream science topics. Not a forum for debating non mainstream personal theories. Since it is clear that you are not interested in learning here, this thread is closed.