Ontology of time

[swansont]

What is time transformation but change in the rate (speeding up or slowing down) of physical processes?

The derivation makes no reference to, and does not depend on, physical processes.

[Iggy]

Maybe the word “year” has become meaningless because of relativistic effects on physical processes.

By definition, the meaning of a year is "31.5576 Ms (megaseconds or 'million seconds')" (definition) where one second is defined as "the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom"[/i] (definition).

 

The definition of "year" in a scientific context actually doesn't contain any reference to the earth or sun.

 

And of course for “Martians” an orbit of Mars is not an earth year. I really don’t believe that an earth year is the universal standard of time, as I’ve said a few times. It (and the “day”) is simply the event duration that all of us earthlings have in common...what “a year” means here on earth.

 

To explore the philosophy of time clearly a few things have to be established. Proper time is a measurement. It is a measurement of a physical process. For example, an oil lamp could burn so that all of the oil is used up. lighting the wick of the lamp when it is full of oil is an event and when the lamp goes dark from running out of oil, that is another event. Between those two events is a duration.

 

Everyone, in all frames of reference, agree on the physical process. They agree that the lamp burned completely -- that there were two events -- that the one event happened before the other. The duration of the physical process, however, is variable and relative to velocity and gravitational potential. This means that someone with an identical lamp in a different reference frame could himself burn, for example, two lamp-fulls of oil between the events in question.

 

The duration between events could also be measured with a mechanical clock. The person in the frame of the first lamp (lamp 1) measuring the duration of its burn could get 5 minutes on a stopwatch. The person in the different frame of reference using an identical stopwatch measuring the burn time of lamp 1 would get 10 minutes.

 

It doesn't matter what units of measure are used or with what physical process they are defined. The units are arbitrary, which makes the number of units equally arbitrary. Relativity works regardless of the units used (you can pick any you like) and that is the reason Einstein said "according to the general theory of relativity the four coordinates of the space-time continuum [space and time] are entirely arbitrary choosable parameters, devoid of any independent physical meaning."

 

Values like "2 lamp-burns", "5 years", or "20 seconds" do not themselves have independent physical meaning. "5 minutes" is not a thing that exists between two events. This is why it is so weird that you say relativity makes a reification of time -- it actually does the opposite. In relativity time is just the measurement of a clock -- that's all.

 

Time dilates because identical clocks disagree about the duration between the same two events. For example, I had a birthday this year and I had a different birthday last year. Between those two events the earth orbited exactly once. Everyone, no matter what frame of reference they are in, would agree that the earth orbited the sun once between those events. If, however, there were an identical solar system to ours near the center of the Milky Way it would measure a different value based on its orbit. It would not orbit exactly once between the events because it would 'tick' at a different rate.

 

I think you would have to understand these basic concepts of relativity and time dilation before you could consider what they imply about time.

Edited June 5, 2011 by Iggy

[owl]

Iggy:

The duration of a bang/crunch cycle depends on the gravitational potential and velocity relative to the CMB of the frame measuring it.

 

Do you think that the event duration (elapsed time) of a Bang/Crunch cycle (or Bang to entropy) has a “life of its own” independent of measurement and transcending all local frames of reference?

I do.

 

michel:

Can you give backup for the idea that "the present is present, i.e., now everywhere", for example, a physics theory consistent with relativity's confirmed predictions and presentism? I would be very interested in looking at that theory.

 

Just the meaning of the words, A: “was,”; B: “is,” and C: “will be,” the meaning of which has not been debunked or made irrelevant by relativity. Transcending the concept of (or focus on) location, the words and realities they denote are, A: “has already happened” (not happening now, in the present), B: happening now (wherever... everywhere), and C: “not yet happening in the present” (again regardless of location in all three tenses.)

 

Iggy:

In relativity time is just the measurement of a clock -- that's all.

And, of course, as already discussed, all physical events are "clocks" in the broadest sense. So, between one instant ("now") and another instant ("now") is "elapsed time" on whatever scale of the "event" in question.

Your statement has the same meaning (or lack thereof) as the often repeated old saw, “Time is that which clocks measure,” which is a meaningless tautology. It doesn’t address “What dilates” in “time dilation”, for instance, the ontological question. Yet we all agree (I think) that clocks “tick” at different rates in different “environments” in the broadest sense, including different velocities and “gravitational environments.”

 

In reply to swansont's statement on time transformation, I asked:

 

What is time transformation but change in the rate (speeding up or slowing down) of physical processes?

swansont answered:

The derivation makes no reference to, and does not depend on, physical processes.

 

If time is not a reference to the "event duration" of physical processes (clocks ticking, planets orbiting, galaxies rotating, cosmic lifespan or cycling), what then... what "transforms?" Sorry if ontology irritates you, but "inquiring minds"... well, they (we) keep inquiring, and this is the subject of this thread.

[Iggy]

Do you think that the event duration (elapsed time) of a Bang/Crunch cycle (or Bang to entropy) has a “life of its own” independent of measurement and transcending all local frames of reference?

Like I explained in my last post, it is not generally assumed that duration is something that exists in and of itself. Einstein held that space-time coordinates do not have an independent, substantial, ‘life of their own’. Relativity, he said, proves this.

 

You might think of it like this... things that have a "life of their own" can be counted. You can count the number of swans in a lake or the number of stars in the Milky Way. You can't count a duration in the same way. If duration had an independent existence then you should be able to count the number of durations between a person's birth and death, but any count would be an arbitrary counting of events.

 

Don't get me wrong, I believe duration is real -- just that it isn't independent -- doesn't have a life of its own. It depends on other things, one of those things being frame of reference.

 

I do.

If you believe duration has a life of its own then you are making a reification of time, which is fine, but it is not supported by relativity.

 

And, of course, as already discussed, all physical events are "clocks" in the broadest sense.

A series of events make a clock.

 

So, between one instant ("now") and another instant ("now") is "elapsed time" on whatever scale of the "event" in question.

You do not understand that an instant is a function of reference frame and there is no absolute reference frame -- therefore no universal instant or universal present instant. People have tried to explain why this is true, but without a basic working knowledge of relativity I don't think it's going to hit home.

 

In relativity time is just the measurement of a clock -- that's all.

Your statement has the same meaning (or lack thereof) as the often repeated old saw, “Time is that which clocks measure,” which is a meaningless tautology.

A rhetorical tautology... that's all it is... that was my point.

 

It doesn’t address “What dilates” in “time dilation”, for instance

That is correct, it does not. Relativity does not introduce any kind of medium or aether that dilates. There are no postulates or assumptions of that sort.

 

Yet we all agree (I think) that clocks “tick” at different rates in different “environments” in the broadest sense, including different velocities and “gravitational environments.”

Velocity is not an environment or an environmental factor. There is no such thing as a "fast environment" or "slow environment". People knew this going back to Galileo in the 1600's.

 

If time is not a reference to the "event duration" of physical processes (clocks ticking, planets orbiting, galaxies rotating, cosmic lifespan or cycling), what then... what "transforms?" Sorry if ontology irritates you, but "inquiring minds"... well, they (we) keep inquiring, and this is the subject of this thread.

It should be possible to derive relativity without reference to clocks and their mechanics or any other physical process.

 

I think you have in your mind that clocks slow down because some force is being applied to them or something physical is interacting with them and affecting whatever mechanism makes them work. Is that right?

[swansont]

If time is not a reference to the "event duration" of physical processes (clocks ticking, planets orbiting, galaxies rotating, cosmic lifespan or cycling), what then... what "transforms?" Sorry if ontology irritates you, but "inquiring minds"... well, they (we) keep inquiring, and this is the subject of this thread.

It's not asking the question that I mind, though I am not particularly interested in it. You'll notice that my answers have been in the realm of physics, not metaphysics. It's giving a straw man of an answer that irritates me.

[owl]

swansont;

It's not asking the question that I mind, though I am not particularly interested in it. You'll notice that my answers have been in the realm of physics, not metaphysics. It's giving a straw man of an answer that irritates me.

 

I wonder why you keep participating in a thread on a subject in which you are not particularly interested. Maybe you just need to try to discredit ontology and insist that the physics is all that matters.

 

Btw, ontology is not metaphysics. It is the study of what qualifies as an existing entity (what an entity is) and the nature thereof in each case; almost the opposite of metaphysics, which is about what is "beyond" (meta) physics.

 

I also notice that you use "straw man" a lot as a label to discredit ontology in general and my arguments in particular. Your reply completely avoids my point. You use ontology (and my challenge) as a straw man without even addressing my direct question:

If time is not a reference to the "event duration" of physical processes (clocks ticking, planets orbiting, galaxies rotating, cosmic lifespan or cycling), what then... what "transforms?"

... Likewise, again, what dilates? And calling the question a straw man argument is not an answer.

[Cap'n Refsmmat]

Btw, ontology is not metaphysics. It is the study of what qualifies as an existing entity (what an entity is) and the nature thereof in each case; almost the opposite of metaphysics, which is about what is "beyond" (meta) physics.

 

on·tol·o·gy, noun: the branch of metaphysics that studies the nature of existence or being as such.

 

http://dictionary.reference.com/browse/Ontology?r=75&src=ref&ch=dic

[swansont]

swansont;

 

 

I wonder why you keep participating in a thread on a subject in which you are not particularly interested. Maybe you just need to try to discredit ontology and insist that the physics is all that matters.

 

I have participated in areas where people have gotten the physics wrong. I have no interest in the ontology, but if you err with the physics which you think supports your position, or denies some other position, you have no hope of moving forward.

[StringJunky]

Like I explained in my last post, it is not generally assumed that duration is something that exists in and of itself. Einstein held that space-time coordinates do not have an independent, substantial, ‘life of their own’. Relativity, he said, proves this.

 

 

Would it be correct to say that time is to space and matter as a wave is to water...you can't take the wave out of water?

Edited June 7, 2011 by StringJunky

[Iggy]

Would it be correct to say that time is to space and matter as a wave is to water...you can't take the wave out of water?

I think it is fair to say that you cannot have time without space and matter. Einstein said also, "People before me believed that if all the matter in the universe were removed, only space and time would exist. My theory proves that space and time would disappear along with matter"

[owl]

Definition of ontology quoted by Cap'n Refsmmat:

on·tol·o·gy, noun: the branch of metaphysics that studies the nature of existence or being as such.

 

I stand corrected. Thank you.

My error came from my background in studying metaphysics as the supposed “spiritual realm”... beyond the “physical realm,” which entails an emphasis on the “meta” as “beyond.” Sorry.

Having partially extracted foot from mouth, I brushed up on my definitions and metaphysical history. Here are more quotes about the place of ontology within metaphysics.

Wikipedia:

Ontology:... "of that which is"...

Traditionally listed as a part of the major branch of philosophy known as metaphysics, ontology deals with questions concerning what entities exist or can be said to exist,...

 

In theory, an ontology is a "formal, explicit specification of a shared conceptualization".[1] An ontology renders shared vocabulary and taxonomy, which models a domain — that is, the definition of objects and/or concepts, and their properties and relations.

 

From Dictionary.com:

1.The branch of metaphysics that studies the nature of existence or being as such.

2.

(loosely) metaphysics.

(my bold.)

 

So anyway, the question, “What is time?” is appropriately within the ontological branch of metaphysics. It is not to be taken for granted as an existing entity ("that which clocks measure") other than the obvious concept of "event duration" (however variable) for all physical processes.

 

Finally (to this point) a paragraph from Wikipedia on the history of science in relation to metaphysics:

 

Prior to the modern history of science, scientific questions were addressed as a part of metaphysics known as natural philosophy. The term science itself meant "knowledge" of, originating from epistemology. The scientific method, however, transformed natural philosophy into an empirical activity deriving from experiment unlike the rest of philosophy. By the end of the 18th century, it had begun to be called "science" to distinguish it from philosophy. Thereafter, metaphysics denoted philosophical enquiry of a non-empirical character into the nature of existence.

 

I think the latter inquiry is still relevant today as in the context of this thread. Even given the “mountain of evidence” empirically established for relativity (quite true), the question, “What, after all, is time?”... is still relevant.

As a footnote, the same applies to the ontology of space.

A bit off topic, but in brief reply to Iggy’s quote in that regard:

 

Einstein (quoted by Iggy):

...

My theory proves that space and time would disappear along with matter.

 

I wonder what we would call that emptiness after everything, even space disappeared. I think that the result of matter disappearing (and the concept of elapsed time as it moved around) would be empty space... absence of "things" in space. How is this wrong? What is space besides the empty whatever... volume (pick a synonym) in which "stuff" exists and moves. This question is only appropriate to this thread as another very similar example of ontology as applied to time.

Edited June 7, 2011 by owl

[md65536]

Your statement has the same meaning (or lack thereof) as the often repeated old saw, "Time is that which clocks measure," which is a meaningless tautology. It doesn't address "What dilates" in "time dilation", for instance, the ontological question.

That which clocks measure, dilates. ie time. If that's unsatisfactory, can you give us a concrete example or speculation or anything of what time might be other than "that which clocks measure"? Is there any reason to suggest it is something more?

 

And a follow-up: Is there any observable or testable prediction or consequence (even if indirect) of such an expanded definition of time? Or is there any way in which you can notice the effects of time, for which it is insufficient to say that it is "that which clocks measure", so that the definition of time used by SR/GR is insufficient?

 

And, in case there is no way to notice the effect of any consequence of an expanded, ontological definition of time, then how would you verify that it was true, especially versus any other supposed ontological definition of time that also can't be verified or falsified, including of course the obvious possible case that it is nothing more?

Edited June 7, 2011 by md65536

[owl]

md65536

 

That which clocks measures, dilates. ie time.

 

The empirical observation is that even the most accurate clocks “tick” at variable rates in different “environments.” There is scientific consensus on this fact. The assumption that, therefore “time dilates” begs the ontological question, “What dilates?" Is "time itself” some kind of malleable medium or entity or is it just event duration, from one instance of “now” to another as in all physical processes, as everything moves (faster or slower in different circumstances.)

 

If that's unsatisfactory, can you give us a concrete example or speculation or anything of what time might be other than "that which clocks measure"? Is there any reason to suggest it is something more?

 

As some of us here have agreed, any physical process can be called a clock in the broadest sense. So even if there were no intelligent life with clocks as we know them, we can say that it “takes time” for all physical processes to happen... for all movement. Ontology asks, What slows down in so called “time dilation” situations besides those physical processes? My argument is that the latter is the reality, while time remains an artifact of measurement, the concept of duration which the phrase “time dilation” erroneously reifies (making time into an entity in and of itself.)

 

And a follow-up: Is there any observable or testable prediction or consequence (even if indirect) of such an expanded definition of time? Or is there any way in which you can notice the effects of time, for which it is insufficient to say that it is

"that which clocks measure", so that the definition of time used by SR/GR is insufficient?

 

I think the above ontology is actually a more restricted sense of time than an expanded one... just elapsed time during all physical movement rather than some unexplained local variable “time environment.”

As for “noticing the effects of time,” I must not understand the question, because we all notice these physical processes happening on all scales, including the human aging process. No doubt the latter must slow down with higher velocity, just as clocks do. And we can expect that those “space cadets” above aged only five years while the whole earth population aged ten years... this without saying “time slowed down” or that they “traveled through time.” This is the ontological criticism of time.

I believe all of the above addresses your last question:

 

And, in case there is no way to notice the effect of any consequence of an expanded, ontological definition of time, then how would you verify that it was true, especially versus any other supposed ontological definition of time that also can't

be verified or falsified?

 

Again, movement/processes “takes time” (and happens faster or slower) without “making something of it” (time.)

 

Another footnote to the Einstein quote above cited by Iggy:

My theory proves that space and time would disappear along with matter.

I am still hoping for some discussion of my criticism of that statement at the bottom of my post yesterday.

To the same point, say we took a small scale example... a box full of objects (matter.) We take all the stuff out of the box and now the box is empty. It makes no sense to say that the space inside the box disappears. Discussion?

[Cap'n Refsmmat]

The empirical observation is that even the most accurate clocks "tick" at variable rates in different "environments." There is scientific consensus on this fact. The assumption that, therefore "time dilates" begs the ontological question, "What dilates?" Is "time itself" some kind of malleable medium or entity or is it just event duration, from one instance of "now" to another as in all physical processes, as everything moves (faster or slower in different circumstances.)

I believe what md65536 was trying to get at was this:

 

We observe time dilation (or something which appears to be time dilation) through empirical observation. We can make predictions about its behavior through mathematics and our current theories of physics. If we propose an answer to the question, "What dilates?", is there any way to test that answer through empirical observation?

 

Clearly at the moment we can observe dilation but do not know what is dilating. If I propose three different answers to that question, is there any way to discern between them experimentally, given that the clocks will show time dilation in exactly the same way no matter which of the three answers is correct?

[swansont]

The empirical observation is that even the most accurate clocks “tick” at variable rates in different “environments.” There is scientific consensus on this fact. The assumption that, therefore “time dilates” begs the ontological question, “What dilates?" Is "time itself” some kind of malleable medium or entity or is it just event duration, from one instance of “now” to another as in all physical processes, as everything moves (faster or slower in different circumstances.)

It has already been pointed out that these environmental factors can be either controlled or compensated for, so there's no point in bringing them up again and again. After you have stripped out those factors you still have time dilation effects, and these effects are independent of the kind of clock you have.

 

As Cap'n R has pointed out, we can measure the dilation without answering the ontological question.

[mpc7555]

It has already been pointed out that these environmental factors can be either controlled or compensated for, so there's no point in bringing them up again and again. After you have stripped out those factors you still have time dilation effects, and these effects are independent of the kind of clock you have.

Ever hear of gravity?

 

And what do you think occurs when the clock is at the center of the Earth? Does it tick at the same rate as it would in 'empty' space because there is no gravity at the center of the Earth? Of course, not. An atomic clock will tick slower at the center of the Earth than it will on the surface of the Earth.

 

The rate at which an atomic clock ticks is determined by the physical state of the space in which it exists.

Edited June 8, 2011 by mpc7555

[Cap'n Refsmmat]

Ever hear of gravity?

 

And what do you think occurs when the clock is at the center of the Earth? Does it tick at the same rate as it would in 'empty' space because there is no gravity at the center of the Earth? Of course, not. An atomic clock will tick slower at the center of the Earth than it will on the surface of the Earth.

 

The rate at which an atomic clock ticks is determined by the physical state of the space in which it exists.

Gravitational time dilation is of course part of general relativity, and its predictions have been tested and verified along with the rest of it.

[mpc7555]

Gravitational time dilation is of course part of general relativity, and its predictions have been tested and verified along with the rest of it.

That has nothing to do with my post.

 

I said the rate at which an atomic clock ticks is determined by the physical state of the space in which it exists.

 

Gravitational force is a physical state of space.

Edited June 8, 2011 by mpc7555

[Cap'n Refsmmat]

So are you saying there's a gravitational effect on clocks apart from the measured and predicted gravitational time dilation?

[mpc866]

So are you saying there's a gravitational effect on clocks apart from the measured and predicted gravitational time dilation?

I am saying the gravitational effect on an atomic clock is the measured and predicted gravitational time dilation.

 

http://en.wikipedia.org/wiki/Time_dilation#Gravitational_time_dilation

 

"Gravitational time dilation There is another case of time dilation, where both observers are differently situated in their distance from a significant gravitational mass, such as (for terrestrial observers) the Earth or the Sun. One may suppose for simplicity that the observers are at relative rest (which is not the case of two observers both rotating with the Earth—an extra factor described below). In the simplified case, the general theory of relativity describes how, for both observers, the clock that is closer to the gravitational mass, i.e. deeper in its "gravity well", appears to go slower than the clock that is more distant from the mass (or higher in altitude away from the center of the gravitational mass). That does not mean that the two observers fully agree: each still makes the local clock to be correct; the observer more distant from the mass (higher in altitude) measures the other clock (closer to the mass, lower in altitude) to be slower than the local correct rate, and the observer situated closer to the mass (lower in altitude) measures the other clock (farther from the mass, higher in altitude) to be faster than the local correct rate. They agree at least that the clock nearer the mass is slower in rate and on the ratio of the difference."

 

The only reason for each observer to make the local clock to be correct is because they are unable or unwilling to understand the rate at which an atomic clock ticks is determined by the physical state of the space in which it exists.

 

If you own a battery operated clock and it ticks slower has time changed or do you replace the batteries? You replace the batteries because you understand what occurred physically in nature to cause the battery operated clock to tick slower. Now, you may say an atomic clock is more accurate than a battery operated clock. The Earth orbiting the Sun clock is more accurate than an atomic clock.

 

As I am going to be banned. This is my last post.

 

 

 

 

 

[Cap'n Refsmmat]

The only reason for each observer to make the local clock to be correct is because they are unable or unwilling to understand the rate at which an atomic clock ticks is determined by the physical state of the space in which it exists.

 

If you own a battery operated clock and it ticks slower has time changed or do you replace the batteries? You replace the batteries because you understand what occurred physically in nature to cause the battery operated clock to tick slower. Now, you may say an atomic clock is more accurate than a battery operated clock. The Earth orbiting the Sun clock is more accurate than an atomic clock.

So you're saying that the gravitational time dilation is actually just the clocks being messed up by gravity, and their measurements are wrong.

 

That has nothing to do with the subject of this thread, so perhaps you'd like to open a new discussion about it in Speculations?

 

As I am going to be banned. This is my last post.

What gave you that impression?

[mpc866]

So you're saying that the gravitational time dilation is actually just the clocks being messed up by gravity, and their measurements are wrong.

 

That has nothing to do with the subject of this thread, so perhaps you'd like to open a new discussion about it in Speculations?

That is exactly what this thread is about. The whole point of this thread is the rate at which clocks tick has nothing to do with time. Perhaps you'd like to re-read the posts by owl. Especially the ones where owl states they agree with much of what I say. Or the ones where owl states the Earth orbiting the Sun is a more correct clock than an atomic clock, which I agree with.

 

What gave you that impression?

I take it you didn't notice this is my third username tonight?

[md65536]

while time remains an artifact of measurement

 

Be careful with your terminology. Time is the measurement. Otherwise we'll be mired in questions like "an artifact of a measurement of what?" and that gets you nowhere. Then all your questions could be answered and you can still imagine there must always be something more to wonder what it is.

 

I think the above ontology is actually a more restricted sense of time than an expanded one... just elapsed time during all physical movement rather than some unexplained local variable "time environment."

 

 

Okay so I thought you were saying that time must be something more than what SR/GR says, but are you instead saying it is something less?

 

Again, I believe it is a mistaken interpretation of SR to say that it suggests that time is an entity, or even that it is unexplained.

 

If SR/GR's definition of time is no good, what can be added, changed, or removed to improve it?

What specific observable (measurable) phenomena might be predicted differently by GR vs. this new definition (Note that all observed phenomena so far are consistent with GR)? If none, then how would you clearly describe the difference between the new definition and GR's definition of time, precisely enough for it to be useful?

 

My point is, how can you define time by anything other than that which can be measured (ie. by a time measuring device)? If you propose some aspect of time that is not a consequence of what is observed, then how can you evaluate its validity? On the other side of the issue, if you propose some aspect that can be removed from GR's definition of time, how do you account for all of the observed phenomena that are consistent with GR?

 

To the same point, say we took a small scale example... a box full of objects (matter.) We take all the stuff out of the box and now the box is empty. It makes no sense to say that the space inside the box disappears. Discussion?

Well sure... the box can define a space. But I think Einstein was talking about removing everything, including such a box.

 

Einstein's saying that space and time don't exist on their own.

If something exists on its own, when considered as independent of other things, this implies that it is an entity (by the very definition of entity), agreed?

But time is not an entity, agreed? Therefore, time does not exist on its own.

Similarly space is not an entity, agreed? Therefore, space does not exist on its own.

 

If you agree with all these things, where's the problem with Einstein's quote?

[DrRocket]

That has nothing to do with my post.

 

I said the rate at which an atomic clock ticks is determined by the physical state of the space in which it exists.

 

Gravitational force is a physical state of space.

 

Any ideal, accurate clock -- atomic, light, pendulm, whatever -- under any condition-- speed, gravitational field, whatever -- ALWAYS ticks at the rate of one second per second. Always.

 

Relativity, particularly general rrelativity, tells us that time is neither universal nor absolute. An accurate clock reliably measures the proper time of its world line. Different clocks, subject to different conditions -- relative speeds, gravitational fields, etc, -- have different world lines and therefore register differences in proper time.

 

Time is not some universal quantity, but is a characteristic of a time-like world line joining two points in spacetime. In general relativity it only makes sense to compare two clocks at two points of intersection of their world lines. There is no exact comparison of "time here" with "time there" -- as is allowable in special relativity. Special relativity is only a local approximation (on the tangent space) to the more exact general theory.

 

Clocks do not "tick slower" in a gravitational field. That makes no sense. Speed of something is [math] \dfrac{change \ in \ something}{change \ in \ time}[/math]. And [math] \dfrac {change \ in\ time}{change \ in \ time} = 1[/math]. Always.

 

 

Confusion arises when Newtonian intuition and Newtonian concepts, like the "flowing river of time" are carried over and inserted naively into a relativistic setting. "Coordinate time" is mistaken for proper time. Clocks measure proper time and nothing but proper time. Proper time is invariant. Coordinate time is not. Ordinary velocity is not invariant. 4-velocity is invariant. Ordinary energy and momentum depend on a choice of coordinates (reference frame). The momentum-energy 4-vector is invariant. If you are going to understand relativity you must invest the time to understand the mathematics in which it is formulated. You cannot even accurately describe the concepts involved in general relativity without using the mathematics of Riemannian geometry (pseudo-Riemannian geometry to be pedantic).

 

This stuff is not intuitive, and if let your intuition be your only guide, you will certainly go astray.

[mpc866]

Any ideal, accurate clock -- atomic, light, pendulm, whatever -- under any condition-- speed, gravitational field, whatever -- ALWAYS ticks at the rate of one second per second. Always.

 

Relativity, particularly general rrelativity, tells us that time is neither universal nor absolute. An accurate clock reliably measures the proper time of its world line. Different clocks, subject to different conditions -- relative speeds, gravitational fields, etc, -- have different world lines and therefore register differences in proper time.

 

Time is not some universal quantity, but is a characteristic of a time-like world line joining two points in spacetime. In general relativity it only makes sense to compare two clocks at two points of intersection of their world lines. There is no exact comparison of "time here" with "time there" -- as is allowable in special relativity. Special relativity is only a local approximation (on the tangent space) to the more exact general theory.

 

Clocks do not "tick slower" in a gravitational field. That makes no sense. Speed of something is [math] \dfrac{change \ in \ something}{change \ in \ time}[/math]. And [math] \dfrac {change \ in\ time}{change \ in \ time} = 1[/math]. Always.

 

 

Confusion arises when Newtonian intuition and Newtonian concepts, like the "flowing river of time" are carried over and inserted naively into a relativistic setting. "Coordinate time" is mistaken for proper time. Clocks measure proper time and nothing but proper time. Proper time is invariant. Coordinate time is not. Ordinary velocity is not invariant. 4-velocity is invariant. Ordinary energy and momentum depend on a choice of coordinates (reference frame). The momentum-energy 4-vector is invariant. If you are going to understand relativity you must invest the time to understand the mathematics in which it is formulated. You cannot even accurately describe the concepts involved in general relativity without using the mathematics of Riemannian geometry (pseudo-Riemannian geometry to be pedantic).

 

This stuff is not intuitive, and if let your intuition be your only guide, you will certainly go astray.

 

This stuff is extremely intuitive.

 

All that needs to occur in order to correctly understand the relationship between the rate at which atomic clocks tick and time is to correctly define what a second is.

 

The present definition is:

 

the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom.

 

The correct definition is:

 

the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom [at sea level].