Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: chiralSPO on 01/05/2018 17:50:19

Please note: This thread may sit on the edge of generally accepted science and speculation. I would like to keep it in this subforum (which is intended for discussions of generally accepted science), so let us agree to be clear about when we are speculating/hypothesizing. Thanks! ;D (also note: While I personally have a fairly advanced understanding of QM, I have only a modest understanding of general relativity, so please bear with me, and know that I am here to learn)
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Time is simultaneously (sorry) a simple concept and a difficult one to grasp. Clearly, our perception (as human beings) of time is not entirely quantitative. There are many different biological and psychological aspects of our perception that I do not want to delve in to. Rather, I would like to discuss purely physical and mathematical interpretations of time.
I have had many questions about time swirling in my head for a while now, and I think I can distill them into two primary questions:
(1) Is time the most fundamental "temporal" dimension, or is it a function of an unrecognized dimension?
This question comes about when trying to conceive of an absolute time scale. Every equation I have come across in my education in the physical sciences deals with dt or Δt, and so is really just dealing with relative time (t = 0 is arbitrary or internally defined, and any indefinite ∫f(t)dt will have that pesky "+ c" term).
Many people point to the Big Bang as the natural t = 0, but this raises at least as many problems as it addresses.
So is time a function of another more fundamental parameter t = G(α), and most of our equations are actually only valid for α, but are comfortably within experimental error of t?
For example let us imagine that α = t +ln(t)/t (unfortunately, there is no algebraic solution for the inverse, but we can solve it graphically, just by swapping the α and t axesit would be nice if someone can recommend a function that has similar properties but can be explicitly solved both ways):
Screen Shot 20180501 at 12.11.47 PM.png (36.26 kB . 570x563  viewed 4419 times)
(If we look at the blue curve pictured above, and consider the abscissa as the α axis and the ordinate is the t axis)
Clearly, consideration of t ≤ 0 gives only nonsensical results, but the function is welldefined for all values of α, and for large positive values of α (or t), α ≈ t. For example, t = 1000 returns α = 1000.006908 (an error of about 7 ppm), and for t = 10^{10} the error is only 2.3×10^{–19}, well beyond the temporal precision of any experiment I know of. And the convergence of dα and dt (or Δα and Δt) will come even faster.
This relation has the obvious shortcoming that it requires some explicit definition of the unit (you will get different answers using years, seconds, or any other arbitrary unit) ie we have traded the problem of an absolute zero for the problem of an absolute 1. Perhaps there may be a fundamental unit of time (and therefore a fundamental unit of space, based on the relationship defined by the speed of light)?
However, this may obviate some of the difficulties that come when considering inflation (the big bang type, and perhaps what we see now). How could we experimentally (or theoretically) test the validity of this type of model?
(2) Are there different "kinds" of time?
Just as there is inertial mass and gravitational mass, which are conceptually different, but appear to be the same, for reasons which (to the best of my knowledge) still elude us. Are there conceptually independent "kinds" of time?

Interesting thoughts.
Do we have the same problem with distance, there is no true origin. All measurements are Δx, Δy or Δz.
Similarly, units are arbitrary.

Interesting thoughts.
Do we have the same problem with distance, there is no true origin. All measurements are Δx, Δy or Δz.
Similarly, units are arbitrary.
Thanks Colin!
I guess I am trying to find a temporal dimension that is more like the spatial ones, where there is no (apparently) meaningful zero. Currently, by defining the Big Bang as t =0 we introduce problems associated with negative times and other nonsensical consequences. Perhaps instead, there is no true temporal origin, and the observations interpreted as the BB are just consequences of the divergence of t and α.

I am going to have to think a little about your questions. This is a doozy.

And following up from Colin's response:
I guess our current system would be similar to finding some point of reference (like a massive object), and defining our spatial coordinates as in spherical coordinates about it. In this case, time would be like r, for which there is nothing meaningful to be gaining by considering r ≤ 0. Spherical coordinate systems, of course, make the most sense when dealing with spaces that have some sort of spherical symmetry: like looking at orbits around a lonely planet, or orbitals about a lonely nucleusthis becomes increasingly cumbersome when considering multiple planets or atoms. (I know that internally vs externallydefined coordinate systems are a big deal when modeling molecules, and I presume that this is similar when looking at orbital systems containing multiple bodies)
Pure speculation: Drawing on the analogy to spherical coordinates, could there be additional dimensions akin to θ and φ? Are they what we think of as spatial dimensions, or are they distinct? Is this how trigonometric functions become involved in GR? And expanding the multibody problem of spherical coordinates: is there an external coordinate system that allows for multiple Big Bangs, each being a local origin?

First of all, is an indefinite integral unsuitable for functions of time? Surely only time intervals make sense so definite integrals are the way to go. I am also thinking about your function for α and t.

I don’t want to appear to be discouraging. We do know for a fact that the quantification of time uses some form of clock, and we know that the rate that a clock measures the passing of time is affected by the relative acceleration of that clock vs some presumed rest clock.
Unfortunately there is no absolute space in which to place our rest clock, and so there is no absolute measure of time. Therefore, time is relative to conditions of local energy density set up by differences in gravitational potential, relative motion, and/or applied forces between two clocks in relative motion. The conditions of each clock in relative motion are therefore different.
I don’t see how you can get to anything fundamental in regard to a time increment from those circumstances, so I personally settle for the concept that time simply passes, but the measure of the rate that time passes is relative to the differing conditions in which our clocks are located.
On the bright side, maybe there is some fundamental increment of energy based on some foundational minimum background energy level. If such an energy level could not be reduced below this as yet unknown natural limit, and if we could place our rest clock there, maybe all other frames could be compared to that clock.

I don’t want to appear to be discouraging. We do know for a fact that the quantification of time uses some form of clock, and we know that the rate that a clock measures the passing of time is affected by the relative acceleration of that clock vs some presumed rest clock.
Unfortunately there is no absolute space in which to place our rest clock, and so there is no absolute measure of time. Therefore, time is relative to conditions of local energy density set up by differences in gravitational potential, relative motion, and/or applied forces between two clocks in relative motion. The conditions of each clock in relative motion are therefore different.
I don’t see how you can get to anything fundamental in regard to a time increment from those circumstances, so I personally settle for the concept that time simply passes, but the measure of the rate that time passes is relative to the differing conditions in which our clocks are located.
On the bright side, maybe there is some fundamental increment of energy based on some foundational minimum background energy level. If such an energy level could not be reduced below this as yet unknown natural limit, and if we could place our rest clock there, maybe all other frames could be compared to that clock.
Thanks Bogie.
I think I may have caused some confusion using the terms "absolute" and "relative." I understand that different frames of reference will have different relative rates at which time passes, and that looking for any sort of Universal Clock is probably futile. My intended meaning of "absolute" and "relative" is more akin to Kelvin vs Celsius temperature scales, in which "absolute" scales are referenced to a meaningful zeropoint, whereas "relative" scales only concern themselves with the difference between two points. (My apologies, if you already understood my meaning, and the confusion is all on my endif so, please clarify).
Your points do still seem quite relevant to my question of whether there can be a meaningful unit of time (an absolute 1). I will have to think more about this aspect. Thank you.

Thanks Bogie.
I think I may have caused some confusion using the terms "absolute" and "relative." I understand that different frames of reference will have different relative rates at which time passes, and that looking for any sort of Universal Clock is probably futile. My intended meaning of "absolute" and "relative" is more akin to Kelvin vs Celsius temperature scales, in which "absolute" scales are referenced to a meaningful zeropoint, whereas "relative" scales only concern themselves with the difference between two points. (My apologies, if you already understood my meaning, and the confusion is all on my endif so, please clarify).
Your points do still seem quite relevant to my question of whether there can be a meaningful unit of time (an absolute 1). I will have to think more about this aspect. Thank you.
I didn't mean to imply you weren't entirely on top of the basics of measuring and comparing the rate that time passes in different frames. I see your point about absolute and relative scales now, and perhaps there is something to uncover along that avenue in regard to a fundament unit of time. Thanks for the thoughtful response.

I didn't mean to imply you weren't entirely on top of the basics of measuring and comparing the rate that time passes in different frames. I see your point about absolute and relative scales now, and perhaps there is something to uncover along that avenue in regard to a fundament unit of time. Thanks for the thoughtful response.
No offense taken :) Your response was entirely reasonable given my ambiguous word choice.

First of all, is an indefinite integral unsuitable for functions of time? Surely only time intervals make sense so definite integrals are the way to go.
Well, one can invoke indefinite integrals to make generic forms of useful functions. For instance, if we know that an object is accelerating at some function f(t), then we can describe the generic velocity as the indefinite integral of f(t)dt. However, after thinking about it more, I think that the example of the integral actually has little to do with my main point, and is largely tangential...
I am also thinking about your function for α and t.
Yes, please do. I would be very interested in your thoughts on this.

Here is an aside. Not directly related to your function but interesting none the less.
https://www.quora.com/WhatistheLaplacetransformoflogt
This also leads to the following.
http://mathworld.wolfram.com/EulerMascheroniConstant.html
Euler is likely the way to go in starting to analyse the equation.

We can arrive at imaginary time which is interesting since that is one way to arrive at negative energy.
http://m.wolframalpha.com/input/?i=integrate%5Bt%2B%28log+t%29%2Ft%5D

Let's break out the interesting part.
http://m.wolframalpha.com/input/?i=integrate%5B%28%28log+t%29%2Ft%29%5E1%5D
Now that is something you wouldn't want to explain to your granny.

Thanks Jeffrey! I had not come across the EulerMascheroni γ before. It will take some time to work through the first two links and digest the content, but looks well worth it!
As for the last two links you sent, it looks like the imaginary components only appear for negative values of t (and the solutions are purely real for values of t > 0). The functions also appear poorly behaved at 0 (jump discontinuity at t = 0 in the imaginary components, and not differentiable at t = 0 (or t = 1 for the second integral) in the real components).
My goal with the proposed transform from t to α was to find a dimension (α) in which the entire range of reals (–∞ to +∞) maps onto only the strictly positive values of t ( t > 0), thereby avoiding the difficulties associated with t ≤ 0.
Unfortunately, with the function I have chosen, there is no algebraic inverse (only numerical or graphical solutions), so determining indefinite integrals is a nonstarter (for definite integrals, numerical and graphical solutions are feasible).
Is there a function y = f(x) for which:
• limit of y as x → –∞ = 0
• limit of y as x → +∞ = x (I know this would be y = x = +∞, but I want x and y to nearly converge well before +∞)
• the function is continuous for all real values of x (–∞ to +∞) and y > 0
• an algebraic solution for f^{–1} can be found: x = f^{–1}(y)
Ideally this function would also be differentiable everywhere (probably would have to be to satisfy the above constraints, but if not, I will still consider solutions that are not differentiable everywhere, but still adhere to the above)

Well you don't ask for much. I'll think about it a while.

Thanks! :D

Pure speculation: Drawing on the analogy to spherical coordinates, could there be additional dimensions akin to θ and φ? Are they what we think of as spatial dimensions, or are they distinct?
Are you thinking that what we perceive as a single time dimension might be the resultant of other, hidden dimensions? Or are you thinking that those other dimentions are what we see as space?
Or something else? :)
Is this how trigonometric functions become involved in GR?
In relativity if you look at Minkowski ST diagrams the worldlines of uniformly accelerating particles are hyperbolic which links to GR.
The trig functions come about because the Lorentz transformations can be treated as hyperbolic rotations.

Quote from: chiralSPO on Yesterday at 18:45:43
Pure speculation: Drawing on the analogy to spherical coordinates, could there be additional dimensions akin to θ and φ? Are they what we think of as spatial dimensions, or are they distinct?
Are you thinking that what we perceive as a single time dimension might be the resultant of other, hidden dimensions? Or are you thinking that those other dimentions are what we see as space?
Or something else?
Yes... Maybe... I really don't know.
One could imagine a 4D spherical coordinate system in which there is one radial dimension (time), and 3 orthogonal angular dimensions [t, θ,φ,ψ]. It could be mapped onto the orthonormal basis set of [t, X, Y, Z], but it isn't immediately clear to me that it would be useful.
Quote from: chiralSPO on Yesterday at 18:45:43
Is this how trigonometric functions become involved in GR?
In relativity if you look at Minkowski ST diagrams the worldlines of uniformly accelerating particles are hyperbolic which links to GR.
The trig functions come about because the Lorentz transformations can be treated as hyperbolic rotations.
Yes, indeed. I am reading up on Minkowski spaces now (this was part of the inspiration for starting this thread). Obviously these are only defined for the observer, placing them at the origin (and only a good local approximation, once thinking about GR).
More pure speculation: If the other angles involved (even if it's just one) then this might (I haven't worked through the math yet) offer a way of performing Lorenzlike transformations for GR: if we treat time like the radius of the nsphere (from circle on up), and think of acceleration/gravitation (or other distortions) as a rotation that shrinks the projection of the radius (ie perceived time = t×cos(θ), where θ relates to the (gravitational) accelerationso in the absence of acceleration, perceived time = t, while for increasing θ the perception of time (elsewhere) contracts (efectively blue shifting the rest of the universe)
I don't know, I think this speculation might just be veering off topic and into New Theories territory....
I really like the idea of Minkowski space being centered at the observer (which it would have to be for relativity), with infinitely extending orthogonal [t, X, Y, Z] dimensions (and it appears to be experimentally valid). My main question is: none of the X, Y, or Z coordinates have any boundaries, so why should t? And therefore, is it possible that the way we have defined t is wrong, and actually we should be thinking in terms of [α, X, Y, Z], which eliminates all boundaries while still being essentially commensurate with what we observe.

In the Minkowski ST diagrams t doesn’t have a boundary, just the same as x.
I’ll have to think about the rest, I have enough problems imagining 4 orthoganal cartesian dimensions without imaging the same for spherical! 8)

We can arrive at imaginary time……
The “Ausies” got there ahead of us! Fred Alan Wolf says of dreamtime:
“Aboriginals believe in two forms of time. Two parallel streams of activity".
Interestingly, the aboriginal term “Alcheringa” is not best translated as “Dreamtime” (which was coined by research worker Frank Gillen). The term “The Dreaming” is preferred by the Indigenous Australian People as being a more accurate translation, and certainly involves two “dimensions” of time.
Forgive that unscientific aside.
Who was it who said: “The truth is that a scientist's understanding of a phenomenon is inversely proportional to the number of math equations he uses to describe it.”
I have a nasty feeling it might have been Louis Savain.
Interesting and valuable as the maths undoubtedly are, how well does this approach address the OP?
As far as we are aware, nothing can happen without time, in which it can happen. How fundamental is that?

This question comes about when trying to conceive of an absolute time scale.
Could it be that there is no “absolute time scale”?
We perceive our Universe as functioning in accordance with the “rules” of relativity, at least, on a scale that is meaningful in our everyday lives. Should we expect anything, other than “c”, to be “absolute”?

If we define a universe in which no forces exist then all frames are inertial. However, if all inertial frames are in relative motion with each other then any particles traveling along with the frame will eventually collide with another particle. Therefore, these collisions act like a force. We have time. If all frames are at rest in relation to one another the same particles still exist but don't move. Where has time gone?

This question comes about when trying to conceive of an absolute time scale.
Could it be that there is no “absolute time scale”?
We perceive our Universe as functioning in accordance with the “rules” of relativity, at least, on a scale that is meaningful in our everyday lives. Should we expect anything, other than “c”, to be “absolute”?
Indeed. I suspect that there isn't an "absolute" time scale. I want to reiterate that my intended meaning of "absolute" and "relative" is with respect to whether the 0 is meaningful or not:
My intended meaning of "absolute" and "relative" is more akin to Kelvin vs Celsius temperature scales, in which "absolute" scales are referenced to a meaningful zeropoint, whereas "relative" scales only concern themselves with the difference between two points.
It would seem that when people invoke the Big Bang as "the beginning of time" that they are declaring some sort of absolute scale, in which everything that can be observed is t > 0, and that all t ≤ 0 is fanciful. My hope is to do away with this boundary condition by exploring the possibility of a temporal dimension that is not the same as what is currently defined as time, which has no bounds.

Hence the mapping. ;)

If we define a universe in which no forces exist then all frames are inertial. However, if all inertial frames are in relative motion with each other then any particles traveling along with the frame will eventually collide with another particle. Therefore, these collisions act like a force. We have time. If all frames are at rest in relation to one another the same particles still exist but don't move. Where has time gone?
Time has not necessarily gone anywhere, but without change (movement) how can we perceive it?
It might be true that there can be no change without time, but time without change? That's a cat of a different colour.

It would seem that when people invoke the Big Bang as "the beginning of time" that they are declaring some sort of absolute scale, in which everything that can be observed is t > 0, and that all t ≤ 0 is fanciful.
Agreed! If the BB was the beginning of time, how could it have happened?
“In the beginning there was nothing, which exploded.” (T. Pratchett). Of course, he would have the answer! :)
My hope is to do away with this boundary condition by exploring the possibility of a temporal dimension that is not the same as what is currently defined as time, which has no bounds.
If it has no bounds; wouldn’t that make it infinite?

If it has no bounds; wouldn’t that make it infinite?
Not necessarily... it just means there's no boundary. One could imagine a loop, or some other type of closed, but still unbounded time...
What I have been describing with my attempts at defining α does seem to be unbounded and open, which would indeed be infinite.

See attached article. I tried to post other articles but they're too big. This site is too stingy!!!

Not necessarily... it just means there's no boundary. One could imagine a loop, or some other type of closed, but still unbounded time...
If time were a loop, wouldn’t it repeat? If that were the case, it would be bounded by its own repetition. If anyone could experience the whole loop, he/she would be able to recognise the start/finish.
In principle, a featureless loop might be said to be boundless. No doubt someone can think of an example.
Good luck identifying infinite time.

Fascinating piece of "history", Pete. If it were not for the comment about dating the discussion some twenty years back, it would have been interesting trying to work out when it was written.
Shame about your other articles. Could you split them into postable size chunks?

Fascinating piece of "history", Pete. If it were not for the comment about dating the discussion some twenty years back, it would have been interesting trying to work out when it was written.
Shame about your other articles. Could you split them into postable size chunks?
Possible, yes.It'd be easier if I put them all on my website and post the URL to it.

Please see the flour articles listed below the title "Articles about time" at
http://www.newenglandphysics.org/other/other.htm

If I have this right we need two conditions for the function.
And
And the function should be continuous. Is this correct?

An interesting but not very pertinent function is f(t) = (t)^1.

An interesting but not very pertinent function is f(t) = (t)^1.
Is this not equivalent to f(x) = –x ? Perhaps there is a typo in your equation? f(x) = (–x)^{x} is definitely an odd one! (all x < 0 are well defined, but then only odd positive integers get real outputs)

If I have this right we need two conditions for the function.
And
And the function should be continuous. Is this correct?
Close! I would like:
And
And the function should be continuous, and f(α) > 0

Ok, got it. How soon do you want it?

An interesting but not very pertinent function is f(t) = (t)^1.
Is this not equivalent to f(x) = –x ? Perhaps there is a typo in your equation? f(x) = (–x)^{x} is definitely an odd one! (all x < 0 are well defined, but then only odd positive integers get real outputs)
Sorry that was just wrong. Should have been f(t) = (t)^{1}

I think Einstein pointed out that time is what prevents everything from happening at once.
So no problem with the Big Bang: it was the event when everything did indeed happen at once.

Ok, got it. How soon do you want it?
No real rushbut it is driving me nuts. :)

Here is something that I haven't attempted to graph yet but may be interesting. It is α = t^{2} + log^{2}(t)t^{2}

This is now interesting. Looks like a gravity well.
http://www.wolframalpha.com/input/?i=t%5E2%2Blog(t%5E2)t%5E2%3D0

The non homogeneous solution.
http://www.wolframalpha.com/input/?i=t%5E2%2Blog(t%5E2)t%5E2%3Du

.....I have discussed this elsewhere (https://www.thenakedscientists.com/forum/index.php?topic=73163.0)
I've had another look at this thread. Now I recall why Alan's quote was the only one I remembered. :)
I have to ask one question, though. If you replaced the word "time" with "change" in all the appropriate places; how much difference would it make to the arcane maths?
(mod edit: you forgot to close the quote, so it was hard to know where the question started. I think I fixed it correctly)

Change and time are not equivalent. Time is a dimension, and change refers to differences within one dimension.
This is most well defined within calculus (sometimes called the math of change), where the symbol ∂ (sometimes d) is used to denote microscopic change, often relating the change of one thing with respect to the change of another.
In this way, we can define instantaneous (microscopic) change of position along a spatial dimension (x) with respect to instantaneous (microscopic) change in time (t) as ∂x/∂t which is equivalent to the velocity in the x direction.
Although time is a very common dimension (variable) to compare changes against, it is not the only one. For instance we can look at the change in altitude with respect to change in forward distance traveled ∂y/∂dx (slope) or the change in cost of making chocolate with respect to the change in the cost of labor ∂$_{chocolate}/∂$_{labor} etc. etc.
What I am trying to learn in this thread is whether our concept of velocity (or any other rate of change with respect to apparent time) is best described as a ∂x/∂dt, or if there is a more fundamental variable (I believe I called it α earlier in the thread) such that ∂t/∂α is welldefined, and ∂x/∂α holds up better to the boundary condition that the big bang appears to impose on ∂t.

(mod edit: you forgot to close the quote, so it was hard to know where the question started. I think I fixed it correctly)
Spoton, thanks.

Thanks Chiral. I knew I was in the wrong thread. :)
I'm fine with your explanation, but I guess we all have a "mumpsimus", or two, lurking somewhere. One of mine is the idea that time is just a measure of rate of change, like inches miles etc are measures of distance.

I had thought about this a lot last year. I came to the conclusion that a continuous function would be impossible because it would always end up with a zero denominator at some point. I may have another look now that I have not been thinking about it for a while.

I'm fine with your explanation, but I guess we all have a "mumpsimus", or two, lurking somewhere. One of mine is the idea that time is just a measure of rate of change, like inches miles etc are measures of distance.
My lack of background maths and physics means that, sometimes, even my “eureka” moments are ephemeral, and this may be an example, but thinking about my post (#47) I spotted an “unconformity”.
I’m comparing time with inches and miles. The real comparison should be between time and length (distance) on the one hand, and (e.g.) seconds and millimetres, on the other. Thus, time by association, can be considered as a dimension.

If we take f(α) to be 1/α then at α = ∞ we have our zero value. You stated that a value of 1 for time was a consideration. At α = 1 we have our value of 1. All negative fractions from α = 1 and approaching zero give an infinite positive sequence that can map to time. Infinite time then terminates at this α = 0 boundary. Crossing into positive α then gives us negative time which descends back to zero. You still have a discontinuity.

I’m comparing time with inches and miles. The real comparison should be between time and length (distance) on the one hand, and (e.g.) seconds and millimetres, on the other. Thus, time by association, can be considered as a dimension.
This is how I understand it to be.

There is a singularity separating positive time from negative time. One time 'direction' will never be able to detect the other.

If we take f(α) to be 1/α then at α = ∞ we have our zero value. You stated that a value of 1 for time was a consideration. At α = 1 we have our value of 1. All negative fractions from α = 1 and approaching zero give an infinite positive sequence that can map to time. Infinite time then terminates at this α = 0 boundary. Crossing into positive α then gives us negative time which descends back to zero. You still have a discontinuity.
Indeed... t = 1/α will not fit the necessary criteria.
Is there a function t = f(α) for which:
• t is strictly positive for all values of α (t > 0)
• limit of t as α → –∞ = 0
• limit of t as α → +∞ = α (I know this would be t = α = +∞, but I want α and t to nearly converge well before +∞)
• the function is continuous for all real values of α (–∞ to +∞)
• an algebraic solution for f^{–1} can be found: α = f^{–1}(t)
Ideally this function would also be differentiable everywhere (probably would have to be to satisfy the above constraints, but if not, I will still consider solutions that are not differentiable everywhere, but still adhere to the above)
I think that t = ln(1+e^{α}) works!
(I found it by realizing that the derivative of the desired curve followed a sigmoid curve, going monotonically from zero to 1, and that therefore the integral of a sigmoid would have the desired properties.)
t = ln(1+e^{α})
• is continuous and differentiable and strictly positive across all reals
• limit of t as α → –∞ = ln(1) = 0
• limit of t as α → +∞ = ln(e^{α}) = α
• has the inverse function α = ln(e^{t} – 1)
Thank you to Bill S for reviving this thread, and to jeffreyH for prompting me to revisit the math!

This is how I understand it to be.
Eureka!!! Mumpsimus not completely exorcised, but still a lot of thinking to do. Thanks for the patience.
There is a singularity separating positive time from negative time. One time 'direction' will never be able to detect the other.
That’s one of the things that will need some thought!

Think of decoherence Chiral. Then treat time as if it would be a equivalence, scaling up Quantum objects to a macroscopic plane gaining that 'local clock'. In that case a Big Bang, no matter where and how it comes to be, indeed is t=0.
But it also tells you that t must be 0 at 'all times'. Making it a choice of from where you measure. You can't measure it at a same scale (QM) though so you become restricted by your (macroscopic) wrist watch, which never stops ticking.
And I think you are correct in splitting it into two concepts, that's what I do too. Time should be a 'property' of SpaceTime, with the 'local clock' being a expression of our macroscopic reality. In relativity it indeed is a 'dimension', that you need for a SpaceTime.
As for " Perhaps there may be a fundamental unit of time (and therefore a fundamental unit of space, based on the relationship defined by the speed of light)? "
Yes, your local clock is a equivalence to 'c', but the question of it thereby also being a 'fundamental unit' seems to me to belong to whether SpaceTime has a 'granularity'.
Is 'c' a granularity?
I like the idea of 'c' being a 'constant' much better, and defining ones local clock as a equivalence then makes it into a constant too, aka 'Proper Time'.
It is of a outmost importance to understand how we define a repeatable experiment' and so 'c'. It's local definitions agreeing with each other that gives us the base from where we find this 'global' definition of a universe. When turned around into ' time dilation's ' and ' length contractions ' by relativity you will need to take a new look at that base. Failing to do so makes you unprepared.
=
Thinking of it this way a 'Big Bang' is the beginning of a cone widening out into 'a local clock'. And presuming that a Big Bang has no defined localization. or turned around, started 'everywhere' as can be proven by using a 'isotropic and homogeneous universe'. Then the 'cone', aka 'Big Bang', isn't something you just can 'time reverse' from the macroscopic to the microscopic finding a 'origin', neither is the 'arrow of time' what you can use to back track it. It's a 'co existence'.
It makes the quantum regime into something entirely different from the way we define a SpaceTime. We use four dimensions for it, length, width, height and 'time'. Exchange 'time' for 'local clocks' macroscopically and make our wristwatches what give us a direction. The 'one way arrow'. That way your clock is no 'illusion' and 'proper time' is the base of our universe. Time becomes very real treating it like this, without it nothing exist.
Another way to look at those 'cones' would then be to use each ones 'history' to give us a 'time scale' of when a 'Big Bang' started. Then as we compare my local 'cone' to yours, and find us in agreement, we come to a same conclusion as we do finding a 'repeatable experiment' to work. It holds at all times and wherever you go to test it.
The 'cone' I'm using is to its nature two folded, it has no arrow in one sense as it is about QM and our macroscopic reality co existing. But we can't get away from our local macroscopic clock so in that sense it is possible to define histories to each 'cone'. And it makes 'scaling' what you use to go from one concept to the other.
It's not that difficult a concept, and it fits. But it makes the 'universe' a even stranger place than what we thought before.
==
PS: I suspect one might be able to do the same for the rest of our 'dimensions'. Leaving them to be a result of, what I like to call, 'scale dependencies'. It makes 'scales' into something different than what we usually define them from, as we do it from presuming 'dimensions' to be their origin. And that one is quite worth thinking of.
It's also a primary reason for trying to be clear from where you define something, locally or 'globally'. People tend to miss doing so, but it's just as important as telling what 'frame of reference' one define it from.

thanks yor_on, there is a lot to digest there, and I want to think more before I respond to your post.
As far as the function I posted earlier, it appears to be one of a class of functions that will all meet the criteria I had posited earlier.
t = log_{β}(1 + β^{α}) meet all of the criteria, for any β > 1
As β increases, α and t become more similar to each other (converging at lower values of α (or t))
For instance:
If we evaluate with the natural base, e, then α and t converge to error < 1ppm by α = 12
If we evaluate in base 10, then α and t converge to < 1ppm by α = 5
While if we evaluate in base 2, then α and t converge to < 1ppm by α = 17
Again, one must be aware that we don't know what the units of α and t are... is this 17 seconds, or 17 quintillion years?
Speculation: Is there a way to fit to z values of Hubble shift to see if instead of expansion, it's actually this deviation? This might help us nail down what β is and what the actual fundamental units of time are?...

Bill: the jargon is the distinction between quantities and units. "Length" is a quantity, "meters" is a unit.
So no problem with time: it's a quantity. Just as length separates points, time separates events, and "seconds" are a unit.
As all the units are defined in terms of the number of cycles of an atomic clock, we have a universal scale for each  now including mass following its SI redefinition.
The most fundamental quantities that are unrelated to each other are also called dimensions, usually signified by square brackets [M], [L] and [T] being the most often encountered, but you can usefully add charge [Q] to produce a fairly complete armoury for engineering analysis.
So back to the question: how fundamental is time? As I see it, it is as fundamental as the other dimensions, none of which requires an absolute frame or origin. If we consider mass to be "that which is subject to gravitational attraction" then zero mass is no more conceptually difficult than zero length or zero time  no need for an origin or any embodiment of negative mass.
Or am I being too naive to see the problem?

time separates events
Are there any scenarios where such separations do not exist? Even one example?
If not can we say that the separation is measured (not caused which you are probably not saying) by time ?
Ad do some of us need to keep reminding ourselves that time is not a "thing" ,more a description?

Time is the most 'real' thing you will meet in your life. It gives you a existence and it ends with your death. Doesn't matter if you're a mathematician. It's here, and can't be transformed locally.
=
Gravity can, not your local clock

@chiralSPO I am impressed! What exactly are your thoughts on a connection with the Hubble shift? Are you assuming a connection to the convergence of α and t? Also, what started you down this path?

Bill: the jargon is the distinction between quantities and units. "Length" is a quantity, "meters" is a unit.
So no problem with time: it's a quantity. Just as length separates points, time separates events, and "seconds" are a unit.
As all the units are defined in terms of the number of cycles of an atomic clock, we have a universal scale for each  now including mass following its SI redefinition.
So far, so good. Add "jargon" to my list of "deficiencies". :)
The most fundamental quantities that are unrelated to each other are also called dimensions,
I’ve been looking for a good definition of dimensions. Thanks.
usually signified by square brackets [M], [L] and [T] being the most often encountered, but you can usefully add charge [Q] to produce a fairly complete armoury for engineering analysis.
Next step, time permitting: Get to grips with dimensional analysis.
So back to the question: how fundamental is time? As I see it, it is as fundamental as the other dimensions, none of which requires an absolute frame or origin. If we consider mass to be "that which is subject to gravitational attraction" then zero mass is no more conceptually difficult than zero length or zero time  no need for an origin or any embodiment of negative mass.
Or am I being too naive to see the problem?
Alan, I suspect you are not the one who is being naïve. It’s much more likely that my questions are naïve, and that you, in common with many other experts, sometimes don’t see the extent of that naivety.
“Conceptually”, I have little difficulty with zero mass, zero length or zero time. I then need to try to relate these concepts to the physical world. This leads to questions like: If something has no mass, or no length, can it be said to exist, other than as a mental concept? Similarly, if something exists for zero time, is it ever “there”?
Then we come back to:
A point on a line has no length. A point on a timeline has no duration. What's the problem?
I have no problem with either of those, in principle. However, in practice, can you show me a point that has no length, but is still there?
And that tends to be as far as it goes.

So back to the question: how fundamental is time? As I see it, it is as fundamental as the other dimensions, none of which requires an absolute frame or origin. If we consider mass to be "that which is subject to gravitational attraction" then zero mass is no more conceptually difficult than zero length or zero time  no need for an origin or any embodiment of negative mass.
Or am I being too naive to see the problem?
I would certainly not say you are being naive.
I liked the analogy to mass at first glance, but after some thought, I am not sure it is a good one. In my mind (happy to be shown wrong), an object with zero mass would be more akin to an object that existed for a duration of 0 time, or that had a radius of 0 length. However, unlike mass, both space and time appear to be descriptors of location within spacetime (I am open to discussion of massspaces, but that may require another thread...)
Our own perception of time is quite unusual, and certainly prone to mistakes. That we have found ways of making devices to measure it certainly has helped a lot, but I still do wonder if we are correctly interpreting what they are measuring. I will use another analogy that involves mass: we perceive weight directly, and it was quite an advancement for society, when it was realized that weight is not a fundamental quantity, and instead is a function of mass and our gravitational environment. My question regarding the fundamentality of time is along the lines of asking whether time is more masslike (fundamental) or weightlike (can be distilled further).

@chiralSPO I am impressed! What exactly are your thoughts on a connection with the Hubble shift? Are you assuming a connection to the convergence of α and t? Also, what started you down this path?
I am still trying to see if it fits (or show that it cannot be, which is equally useful, but a little less interesting...)
I started down this path because I wondered if the apparent expansion (current and ancient) and big bang both could be explained in a way different from the currently accepted model. Questions like "what happened before the big bang?" can be answered more easily as "nothing" because the big bang would be an infinitely long period (in α time), which is identified only by how different the α and t values are. The concept of "rapid inflation" immediately after the big bang could potentially be reinterpreted as a period of time for which α and t were very different.
If "time" had been going more slowly before, then light emitted longer ago could appear to have lower frequency, even if there isn't any expansion (ongoing or ancient). This model could account for red shifts: ∂t/∂α < 1 for all α (and all t), and ∂t/∂α increases monotonically, so as α (or t) increases, so does ∂t/∂α. However, this model does not account for accelerating expansion (indeed, it was designed to converge such that α = t for sufficiently large values, and assuming that we are in that sufficiently advanced region). There are ways to tweak this model, but of course, once we start adding parameters in willy nilly, we can make a model that will reproduce anything...
I am not optimistic that this model will turn cosmology upside down, but I am interested to see how far this line of reasoning can go before it fails theoretical or experimental tests.

Go for it!

Consider a photon to be an object with zero mass. Some of those reaching us now, were launched umpteen billion years ago, so they don't exist for zero time!

Consider a photon to be an object with zero mass. Some of those reaching us now, were launched umpteen billion years ago, so they don't exist for zero time!
I don't think you understood what I meant.
If I understood correctly, you had said something along the lines of, 'why is zero time any harder to understand than zero mass?' To which I responded, 'that analogy is not quite right: An object existing for a length of zero time is not that same as an object existing at t = 0"
Do you see why I differentiate between the usage of time as it pertains to the duration of an event or existence, and the usage of time as it pertains to a location of an event on a timeline?
Something that has the property of zero mass, is analogous to something that has the property of zero volume (not analogous to being at the origin of a spatial coordinate system), and is analogous to something that has the property of zero duration (not being at the origin of a timeline).

Chiral, you write : " If "time" had been going more slowly before, then light emitted longer ago could appear to have lower frequency " But I'm not sure relative what? light?
Then light need one invariant 'clock rate', or 'wavelength/Frequency' that then gets manipulated by this otherwise 'universal time change' you're wondering about, wouldn't it?
=
Or you're thinking of early light then being misinterpreted as it reach us in 'fast time'?
I'm not sure, but it's a interesting idea.
=
Let me translate it to this. Isn't that the same as to suggest that 'c' is a variable of sorts, although at all times keeping its 'proportion' relative all frames of reference, meaning that 'c' is 'c', both then and now. Seems a hard thing to test.

Chiral, you write : " If "time" had been going more slowly before, then light emitted longer ago could appear to have lower frequency " But I'm not sure relative what? light?
Then light need one invariant 'clock rate', or 'wavelength/Frequency' that then gets manipulated by this otherwise 'universal time change' you're wondering about, wouldn't it?
=
Or you're thinking of early light then being misinterpreted as it reach us in 'fast time'?
I'm not sure, but it's a interesting idea.
=
Let me translate it to this. Isn't that the same as to suggest that 'c' is a variable of sorts, although at all times keeping its 'proportion' relative all frames of reference, meaning that 'c' is 'c', both then and now. Seems a hard thing to test.
The second one (misinterpretation by us now in "fast time") is how I am trying to think about it.
I am definitely struggling with what it would mean for time to change. Would the frequency of the light shift as well, keeping up with time, and ultimately giving no difference? How can I reconcile this theory with the photon's point of view, in which its journey is instantaneous?
I think I am out of my league!

I think you have a point actually. The first thing you need to prove univocally would be that we actually have a locally slow versus fast times depending on mass and speeds. But that's me :)
After that you will need to prove that it is a 'field' with excitations. Think of it undulating and count in 'time' as part of that field. It would actually be easier if you stayed away from the idea of locally fast and slow time and instead referred to it the way I do, as 'proper time' being special.
You don't want 'propagation' for it Chiral, what you want is something expressing itself as a propagation, proportional to the 'time rate' you set. That takes care of 'speeds'. It's a field you're after in where those excitations observer dependently express themselves as waves or 'photons', but always proportionally to the 'time rate' you set.
Then let it undulate.
Now you just need to prove that this will produce your red shift at this 'faster' proper time/'undulation'.
Maybe :)
A hard one to prove I think, but very nice all the same.
In my terms 'slow' and 'fast' time is when considering it from a 'global perspective'. If you stick with the local definition then 'proper time' is what you use for proving it. Because you're discussing a red shift, right? Not a 'universal globally explainable' TOE. Those two are like mirrors of each other, with the local interpretation being the simplest. Actually logic tells me that if you get it right locally there will be a way to translate it 'globally' too, but that one will be a lot more complicated.
Think of using a local interpretation as doing away with observer dependencies. There are no observer dependencies if you just stay local ignoring global interpretations. The rest becomes a question of making it fit.
At a quantum regime it becomes trickier when considering super positions. Then again, there are no subtleties to it if you just accept that outcomes too then must be a function of time.
As for you worrying about " How can I reconcile this theory with the photon's point of view, in which its journey is instantaneous? " You don't have a frame of reference for a photon, as you well know Chiral :) It has a 'origin/recoil' and a 'absorption'. Any proof to otherwise will be a indirect proof, colored by expectations. It's 'c' and as long as the 'proportions' relative all other constants etc are correct it shouldn't be noticeable as differing with time. Unless we now presume the cosmological red shift being a 'proof' of your ideas.

Chiral, you write : " If "time" had been going more slowly before, then light emitted longer ago could appear to have lower frequency " But I'm not sure relative what? light?
Then light need one invariant 'clock rate', or 'wavelength/Frequency' that then gets manipulated by this otherwise 'universal time change' you're wondering about, wouldn't it?
=
Or you're thinking of early light then being misinterpreted as it reach us in 'fast time'?
I'm not sure, but it's a interesting idea.
=
Let me translate it to this. Isn't that the same as to suggest that 'c' is a variable of sorts, although at all times keeping its 'proportion' relative all frames of reference, meaning that 'c' is 'c', both then and now. Seems a hard thing to test.
The second one (misinterpretation by us now in "fast time") is how I am trying to think about it.
I am definitely struggling with what it would mean for time to change. Would the frequency of the light shift as well, keeping up with time, and ultimately giving no difference? How can I reconcile this theory with the photon's point of view, in which its journey is instantaneous?
I think I am out of my league!
The deeper the source of light is in a gravity well the stronger the effect of time dilation. We have no problem with that idea of slower time. The wavelength is affected on its way out into 'faster' time. It is the same for your idea I would imagine. If you think you are out of your depth move to shallower waters.

So I thought about this more:
The deviation from time, is represented by the slope of this curve, dt/dα, which is best expressed as the logistic function:
For F(α)= log_{x}(1+x^{α}) = ln(1+x^{α})/ln(x), so I think that dt/dα = dF(α)/dα = G(α) = 1/(1+x^{α}) – ln(x) did I do that right?
Thus the rate of time that we observe now divided by the rate of time y years ago is represented by
H(α, x, y) = (1/(1+x^{α}) – ln(x))/(1/(1+x^{α–y}) – ln(x)) did I do that right?
My hope is that we can fit this function to observed data (red shifts, inflationary phase etc.) to solve for α (what “ultimate time” is it now?), and x (how quickly did α and t converge?)
I would be happy for folks here to poke holes in this as best as possible, and then I have found some cosmologists I can reach out to, once I am sufficiently sure I won't embarrass myself right off!
Rather than finding shallower waters, I will call for the life guard! ;D

H(α, x, y) = (1/(1+xα) – ln(x))/(1/(1+xα–y) – ln(x))
Actually, I needed to account for the fact that y needs to be in terms of α, not t.
So, based on how we understand years, in term of t, this should be:
H(α, x, y) = (1/(1+xα) – ln(x))/(1/(1+xα–(log_{x}(x^{y}–1)) – ln(x))
I think...

I have been thinking about the concept rather than the mathematics. Here are some thoughts. We only have relative velocities which are dependent upon the frame of the observer. All frames non local to the observer are in the past due to the speed limit of information exchange. Thus the relative velocities we measure are all in the past. Since α diverges from t into the past then this must be taken into account when comparing those velocities. What impact, if any, does this have on the accelerated expansion of the universe? I will try to look at the mathematics you posted when I get a chance next weekend.

Have you tried plotting the function? What does it look like?

I know I’m way out of my depth in this thread, but “…thinking about the concept rather than the mathematics” might give me a chance to clarify some of my thoughts.
A is in motion, relative to B.
A measures time as passing at 1s/s, in her RF.
B measures time as passing at 1s/s, in his RF.
A and B both measure time in the other’s RF as being dilated.
SR says that both are “right”.
Thus the relative velocities we measure are all in the past.
The measurements made by A and B, of time in the other’s RF, are in the past, relative to each other, and are both right, so there is no “absolute” past.
This must demonstrate that there is no universal rate of “passage of time” that can be identified.
The rate of expansion of the universe can be measured only in terms of the rates of motion of given bodies, relative to other bodies.
In every case, time dilation will apply to the measurement results.
If this line of reasoning is correct, there is no “absolute” time; so, what is it that might, or might not, be fundamental?

A is in motion, relative to B.
A measures time as passing at 1s/s, in her RF.
B measures time as passing at 1s/s, in his RF.
How could either of them possibly measure that? What would they expect it look like to them to measure a different value?
It's like verifying that your measuring tape measures one meter per meter. We know, because we held a tape measure up to it.
A and B both measure time in the other’s RF as being dilated.
No. A and B each measure the other clock as dilated in their own frame, not in the other frame.
The measurements made by A and B, of time in the other’s RF, are in the past, relative to each other, and are both right, so there is no “absolute” past.
A and B are frames or observers, and not events. What you measure is events, and those measured events are in the past of the measurement events. This is true of those two events in any frame.
This must demonstrate that there is no universal rate of “passage of time” that can be identified.
The above example does not demonstrate this, either way. There could be a universal rate.
The rate of expansion of the universe can be measured only in terms of the rates of motion of given bodies, relative to other bodies.
That rate is actually a good way to determine universal time, because in any nonisotropic foliation of spacetime (translation: in any nonpreferred frame), the expansion rate is not uniform. It is greater one way than the other.
If this line of reasoning is correct, there is no “absolute” time; so, what is it that might, or might not, be fundamental?
Absolute time has been argued. Problem is, all the proponents of it give a reference frame for it, but do not say how much our clocks are dilated relative to that absolute time. I personally find this hilarious.

Halc;
How could either of them possibly measure that? What would they expect it look like to them to measure a different value?
A and B moving at constant velocity of .3c and .6c.
They have synchronized their clocks. Gray hyperbolic lines are isobars of constant time.
Each sends a signal at .68 to request a time signal from the other. Each receives a reading of 1.00 at 1.47. Being in a pseudo rest frame, the SR convention requires the observer to assign the reading (clock event) to half the total transit time, (1.47+.68)/2 = 1.08 (red).
Each concludes the distant clock is running slower than their local clock.
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Have you tried plotting the function? What does it look like?
Yes, here are two different views of three functions (with different bases):
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How would the relationship between α and t relate to time dilation? Would α at negative infinity relate somehow to zero point energy?

A and B moving at constant velocity of .3c and .6c.
You're answering a different question. A is stationary, and is trying to measure the rate that time passes for his own clock, not some other clock. That's like trying to measure the dilation of your own meterstick.

You can map your function onto a spacetime diagram. As α converges with t there is a connection to the speed of light. The function approaches a lightlike path. This will only match at α = ∞. This may be the connection to both time dilation and a fundamental time scale.
EDIT: It seems to me that the green line functions are closer to a match with inflation. That is if you take the connection with spacetime diagrams into consideration.
That way you don't affect the accelerating expansion idea. When α = 0 this could be like a Planck scale equivalent. Before that we are barred from knowing anything. This would be the big bang initiation. Then inflation which quickly converges α and t.

Halc; thanks for your response to #75. It highlights the fact that I cobbled together that post in a hurry and expressed some things badly. I'm trying to find time to go through both posts thoroughly to get my thinking straight, but at present, it looks more as though my days of posting in TNS are numbered. :(

A is in motion, relative to B.
A measures time as passing at 1s/s, in her RF.
B measures time as passing at 1s/s, in his RF.
How could either of them possibly measure that? What would they expect it look like to them to measure a different value?
It's like verifying that your measuring tape measures one meter per meter. We know, because we held a tape measure up to it.
]
A has no way of measuring time as passing at any rate, other than 1s/s in her RF.
B’s position is the same in his RF.
A and B both measure time in the other’s RF as being dilated.
No. A and B each measure the other clock as dilated in their own frame, not in the other frame.
This is point I was working towards. Pop. Sci. books often say things like: “A sees B’s clock as running slower…”. Although we know that A cannot observe B’s clock; we tend to accept this statement, because it is a thought experiment.
Are we, in fact, saying that A calculates that B’s clock would be perceived as running slower than hers, if she could see it; and that this, and any calculation of the amount of the difference, are based on the equations of SR?
Of course, we know, from (e.g.) satnav, that these equations reflect “reality”, so this is probably nitpicking. I’m not really after BC’s Pedantry Award. :)
The measurements made by A and B, of time in the other’s RF, are in the past, relative to each other, and are both right, so there is no “absolute” past.
A and B are frames or observers, and not events. What you measure is events, and those measured events are in the past of the measurement events. This is true of those two events in any frame.
This arose from Jeffrey’s observation that: “All frames non local to the observer are in the past due to the speed limit of information exchange.”
If we identify A and B as intervisible, physical objects, and as observers occupying those objects; we can consider optical observations (either direct, or via light signals), and “observations” via radio signals. In all cases, the information received by the observer will be relevant to an event that took place in the past, relative to the observer’s present.
This must demonstrate that there is no universal rate of “passage of time” that can be identified.
The above example does not demonstrate this, either way. There could be a universal rate.
This provides an illustration of our inability to identify a universal rate of “passage of time”.
The rate of expansion of the universe can be measured only in terms of the rates of motion of given bodies, relative to other bodies.
That rate is actually a good way to determine universal time, because in any nonisotropic foliation of spacetime (translation: in any nonpreferred frame), the expansion rate is not uniform. It is greater one way than the other.
I think you’ve lost me there.
Doesn’t SR say that all RFs are nonpreferred frame?
Isn’t the expansion rate of the universe measured as being the same in every direction?
Given that these points are correct: where might we find a “nonisotropic foliation of spacetime” in which to observe the expansion rate as nouniform?
More to return to, but out of time.

How could either of them possibly measure that? What would they expect it look like to them to measure a different value?
It's like verifying that your measuring tape measures one meter per meter. We know, because we held a tape measure up to it.
]
A has no way of measuring time as passing at any rate, other than 1s/s in her RF.
My point was that it wasn't measured at all, just assumed. If it was measured, then one could ask what it would look like if a different value (say 0.8 s/s in her own RF) was measured.
A and B both measure time in the other’s RF as being dilated.
No. A and B each measure the other clock as dilated in their own frame, not in the other frame.
This is point I was working towards. Pop. Sci. books often say things like: “A sees B’s clock as running slower…”.
But that would be in A's frame, not B's frame. "A sees" is a reference to A's frame. A does not 'see' B's clock running slower in B's frame, which is implied by how you initially worded it. That's what I was correcting.
Although we know that A cannot observe B’s clock; we tend to accept this statement, because it is a thought experiment.
Very few thought experiments have people looking at clocks that are not in their presence since little can be determined from that. For instance, if B is coming towards me, his clock actually runs slow in my frame due to the speed, but it appears to be running fast due to Doppler effect, which is a far greater effect. How else is the twin that travels going to expect the stationary twin's clock to read a greater value if that clock in fact always runs slower than the travelling twin's clock in the traveler's frame? If he watches the distant clock the whole time, at some point it is going to need to appear to run faster. Similarly, the twin back home will see the returning twin's clock run faster, despite the fact that the comparison when they meet still showing much less elapsed time on the traveling clock.
Point is: Don't look at distant clocks. It doesn't tell you what time it reads and it certainly doesn't tell you the rate at which it runs.
Are we, in fact, saying that A calculates that B’s clock would be perceived as running slower than hers, if she could see it; and that this, and any calculation of the amount of the difference, are based on the equations of SR?
Of course, we know, from (e.g.) satnav, that these equations reflect “reality”, so this is probably nitpicking. I’m not really after BC’s Pedantry Award. :)
Well thank goodness you made A female, since only via gender pronouns am I able to parse which clock you're talking about.
It isn't really about perception. It is about what is actually happening in a given frame. So B's moving clock is slower (not perceived to be slower) in A's frame because it is moving in A's frame, and yes, per the mathematics of SR. As for perception, it all depends if B's clock is getting closer or not, and not so much on its speed. Approaching clocks usually appear to run faster even though they're not.
The measurements made by A and B, of time in the other’s RF, are in the past, relative to each other, and are both right, so there is no “absolute” past.
Events in the pastlightcone of event X are in the absolute past of event X. I say absolute, because this is a frameindependent fact. There is never a pair of frame where some event is in X's past light cone in one frame but not in that cone in another. Ditto for future light cones. Events are frame independent since they don't have a velocity.
If we identify A and B as intervisible, physical objects, and as observers occupying those objects; we can consider optical observations (either direct, or via light signals), and “observations” via radio signals. In all cases, the information received by the observer will be relevant to an event that took place in the past, relative to the observer’s present.
Yes, true by (unproven) principle of locality.
This must demonstrate that there is no universal rate of “passage of time” that can be identified.
The above example does not demonstrate this, either way. There could be a universal rate.
This provides an illustration of our inability to identify a universal rate of “passage of time”.
Well, there's a nonlocal way to determine a reasonable candidate for a universal frame, so from that you'd think one could determine a universal rate of time passage, but I've not seen anybody compute it. Somebody must have, but I my search attempts have failed.
Doesn’t SR say that all RFs are nonpreferred frame?
In SR, the 'S' is for the special case of gravityfree flat space, and reality is neither, so SR does not apply to the universe except locally where these conditions can be approximated. So there is no local test for a preferred frame.
GR very much has a preferred frame (which isn't inertial), and I think it annoyed Einstein to admit it.
Isn’t the expansion rate of the universe measured as being the same in every direction?
Only in the preferred frame, and then only on average. Locally, expansion happens more in empty places than in say galaxies where mass is concentrated.
Given that these points are correct: where might we find a “nonisotropic foliation of spacetime” in which to observe the expansion rate as nouniform?
The frame of Earth meets that qualification. The microwave background is definitely more red shifted in one direction than the other. From that we can determine our absolute speed of something like 400 km/sec, slower than the ~600 km/sec speed of the galaxy. It seems we're on the side of the galaxy that rotates away from the direction of motion.

That's sad to hear Bill and I hope it's wrong, for once.
Keep on posting your thoughts man.

Bill: A is in motion, relative to B.
A measures time as passing at 1s/s, in her RF.
B measures time as passing at 1s/s, in his RF.
Halc: How could either of them possibly measure that? What would they expect it look like to them to measure a different value?
[by measuring transit time of light to mirrors located a distance d in opposite directions. It would of course be redundant.]
Bill: A and B both measure time in the other’s RF as being dilated
Halc: No. A and B each measure the other clock as dilated in their own frame, not in the other frame.
[The purpose of the experiment is to measure the rate of the remote moving clock. That's what the graphic shows, in agreement with what he means. Since the remote clock is not part of the local frame, if it is running slow relative to the local clock, then so are all other EM processes in the remote frame.]
Bill: If this line of reasoning is correct, there is no “absolute” time; so, what is it that might, not, be fundamental?
Halc: Absolute time has been argued. Problem is, all the proponents of it give a reference frame for it, but do not say how much our clocks are dilated relative to that absolute time. I personally find this hilarious.
[If there is a universal physical process that synchronizes/coordinates events in some detectable manner, it hasn't been discovered yet. Universal time was possible when light speed was thought to be instantaneous.
Today: Where is the absolute origin of coordinates, or the center of the universe? Using remote clock time requires synchronization, and that is the obstacle since there is only relative synchronization, and only in the case of inertial motion.
The revelation of Relativity is, motion alters measurement and perception. After 100+ yrs. of experimental verification, the general public can't or refuses to accept it.]

A is in motion, relative to B.
A measures time as passing at 1s/s, in her RF.
B measures time as passing at 1s/s, in his RF.
: How could either of them possibly measure that? What would they expect it look like to them to measure a different value?
[by measuring transit time of light to mirrors located a distance d in opposite directions. It would of course be redundant.]
I don't think that works. If time passed slower for me (due to say being in a uniform gravity well), distances would dilate and my measurement of distance d would be proportionally wrong.
Good answer though....
How about if I watch a distant but stationary clock that runs faster than mine? That would tell me that my clock is running slower than that other one, but still no value for the rate of my own since I don't know the rate that time passes for that distant clock either. But it is at least a way to demonstrate I'm not running at full tilt.
The purpose of the experiment is to measure the rate of the remote moving clock. That's what the graphic shows, in agreement with what he means.
Yes. Bill has since posted that he meant that, but worded it as something else.
[If there is a universal physical process that synchronizes/coordinates events in some detectable manner, it hasn't been discovered yet. Universal time was possible when light speed was thought to be instantaneous.
But there is something that synchronizes all events (objectively orders them). It just doesn't say how far apart they are: It doesn't specify the objective rate of time flow. Hence we can know if event A happened objectively before B, but not necessarily how much time exists between the two as measured by a hypothetical clock not dilated at all.
There are all sorts of relativity deniers on this site claiming such absolute metaphysics with aether and such, but none of them seem to be able to tell me how long after A that B occurs.
Today: Where is the absolute origin of coordinates, or the center of the universe?
That's pretty easy if you think about it. But an origin doesn't tell you where the other axes lie. I can draw a dot (origin) on an irregular piece of paper and I still cannot give the coordinates of random location B without assignment of which way is the X and Y axis. Anyway, an absolute frame does not necessarily provide an absolute origin, but your question sort of implies that it should.
Using remote clock time requires synchronization, and that is the obstacle since there is only relative synchronization, and only in the case of inertial motion.
Clocks are typically synced to local events, not to other clocks. Clock rates can be objectively compared to each other if they're stationary relative to each other, not necessarily inertial. So two clocks at either end of an accelerating ship will run at some objective rate relative to each other since they are always stationary relative to each other in their own frames (but not in other frames).
The revelation of Relativity is, motion alters measurement and perception. After 100+ yrs. of experimental verification, the general public can't or refuses to accept it.]
I think that the general public has insufficient use for it to bother understanding it. They may know there is a theory called relativity, but they couldn't describe what it means. This site is not frequented by that typical 'general public'.

Absolutes in physics tend to be out of reach. Massive particles reaching the speed of light or temperature being lowered to absolute zero come to mind. It should be the same with an absolute frame of reference.

Thanks for the encouraging comments, yor_on. I'll do my best to stay with it. Might keep dementia at bay. :)

t = log_{10}(1 + 10^{a})
For: Every time we go back an order of magnitude in time towards the Big Bang, the mass/energy density of the universe increases by 3 orders of magnitude, and quite different events and even different physics dominates. So this logarithmic way of looking back at the big bang is a useful way to view it.
Against: Isn't this just a more sophisticated way of avoiding discussion on t=0 (let alone t<0)?

t = log_{10}(1 + 10^{a})
For: Every time we go back an order of magnitude in time towards the Big Bang, the mass/energy density of the universe increases by 3 orders of magnitude, and quite different events and even different physics appears. So this logarithmic way of looking back at the big bang is a useful way to view it.
Against: Isn't this just a more sophisticated way of avoiding discussion on t=0 (let alone t<0)?
Glad to hear about your for. Funny thing is, your Against is the original for that I was aiming for. I will accept that it might just be a cop out, but I do think there is something to be gained by using the the log approach. By invoking this reparametrization, we might be able to avoid the problems associated with t ≤ 0...

I'm wondering Chiral. This is collected thoughts on 'c' as a variable. http://www.ldolphin.org/cdkconseq.html
with a time dilation you could argue that 'c' changes too, from the 'eyes of a God' so to speak. See if you can find something interesting :)

I'm wondering Chiral. This is collected thoughts on 'c' as a variable. http://www.ldolphin.org/cdkconseq.html
with a time dilation you could argue that 'c' changes too, from the 'eyes of a God' so to speak. See if you can find something interesting :)
Your link is likely related to creationism and therefore of dubious value. Constants are named so because they do not change. Unless they want to convince everyone the earth is only 6000 years old.

interesting... Thanks for the lead, yor_on, I will check it out. And thanks for the warning jeffereyH, I will be skeptical...

Seems Barry Setterfield is a creationist indeed. But it's still interesting reading Jeffrey. If you look at what I wrote, 'c' will be 'c', presumably, only as long as we find all values in a balance relative it. And I would say that this is the question that is discussed there. Everybody have opinions, doesn't mean that one is more true than another. The best approach to any question is to test, validate, and search anew. I'm guessing that there is a lot of good stuff there that one can use
=
You can also think of it this way. 'c' is a variable in that it is is observer dependent. Most people treat the universe as a generally 'objective' playground, defining 'constants' as if they are objective facts as seen from a 'outside'.
That's not true, if we had the 'eyes of a God' we would find observer dependencies redefining 'c' everywhere, as defined from a 'objective', generally same universe. That's also what's so surprising, that the constants we trust in are the same for any frame of reference.
We have two good approximations for what makes this universe 'the same', SpaceTime Intervalls and LorentzFitzgerald transformations. Both of those are a logic defining how to treat 'events' giving us proper time/length etc. They are not a 'generally same' 'objective' universe though, but they are a proof of us sharing a communication, exchanging signals. And yes, they are a proof of 'locality' both of them, because what they lead us to is that your observer is equivalent to mine, both share a same ground level. Proper time and proper length.
And if you like, that's the groundwork for defining a 'constant'. What more is that I think it a good argument for the utter futility of defining a 'outside' to this universe. It wouldn't make sense from a 'outside', not to me anyway :)
==
It's a very strange universe Jeffrey.

'c' is a variable in that it is is observer dependent.
My understanding is that this is not the case. The theories of special and general relativity are built around the concept that all observers agree on c, no matter what reference frame they are in...

'c' is a variable in that it is is observer dependent.
My understanding is that this is not the case. The theories of special and general relativity are built around the concept that all observers agree on c, no matter what reference frame they are in...
Yes. Time dilation depends upon the value of c. Otherwise we would still be using Galilean relativity.

Central Postulates of Relativity: (SR)
The laws of physics are the same for all uniformly moving observers.
The speed of light is the same for all observers.
Yes, but I'm not stating that 'c' won't be 'c' locally measured. I'm stating that there is no golden standard for a uniform motion, from that follows that 'c' is a relation to your acceleration, not a relation to a 'relative motion'. I'm also stating that although relative motion can't be defined locally measured, we can still prove different 'speeds'.
=
Think of it in 'black box scenarios' to see how I mean.

Combine those statements and the conclusion will lead you to observer dependencies.

That's also one of the reasons I look at 'proper time' and 'proper length' as something really important for defining locality, SpaceTime as 'one common universe' and relativity. Another way to prove the idea is to set up a two mirror experiment in uniform motion, measure, then accelerate realtive some suns blue shift, to then do a new two mirror experiment inside and at rest with the ship. There will neither be found a different speed of light, nor a blue shift. So your (new) uniform motion does not change your local measurement. But as you know you've accelerated between measurements you now have to find an explanation for the result.
The explanation is that all uniform motions are equivalent.

Combine those statements and the conclusion will lead you to observer dependencies.
You need to give more context. I don't know to which post you are referring, or which statements.

The one above it :)

Uniform motion is not locally measurable. You need to introduce frames of reference to define different speeds, which doesn't mean that any of those frames by themselves suddenly found it changing locally. Two different things actually, and when you measure 'c' in a two mirror experiment you always do it locally.
=
you can by using frames of reference define it 'globally' but it becomes questionable, the same way an ' eye of a God ' (a 'outside') is questionable. That's not the way we define it geometrically, we do it from the inside.

Another way to prove the idea is to set up a two mirror experiment in uniform motion, measure,
Measure what? You've not really described the experiment. Possibly two mirrors involved that are stationary relative to each other, but even that is not clear.
then accelerate realtive some suns blue shift,
What does this mean? Acceleration is fairly absolute. 'a sun's blue shift' is not something that defines a frame and thus a relation. I can increase my speed relative to some sun, but not relative to its blue shift.
to then do a new two mirror experiment inside and at rest with the ship. There will neither be found a different speed of light, nor a blue shift.
So the experiment (whatever it is) is fairly local, and yes, should not yield a different result. Principle of relativity would assert this.
The explanation is that all uniform motions are equivalent.
Under SR, yes, not under GR. My clock (on a long nonspinning planet) runs at a different rate than does one on the 4th floor. Accelerate that planet to some different velocity, that fact is still true. Either observer can look at the other clock and see that the lower one falls steadily behind the upper one. The two frames are not equivalent, despite being stationary relative to each other.

Combine those statements and the conclusion will lead you to observer dependencies.
I think only the first statement is required for there to be observer dependencies. Such things have been known for at least 4 centuries. My velocity is frame dependent, by definition, long before relativity theory extended the principle to light.

You need to check up on 'two mirror experiments' Halc. They are so defined :)
You can pick any sun you like in front of you, I could also have written that one could put a scale under ones feet to check if one accelerated, I didn't, should I?. And yes, it's SR, I stated that in my first reply to those wondering what I meant by 'c' being both a local constant at the same time I discussed it as 'observer dependent'. The first is 'locally defined', the second is 'globally defined'.
How hard can it be to get it?
" Central Postulates of Relativity: (SR)
The laws of physics are the same for all uniformly moving observers.
The speed of light is the same for all observers.
Yes, but I'm not stating that 'c' won't be 'c' locally measured. I'm stating that there is no golden standard for a uniform motion, from that follows that 'c' is a relation to your acceleration, not a relation to a 'relative motion'. I'm also stating that although relative motion can't be defined locally measured, we can still prove different 'speeds'.
=
Think of it in 'black box scenarios' to see how I mean. "
another angle on the problem.
Assume yourself to be infinitely close to the speed of light in a vacuum (uniform motion).
Setup a two way mirror experiment inside and at rest with your ship
What will it measure?
Or as I think Einstein once wondered, what happens to light if I look into a mirror at 'c', Will I still see myself.

Uniform motion is not locally measurable.
Per the equivalence principle, it is indistinguishable from a uniform gravitational field. In SR, there is no gravity, so uniform motion is very much locally measurable. It is the absence of acceleration, and acceleration is absolute. There are local tests for it in SR.

You need to check up on 'two mirror experiments' Halc. They are so defined :)
Tried that, but I get lots of irrelevant hits. There is a Foucault experiment I've done myself with one spinning mirror (a prism in my case) and one fixed mirror, but I'm not sure you're referring to that. There seems to be no famous 'two mirror experiment'.
Let's just say some local measurement of light speed, which is what the thing I did is.
I could also have written that one could put a scale under ones feet to check if one accelerated, I didn't, should I?
There you go. That's an absolute test for acceleration. That scale will read your weight in any frame.
I'm not stating that 'c' won't be 'c' locally measured. I'm stating that there is no golden standard for a uniform motion
Why not? Motion that is uniform in one inertial frame is also uniform in any other inertial frame. That follows from Newton's first law.
from that follows that 'c' is a relation to your acceleration, not a relation to a 'relative motion'.
Perhaps you could give examples of this, because I just don't know what you mean by those words.
Think of it in 'black box scenarios' to see how I mean. "
Didn't help...
Assume yourself to be infinitely close to the speed of light in a vacuum (uniform motion).
I already am. This isn't hard to imagine. Just pick a frame in which I'm going this arbitrarily high speed.
Setup a two way mirror experiment inside and at rest with your ship. What will it measure?
It will measure light speed as c, assuming that's what the twowaymirror test does. It is a twowaymirror test now? It was a twomirror test before.
Or as I think Einstein once wondered, what happens to light if I look into a mirror at 'c', Will I still see myself.
Einstein did not wonder that. He would not posit himself or a mirror (or both??) moving at c. Relative to what? Each other? You don't see yourself in a mirror moving at somewhat high speed relative to yourself. Too much red or blue shift, and the visible image shifts into ranges outside of human eye sensitivity.

I'm wondering Chiral. This is collected thoughts on 'c' as a variable. http://www.ldolphin.org/cdkconseq.html
with a time dilation you could argue that 'c' changes too, from the 'eyes of a God' so to speak. See if you can find something interesting :)
from the paper:
"The permeability of space was apparently related in some way to the stretching out of free space at the time of creation (Genesis 1:68, Psalm 104:2)".
Genesis is not about creation of the universe, but the preparation of earth for life forms.
Psalm 104:2: isn't about the earth, but 104:7 is.
This is interpretation to suit their agenda.

Halck and Phyti, this is just redirecting the thread into something that could be discussed somewhere else. When I gave that link it wasn't because of whether the guy writing it had opinions of his own. It was because I found some value in the questions and answers. And when it comes to my thoughts I shouldn't have discussed them here.
Let's get back to Chiral's Idea instead.

Thanks for bringing it back (I'm not opposed to having some tangents along the way, but the closer we can stick to the main question, the more likely it is that I will learn the answer) :D

I think at this point it is worth waiting to see what a cosmologist thinks.

chiraSPO;
e naturTime is simultaneously (sorry) a simple concept and a difficult one to grasp. Clearly, our perception (as human beings) of time is not entirely quantitative. There are many different biological and psychological aspects of our perception that I do not want to delve into. Rather, I would like to discuss purely physical and mathematical interpretations of time.
I have had many questions about time swirling in my head for a while now, and I think I can distill them into two primary questions:
(1) Is time the most fundamental "temporal" dimension, or is it a function of an unrecognized dimension?
This question comes about when trying to conceive of an absolute time scale. Every equation I have come across in my education in the physical sciences deals with dt or Δt, and so is really just dealing with relative time (t = 0 is arbitrary or internally defined, and any indefinite ∫f(t)dt will have that pesky "+ c" term).
Many people point to the Big Bang as thal t = 0, but this raises at least as many problems as it addresses.
[Time is not a dimension in the same sense as spatial extent. It's a measurement of activity. The method of measurement can be any periodic process and is typically a device (clock) which produces periodic clock events, with the period defined to suit an area of human activity. Eg. the hour and minute for common daily human activity, seasons for agriculture activity, or the nanosecond for scientific research. The clock period is equivalent to the uniformly spaced marks of a ruler used to measure spatial intervals. The comparison is even more obvious when measuring distance using light. This is an operational definition of time and is consistent with a history of using the motion of astronomical objects to measure time.
Applied time is a correspondence convention, assigning a clock event to an event of interest. It is a personal diary, or any historical records, in a variety of mediums.
Mathematical expressions use time as a correspondence and as a variable. 'As a function of time' is just a convenient figure of speech. Time (clock events) are assigned after the event of interest, so how can it be a causal factor?
The theory of Special Relativity demonstrates there is no absolute time or simultaneity, but subjective time, which is affected by motion in space, which results from the independent speed of light. Einstein did not explicitly refer to SR or GR as a theory of perception, but with the observer as the primary component, it definitely is such. Just as in quantum theory, the observer is part of the measurement process.
If timekeeping only has meaning to humans, then time before their appearance has no meaning. Anything prior is pure speculation.]

I don't know Chiral, we need a experiment that might work?
I think that's the thing you need for the proposal
The 'energy' at a Big Bang should be limitless right?
Somewhat alike a time dependency maybe ?

Sounds simple, doesn't it?
But what frame of reference will you use?
Now?

Phyti, in general, I have no problem with the content of your post, but would like clarity on a couple of points.
The clock period is equivalent to the uniformly spaced marks of a ruler used to measure spatial intervals.
Agreed; but space “exists” independently of any marks on a ruler, are you proposing that the “existence” of time is dependent on measuring instruments?
…. Time (clock events) are assigned after the event of interest, so how can it be a causal factor?
Would it not be right to say that it is the measurement/recognition of the time interval in which the event occurred, that is assigned after the event?
I agree that assigning a time to an event does not establish any sort of causality, but isn’t time necessary (whether it is measured, or not) to enable change can happen?

Bill;
Phyti, in general, I have no problem with the content of your post, but would like clarity on a couple of points.
Phyti;
The clock period is equivalent to the uniformly spaced marks of a ruler used to measure spatial intervals.
Bill;
Agreed; but space “exists” independently of any marks on a ruler, are you proposing that the “existence” of time is dependent on measuring instruments?
[response]
['Space' exists, but if it has no known structure, i.e. no elements to serve as references, then we are limited to measuring the differences in location of objects in space aka distance. We use a defined standard of distance, a ruler or a specified number of wavelengths of light of a given frequency (equal to a unit of 'time').
The clock supplies a standard interval between 'ticks' that provides a perspective of the rate of activities. A race car completes a mile course in 30 sec, moving fast at 120 mph. A store clerk notices an hour go by with no customers, business is slow.
An hour glass, water clock, sun dial, a burning candle, earth rotation...all examples of physical processes used as clocks, practical devices for scheduling human activity.
'Time' as applied by human convention requires measurement. Eg, a worker wants to be compensated for his hours of labor. Time can be classified as record keeping/accounting for human activities. A process, not a physical thing.]
Phyti;
…. Time (clock events) are assigned after the event of interest, so how can it be a causal factor?
Bill;
Would it not be right to say that it is the measurement/recognition of the time interval in which the event occurred, that is assigned after the event?
I agree that assigning a time to an event does not establish any sort of causality, but isn’t time necessary (whether it is measured, or not) to enable change can happen?
[Only if you see 'time' as an activating agent or force.]
–
Points to ponder:
Consider two identical atomic clocks, one on floor 1 and one on floor 2. If there is a universal time agent, why don't they both run at the same rate?
Why do they vary when moved, in any direction?
Radioactive particles decay at random. How would 'time' do that?
We don't need 'time' to explain these. We have gravity and independent light speed, and quantum behavior.
a=g
v=gt
x=gt2/2
math definition (abstract figure of speech): "v and x are functions of t".
observational truth: "an object falls to the ground via the gravitational field".
'time' played no part in the process of falling, but is convenient for measuring.
Eg:
A small mass is released from a height, and recorded by a video device which time stamps each frame.
A graph plots the height on a horizontal axis and the corresponding ‘time’ on a vertical axis , both with a uniformly spaced scale. The graph will show a curved trajectory, indicating acceleration of the mass.
homework:
Imagine being isolated in a cave, with the essential stuff to survive, but not receiving any cues from outside. You have to write an account of your experiences until someone signals via a communication system on the surface. How do you record the time of events in the account?.

OTEOMB, A. Einstein,1905, par 1:
"Now we must bear carefully in mind that a mathematical description of this kind has no physical meaning unless we are quite clear as to what we understand by ``time.'' We have to take into account that all our judgments in which time plays a part are always judgments of “simultaneous events"
In SR, the time of an event is the awareness (perception) of the event according to a local clock. The awarenesss of an event can only be after its occurrence. Additional distance info is required to assign a time to the occurrence event.
If none of this informs, you might check ‘Father Time’ on Wiki.
He should know!

If none of this informs…….
Thanks, it is interesting and informative. There’s just one question it doesn’t answer.
Radioactive particles decay at random. How would 'time' do that?
I certainly don’t see time as an activating agent or force. My answer to this question would be: It doesn’t.
A small mass is released from a height, and recorded by a video device which time stamps each frame.
If time exists only as a measure of events that have already happened; how can the events happen? How can your “small mass” change its position in a timeless environment?

Bill;
Water is lifted from oceans, lakes, etc. via sunlight, carried via winds to different locations.
At higher elevations the vapor cools, condenses on dust, falls to ground via gravity, seeks lowest suface and returns to those reservoirs of water.
It's a sequence of events enabled by physical processes already in place. One of many natural cycles. Where would we be without natural recycling!

Phyti, I have no problem with any of that. What I don't see is how these cycles could operate in a timeless environment.
Cycles involve change. How can there be change if there is no time in which it can happen?

Having looked, briefly, at this thread, thoughts about the "madness" of repeating the same thing, and expecting a different result come to mind.

You know Chiral, that isn't that far away from how I think of 'c' myself. What differs us is that you use what I would call a 'global approach' to it whereas I start to think of it in local terms. Maybe you could think of it in terms of frequencies? What would happen to them if 'time' runs slower at a 'origin' than 'now'? Everything should blue shift to us measuring at this time, right? And the closer we get from the 'early light' to 'now' the less blue shifted the light should be.. If I now got it right :)

What would happen to them if 'time' runs slower at a 'origin' than 'now'? Everything should blue shift to us measuring at this time, right?
Relativistic light shift always results in a redshift due to "'time' running slower at a 'origin'" as you put it, but the visible frequency of the emitted light as seen by some observer is more dependent on the Doppler effect than the lesser relativistic effect. Translation, light from approaching sources appears blue shifted from the frequency of that light in the frame of the emitter.

I am not discussing a Black Hole, and light reflected or released Halc. I'm thinking of it in terms of a 'slower' 'time', as observed 'now'. Even if 'c' still stay 'c at all 'times'' the view point from 'now' should resolve in a apparent blue shift for us, as it seems to me
=
yes, I see how you thought there. The way I think of it here is one from where you roll a movie faster. Everything speeds up relative the observer.
==
Or maybe it would be less blue shifted, although if you count in a inflation it seems to me that this should compress, no, I'm not sure how to think about that one. But thinking of it in those terms should get you to a blue shift anyway. Thinking of it in terms of a 'infinite point singularity' aka a 'white hole' you get a red shift, but that one does not include Chiral's scenario, the way I look at it now.
http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/universe.html

Actually Chiral. You could go out from a accepted model of the cosmological redshift, as defined by a "static 'c' " in main stream physics. then back track 'now' to the Big Bang, and see if there is something that would turn out differently if 'time' indeed has 'speed up'. What makes it tricky is this balance you would need relative all other constants, keeping them the same except 'time' then. With a 'slower speed' of time comes a (apparently) faster 'c' presuming it to be a natural constant, unrelated to 'time'. If you connect it to 'time' though it will keep its balance invariant as a 'clock'. But that doesn't stop us watching the 'cosmological movie' from finding 'things' being 'speed up', as it seems to me?
=
I'm discussing it in terms of a apparent blue shift here, as that is the analogy to a higher 'speed' for light. But? I'm not sure that would work If you could zoom in on something happening 'then'. Everything should be 'speed up' to us, shouldn't it?
Actually, thinking of finding it this way, using main stream physics for defining it, might be considered as 'constants' having changed.

Oops! I left the link out of #121.
https://www.thenakedscientists.com/forum/index.php?topic=53002.msg445400#msg445400

Phyti, I have no problem with any of that. What I don't see is how these cycles could operate in a timeless environment.
Cycles involve change. How can there be change if there is no time in which it can happen?
You are in that group that interprets 'time' as a causal entity. It's like trying to separate Linus from his security blanket.
We can add seeds, programs that produce plants, another cyclic process, DNA for animal and human reproduction. Animal behavior, more programs, also cyclical. Do you see a trend here, processes in place that 'make things happen'.You get more variety when human thought intervenes.
Eg., man does not want to ride a horse, invents carriage.

We need time to see how fast things happen. Time is not a cause and has no effects. It can be affected by velocity. This is however a non local effect. Local time is always a constant.

Relativistic light shift always results in a redshift
Not true. The PoundRebka experiment shows a blue shift in one direction, red in the other.

Relativistic light shift always results in a redshift
Not true. The PoundRebka experiment shows a blue shift in one direction, red in the other.
The PoundRebka experiment concerns gravitational shift. I was speaking of relativistic shift due to motion. I stand corrected.

Chiral, keep on thinking
you're a gentleman, and a deep thinker.
Explore is what we do
Then we die :)

Hi All, there is some great discussion hereand I will contribute to it more when I have gotten some answers from a friend who knows more about cosmology than I do! In the mean time, I noticed that this thread kinda went off on a tangent, so I have taken the liberty of splitting it here. Apologies, if there are relevant posts in the bit that I removed....

I have been thinking about relativistic gamma in relation to this.

I have been thinking about relativistic gamma in relation to this.
Since a time value of positive infinity can never be reached we never have a relativistic gamma value at 1. This ties into conservation of energy.

I don’t want to appear to be discouraging. We do know for a fact that the quantification of time uses some form of clock, and we know that the rate that a clock measures the passing of time is affected by the relative acceleration of that clock vs some presumed rest clock.
Unfortunately there is no absolute space in which to place our rest clock, and so there is no absolute measure of time. Therefore, time is relative to conditions of local energy density set up by differences in gravitational potential, relative motion, and/or applied forces between two clocks in relative motion. The conditions of each clock in relative motion are therefore different.
I don’t see how you can get to anything fundamental in regard to a time increment from those circumstances, so I personally settle for the concept that time simply passes, but the measure of the rate that time passes is relative to the differing conditions in which our clocks are located.
On the bright side, maybe there is some fundamental increment of energy based on some foundational minimum background energy level. If such an energy level could not be reduced below this as yet unknown natural limit, and if we could place our rest clock there, maybe all other frames could be compared to that clock.
Is see the thread is revived, and the members have taken it in a couple of directions since the OP_, I have been reflecting on the topic, and on what I contributed earlier, and thought it wouldn’t hurt to add to my earlier reply.
I’ve revised my thinking beyond where I said, “I don’t see how you can get to anything fundamental in regard to a time increment from those circumstances…”
Actually, after coming back to the topic, I can hypothesize a circumstance where any two events that are separated in time and space can be reconciled to a given instant of time in a third frame of reference. A clock in that frame of reference would be in motion relative to the points in space and time where the two given events occur, and the frame would be identified by invoking the concept of the “simultaneity of relativity”.
It is a little complicated, and quite alternative, and off on another tangent, so I’ll simply say this for what it is worth: The moving point in space (the new frame of reference from which the two given events are seen to be occurring simultaneously) is a continual point of reference from which time is synchronized for those two events.
From that moving third frame of reference, any increment of time on a clock in that moving third frame could be considered fundamental relative to the two given events, given the application of the concept of the simultaneity of relativity.
If you can see that line of reasoning, then you might see that there is a point in space and time, relative to any set of two events, where there is an absolute increment of time passing relative to the two specific events. The concept can be applied to any two events, but the frame of reference containing the point in space and time from which absolute time is associated with each set of events would be unique.
So I would amend my \earlier statement to say that though there is no general absolute space and time, if you isolate any two events, there is a frame of reference where there is a time increment that is absolute for each unique set of events.
Edit: I should have ended this post with this explanation … If you turn around the concept of the relativity of simultaneity in your mind, it can become the concept of the simultaneity of relativity, and when you go there, you might be able to see that not even the absence of absolute time and space is absolute. This might be an unwelcome tangent in a thread in this subforum.
Edit 2
A further explanation of what is going on with the act of turning around the concept of the relativity of simultaneity:
When discussing the relativity of simultaneity, you are addressing the occurrence of one event that has two or more observers in different locations relative to the location of the event. The idea is that any two observers in separate locations will not observe the event simultaneously.
What I mean by “turning that around” is that you are addressing two (or more) events and finding a location relative to those two events that makes them seem to be occurring simultaneously. That location is what I call the third frame and it is any inertial frame where an observer would report that that the two separate events appeared to occur simultaneously.

The problem with relativistic gamma is that it can't be applied in terms of velocity since here it is related to a ratio. I need to think this through in terms of expansion of the universe. It would make more sense related to frequency somehow. This is the problem with not thinking things through.

One conclusion I am contemplating is that time is not fundamental in regard to the rate that it is measured to be passing on a given clock, because various changes will affect the rate that the clock will measure the passing of time. For example, if that clock is moved from location to location (accelerated/decelerated relative to the home conditions), or if the local conditions at the home location of the clock change relative to the original conditions, the clock will measure the passing of time at different rates.

However, though the local conditions can be variable, in an environment where the conditions are constant, the rate that time would be measured to pass would be constant. That brings me to the conclusion that there is a fundamental aspect to time, which is that time will continually pass in any environment, in spite of the fact that the local conditions can affect the rate that time is perceived to be passing.

One conclusion I am contemplating is that time is not fundamental in regard to the rate that it is measured to be passing on a given clock, because various changes will affect the rate that the clock will measure the passing of time. For example, if that clock is moved from location to location (accelerated/decelerated relative to the home conditions),
No, the real problem is the other way round. The moving clock ticks at a constant rate (the fundamental time if you like), it is the other clocks (whether considering themselves at rest or moving) that measure that clock’s time as different to their own. Each clock records its own proper time as it moves along its worldline. So, the “various changes” do not “affect the rate that clock is measuring the passing of time” only the rate that other clocks measure it.

No, the real problem is the other way round. The moving clock ticks at a constant rate (the fundamental time if you like), it is the other clocks (whether considering themselves at rest or moving) that measure that clock’s time as different to their own. Each clock records its own proper time as it moves along its worldline. So, the “various changes” do not “affect the rate that clock is measuring the passing of time” only the rate that other clocks measure it.
Thank you Colin2B.
Then if I have a very accurate clock in my pocket, no matter where I take it, I will not be able to tell if it is ticking faster or slower as I move from one energy density level to another, i.e., from a valley to a mountain top. It will simply tick away at its own "proper" time, and I will be none the wiser that synchronized clocks, when separated as they are moved to other environments, will not agree, until I compare them when they come back together.
The old adage holds true that a person with one watch always knows what time it is, but a person with two watches is never really sure :) .

Not quite. If you separate a pair of identical clocks, move one to a different gravitational potential, and exchange time signals between them, each sees the other as running at a different rate. No need to bring them back together.

Not quite. If you separate a pair of identical clocks, move one to a different gravitational potential, and exchange time signals between them, each sees the other as running at a different rate. No need to bring them back together.
This is correct. A clock at the top of a building or at either end of an accelerating ship can be compared to the one at the bottom at any time and the rate difference noted.
For dilation due to motion, you need to reunite them to see which is the faster/slower of the two. A pair of separating clocks will both run slower in relation to each other, both in appearance and relativistically.
In the twins experiment, the twin back home is always aging slower than the one in the ship in any inertial frame of the ship, which would be demonstrated only by comparing the two clocks in each others presence without changing the ship's frame.