[jeffreyH]

@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 S]

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. 

[chiralSPO (OP)]

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 mass-spaces, 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 mass-like (fundamental) or weight-like (can be distilled further).

[chiralSPO (OP)]

@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.

[jeffreyH]

Go for it!

[alancalverd]

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!

[chiralSPO (OP)]

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).

[yor_on]

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.

[chiralSPO (OP)]

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!

[yor_on]

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.

[jeffreyH]

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.

[chiralSPO (OP)]

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! 

[chiralSPO (OP)]

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...

[jeffreyH]

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.

[jeffreyH]

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

[Bill S]

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?

[Halc]

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 non-isotropic foliation of spacetime (translation: in any non-preferred 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.

[guest4091]

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.

sync signals.gif (6.26 kB . 474x585 - viewed 703 times)

[chiralSPO (OP)]

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

Yes, here are two different views of three functions (with different bases):

Screen Shot 2019-01-30 at 12.23.16 PM.png (110.05 kB . 1254x810 - viewed 745 times)

Screen Shot 2019-01-30 at 12.23.39 PM.png (101.13 kB . 1250x792 - viewed 746 times)

[jeffreyH]

How would the relationship between α and t relate to time dilation? Would α at negative infinity relate somehow to zero point energy?